survival/0000755000175100001440000000000013070772231012145 5ustar hornikuserssurvival/inst/0000755000175100001440000000000013070714003013113 5ustar hornikuserssurvival/inst/CITATION0000755000175100001440000000111412763545562014274 0ustar hornikusersbibentry(bibtype="Manual", title = "A Package for Survival Analysis in S", author= person(c("Terry M"), "Therneau"), year =2015, note ="version 2.38", url="https://CRAN.R-project.org/package=survival", key= "survival-package" ) bibentry(bibtype= "Book", title="Modeling Survival Data: Extending the {C}ox Model", author=c(person(c("Terry M.", "Therneau")), person(c("Patricia M.", "Grambsch"))), year = "2000", publisher= "Springer", address = "New York", isbn = "0-387-98784-3", key = "survival-book" ) survival/inst/NEWS.Rd0000755000175100001440000017640613070713571014210 0ustar hornikusers\name{NEWS} \title{NEWS file for the survival package} \section{Changes in version 2.41-3}{ \itemize{ \item A check for infinite loglik was incorrect in agfit4.c, and could fail to detect the need for step halving. It required a very unusual data set to trigger this. \item The survfit routine would fail for interval censored data, on a group that had only a single step in the curve. (Needed to add drop=FALSE to a matrix subscript.) \item Minor change to Surv to ensure that its check for difftime objects will not trigger a "length >1 inside an if ()" warning. \item The summary.survfit function had n.censor wrong when there were multiple curves and censor=TRUE (spurious NA values). Added more lines to the test suite. \item Pointed out by Mikko Korpela: the dynamic symbols check added in 2.41-0 requires R version 2.16 or later. Add an ifdef to init.c that checks the version of R, mimicing a similar line in the MASS library. }} \section{Changes in version 2.41-2}{ \itemize{ \item Fix two memory leaks and an uninitialized array, found by B Ripley. \item With Surv(a,b, type='interval2') and a or b infinite, the infinite values were incorrectly retained rather then being transformed into left or right censoring. The downstream survfit and/or survreg results could then sometimes be in error. \item Update cch to correctly deal with nearly tied times, in line with the many changes in version 2.40. \item Update the README.md file, for github users who didn't read noweb/Readme and then get R CMD build errors. } } \section{Changes in version 2.41-0}{ \itemize{ \item Per request if the R-core, add R_useDynamicSymbols(dll,FALSE) to the initialization. This prevents .Call from accessing the library when its first argument is a character string. The reason is to stop accidental linking to the routines. \item Fix a bug in tmerge, if data2 was not sorted by time within id then a tdc(time, x) call's outcomte was incorrect. Add the ability to use a factor as the second variable in a tdc call, and add the tdcstart option. \item Expose the aeqSurv routine, which is used rectify tied time issues. \item The survfit routines now save the start.time option (if used) in the output object. This is then used as a default starting point for the x-axis in any plots. \item Allow survfit.matrix to use different p0 values for different curves. \item Add type="survival" to predict.coxph }} \section{Changes in version 2.40-2}{ \itemize{ \item Fix an error in the finegray routine: with strata() the resulting data sets could have incorrect status values. Pointed out by Mark Donoghoe. Added a strata test to tests/finegray.R. \item Remove many "is.R" and "oldClass" calls (vestiges of Splus). \item The summary.pyears routine now prints pandoc style tables. \item Fix multiple spelling errors in the Rd files; contributed by Luca Braglia. \item For a multi-state curve, the cumhaz component accidentally had the final state removed. All values were correct, simply an overzealous trimming of the final result. \item Add a short vignette describing the issue with round off error and tied survival times. \item Errors in survSplit: a factor status was not propogated, and a missing time gave a spurious error message. }} \section{Changes in version 2.40-1}{ \itemize{ \item For multi-state survival with a big data set and the influence=TRUE option, the resulting object could be so long that it overflowed an integer counter in the C code. Add a check in the R code and a caution in the help file. } } \section{Changes in version 2.40-0}{ \itemize{ \item Code changes to void the new warnings for multiplication of a vector * (1 by 1 matrix). \item Add a more thorough test case for multi-state survival: not all subjects start in the same state, delayed entry, and case weights that change within a subject. This uncovered some errors. More carefully document the influence option. \item Consistently deal with "almost tied" survival times in the survfit and coxph routines. Uses the same rule and tolerance as the all.equal function to declare two time value equal. The issue arises due to round off errors, e.g., from cacluations using days/365.25. \item Add the statefig function and a multi-state vignette. \item The rsurvreg function was not exported. NAMESPACE fix. \item Fix some labeling errors in the graphs for the adjusted survival curves vignette (consequences of the xscale change in 2.38-5). \item Update multi-state survival so that the robust (default) variance for a weighted data set treats these as sampling weights rather than case weights. This makes it consistent with the behavior of coxph. (Multiplication of all the weights by a constant now leaves the variance unchanged.) (9/2016) \item Surv(time, status) would fail when status was a factor with only two levels. This was due to an assumption that no user would ever want this, i.e., ever do it on purpose, and so it must be a mistake which should be caught. This was a bad assumption. \item Add the start.time argument to survfit.coxph. 10Sep2017 }} \section{Changes in version 2.39-5}{ \itemize{ \item The summary.survfit routine assumed that the times argument was sorted, contrary to the documentation. Pointed out by Torsten Hothorn. \item The tmerge function would fail if the time variable was a Date object. It was due to the fact that as.Date(as.numeric(x)) fails when x is a date. (A design flaw in Date, IMHO). There were also flaws when both the first and second data set were not sorted by id; added a more complete test case for this. \item An earlier change in dim.survfit had felled the survfit.matrix function: it incorrectly assumed strata when there were none. Unfortunately this didn't generate an error but rather multiple copies of a single curve (and an incomprehensible explanation of this single curve in the vignette). Pointed out by E Lundt. \item print.summary.survfitms would complain if only a single time was returned. A case where drop=FALSE was needed. \item Add a test for survSplit to ensure that it works with both the formula based and old interface. Add documention on how variable names are chosen to the help file. \item Error in subscripting survival curves: if fit was a survfit curve from left-truncated data, fit[k] had an incorrect n.enter component. (An old error, which shows how rarely that component is used.) Pointed out by Beth Atkinson. \item Remove n.enter from the default printout of summary.survfit, to make the printout more compact. It remains in the summary object but was very rarely used. \item Update the points.survfit function to handle multiple colors and/or plotting characters. If a survfit object has multiple curves we cycle through these in the same manner as matpoints would. }} \section{Changes in version 2.39-4}{ \itemize{ \item Create a stronger test suite for summary.survfit, and use it to actually fix the error that 2.39-3 claimed to fix. This uncovered a long-standing inaccuracy with n.risk for in-between time points. \item Add a section on monotone splines to the splines vignette. }} \section{Changes in version 2.39-3}{ \itemize{ \item For multi-state curves, the returned n.event component lost its dimensions if any of the curves had only one observation. \item Fix error in summary.survreg. For multiple curves and requested time points at or before the first time point in the data, the values from curve 1 was used for all. Pointed out by T Eigentler. \item Fix an unitialized variable in C code, pointed out by Brian Ripley. }} \section{Changes in version 2.39-2}{ \itemize{ \item Small updates based on feedback from CRAN }} \section{Changes in version 2.39-1}{ \itemize{ \item Label the output dimnames from pyears with the variable names from the model. This makes it easier to read. \item Replace any refrences to model.frame with "stats::model.frame" (all 38 of them). The model.frame function uses non-standard evaluation rules, and holding its hand like this is the only way to ensure that we don't call a user function of the same name. \item The Surv function would almost always label the columns of the resulting matrix, and the glmnet function depended on this. It now always labels them per a request from Trevor Hastie. \item Add the finegray function and expand the competing risks vignette to document it. \item Add a check to the quantile.survfit function for multi-state models; quantiles are not well defined for this case. \item Changes to the iteration path and convergence tests for coxph models with (start, stop] data, driven by two user examples that failed. The data sets had serious statistical issues of collinearity and/or outliers such that the final fits are not practically useful, but now the routine finishes gracefully instead of dying. The upshot is much more care about the order in which additions and subtractions of large numbers are done so as to avoid cancellation error. \item Fix an error to summary.survfit with the times argument: for intermediate time points it would sometimes choose the wrong value for the number at risk. (Number at risk is a left continuous function.) }} \section{Changes in version 2.38-5}{ \itemize{ \item Add more graphical arguments to plot.cox.zph in response to a user request. \item Remove some of last vestiges of Splus support from the header files for the C code, per a request from R core to remove mention of S.h. \item Multiple updates and corrections to the tmerge function, including improvements to the vignette. (As a result of using it in a class where the TA tried out all manner of combinations.) \item Update survSplit: it now handles all types of status variables (0/1, TRUE/FALSE, factors), the id and episode arguments are useful for start/stop data, the data retains its original sort order (new observations are inserted rather than put at the end), and the function is illustrated in a vignette. \item Add the conf.times argument to plot.survfit. This allows for confidence bars at specified times, which are useful when the plot is crowded. \item Survfit changes that are NOT backward compatable! \itemize{ \item Change the default for mark.time to FALSE \item Change the behavior of xscale so that it matches that of yscale, i.e., it changes only the label and not the underlying scale. Follow on annotations such as legend or locator are in the orignal scale of the data. \item For a matrix of curves, e.g. competing risks, print and plot them in column major order rather than row major, so as to match the usual R behavior. } \item Fix an error in the help page for the cohort argument of survexp, pointed out by Karl Ove Hufthammer. \item The anova and logLik functions would fail when given a null model (right hand side of 1 or only an offset). Pointed out by Karl Ove Hufthammer. \item The recently added code to generate an error when the same variable appears on both sides of a formula in coxph (a good idea) caused a failure if there was offset statement that contains a '-' sign. Pointed out by Abra Jeffers. }} \section{Changes in version 2.38-3}{ \itemize{ \item Add more imports to the NAMESPACE file per a request from CRAN \item Add a length method for Surv objects. Requested by Max Kuhn. (2015/6/17). \item Fix an error in neardate. When both input data sets were unsorted the last match could be wrong. }} \section{Changes in version 2.38-2}{ \itemize{ \item Change print.coxph to use the printCoefmat routine, which l leads to nicer p-values. Other print routines will follow unless there is an outcry. (But I forced signif.stars=FALSE: my tolerance of bad practice has limits.) \item Make those parts of the competing risks vignette which depend on the cmprsk library conditional. Otherwise the build fails for those without the pacakge. \item The coxph function could fail converge for a set of very collinear predictors when using (start, stop) data; revealed in a test case sent by G Borstrom. This was due to deficiency in a check for near infinite coefficients, which had already been updated for some but not all cases. (2015/6/3) \item Update anova.coxph to use the model.frame.coxph function; the current code had scoping errors if embedded in a function. Add an anova.coxph.penal function to correctly handle models with pspline terms. \item Fix an error in the tmerge function. Using the options argument would generate a spurious error. \item Pyears could fail on very long formulas due to a deparse() issue. \item Add the number of observations used and deleted due to missing to summary.pyears. \item Allow the combination of a null coxph model (~1 on the right) and the exact calculation for tied times. No one had ever asked for this before. (2015/3/25) \item Shorten the default printout for survfit. The records, n.max and n.start columns are often the same: if so suppress duplicates. \item Move the anova.coxphlist function from the survival package to coxme. (2015/3/3) \item Change the logLik method for coxph models so that the nobs component is the number of events rather than the number of rows in the data. This is superior for follow on methods such as AIC. \item Add a test to the coxexact.c routine for too large a data set; too many tied times could lead to integer overflow. "Fixing" the error is not sensible: the computation for such a data set would take decades. Add some more explanation to the help pages as well. }} \section{Changes in version 2.38-1}{ \itemize{ \item Fix an error discovered by CRAN, which triggered a core dump for them on a particular manual page (but never for me). The linear predictors from a frailty model contained NA values (incorrect), leading to failure in survConcordance.fit. (2015/2/16). \item An error was found in the mgus data set (a progression after death). Now corrected, and added a little more follow-up time for some subjects. \item Add error check for infitinte weights or offsets. This in respose to a bug report where someone did this on purpose, trying to mimic cure fractions, and then found that survfit.coxph failed. \item Robust variance is not supported for a coxph model with the "exact" approximation. (Rarely requested and a lot of work to add.) Add an error message to clogit(), so users get a more useful notice of the issue rather than a late error from residuals.coxph. \item Update the rats data set: it now includes both female and male litters so as to match the documentation. \item The term frailty(x) would fail if x were a factor, and not all levels were present. Pointed out by Theodor Balan. \item Fix error of "abs" instead of "fabs" in the agfit4.c code; pointed out to me by CRAN. \item Replace all instances of the obsolete prmatrix function. \item Modify pyears to allow cbind(time, count) as the response, giving a cumulative sum of counts, when the counts per observation may be other than 0/1. \item The lines.survfit function was incorrect for data sets that used the start.time option and xscale (it neglected to rescale the start time.) \item An increasingly common error is for user to put the time variable on both sides of a coxph equation in the mistaken belief that this is a way to create time-dependent coefficients. Generate a warning message for this case. \item Update the basehaz function to a simple alias for "survfit". Prior versions called surfit but then only returned part of the object. Update 2/2015: reverted the change. It turns out that 6 different packages that depend on survival also depended on the old behavior. \item Make the default value for the shortlabel argument of strata() more nuanced. If the argument is a single factor, assume that we don't need to prepend the variable name to its levels. \item Return the weights vector, if present, as part of the survreg object. \item For interval censored points and the symmetric distributions (Gaussian and logistic) response type residuals were incorrect. Silly error: needed (x-mean)/scale not x/scale - mean. \item Martingale residuals could be incorrect for the case of model with (start, stop] data and a pspline term. Refactor the code so that all of the possible code paths call the same C routine to do the residuals. Add a new test for this case, and further tests to verify that predict(type='expected') and residuals agree. \item Fix bug pointed out by D Dunker: if a model had both tt() and cluster() terms it would fail with a length error. \item Fix a rare bug in plot.survfit: if a multistate curve rose and then later fell to exactly the same value, the line would be incorrect. \item Add calls to the R_CheckUserInterrupt to several routines, so that long calculations can be interrupted by the user. \item The anova.coxph function would fail if the original call had a subset argument. Pointed out by R Fisher. 11May2014 }} \section{Changes in version 2.37-7}{ \itemize{ \item Remove a dependency on the survey package from the adjusted survival curves vignette, at the request of CRAN. (The base + required bundle needs to be capable of a stand-alone build.) \item Fix error in calcuation of the y-axis range for survival curve plots whenever the "fun" argument could produce infinite values, e.g., complimentary log-log plots transform 1 to -Inf. Pointed out by Eva Boj del Val. (Add finite=TRUE to range() call). }} \section{Changes in version 2.37-6}{ \itemize{ \item The plot for competing risk curves could have a spurious segment. (Found within 3 hours of submitting 2.37-5 to CRAN.) \item The lines method for survexp objects was defaulting to a step function, restore the documented default of a connected line. \item Add a levels method for tcut objects. 14Jan2014 } } \section{Changes in version 2.37-5}{ \itemize{ \item Add vignette on adjusted survival curves. \item Add vignette concerning "type 3" tests. \item Make the tt() function invisible outside of a coxph formula. There was a complaint about conflicts with another package, and there is not really a good reason to have it be a global name. An R-devel discussion just over 1 year ago showed how to accomplish this. \item The modeling routines are set in two parts, e.g., coxph sets up the model and coxph.fit does the work. Export more of the ".fit" routines to make it easier for other packages to build on top of this one. \item Updates to the model.matrix and model.frame logic for coxph. A note from F Harrell showed that I was not correctly dealing with the "assign" attribute when there are strata * factor interactions. This led to cleanup in other cases that I had missed but which never had proven fatal. Also added support for tt() terms to the stand alone model.matrix and model.frame functions. (Residuals for tt models are still not available, but this was a necessary first step to that end.) 26Dec13 \item The Surv function now remembers attributes of the input variables that were passed to it; they are saved as "inputAttributes". This allows the rms package, for instance, to retain labels and units through the call. \item Update summary.coxph.penal to produce an object, which in turn has a print method, i.e., make it a "standard" summary function. \item Add a logLik method for coxph and survfit objects. \item Allow for Inf as the end of the time interval, for interval censored data in the Surv function. \item The predict.coxph function would fail if it had both a newdata and a collapse argument. Pointed out by Julian Bothe. 25Sep13 \item Survexp can now produce expecteds based on a stratified Cox model. Add the 'individual.s' and 'individual.h' options to return indivudual survival and cumulative hazard estimates, respectively. The result of survfit now (sometimes) includes the cumulative hazard. This will be expanded. 29Jul13 2 \item Change code in the coxpenal.fit routine: the use of a vector of symbols as arguments to my .C calls was confusing to a new CRAN consistency check. Both the old and new are legal R; but the old was admittedly an unusual construction and it was simpler to change it. \item Fix a bug in survfit.coxph pointed out by Chris Andrews, whose root cause was incorrect curve labels when the id option is used. 27Jun13 \item Add rsurvreg routine. \item Change survfit.coxph routine so that it detects whether newdata contains or does not contain strata variables, and acts accordingly. If newdata does containe strata then the output will contain only those data-value and strata combinations specified by the user. Retain strata levels in the coxph routine for use in the survfit routine, to correctly reconstruct strata levels. Warn about curves with interactions. 18Ju13 \item Add a dim method for survival curves. \item For competing risks curves that use the istate option, the plotted curves now start with the correct (initial) prevalence of each state. 22May13 \item The survreg function failed with the "robust=T" option. Pointed out by Jon Peck. Test case added. 6May13 \item Kazuki Yoshida pointed out that rep() had no method for Surv objects. This caused the survSplit routine to fail if the data frame contained a Surv object. 3May13 \item Per a request from Milan Bouchet-Valet fix an issue in survfit that arose when the OutDec option is set to ',': it did not correctly convert times back from character to numeric. \item The plot.survfit function now obeys "cex" for the size of the marks used for censored observations. }} \section{Changes in version 2.37-4}{ \itemize{ \item Subscripting error in predict.coxph for type=expected, se=T, strata in the model, newdata, and multiple strata in the new data set. Pointed out by Chris Andrews. The test program has been tweaked to include multiple strata in newdata. }} \section{Changes in version 2.37-3}{ \itemize{ \item Minor flaw in [.survfit. If "fit" had multiple curves, and fit$surv was a matrix, and one of those curves had only a single observation time, fit[i,] would collapse columns when "i" selected that curve, though it shouldn't. \item Changed all of the .C and .Call statements to make use of "registered native routines", per R-core request. Add file src/init.c \item Error in plot.survfit pointed out by K Hoggart -- the "+" signs for censored observations were printing one survival time to the left of the proper spot. Eik Vettorazi found another error if mark.time is a vector of numerics. These are the results of merging the code for plot, lines and points due to some discrepancies between them, plus not having any graphical checks in the test suite. \item Repair an error in using double subscripts for the survfitms objects. \item Add the US population data set, with yearly totals by age and sex for 2000 onward. It is named uspop2, since there is already a "uspop" data set containing decennial totals from 1790 to 1970. \item Not all combinations of strata Y/N and CI Y/N worked in the quantile.survfit function, pointed out by Daniel Wallschlaeger (missing a function argument in one if-else combination). Added a new test routine that verifies all paths. \item The first example in predict.survreg help file needed to have \code{I(age^2)} instead of \code{age^2} in the model: R ignores the second form. (I'm almost sure this worked at one time, perhaps in Splus). It also needed different plot symbols to actually match the referenced figure. Pointed out by Evan Newell. \item Fix a long-standing problem with cch pointed out by Ornulf Borgan leading to incorrect standard errors. A check in the underlying coxph routines to deal with out of bounds exponents, added in version 2.36-6, interacted badly with the -100 offset used in cch. It only affected models using (start, stop) survival times. }} \section{Changes in version 2.37-2}{ \itemize{ \item Two bugs were turned up by running tests for all the packages that depend on survival (158 of them). }} \section{Changes in version 2.37-1}{ \itemize{ \item Add a new multi-state type to the Surv object. Update the survfit routine to work with it. The major change is addition of a proper variance for this case. More functionality is planned. \item Remove the fr_colon.R test program. It tests an ability that has been superseded by coxme, on a numerically touchy data set, and it was slow besides. For several other tests that produce warning messages and are supposed to produce said messages, add extra comments to that effect so testers will know it is expected. \item The code has had several "if.R" clauses to accomodate Splus vs R differences, which are mostly class vs oldClass. These are now being removed as I encounter them; since our institution no longer uses Splus I can no longer test the clauses' validity. \item The fast subsets routine coxexact.fit incorrectly returned the linear predictor vector in the (internal) sorted order rather than data set order. Pointed out by Tatsuki Koyama, affecting the result of a clogit call. 6Nov2012 \item Jason Law pointed out that the sample data set "rats" is from the paper by Mantel et.al, but the documentation was for a data set from Gail, Santner and Brown. Added the Gail data as rats2 and fixed the documentation for rats. \item For predict.coxph with type="terms", use "sample" as the default value for the reference option. For all others the default remains "strata", the current value. Type terms are nearly always passed forward for further manipulation and per strata centering can mess things up: termplot() for instance will no longer show a smooth function if the results are recentered within strata. \item Fix bug in summary.aareg, which was unhappy (without cause) if the maxtime option was used for a fit that did not include the dfbeta option. Pointed out by Asa Johannesen. \item The coxph fitting functions would report an error for a null model (no X variables) if init was specified as numeric(0) rather than NULL. \item Update the description and citation files to use the new "person" function described in the R Journal. Also add the ByteCompile directive per suggestion of R core. \item Allow an ordinary vector as the left hand side of survConcordance. \item Update anova.coxphlist to reject models with a robust variance. \item The survfit function had an undocumented backwards-compatability that allows the newdata argument to be a vector with no names. An example from Damon Krstajic showed that this does not work when the original model has a matrix in the formula. Removed the feature. (This is for survfit.coxph.) Also clarified the code and its documentation about what is found where -- environments, formulas, and the arguments of eval, which fixes a problem pointed out by xxx where the result of a Surv call is used in the coxph formula. \item Fix an issue in summary.survfit pointed out by Frank Harrell. The strata variable for the output always had its labels in sorted order, even when a factor creating the survival curves was otherwise. (This was due to a call to factor() in the code.) The print routine would then list curves in sorted order, which might well be contrary to the user's wishes. The curves were numerically correct. \item Add the anova.coxmelist function to the namespace so that it is visible. If someone has a list of models the first of which was a coxph fit and the list includes coxme fits, then anova.coxph will be the function called by R, and it will call anova.coxmelist. \item Fix a bug pointed out by Yi Zhang and Mickael Hartweg. If a coxph model used an offset, then a predicted survival curve that used newdata (and the offset variable of course) would be wrong, e.g. survival values > 1. A simple misplaced parenthesis was the cause. A recent paper by Langholz shows how to get absolute survival from case-control data using an offset, which seems to have suddenly made this feature popular. \item Per further interaction with Yi Zhang, a few items were missing from the S3methods in the NAMESPACE file: as.matrix.Surv, model.matrix.coxph, model.matrix.survreg, model.frame.survreg. }} \section{Changes in version 2.36-14}{ \itemize{ \item A supposedly cosmetic change to coxph in the last release caused formulas with a "." on the right hand side to fail. Fix this and add a case with "." to the test suite. } } \section{Changes in version 2.36-13}{ \itemize{ \item Add the anova.coxmelist function. This is in the survival package rather than in coxme since "anova(fit1, fit2)" is valid when fit1 is a coxph and fit2 a coxme object, a case which will cause this function to be called by way of anova.coxph. \item More work on "predvars" handling for the pspline function, when used in predict calls. Add a new test of this to the suite, and the makepredictcall method to the namespace. Fixes a bug pointed out by C Crowson. \item Deprecate the "robust" option of coxph. When there are multiple observations per subject it is almost surely the wrong thing to do, while adding a "cluster(id)" term does the correct thing. When there is only one obs per subject both methods work correctly. \item Add documentation of the output structure to the aareg help file. \item Change ratetableDate so that it still allows use of chron objects, but doesn't need the chron library. This eliminates a warning messge from the package checks, but is also a reasonable support strategy for a moribund package. (Some of the local users keep datasets for a long long time.) \item Fix a bug in summary.survfit for a multiple-strata survival object. If one of the curves had no data after application of the times argument, an output label was the wrong length. \item Fix a bug pointed out by Charles Berry: predict for a Cox model which has strata, and the strata is a factor with not all its levels represented in the data. I had a mistake in the subscripting logic: number of groups is not equal to max(as.integer(strata)). \item Changes to avoid overflow in the exponent made in 2.36-6 caused failure for one special usage: in case-cohort designs a dummy offset of -100 could be added to some observations. This was being rounded away. The solution is to 1: have coxsafe not truncate small exponents and 2: do not recenter user provided offset values. \item Fix bug in survfit.coxph. Due to an indexing error I would sometimes create a huge scratch vector midway through the calculations (size = max value of "id"); the final result was always correct however. Data set provided by Cindy Crowson which had a user id in the billions. \item Fix bug pointed out by Nicholas Horton: predictions of type expected, with newdata, from a Cox model without a strata statement would fail with "x not found". A misplaced parenthesis from an earlier update caused it to not recreate the X matrix even though it was needed later. Also add some further information to the predict manual page to clarify an issue with frailty terms. }} \section{Changes in version 2.36-12}{ \itemize{ \item Fix a bug in the new fast subsets code. The test suite had no examples of strata + lots of tied times, so of course that's the case where I had an indexing error. Add a test case using the clogit function, which exercises this. \item Further memory tuning for survexp. }} \section{Changes in version 2.36-11}{ \itemize{ \item Make survexp more efficient. The X matrix was being modified in several places, leading to multiple copies of the data. When the data set was large this would lead to a memory shortage. \item Cause anova.coxph to call anova.coxme when a list of models has both coxph and coxme objects. \item Add the quantile.survfit function. This allows a user to extract arbitrary quantiles from a fitted curve (and std err). \item Fix an error in predict.coxph. When the model had a strata and the newdata and reference="sample" arguments were used, it would (incorrectly) ask for a strata variable in the new data set. \item Incorporate the fast subsets algorithm of Gail et al, when using coxph with the "exact" option. The speed increase is profound though at the cost of some memory. Reflect this in the documentation for the clogit routine. Note that the fast computation is not yet implemented for (start,stop) coxph models. \item Change the C routine used by coxph.fit from .C to .Call semantics to improve memory efficiency, in particular fewer copies of the X matrix. \item Add scaling to the above routine. This was prompted by a user who had some variables with a 0-1 range and others that were 0 - 10^7, resulting in 0 digits of accuracy in the variance matrix. (Economics data). \item Comment out some code sections that are specific to Splus. This reduced the number of "function not found" warnings from R CMD check. }} \section{Changes in version 2.36-10}{ \itemize{ \item 30 Sept 2011: The na.action argument was being ignored in predict.coxph; pointed out by Cindy Crowson. \item The log-likelihood for survreg was incorrect when there are case weights in the model. The error is a fixed constant for any given data set, so had no impact on tests or inferences. The error and correction were pointed out by Robert Kusher. \item A variable name was incorrect in survpenal.fit. This was in a program path that had never been traversed until Carina Salt used survreg with a psline(..., method='aic') call, leading to a "variable not found" message. \item Punctuation error in psline made it impossible for a user to specify the boundary.knots argument. Pointed out by Brandon Stewart. \item Add an "id" variable to the output of survobrien. \item The survfitCI routine would fail for a curve with only one jump point (a matrix collapsed into a vector). \item Fix an error in survfit.coxph when the coxph model has both a strata by covariate interaction and a cluster statement. The cluster term was not dropped from the Terms object as it should have been, led to a spurious "variable not found" error. Pointed out by Eva Bouguen. \item If a coxph model with penalized terms (frailty, pspline) also had a redundant covariate, the linear predictor would be returned as NA. Pointed out by Pavel Krivitsky. }} \section{Changes in version 2.36-9}{ \itemize{ \item Due to a mistake in my script that submits to CRAN, the fix in 2.36-8 below was actually not propogated to the CRAN submission. \item Fix an error in the Cauchy example found in the survreg.distributions help page, pointed out by James Price. \item Update the coxph.getdata routine to use the model.frame.coxph and model.matrix.coxph methods. \item Add the concordance statistic to the printout for penalized models. }} \section{Changes in version 2.36-8}{ \itemize{ \item Unitialized variable in calcuation of the variance of the concordance. Found on platform cross-checking by Brian Ripley. \item Changed testci to use a fixed file of results from cmprsk rather than invoking that package on-the-fly. Suggested by the CRAN maintainers. } } \section{Changes in version 2.36-7}{ \itemize{ \item Due to changes in R 2.13 default printout, the results of many of the test programs change in trivial way (one more or fewer digits). Update the necessary test/___.Rout.save files. Per the core team's suggestion the dependency for the package is marked as >=2.13. }} \section{Changes in version 2.36-6}{ \itemize{ \item An example from A Drummond caused iteration failure in coxph: x=c(1,1,1,0,1, rep(0,35)), time=1:40, status=1. The first iteration overshoots the solution and lands on an almost perfectly linear part of the loglik surface, which made the second iteration go to a huge number and exp() overflows. A sanity check routine coxsafe is now invoked on all values of the linear predictor. \item 1 April: Fix minor bug in survfit. For left censored data where all the left censored are on the very left, it would give a spurious warning message when trying to create a 0 row matrix that it didn't need or use. Pointed out by Steve Su. \item 31 March 2011: One of the plots in the r_sas test was wrong (it's been a long time since I visually checked these). The error was in predict.survreg; it had not taken into account a change in R2.7.1: the intercept attribute is reset to 1 whenever one subscripts a terms object, leading to incorrect results for a model with "-1" in the formula and a strata(): the intercept returned when removing the strata. I used this opportunity to move most of the logic into model.frame.survreg and model.matrix.survreg functions. Small change to the model.frame.coxph and model.matrix.coxph functions due to a better understanding of xlevels processing. \item Round off error issue in survfit: it used both unique(time) and table(time), and the resulting number of unique values is not guarranteed to be the same for times that differ by a tiny amount. Now times are coverted to a factor first. Peter Savicky from the R core team provided a nice discussion of the issue and helped me clarify how best to deal with it. The prior fix of first rounding to 15 digits was good enough for almost every data set -- except the one found by a local user just last week. \item Round off error in print.survfit pointed out by Micheal Faye. If a survival value was .5 in truth, but .5- eps due to round off the printed median was wrong. But it was ok for .5+eps. Simple if-then logic error. \item Re-fix a bug in survfit. It uses both unique and table in various places, which do not round the same; I had added a pre-rounding step to the code. A data set from Fan Chun showed that I didn't round quite enough. But the prior rounding did work for a time of 2 vs (sqrt(2))^2: this bug is very hard to produce. I now use as.numeric(as.character(factor(x))), which induces exactly the same rounding as table, since it is the same compuation path. \item Further changes to pspline. The new Boundary.knots argument allows a user to set the boundary knots inside the range of data. Code for extrapolation outside that range was needed, essentially a copy of the code found in ns() for the same issue. Also added a psplineinverse function, which may be useful with certain tt() calls in coxph. \item 10 Mar 2011: Add the capablilty for time-dependent transformations to coxph, along with a small vignette describing use of the feature. This code is still incompletely incorporated in that the models work but other methods (residuals, predict, etc) are not yet defined. \item 8 Mar 2011: Expand the survConcordance function. The function now correctly handles strata and time dependent covariates, and computes a standard error for the estimate. All computation is based on a balanced binary tree strucure, which leads to computation in \eqn{O(n \log_2(n))}{O(n log(n))} time. The \code{coxph} function now adds concordance to its output, and \code{summary.coxph} displays the result. \item 8 Mar 2011: Add the "reference" option to predict.coxph, a feature and need pointed out by Stephen Bond. \item 4 Mar 2011: Add a makepredictcall method for pspline(), which in turn required addition of a Boundary.knots argument to the function. \item 25 Feb 2011: Bug in pyears pointed out by Norm Phillips. If a subject started out with "off table" time, their age was not incremented by that amount as they moved forward to the next "in table" cell of the result. This could lead to using the wrong expected rate from the rate table. } } \section{Changes in version 2.36-5}{ \itemize{ \item 20 Feb 2011: Update survConcordance to correctly handle case weights, time dependent covariates, and strata. \item 18 Feb 2011: Bug in predict.coxph found by a user (1 day after 36-4!). If the coxph call had a subset and predict used newdata, the subset clause was "remembered" in the newdata construction, which is not appropriate. }} \section{Changes in version 2.36-4}{ \itemize{ \item 17 Feb 2011: Fix to predict.coxph. A small typo that only was exercised if the coxph model had x=T. Discovered via induced error in the rankhazard package. Added lines to the test suite to test for this in the future. \item Removed some files from test and src that are no longer needed. \item Update the configure script per suggestion from Kurt H. }} \section{Changes in version 2.36-3}{ \itemize{ \item 13 Feb 2011: Add the rmap argument to pyears, as was done for survexp, and update the manual pages and examples. Fix one last bug in predict.coxph (na.action use). Passes all the tests for inclusion on the next R release. \item 8 Feb 2011: Change the name of the new survfit.coxph.fit routine to survfitcoxph.fit; R was mistaking it for a survfit method. Fix errors in predict.coxph when there is a newdata argument, including adding yet another test program. \item 1 Feb 2011: Fix bugs in coxph and survreg pointed out by Heinz Tuechler and dtdenes@cogpsyphy.hu, independently, that were the same wrong line in both programs. With interactions, a non-penalized term could be marked as penalized due to a mismatched vector length, leading to a spurious error message later in the code. \item 1 Feb 2011: Update survfit.coxph to handle the case of a strata by covariate interaction. All prior releases of the code did this wrong, but it is a very rare case (found by Frank Harrell). Added a new test routine coxsurv4. Also found a bug in [.survfit; for a curve with both strata and multiple columns, as produced by survfit.coxph, it could drop the n.censored item when subscripting. A minor issue was fixed in coxph: when iter=0 the output coefficient vector should be equal to the input even when the variance is singular. \item 30 Jan 2011: Move the noweb files to a top level directory, out of inst/. They don't need to be copied to binary installs. \item 22 Jan 2011: Convert the Changelog files to the new inst/NEWS.Rd format. \item 1 Jan 202011: The match.ratetable would fail when passed a data frame with a character variable. This was pointed out by Heinz Tuechler, who also did most of the legwork to find it. It was triggered by the first few lines of tests/jasa.R (expect <- ....) when options(stringsAsFactors=FALSE) is set. } } \section{Changes in version 2.36-2}{ \itemize{ \item 20 Dec 2010: Add more test cases for survfit.coxph, which led to significant updates in the code. \item 18 Nov 2010: Add nevent to the coxph output and printout in response to a long standing user request. \item 14 Dec 2010: Add an as.matrix method for Surv objects. \item 11 Nov 2010: The prior changes broke 5 packages: the dependencies form a bigger test suite than mine! 1. Survival curve for a coxph model with sparse frailty fit; fixed and added a new test case. 2. survexp could fail if called from within a function due to a scoping error. 3. "Tsiatis" was once a valid type (alias for 'aalen') for survfit.coxph; now removed from the documentation but the code needed to be backwards compatable. The other two conflicts were fixed in the packages that call survival. There are still issues with the rms package which I am working out with Frank H. } } \section{Changes in version 2.36-1}{ \itemize{ \item{27 Oct 2010: Finish corrections and test to the new code. It now passes the checks. The predict.coxph routine now does strata and standard errors correctly, factors propogate through to predictions, and numerous small errors are addressed. Predicted survival curves for a Cox model has been rewritten in noweb and expanded. Change the version number to 2.36-1.} \item{17 Oct 2010: Per a request from Frank Harrell (interaction with his library), survfit.coxph no longer reconstructs the model frame unless it really needs it: in some cases the 'x' and 'y' matrices may be sufficient, and may be saved in the result. Add an argument "mf" to model.matrix.coxph for more efficient interaction when a parent routine has already recovered the model frame. In general, we are trying to make use of model.matrix.coxph in many of the routines, so that the logic contained there (remove cluster() calls, pull out strata, how to handle intercepts) need not be replicated in multiple places.} \item{12 Oct 2010: Fix a bug in the modified lower limits for survfit (Dory & Korn). A logical vector was being inadvertently converted to numeric. Pointed out by Andy Mugglin. A new case was added to the test suite. } } } \section{Changes in version 2.35}{ \itemize{ \item{15 July 2010: Add a coxph method for the logLik function. This is used by the AIC function and was requested by a user.} \item{29 July 2010: Fix 2 bugs in pyears. The check for a US rate table was off (minor effect on calculations), and there was a call to julian which assumed that the origin argument could be a vector. } \item{21 July 2010: Fix a problem pointed out by a user: calling survfit with almost tied times, e.g., c(2, sqrt(2)^2), could lead to an inconsistent result. Some parts of the code saw these as 2 unique values per the unique() function, some as a single value using the results of table(). We now pre-round the input times to one less decimal digit than the max from .Machine$double.digits. Also added the noweb.R processing function from the coxme package, so that the noweb code can be extracted "on the fly" during installation using commands in the configure and cleanup scripts. } \item{11 July 2010: A rewrite of the majority of the survfit.coxph code. The primary benefits are 1: finally tracked down and eliminated the bug for standard errors of case weights + Cox survival + Efron method; 2: the individual=TRUE and FALSE options now use the same underlying code for curves, before there were some options valid only for one or the other; 3: code was rewritten using noweb with a considerable increase in documentation; 4: during the verification process some errors were found in the test suite and corrected, e.g., a typo in my book led to failure of an all.equal test in book4.R. Similar to the rewrite for survfit several years ago, the new code has far less use of .C to help transparency.} \item{21 May 2010: Fix bug in summary.survfit. For a survival curve from a Cox model with start,stop data, the 'times' argument would generate an error.} \item{24 May 2010: Fix an annoyance in summary.survfit. When the survival data had an event or censor at time 0 and summary is called with a times argument, then my constructed call to approx() would have duplicate x values. The answer was always right, but approx has begun to print a bothersome warning message. A small change to the constructed argument vector avoids it.} \item{7 April 2010: Minor bug pointed out by Fredrik Lundgren. In survfit if the method was KM (default) and error = Tsiatis an error message results. Simple fix: code went down the wrong branch.} \item{24 Feb 2010: Serious bug pointed out by Kevin Buhr. In Surv(time1, time2,stat) if there were i) missing values in time1 and/or time2, ii) illegal value sets with time1 >=time2, and iii) all the instances of ii do not preceed all the instances of i, then the wrong observation (not the illegal) will be thrown out. Repaired, and a new test added. Minor updates to 3 test files: survreg2, testci, ratetable.} \item{8 Feb 2010: Bug pointed out by Heinz Tuechler -- if a subscript was dropped from a rate table the 'type' attribute got dropped, e.g. survexp.usr[,1,,].} \item{26 Jan 2010: At the request of Alex Bokov, added the xmax, xscale, and fun arguments to points.survfit.} \item{26 Jan 2010: Fix bug pointed out by Thomas Lumley -- with case weights <1 a Cox model with (start, stop) input would inappropriately decide it needed to do step halving to find a solution, eventually failing to converge. It was treating a loglik >0 as an indication of failure, but such values arise for small case weights. Let L(w) be the loglik for a data set where everyone is given a weight of w, then L(w)= wL(1) - d log(w) where d=number of deaths in the data. For small enough w positivity of L(w) is certain.} \item{25 Jan 2010: Fix bug in summary.ratetable pointed out by Heinze Tuechler. Added a call to the function to the test suite as well.} \item{15 Dec 2009: Two users pointed out a bug that crept into survreg() with a cluster statement, when a t(x)%*%x was replaced with crossprod. A trivial fix, but in response I added another test that more formally checks the dfbeta residuals and found a major oversight for the case of multiple strata. } \item{14 Dec 2009: 1.Fix bug in frailty.xxx, if there is a missing value in the levels it gets counted by "length(unique(x))" (frailty is called before NA removal.) 2.SurvfitCI had an incorrect CI with case weights, and 3. in survreg a call to resid instead of residuals.survreg, before the class was attached.} \item{11 Nov 2009: The 'type' argument does not make sense for plot.survfit. (If type='p', should one plot the tops of the step function, the bottoms, or both?). Make it explicitly disallowed in response to an R-help query, rather than the confusing error message that currently arose.} \item{28 Oct 2009: The basehaz function would reorder the labels of the strata factor. Not a bug really, but a "why do this?" Unintended consequence of a character -> factor conversion.} \item{1 Oct 2009: Fix a bug pointed out by Ben Domingue. There was one if-then-else path into step-halving in the frailty.controldf routine that would refer to a non-existent variable. A very rarely followed path, obviously, and with the obvious fix. The mathematics of the update was fine.} \item{30 Sep 2009: For coxph and model.matrix.coxph, re-attach the attributues lost from the X matrix when the intercept is removed, i.e., X <- X[,1]. In particular, some downstream libraries depend on the assign attribute. For predict.coxph remove an earlier edit so that a single variable model + type='terms' returns a matrix, not a vector. This is expected by the termplot() function. It led to a whole lot of changes in the test suite results, though, due to more "matrix" printouts.} \item{4 Sep 2009: Added a model.matrix.coxph and model.frame.coxph methods. The model.matrix.default function ceased to work for coxph models sometime between R 2.9 and 2.9.2 (best guess). This wasn't picked up in the test suite but rather by failure of 3 packages that depend on survival. Also added a test. Update CRAN since this broke other's packages.} \item{20 Aug 2009: One more fix to predict.coxph. It needed to use delete.response(Terms) rather than Terms, so as to not look for (unnecessarily) the response variable when the newdata argment is used. Pointed out by Michael Conklin.} \item{17 Aug 2009: Small bug in survfit.coxph.null pointed out by Frank Harrell. The 'n' component would be missing if the input data included strata, i.e., the initial model had used x=TRUE. He also pointed out the fix.} \item{10 June 2009: Fix an error pointed out by Nick Reich, who was the first to use interval censored data + user defined distribution in survreg, jointly. There was no test case and creating one uncovered several errors (but only for this combination). All the error cases led to catastrophic failure, highlighting the extreme rarity of a user requesting this combination.} \item{2 June 2009: Surv(time1, time2, status, type='interval') would fail for an NA status code. Pointed out by Achim Zeilus.} \item{22 May 2009: Allow single subscripts to rate tables, e.g. survexp[1:10: . Returns a simple vector of values. The str() function does this to print out a short summary. Problem pointed out by Heinz Tuechler.} \item{21 May 2009: Create a test case for factor variables/newdata/predict for coxph and survreg. This led to a set of minor fixes; the code is now in line with the R standard for model functions. One consequence is that model.frame.coxph and model.frame.survreg are no longer needed, so have been removed.} \item{20 May 2009: The manual page for survfit was confusing, since it tries to document both the standard KM (formula method) and the coxph method. I've split them out so that now survfit documents only the basic method and points a user the appropriate specialized page.} \item{1 May 2009: The anova.coxph function was incorrect for models with a strata term. Fixed this, and made chisquare tests the default.} \item{22 April 2009: The coxph code had an override to iter and eps, making both of them more strict for a penalized model. However, the overall default values have changed over time, so that these lines actually decreased accuracy - the opposite of their intent. Removed the lines. Also removed the iter.miss and eps.miss components (on which this check depended) from coxph.control, which makes that function match its documentation.} } } \section{Changes in version 2.34 and earlier}{ \subsection{Merge of the TMT source code tree with the Lumley code tree}{ \itemize{ \item Issues/decisions in remerging the Mayo and R code: For most of routines, it was easier to start with the Lumley code and add the Therneau fixes. This is because Tom had expanded a lot of partial matches, e.g., fit$coef in the TT code vs fit$coefficients. Routines with substantial changes were, of course, a special case. The most common change is an is.R() construct to choose class vs oldClass. \item xtras.R: Move anova.coxph and anova.coxphlist to their own source files. The remainder of the code is R only. \item survsum: removed from package \item survreg.old: has been removed from the package \item survfit.s: Depreciate the "formula with no ~1" option Mayo code for [ allows for reordering curves Separate out the R "basehaz" function as a separate source file \item survfit.km.s: The major change of did not get copied into R, so lots of changes. R had "new.time" and Splus 'start.time' for the same argument. Allow them both as synonyms. The output structure also changed: adapt the new one. This is mostly some name changes in the components, removing unneeded redundancies created by a different programmer. \item survfit.coxph.s: TMT code finally fixed the "Can't (yet) to case weights" problem. There must have been 10 years been the intent and execution. \item survexp.s: Add "bareterms" function from R, which replaces a prior use of terms.inner (in Splus but not R). \item survdiff.s: R code had the old (incorrect) expected <- sum(1-offset), since corrected to sum(-log(offset)) . \item{summary.coxph.s: This was a mess, since Tom and I had independently made the addition of a print.summary.coxph function. Below, TMT means that it was the choice in the Splus code, TL means that it was the choice in R 1. Put the coef=T argument in the print function, not summary (TMT) 2. Change the output's name from coef to coefficients (suggestion of Peter Dalgaard). Also change one column name to Pr(>|z|) for R. 3. Remove last vestiges of a reference to the 'icc' component (TMT) 4. Do not include score, rscore, naive.var in the result (TL) 5. Do include loglik in the result (TMT) 6. Compute the test statistics (loglik, Wald, etc) in the summary function rather than in the print.summary function (TL) 7. Remove the digits option from summary, it belongs in print.summary. (neither)} \item{strata.s: R code added a sep argument, this is ok R changed the character string NA to as.character(NA). Not okay 1. won't work with Splus, 2. This is a label, designed for printing, and so it should be a character string. } \item{residuals.coxph.s: R had added type='partial'. (Which I'm not very partial to, from their statistical properties. But they are legal, and I assume that someone requested them).} \item{print.survfit.s: Rewritten as a part of the general survival rewrite. Created the function 'survmean' which does most of the work, and is shared by print and summary, so that the values from 'print' are now available. Fix the minmin function: min(NULL) gives NA in Splus, which is the right answer for a non-estimable median, but Inf in R. Explicitly deal with this case, and add a bunch of comments. R had the print.rmean option, this has been expanded to a more general rmean option that allows setting the cutoff point. R added a print.n option with 3 choices, my code includes all 3 in the output. } \item{lines.survfit.s: The S version has a new block of code for guessing "firstx" more intellegently when it is missing. (Or, one hopes is is more intellegent!)} \item{coxph.control.s: The R code had tighter tolerances (eps= 1e-9) than Splus (1e-4) and a higher iterationn count (20 vs 10). Set eps to 1e-8 and iter to 15, mostly bending to the world. The tighter iteration is defensible, but I still maintain that a Cox model that takes >10 iterations is not going to finish if you give it 100. The likelihood surface is almost perfectly quadratic near the minimum. (Not true for survreg by the way).} \item{: In Surv, the Mayo code creates NA's out of invalid status values or start,stop pairs, rather than a stop and error message. This is to allow for example coxph(Surv(time1,time2, status).... , subset=(goodlines)) succeed, when "goodlines" is the subset with correct values.} } } \subsection{Older changes}{ \itemize{ \item{25SepO7: How embarrassing -- someone pointed out that I had Dave Harrington's name spelled wrong in the options to survfit.coxph!} \item{9Jul07: In a model with offsets, survreg mistakenly omitted the offset from the returned linear.predictor component.} \item{10May07: Change summary.coxph so that it returns an object of class summary.coxph, and add a print method for that object.} \item{22Jun06: Update match.ratetable, so that more liberal matches are now allowed. For instance, 'F', 'f', 'female', 'fem', 'FEMA', etc are now all considered matches to the dimname "female" in survexp.us.} \item{26Apr06: Fix bug in summary.survfit, pointed out by Bob Treder. With the times option, the value of n.risk would be wrong for "in between" times; e.g., the data had events and/or censoring at times 10, 20,... and we asked for printout at time 15. It should give n.risk at time 20, it was returning the value at time 10. Interestingly, the code had a very careful treatment of this case, along with an example in the comments, and the "the right answer is" part of the comment was wrong! So the code correctly computed an incorrect answer. Added another test case to the test suite, survtest2.} \item{21Apr06: Fix problem in [.survfit, pointed out by Thomas Lumley. If fit <- survfit(Surv(time, status) ~ ph.ecog, lung), then fit[2:1] did not reorder the output correctly. I had never tested putting the subscripts in non-increasing order.} \item{7Feb06: Fix a problem in the coxph iteration (coxfit2.c, coxfit5, agfit3, agfit5, agexact). It will likely never catch anyone again, even if I didn't fix it. In a particular data set, beta overshot and step halving was invoked. During step halving, a loglik happened to occur that was within eps of the prior step's loglik --- and the routine decided, erroneously, that it had converged! (A nice quadratic curve, a first guess b1 to the left of the desired max of the curve. The next guess b2 overshot and ends up with a lower loglik, on the right side of the max. Back up to the midpoint of b1 and b2, and this guess, still to the right of the max (still too large) has EXACTLY the same value of y as b1 did, but on the other side of the max from b1. "Last two guesses give the same answer, I'm done" said the routine).} \item{27Sep05: Found and fixed a nasty bug in survfit. When method='fh2' and there were multiple groups I had a subscripting bug, leading to vectors that were supposed to be the same length, but weren't, passed into C. The resulting curves were obviously wrong -- survival precipitously drops to zero.} \item{5May05: Add the drop=F arg to one subscripting selection in survfit.coxph. temp <- (matrix(surv$y, ncol=3))[ntime,,drop=F] If you selected only 1 time point (1 row) in the final output, the code would fail. Pointed out by Cindy Crowson.} \item{18Apr05: Bug in survfit.turnbull. The strata variable was not being filled in (number of points per curve). So if multiple curves were generated at once, i.e., with something on the right hand side of ~ in the formula, all the downstream print/plot functions would not work with the result.} \item{8Feb05: Fix small typo in is.ratetable, introduced on 24Nov04: (Today was the first time I added to the standard library, and thus ended up using the non-verbose mode.)} \item{8Feb05: Add the data.frame argument to pyears. This causes the output to contain a dataframe rather than a set of arrays. It is useful for further processing of the data using Poisson regression.} \item{7Feb05: Modified print.ratetable to be more useful. It now tells about the ratetable, rather than printing all of its values.} \item{8Dec04: Fix a small bug in survfit.turnbull. If there are people left censored before the first time point of any other kind (interval, exact, or right censored), the the plotted height of the curve from "rightmost left censoring time" to "leftmost event time", that is the flat tail on the left, was at the wrong height. Added another test to testreg/reliability.s for this.} \item{24Nov04: Change is.ratetable to give longer messages} } } } survival/inst/COPYRIGHTS0000755000175100001440000000024112257335007014542 0ustar hornikusersCopyright 2000 Mayo Foundation for Medical Education and Research. 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\SweaveOpts{prefix.string=adjcurve,width=6,height=4} \setkeys{Gin}{width=\textwidth} %\VignetteIndexEntry{Adjusted Survival Curves} <>= options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text require(survival, quietly=TRUE) fdata <- flchain[flchain$futime > 7,] fdata$age2 <- cut(fdata$age, c(0,54, 59,64, 69,74,79, 89, 110), labels = c(paste(c(50,55,60,65,70,75,80), c(54,59,64,69,74,79,89), sep='-'), "90+")) @ \title{Adjusted Survival Curves} \author{Terry M Therneau, Cynthia S Crowson, Elizabeth J Atkinson} \date{Jan 2015} \newcommand{\myfig}[1]{\includegraphics[height=!, width=\textwidth] {adjcurve-#1.pdf}} \begin{document} \maketitle \section{Introduction} Suppose we want to investigate to what extent some factor influences survival, as an example we might compare the experience of diabetic patients who are using metformin versus those on injected insulin as their primary treatment modality. There is some evidence that metformin has a positive influence, particularly in cancers, but the ascertainment is confounded by the fact that it is a first line therapy: the patients on metformin will on average be younger and have had a diabetes diagnosis for a shorter amount of time than those using insulin. ``Young people live longer'' is not a particularly novel observation. The ideal way to test this is with a controlled clinical trial. This is of course not always possible, and assessments using available data that includes and adjusts for such confounders is also needed. There is extensive literature --- and debate --- on this topic in the areas of modeling and testing. The subtopic of how to create honest survival curve estimates in the presence of confounders is less well known, and is the focus of this note. Assume that we have an effect of interest, treatment say, and a set of possible confounding variables. Creation a pair of adjusted survival curves has two parts: definition of a reference population for the confounders, and then the computation of estimated curves for that population. There are important choices in both steps. The first, definition of a target, is often not explicitly stated but can be critical. If an outcome differs with age, myocardial infarction say, and two treatments also had age dependent efficacy, then the comparison will depend greatly on whether we are talking about a population of young, middle aged, or older subjects. The computational step has two main approaches. The first, sometimes known as \emph{marginal} analysis, first reweights the data such that each subgroup's weighted distribution matches that of our population target. An immediate consequence is that all subgroups will be balanced with respect to the confounding variables. We can then proceed with a simple analysis of survival using the reformulated data, ignoring the confounders. The second approach seeks to understand and model the effect of each confounder, with this we can then correct for them. From a comprehensive overall model we can obtain predicted survival curves for any configuration of variables, and from these get predicted overall curves for the reference population. This is often called the \emph{conditional} approach since we are using conditional survival curves given covariates $x$. A third but more minor choice is division of the covariates $x$ into effects of interest vs. confounders. For instance, we might want to see separate curves for two treatments, each adjusted for age and sex. The reference population will describe the age and sex distribution. For simplicity we will use $x$ to describe all the confounding variables and use $c$ for the control variable(s), e.g. treatment. The set $c$ might be empty, producing a single overall curve, but this is the uncommon case. As shown below, our two methods differ essentially in the \emph{order} in which the two necessary operations are done, balancing and survival curve creation. \begin{center} \begin{tabular}{rccc} Marginal: & balance data on $x$ & $\longrightarrow$ & form survival curves for each $c$\\ Conditional: & predicted curves for $\{x,c\}$ subset & $\longrightarrow$ & average the predictions for each $c$ \end{tabular} \end{center} We can think of them as ``balance and then model'' versus ``model then balance''. An analysis might use a combinations of these, of course, balancing on some factors and modeling others. All analyses are marginal analyses with respect to important predictors that are unknown to us, although in that case we have no assurance of balance on those factors. \begin{figure}[tb] \myfig{flc1} \caption{Survival of \Sexpr{nrow(flchain)} residents of Olmsted County, broken into three cohorts based on FLC value.} \label{flc1} \end{figure} \section{Free Light Chain} Our example data set for this comparison uses a particular assay of plasma immunoglobulins and is based on work of Dr Angela Dispenzieri and her colleagues at the Mayo Clinic \cite{Dispenzieri12}. In brief: plasma cells (PC) are responsible for the production of immunoglobulins, but PC comprise only a small portion ($<1$\%) of the total blood and marrow hematapoetic cell population in normal patients. The normal human repertoire is estimated to contain over $10^{8}$ unique immunoglobulins, conferring a broad range of immune protection. In multiple myeloma, the most common form of plasma cell malignancy, almost all of the circulating antigen will be identical, the product of a single malignant clone. An electrophoresis examination of circulating immunoglobulins will exhibit a ``spike'' corresponding to this unique molecule. This anomaly is used both as a diagnostic method and in monitoring the course of the disease under treatment. The presence of a similar, albeit much smaller, spike in normal patients has been a long term research interest of the Mayo Clinic hematology research group \cite{Kyle93}. In 1995 Dr Robert Kyle undertook a population based study of this, and collected serum samples on 19,261 of the 24,539 residents of Olmsted County, Minnesota, aged 50 years or more \cite{Kyle06}. In 2010 Dr. Angela Dispenzieri assayed a sub fraction of the immunoglobulins, the free light chain (FLC), on 15,748 of these subjects who had sufficient remaining sera from the original sample collection. All studies took place under the oversight of the appropriate Institutional Review Boards, which ensure rigorous safety and ethical standards in research. A subset of the Dispenzieri study is available in the survival package as data set \texttt{flchain}. Because the original study assayed nearly the entire population, there is concern that some portions of the anonymized data could be linked to actual subjects by a diligent searcher, and so only a subset of the study has been made available as a measure to strengthen anonymity. It was randomly selected from the whole within sex and age group strata so as to preserve the age/sex structure. The data set contains 3 subjects whose blood sample was obtained on the day of their death. It is rather odd to think of a sample obtained on the final day as ``predicting'' death, or indeed for any results obtained during a patient's final mortality cascade. There are also a few patients with no follow-up beyond the clinic visit at which the assay occurred. We have chosen in this analysis to exclude the handful of subjects with less than 7 days of follow-up, leaving \Sexpr{nrow(fdata)} observations. \begin{table} \centering \begin{tabular}{l|cccc} & 50--59 & 60--69 & 70--79 & 80+ \\ \hline <>= group3 <- factor(1+ 1*(fdata$flc.grp >7) + 1*(fdata$flc.grp >9), levels=1:3, labels=c("FLC < 3.38", "3.38 - 4.71", "FLC > 4.71")) age1 <- cut(fdata$age, c(49,59,69,79, 110)) levels(age1) <- c(paste(c(50,60,70), c(59,69,79), sep='-'), '80+') temp1 <- table(group3, age1) temp2 <- round(100* temp1/rowSums(temp1)) pfun <- function(x,y) { paste(ifelse(x<1000, "\\phantom{0}", ""), x, " (", ifelse(y<10, "\\phantom{0}", ""), y, ") ", sep="") } cat(paste(c("FLC $<$ 3.38", pfun(temp1[1,], temp2[1,])), collapse=" & "), "\\\\\n") cat(paste(c("FLC 3.38--4.71", pfun(temp1[2,], temp2[2,])), collapse=" & "), "\\\\\n") cat(paste(c("FLC $>$ 4.71", pfun(temp1[3,], temp2[3,])), collapse=" & "), "\n") @ \end{tabular} \caption{Comparison of the age distributions (percents) for each of the three groups.} \label{tflc1} \end{table} Figure \ref{flc1} shows the survival curves for three subgroups of the patients: those whose total free light chain (FLC) is in the upper 10\% of all values found in the full study, those in the 70--89th percentile, and the remainder. There is a clear survival effect. Average free light chain amounts rise with age, however, at least in part because it is eliminated through the kidneys and renal function declines with age. Table \ref{tflc1} shows the age distribution for each of the three groups. In the highest decile of FLC (group 3) over half the subjects are age 70 or older compared to only 23\% in those below the 70th percentile. How much of the survival difference is truly associated with FLC and how much is simply an artifact of age? (The cut points are arbitrary, but we have chosen to mimic the original study and retain them. Division into three groups is a convenient number to illustrate the methods in this vignette, but we do not make any claim that such a categorization is optimal or even sensible statistical practice.) The R code for figure 1 is shown below. <>= fdata <- flchain[flchain$futime >=7,] fdata$age2 <- cut(fdata$age, c(0,54, 59,64, 69,74,79, 89, 110), labels = c(paste(c(50,55,60,65,70,75,80), c(54,59,64,69,74,79,89), sep='-'), "90+")) fdata$group <- factor(1+ 1*(fdata$flc.grp >7) + 1*(fdata$flc.grp >9), levels=1:3, labels=c("FLC < 3.38", "3.38 - 4.71", "FLC > 4.71")) sfit1 <- survfit(Surv(futime, death) ~ group, fdata) plot(sfit1, mark.time=F, col=c(1,2,4), lty=1, lwd=2, xscale=365.25, xlab="Years from Sample", ylab="Survival") text(c(11.1, 10.5, 7.5)*365.25, c(.88, .57, .4), c("FLC < 3.38", "3.38 - 4.71", "FLC > 4.71"), col=c(1,2,4)) @ \section{Reference populations} There are a few populations that are commonly used as the reference group. \begin{enumerate} \item Empirical. The overall distribution of confounders $x$ in the data set as a whole. For this study we would use the observed age/sex distribution, ignoring FLC group. This is also called the ``sample'' or ``data'' distribution. \item External reference. The distribution from some external study or standard. \item Internal reference. A particular subset of the data is chosen as the reference, and other subsets are then aligned with it. \end{enumerate} Method 2 is common in epidemiology, using a reference population based on a large external population such as the age/sex distribution of the 2000 United States census. Method 3 most often arises in the case-control setting, where one group is small and precious (a rare disease say) and the other group (the controls) from which we can sample is much larger. In each case the final result of the computation can be thought of as the expected answer we ``would obtain'' in a study that was perfectly balanced with respect to the list of confounders $x$. Population 1 is the most frequent. \section{Marginal approach} \begin{table} \centering \begin{tabular}{crrrrrrrr} \multicolumn{3}{c}{Females} \\ & \multicolumn{8}{c}{Age} \\ FLC group & 50--54& 55--59& 60--64 & 65--69 & 70--74 & 75--79 & 80--89& 90+ \\ \hline <>= tab1 <- with(fdata, table(group, age2, sex)) cat("Low&", paste(tab1[1,,1], collapse=" &"), "\\\\\n") cat("Med&", paste(tab1[2,,1], collapse=" &"), "\\\\\n") cat("High&", paste(tab1[3,,1], collapse=" &"), "\\\\\n") @ \\ \multicolumn{3}{c}{Males} \\ % & 50--54& 55--59& 60--64 & 65--69 & 70--74 & 75--79 & 80--89& 90+ \\ \hline <>= cat("Low&", paste(tab1[1,,2], collapse=" &"), "\\\\\n") cat("Med&", paste(tab1[2,,2], collapse=" &"), "\\\\\n") cat("High&", paste(tab1[3,,2], collapse=" &"), "\n") @ \end{tabular} \caption{Detailed age and sex distribution for the study population} \label{tab2} \end{table} \subsection{Selection} One approach for balancing is to select a subset of the data such that its distribution matches the referent for each level of $c$, i.e., for each curve that we wish to obtain. As an example we take a case-control like approach to the FLC data, with FLC high as the ``cases'' since it is the smallest group. Table \ref{tab2} shows a detailed distribution of the data with respect to age and sex. The balanced subset has all \Sexpr{tab1[3,1,1]} females aged 50--54 from the high FLC group, a random sample of \Sexpr{tab1[3,1,1]} out of the \Sexpr{tab1[1,1,1]} females in the age 50--54 low FLC group, and \Sexpr{tab1[3,1,1]} out of \Sexpr{tab1[2,1,1]} for the middle FLC. Continue this for all age/sex subsets. We cannot \emph{quite} compute a true case-control estimate for this data since there are not enough ``controls'' in the female 90+ category to be able to select one unique control for each case, and likewise in the male 80-89 and 90+ age groups. To get around this we will sample with replacement in these strata. \begin{figure}[tb] \myfig{flc2} \caption{Survival curves from a case-control sample are shown as solid lines, dashed lines are curves for the unweighted data set (as found in figure \ref{flc1}).} \label{flc2} \end{figure} <>= temp <- with(fdata, table(group, age2, sex)) dd <- dim(temp) # Select subjects set.seed(1978) select <- array(vector('list', length=prod(dd)), dim=dd) for (j in 1:dd[2]) { for (k in 1:dd[3]) { n <- temp[3,j,k] # how many to select for (i in 1:2) { indx <- which(as.numeric(fdata$group)==i & as.numeric(fdata$age2) ==j & as.numeric(fdata$sex) ==k) select[i,j,k] <- list(sample(indx, n, replace=(n> temp[i,j,k]))) } indx <- which(as.numeric(fdata$group)==3 & as.numeric(fdata$age2) ==j & as.numeric(fdata$sex) ==k) select[3,j,k] <- list(indx) #keep all the group 3 = high } } data2 <- fdata[unlist(select),] sfit2 <- survfit(Surv(futime, death) ~ group, data2) plot(sfit2,col=c(1,2,4), lty=1, lwd=2, xscale=365.25, xlab="Years from Sample", ylab="Survival") lines(sfit1, col=c(1,2,4), lty=2, lwd=1, xscale=365.25) legend(730, .4, levels(fdata$group), lty=1, col=c(1,2,4), bty='n', lwd=2) @ %\begin{table}[tb] \centering % \begin{tabular}{ccccccc} % &\multicolumn{2}{c}{FLC low} & \multicolumn{2}{c}{FLC med}& % \multicolumn{2}{c}{FLC high} \\ % & Total & Subset & Total & Subset & Total & Subset \\ \hline %<>= %tab3 <- with(fdata, table(age2, group)) %tab3 <- round(100*scale(tab3, center=F, scale=colSums(tab3))) %tab4 <- with(data2, table(age2, group)) %tab4 <- round(100*scale(tab4, center=F, scale=colSums(tab4))) %tab5 <- cbind(tab3[,1], tab4[,1], tab3[,2], tab4[,2], tab3[,3], tab4[,3]) %pfun <- function(x) paste(ifelse(x<10, paste("\\phantom{0}", x), x), % collapse=" &") %dtemp <- dimnames(tab5)[[1]] %for (j in 1:7) % cat(dtemp[j], " &", pfun(tab5[j,]), "\\\\\n") %cat(dtemp[8], " & ", pfun(tab5[8,]), "\n") %@ %\end{tabular} %\caption{Age distributions (\%) of the original data set along with that of % the subset, for the three FLC groups.} %\label{tflc2} %\end{table} The survival curves for the subset data are shown in figure \ref{flc2}. The curve for the high risk group is unchanged, since by definition all of those subjects were retained. We see that adjustment for age and sex has reduced the apparent survival difference between the groups by about half, but a clinically important effect for high FLC values remains. The curve for group 1 has moved more than that for group 2 since the age/sex adjustment is more severe for that group. <>= # I can't seem to put this all into an Sexpr z1 <- with(fdata,table(age, sex, group)) z2<- apply(z1, 1:2, min) ztemp <- 3*sum(z2) z1b <- with(fdata, table(age>64, sex, group)) ztemp2 <- sum(apply(z1b, 1:2, min)) @ In actual practice, case-control designs arise when matching and selection can occur \emph{before} data collection, leading to a substantial decrease in the amount of data that needs to be gathered and a consequent cost or time savings. When a data set is already in hand it has two major disadvantages. The first is that the approach wastes data; throwing away information in order to achieve balance is always a bad idea. Second is that though it returns an unbiased comparison, the result is for a very odd reference population. One advantage of matched subsets is that standard variance calculations for the curves are correct; the values provided by the usual Kaplan-Meier program need no further processing. We can also use the usual statistical tests to check for differences between the curves. <<>>= survdiff(Surv(futime, death) ~ group, data=data2) @ \subsection{Reweighting} \label{sect:logistic} A more natural way to adjust the data distribution is by weighting. Let $\pi(a,s)$, $a$ = age group, $s$ = sex be a target population age/sex distribution for our graph, and $p(a,s,i)$ the observed probability of each age/sex/group combination in the data. Both $\pi$ and $p$ sum to 1. Then if each observation in the data set is given a case weight of \begin{equation} w_{asi} = \frac{\pi(a,s)}{p(a,s,i)} \label{wt1} \end{equation} the weighted age/sex distribution for each of the groups will equal the target distribution $\pi$. An obvious advantage of this approach is that the resulting curves represent a tangible and well defined group. As an example, we will first adjust our curves to match the age/sex distribution of the 2000 US population, a common reference target in epidemiology studies. The \texttt{uspop2} data set is found in later releases of the survival package in R. It is an array of counts with dimensions of age, sex, and calendar year. We only want ages of 50 and over, and the population data set has collapsed ages of 100 and over into a single category. We create a table \texttt{tab100} of observed age/sex counts within group for our own data, using the same upper age threshold. New weights are the values $\pi/p$ = \texttt{pi.us/tab100}. <<>>= refpop <- uspop2[as.character(50:100),c("female", "male"), "2000"] pi.us <- refpop/sum(refpop) age100 <- factor(ifelse(fdata$age >100, 100, fdata$age), levels=50:100) tab100 <- with(fdata, table(age100, sex, group))/ nrow(fdata) us.wt <- rep(pi.us, 3)/ tab100 #new weights by age,sex, group range(us.wt) @ There are infinite weights! This is because the US population has coverage at all ages, but our data set does not have representatives in every age/sex/FLC group combination; there are for instance no 95 year old males in in the data set. Let us repeat the process, collapsing the US population from single years into the 8 age groups used previously in table \ref{tab2}. Merging the per age/sex/group weights found in the 3-dimensional array \texttt{us.wt} into the data set as per-subject weights uses matrix subscripts, a useful but less known feature of R. <<>>= temp <- as.numeric(cut(50:100, c(49, 54, 59, 64, 69, 74, 79, 89, 110)+.5)) pi.us<- tapply(refpop, list(temp[row(refpop)], col(refpop)), sum)/sum(refpop) tab2 <- with(fdata, table(age2, sex, group))/ nrow(fdata) us.wt <- rep(pi.us, 3)/ tab2 range(us.wt) index <- with(fdata, cbind(as.numeric(age2), as.numeric(sex), as.numeric(group))) fdata$uswt <- us.wt[index] sfit3a <-survfit(Surv(futime, death) ~ group, data=fdata, weight=uswt) @ \begin{figure}[tb] \myfig{flc3a} \caption{Population totals for the US reference (red) and for the observed data set (black).} \label{flc3a} \end{figure} A more common choice is to use the overall age/sex distribution of the sample itself as our target distribution $\pi$, i.e., the empirical distribution. Since FLC data set is population based and has excellent coverage of the county, this will not differ greatly from the US population in this case, as is displayed in figure \ref{flc3a}. <>= tab1 <- with(fdata, table(age2, sex))/ nrow(fdata) matplot(1:8, cbind(pi.us, tab1), pch="fmfm", col=c(2,2,1,1), xlab="Age group", ylab="Fraction of population", xaxt='n') axis(1, 1:8, levels(fdata$age2)) tab2 <- with(fdata, table(age2, sex, group))/nrow(fdata) tab3 <- with(fdata, table(group)) / nrow(fdata) rwt <- rep(tab1,3)/tab2 fdata$rwt <- rwt[index] # add per subject weights to the data set sfit3 <- survfit(Surv(futime, death) ~ group, data=fdata, weight=rwt) temp <- rwt[,1,] #show female data temp <- temp %*% diag(1/apply(temp,2,min)) round(temp, 1) #show female data @ \begin{figure}[tb] \myfig{flc3} \caption{Survival curves for the three groups using reweighted data are shown with solid lines, the original unweighted analysis as dashed lines. The heavier solid line adjusts to the Olmsted population and the lighter one to the US population.} \label{flc3} \end{figure} <>= plot(sfit3, mark.time=F, col=c(1,2,4), lty=1, lwd=2, xscale=365.25, xlab="Years from Sample", ylab="Survival") lines(sfit3a, mark.time=F, col=c(1,2,4), lty=1, lwd=1, xscale=365.25) lines(sfit1, mark.time=F, col=c(1,2,4), lty=2, lwd=1, xscale=365.25) legend(730, .4, levels(fdata$group), lty=1, col=c(1,2,4), bty='n', lwd=2) @ The calculation of weights is shown above, and finishes with a table of the weights for the females. The table was scaled so as to have a minimum weight of 1 in each column for simpler reading. We see that for the low FLC group there are larger weights for the older ages, whereas the high FLC group requires substantial weights for the youngest ages in order to achieve balance. The resulting survival curve is shown in figure \ref{flc3}. The distance between the adjusted curves is similar to the results from subset selection, which is as expected since both approaches are correcting for the same bias, but results are now for an overall population distribution that matches Olmsted County. The curves estimate what the results would have looked like, had each of the FLC groups contained the full distribution of ages. Estimation based on reweighted data is a common theme in survey sampling. Correct standard errors for the curves are readily computed using methods from that literature, and are available in some software packages. In R the \texttt{svykm} routine in the \texttt{survey} package handles both this simple case and more complex sampling schemes. Tests of the curves can be done using a weighted Cox model; the robust variance produced by \texttt{coxph} is identical to the standard Horvitz-Thompsen variance estimate used in survey sampling \cite{Binder92}. The robust score test from \texttt{coxph} corresponds to a log-rank test corrected for weighting. (In the example below the svykm function is only run if the survey package is already loaded, as the variance calculation is very slow for this large data set.) <<>>= id <- 1:nrow(fdata) cfit <- coxph(Surv(futime, death) ~ group + cluster(id), data=fdata, weight=rwt) summary(cfit)$robscore if (exists("svykm")) { #true if the survey package is loaded sdes <- svydesign(id = ~0, weights=~rwt, data=fdata) dfit <- svykm(Surv(futime, death) ~ group, design=sdes, se=TRUE) } @ Note: including the \texttt{cluster} term in the coxph call causes it to treat the weights as resampling values and thus use the proper survey sampling style variance. The default without that term would be to treat the case weights as replication counts. This same alternate variance estimate is also called for when there are correlated observations; many users will be more familiar with the cluster statement in that context. \paragraph{Inverse probability weighting} Notice that when using the overall population as the target distribution $\pi$ we can use Bayes rule to rewrite the weights as \begin{align*} \frac{1}{w_{asi}} &= \frac{{\rm Pr}({\rm age}=a, {\rm sex} =s, {\rm group}=i)} {{\rm Pr}({\rm age}=a, {\rm sex} =s)} \\ &= {\rm Pr}({\rm group}=i | {\rm age}=a, {\rm sex} =s) \end{align*} This last is precisely the probability estimated by a logistic regression model, leading to \emph{inverse probability weighting} as an alternate label for this approach. We can reproduce the weights calculated just above with three logistic regression models. <>= options(na.action="na.exclude") gg <- as.numeric(fdata$group) lfit1 <- glm(I(gg==1) ~ factor(age2) * sex, data=fdata, family="binomial") lfit2 <- glm(I(gg==2) ~ factor(age2) * sex, data=fdata, family="binomial") lfit3 <- glm(I(gg==3) ~ factor(age2) * sex, data=fdata, family="binomial") temp <- ifelse(gg==1, predict(lfit1, type='response'), ifelse(gg==2, predict(lfit2, type='response'), predict(lfit3, type='response'))) all.equal(1/temp, fdata$rwt) @ If there were only 2 groups then only a single regression model is needed since P(group 2) = 1 - P(group 1). Note the setting of na.action, which causes the predicted vector to have the same length as the original data even when there are missing values. This simplifies merging the derived weights with the original data set. An advantage of the regression framework is that one can easily accommodate more variables by using a model with additive terms and only a few selected interactions, and the model can contain continuous as well as categorical predictors. The disadvantage is that such models are often used without the necessary work to check their validity. For instance models with \texttt{age + sex} could have been used above. This makes the assumption that the odds of being a member of group 1 is linear in age and with the same slope for males and females; ditto for the models for group 2 and group 3. How well does this work? Since the goal of reweighting is to standardize the ages, a reasonable check is to compute and plot the reweighted age distribution for each flc group. \begin{figure}[tb] \myfig{flc4} \caption{The re-weighted age distribution using logistic regression with continuous age, for females, FLC groups 1--3. The target distribution is shown as a ``+''. The original unadjusted distribution is shown as dashed lines.} \label{flc4} \end{figure} Figure \ref{flc4} shows the result. The reweighted age distribution is not perfectly balanced, i.e., the `1', `2' and `3' symbols do no exactly overlay one another, but in this case the simple linear model has done an excellent job. We emphasize that whenever the reweighting is based on a simplified model then such a check is obligatory. It is quite common that a simple model is not sufficient and the resulting weight adjustment is inadequate. Like a duct tape auto repair, proceeding forward as though the underlying problem has been addressed is then most unwise. <>= lfit1b <-glm(I(gg==1) ~ age + sex, data=fdata, family="binomial") lfit2b <- glm(I(gg==2) ~ age +sex, data=fdata, family="binomial") lfit3b <- glm(I(gg==3) ~ age + sex, data=fdata, family="binomial") # weights for each group using simple logistic twt <- ifelse(gg==1, 1/predict(lfit1b, type="response"), ifelse(gg==2, 1/predict(lfit2b, type="response"), 1/predict(lfit3b, type="response"))) tdata <- data.frame(fdata, lwt=twt) #grouped plot for the females temp <- tdata[tdata$sex=='F',] temp$gg <- as.numeric(temp$group) c1 <- with(temp[temp$gg==1,], tapply(lwt, age2, sum)) c2 <- with(temp[temp$gg==2,], tapply(lwt, age2, sum)) c3 <- with(temp[temp$gg==3,], tapply(lwt, age2, sum)) xtemp <- outer(1:8, c(-.1, 0, .1), "+") #avoid overplotting ytemp <- 100* cbind(c1/sum(c1), c2/sum(c2), c3/sum(c3)) matplot(xtemp, ytemp, col=c(1,2,4), xlab="Age group", ylab="Weighted frequency (%)", xaxt='n') ztab <- table(fdata$age2) points(1:8, 100*ztab/sum(ztab), pch='+', cex=1.5, lty=2) # Add the unadjusted temp <- tab2[,1,] temp <- scale(temp, center=F, scale=colSums(temp)) matlines(1:8, 100*temp, pch='o', col=c(1,2,4), lty=2) axis(1, 1:8, levels(fdata$age2)) @ \paragraph{Rescaled weights} As the weights were defined in equation \ref{wt1}, the sum of weights for each of the groups is \Sexpr{nrow(fdata)}, the number of observations in the data set. Since the number of subjects in group 3 is one seventh of that in group 1, the average weight in group 3 is much larger. An alternative is to define weights in terms of the \emph{within} group distribution rather than the overall distribution, leading to the rescaled weights $w^*$ \begin{align} w^* &= \frac{\pi(a,s)}{p(a,s|i)} \label{wt2} \\ &= \frac{{\rm P}({\rm group}=i)} {{\rm P}({\rm group}=i | {\rm age}=a, {\rm sex}=s)} \label{wt2b} \end{align} Each group's weights are rescaled by the overall prevalence of the group. In its simplest form, the weights in each group are scaled to add up to the number of subjects in the group. <<>>= # compute new weights wtscale <- table(fdata$group)/ tapply(fdata$rwt, fdata$group, sum) wt2 <- c(fdata$rwt * wtscale[fdata$group]) c("rescaled cv"= sd(wt2)/mean(wt2), "rwt cv"=sd(fdata$rwt)/mean(fdata$rwt)) cfit2a <- coxph(Surv(futime, death) ~ group + cluster(id), data=fdata, weight= rwt) cfit2b <- coxph(Surv(futime, death) ~ group + cluster(id), data=fdata, weight=wt2) round(c(cfit2a$rscore, cfit2b$rscore),1) @ The rescaling results in weights that are much less variable across groups. This operation has no impact on the individual survival curves or their standard errors, since within group we have multiplied all weights by a constant. When comparing curves across groups, however, the rescaled weights reduce the standard error of the test statistic. This results in increased power for the robust score test, although in this particular data set the improvement is not very large. \section{Conditional method} In the marginal approach we first balance the data set and then compute results on the adjusted data. In the conditional approach we first compute a predicted survival curve for each subject that accounts for flc group, age and sex, and then take a weighted average of the curves to get an overall estimate for each flc group. For both methods a central consideration is the population of interest, which drives the weights. Modeling has not removed the question of \emph{who} these curves should represent, it has simply changed the order of operation between the weighting step and the survival curves step. \subsection{Stratification} Our first approach is to subset the data into homogeneous age/sex strata, compute survival curves within each strata, and then combine results. We will use the same age/sex combinations as before. The interpretation of these groups is different, however. In the marginal approach it was important to find age/sex groups for which the probability of membership within each FLC group was constant within the strata (independent of age and sex, within strata), in this case it is important that the survival for each FLC group is constant in each age/sex stratum. Homogeneity of membership within each stratum and homogeneity of survival within each stratum may lead to different partitions for some data sets. Computing curves for all the combinations is easy. <>= allfit <- survfit(Surv(futime, death) ~ group + age2 + sex, fdata) temp <- summary(allfit)$table temp[1:6, c(1,4)] #abbrev printout to fit page @ The resultant survival object has 48 curves: 8 age groups * 2 sexes * 3 FLC groups. To get a single curve for the first FLC group we need to take a weighted average over the 16 age/sex combinations that apply to that group, and similarly for the second and third FLC subset. Combining the curves is a bit of a nuisance computationally because each of them is reported on a different set of time points. A solution is to use the \texttt{summary} function for survfit objects along with the \texttt{times} argument of that function. This feature was originally designed to allow printout of curves at selected time points (6 months, 1 year, \ldots), but can also be used to select a common set of time points for averaging. We will arbitrarily use 4 per year, which is sufficient to create a visually smooth plot over the time span of interest. By default \texttt{summary} does not return data for times beyond the end of a curve, i.e., when there are no subjects left at risk; the \texttt{extend} argument causes a full set of times to always be reported. As seen in the printout above, the computed curves are in sex within age within group order. The overall curve is a weighted average chosen to match the original age/sex distribution of the population. <>= xtime <- seq(0, 14, length=57)*365.25 #four points/year for 14 years smat <- matrix(0, nrow=57, ncol=3) # survival curves serr <- smat #matrix of standard errors pi <- with(fdata, table(age2, sex))/nrow(fdata) #overall dist for (i in 1:3) { temp <- allfit[1:16 + (i-1)*16] #curves for group i for (j in 1:16) { stemp <- summary(temp[j], times=xtime, extend=T) smat[,i] <- smat[,i] + pi[j]*stemp$surv serr[,i] <- serr[,i] + pi[i]*stemp$std.err^2 } } serr <- sqrt(serr) plot(sfit1, lty=2, col=c(1,2,4), xscale=365.25, xlab="Years from sample", ylab="Survival") matlines(xtime, smat, type='l', lwd=2, col=c(1,2,4),lty=1) @ \begin{figure}[tb] \myfig{flc5} \caption{Estimated curves from a stratified model, along with those from the uncorrected fit as dashed lines.} \label{flc5} \end{figure} Figure \ref{flc5} shows the resulting averaged curves. Overlaid are the curves for the unadjusted model. Very careful comparison of these curves with the weighted estimate shows that they have almost identical spread, with just a tiny amount of downward shift. There are two major disadvantages to the stratified curves. The first is that when the original data set is small or the number of confounders is large, it is not always feasible to stratify into a large enough set of groups that each will be homogeneous. The second is a technical aspect of the standard error estimate. Since the curves are formed from disjoint sets of observations they are independent and the variance of the weighted average is then a weighted sum of variances. However, when a Kaplan-Meier curve drops to zero the usual standard error estimate at that point involves 0/0 and becomes undefined, leading to the NaN (not a number) value in R. Thus the overall standard error becomes undefined if any of the component curves falls to zero. In the above example this happens at about the half way point of the graph. (Other software packages carry forward the se value from the last no-zero point on the curve, but the statistical validity of this is uncertain.) To test for overall difference between the curves we can use a stratified test statistic, which is a sum of the test statistics computed within each subgroup. The most common choice is the stratified log-rank statistic which is shown below. The score test from a stratified Cox model would give the same result. <<>>= survdiff(Surv(futime, death) ~ group + strata(age2, sex), fdata) @ \subsection{Modeling} The other approach for conditional estimation is to model the risks due to the confounders. Though we have left it till last, this is usually the first (and most often the only) approach used by most data analysts. Let's start with the very simplest method: a stratified Cox model. <>= cfit4a <- coxph(Surv(futime, death) ~ age + sex + strata(group), data=fdata) surv4a <- survfit(cfit4a) plot(surv4a, col=c(1,2,4), mark.time=F, xscale=365.25, xlab="Years post sample", ylab="Survival") @ This is a very fast and easy way to produce a set of curves, but it has three problems. First is the assumption that this simple model adequately accounts for the effects of age and sex on survival. That is, it assumes that the effect of age on mortality is linear, the sex difference is constant across all ages, and that the coefficients for both are identical for the three FLC groups. The second problem with this approach is that it produces the predicted curve for a single hypothetical subject of age \Sexpr{round(cfit4a[['means']][1], 1)} years and sex \Sexpr{round(cfit4a[['means']][2],2)}, the means of the covariates, under each of the 3 FLC scenarios. However, we are interested in the adjusted survival of a \emph{cohort} of subjects in each range of FLC, and the survival of an ``average'' subject is not the average survival of a cohort. The third and most serious issue is that it is not clear exactly what these ``adjusted'' curves represent --- exactly who \emph{is} this subject with a sex of \Sexpr{round(cfit4a[['means']][2],2)}? Multiple authors have commented on this problem, see Thomsen et al \cite{Thomsen91}, Nieto and Coresh \cite{Nieto96} or chapter 10 of Therneau and Grambsh \cite{Therneau00} for examples. Even worse is a Cox model that treated the FLC group as a covariate, since that will impose an additional constraint of proportional hazards across the 3 FLC groups. \begin{figure} \myfig{flc6} \caption{Curves for the three groups, adjusted for age and sex via a risk model. Dotted lines show the curves from marginal adjustment. Solid curves are for the simple risk model \texttt{cfit4a}.} \label{flc6} \end{figure} We can address this last problem problem by doing a proper average. A Cox model fit can produce the predicted curves for any age/sex combination. The key idea is to produce a predicted survival curve for every subject of some hypothetical population, and then take the average of these curves. The most straightforward approach is to retrieve the predicted individual curves for all \Sexpr{nrow(fdata)} subjects in the data set, assuming each of the three FLC strata one by one, and take a simple average for each strata. For this particular data set that is a bit slow since it involves \Sexpr{nrow(fdata)} curves. However there are only 98 unique age/sex pairs in the data, it is sufficient to obtain the 98 * 3 FLC groups unique curves and take a weighted average. We will make use of the survexp function, which is designed for just this purpose. Start by creating a data set which has one row for each age/sex combination along with its count. Then replicate it into 3 copies, assigning one copy to each of the three FLC strata. <>= tab4a <- with(fdata, table(age, sex)) uage <- as.numeric(dimnames(tab4a)[[1]]) tdata <- data.frame(age = uage[row(tab4a)], sex = c("F","M")[col(tab4a)], count= c(tab4a)) tdata3 <- tdata[rep(1:nrow(tdata), 3),] #three copies tdata3$group <- factor(rep(1:3, each=nrow(tdata)), labels=levels(fdata$group)) sfit4a <- survexp(~group, data=tdata3, weight = count, ratetable=cfit4a) plot(sfit4a, mark.time=F, col=c(1,2,4), lty=1, lwd=2, xscale=365.25, xlab="Years from Sample", ylab="Survival") lines(sfit3, mark.time=F, col=c(1,2,4), lty=2, lwd=1, xscale=365.25) legend(730,.4, c("FLC low", "FLC med", "FLC high"), lty=1, col=c(1,2,4), bty='n', lwd=2) @ Figure \ref{flc6} shows the result. Comparing this to the prior 3 adjustments shown in figures \ref{flc3}, \ref{flc4}, and \ref{flc5} we see that this result is different. Why? Part of the reason is due to the fact that $E[f(X)] \ne f(E[X])$ for any non-linear operation $f$, so that averages of survival curves and survival curves of averages will never be exactly the same. This may explain the small difference between the stratified and the marginal approaches of figures \ref{flc3} and \ref{flc5}, which were based on the same subsets. The Cox based result is systematically higher than the stratified one, however, so something more is indicated. Aside: An alternate computational approach is to create the individual survival curves using the \texttt{survfit} function and then take averages. <<>>= tfit <- survfit(cfit4a, newdata=tdata, se.fit=FALSE) curves <- vector('list', 3) twt <- c(tab4a)/sum(tab4a) for (i in 1:3) { temp <- tfit[i,] curves[[i]] <- list(time=temp$time, surv= c(temp$surv %*% twt)) } @ The above code is a bit sneaky. I know that the result from the survfit function contains a matrix \texttt{tfit\$surv} of 104 columns, one for each row in the tdata data frame, each column containing the curves for the three strata one after the other. Sub setting \texttt{tfit} results in the matrix for a single flc group. Outside of R an approach like the above may be needed, however. \begin{figure} \myfig{flc6b} \caption{Left panel: comparison of Cox model based adjustment (solid) with the curves based on marginal adjustment (dashed). The Cox model curves without (black) and with (red) an age*sex interaction term overlay. Right panel: plot of the predicted relative risks from a Cox model \texttt{crate} versus population values from the Minnesota rate table.} \label{flc6b} \end{figure} So why are the modeling results so different than either reweighting or stratification? Suspicion first falls on the use of a simple linear model for age and sex, so start by fitting a slightly more refined model that allows for a different slope for the two sexes, but is still linear in age. In this particular data set an external check on the fit is also available via the Minnesota death rate tables, which are included with the survival package as \texttt{survexp.mn}. This is an array that contains daily death rates by age, sex, and calendar year. <>= par(mfrow=c(1,2)) cfit4b <- coxph(Surv(futime, death) ~ age*sex + strata(group), fdata) sfit4b <- survexp(~group, data=tdata3, ratetable=cfit4b, weights=count) plot(sfit4b, fun='event', xscale=365.25, xlab="Years from sample", ylab="Deaths") lines(sfit3, mark.time=FALSE, fun='event', xscale=365.25, lty=2) lines(sfit4a, fun='event', xscale=365.25, col=2) temp <- median(fdata$sample.yr) mrate <- survexp.mn[as.character(uage),, as.character(temp)] crate <- predict(cfit4b, newdata=tdata, reference='sample', type='lp') crate <- matrix(crate, ncol=2)[,2:1] # mrate has males then females, match it # crate contains estimated log(hazards) relative to a baseline, # and mrate absolute hazards, make both relative to a 70 year old for (i in 1:2) { mrate[,i] <- log(mrate[,i]/ mrate[21,2]) crate[,i] <- crate[,i] - crate[21,2] } matplot(mrate, crate, col=2:1, type='l') abline(0, 1, lty=2, col=4) @ The resulting curves are shown in the left panel of figure \ref{flc6b} and reveal that addition of an interaction term did not change the predictions, and that the Cox model result for the highest risk group is distinctly different predicted survival for the highest FLC group is distinctly different when using model based prediction. The right hand panel of the figure shows that though there are slight differences with the Minnesota values, linearity of the age effect is very well supported. So where exactly does the model go wrong? Since this is such a large data set we have the luxury of looking at subsets. This would be a very large number of curves to plot --- age by sex by FLC = 48 --- so an overlay of the observed and expected curves by group would be too confusing. Instead we will summarize each of the groups according to their observed and predicted number of events. <>= obs <- with(fdata, tapply(death, list(age2, sex, group), sum)) pred<- with(fdata, tapply(predict(cfit4b, type='expected'), list(age2, sex, group), sum)) excess <- matrix(obs/pred, nrow=8) #collapse 3 way array to 2 dimnames(excess) <- list(dimnames(obs)[[1]], c("low F", "low M", "med F", "med M", "high F", "high M")) round(excess, 1) @ The excess risks, defined as the observed/expected number of deaths, are mostly modest ranging from .8 to 1.2. The primary exception exception is the high FLC group for ages 50--59 which has values of 1.6 to 2.5; the Cox model fit has greatly overestimated the survival for the age 50--54 and 55--59 groups. Since this is also the age category with the highest count in the data set, this overestimation will have a large impact on the overall curve for high FLC subset, which is exactly where the the deviation in figure \ref{flc6b} is observed to lie. There is also mild evidence for a linear trend in age for the low FLC females, in the other direction. Altogether this suggests that the model might need to have a different age coefficient for each of the three FLC groups. <<>>= cfit5a <- coxph(Surv(futime, death) ~ strata(group):age +sex, fdata) cfit5b <- coxph(Surv(futime, death) ~ strata(group):(age +sex), fdata) cfit5c <- coxph(Surv(futime, death) ~ strata(group):(age *sex), fdata) options(show.signif.stars=FALSE) # see footnote anova(cfit4a, cfit5a, cfit5b, cfit5c) temp <- coef(cfit5a) names(temp) <- c("sex", "ageL", "ageM", "ageH") round(temp,3) @ The model with separate age coefficients for each FLC group gives a major improvement in goodness of fit, but adding separate sex coefficients per group or further interactions does not add importantly beyond that. \footnote{There are certain TV shows that make one dumber just by watching them; adding stars to the output has the same effect on statisticians.} \begin{figure} \myfig{flc7} \caption{Adjusted survival for the 3 FLC groups based on the improved Cox model fit. Dashed lines show the predictions from the marginal model.} \label{flc7} \end{figure} A recheck of the observed/expected values now shows a much more random pattern, though some excess remains in the upper right corner. The updated survival curves are shown in figure \ref{flc7} and now are in closer concordance with the marginal fit. <>= pred5a <- with(fdata, tapply(predict(cfit5a, type='expected'), list(age2, sex, group), sum)) excess5a <- matrix(obs/pred5a, nrow=8, dimnames=dimnames(excess)) round(excess5a, 1) sfit5 <- survexp(~group, data=tdata3, ratetable=cfit5a, weights=count) plot(sfit3, fun='event', xscale=365.25, mark.time=FALSE, lty=2, col=c(1,2,4), xlab="Years from sample", ylab="Deaths") lines(sfit5, fun='event', xscale=365.25, col=c(1,2,4)) @ One problem with the model based estimate is that standard errors for the curves are complex. Standard errors of the individual curves for each age/sex/FLC combination are a standard output of the survfit function, but the collection of curves is correlated since they all depend on a common estimate of the model's coefficient vector $\beta$. Curves with disparate ages are anti-correlated (an increase in the age coefficient of the model would raise one and lower the other) whereas those for close ages are positively correlated. A proper variance for the unweighted average has been derived by Gail and Byar \cite{Gail86}, but this has not been implemented in any of the standard packages, nor extended to the weighted case. A bootstrap estimate would appear to be the most feasible. \section{Conclusions} When two populations need to be adjusted and one is much larger than the other, the balanced subset method has been popular. It is most often seen in the context of a case-control study, with cases as the rarer group and a set of matched controls selected from the larger one. This method has the advantage that the usual standard error estimates from a standard package are appropriate, so no further work is required. However, in the general situation it leads to a correct answer but for the wrong problem, i.e., not for a population in which we are interested. The population reweighted estimate is flexible, has a readily available variance in some statistical packages (but not all), and the result is directly interpretable. It is the method we recommend in general. The approach can be extended to a large number of balancing factors by using a regression model to derive the weights. Exploration and checking of said model for adequacy is an important step in this case. The biggest downside to the method arises when there is a subset which is rare in the data sample but frequent in the adjusting population. In this case subjects in that subset will be assigned large weights, and the resulting curves will have high variance. The stratified method is closely related to reweighting (not shown). It does not do well if the sample size is small, however. Risk set modeling is a very flexible method, but is also the one where it is easiest to go wrong by using an inadequate model, and variance estimation is also difficult. To the extent that the fitted model is relevant, it allows for interpolation and extrapolation to a reference population with a different distribution of covariates than the one in the training data. It may be applicable in cases such as rare subsets where population reweighting is problematic, with the understanding that one is depending heavily on extrapolation in this case, which is always dangerous. \section{A note on type 3 tests} One particular software package (not R) and its proponents are very fond of something called ``type 3'' tests. Said tests are closely tied to a particular reference population: \begin{itemize} \item For all continuous covariates in the model, the empirical distribution is used as the reference. \item For all categorical adjusters, a uniform distribution over the categories is used. \end{itemize} Figure \ref{flc8} shows the fit from such a model. Not surprisingly, the predicted death rate is very high: 1/4 of our population is over 80 years old! The authors do not find such a prediction particularly useful since we don't ever expect to see a population like this (it's sort of like planning for the zombie apocalypse), but for those enamored of type 3 tests this shows how to create the corresponding curves. <>= # there is a spurious warning from the model below: R creates 3 unneeded # columns in the X matrix cfit6 <- coxph(Surv(futime, death) ~ strata(group):age2 + sex, fdata) saspop <- with(fdata, expand.grid(age2= levels(age2), sex= levels(sex), group = levels(group))) sfit6 <- survexp(~group, data=saspop, ratetable=cfit6) plot(sfit6, fun='event', xscale=365.25, mark.time=FALSE, lty=1, col=c(1,2,4), xlab="Years from sample", ylab="Deaths") lines(sfit5, fun='event', xscale=365.25, lty=2, col=c(1,2,4)) @ \begin{figure} \myfig{flc8} \caption{Adjusted survival for the 3 FLC groups based on a fit with categorical age, and predicting for a uniform age/sex population. Dashed lines show the predictions from the marginal model.} \label{flc8} \end{figure} \newpage \bibliographystyle{plain} \bibliography{refer} \end{document} survival/inst/doc/compete.R0000644000175100001440000003335713070713770015464 0ustar hornikusers### R code from vignette source 'compete.Rnw' ################################################### ### code chunk number 1: compete.Rnw:23-29 ################################################### options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=10) #text in graph about the same as regular text options(contrasts=c("contr.treatment", "contr.poly")) #ensure default require("survival") ################################################### ### code chunk number 2: sfig1 ################################################### getOption("SweaveHooks")[["fig"]]() # A note to readers of this code: drawing multi-state figures in this # way via polygon and arrows statements is a major PITA. Don't mimic # the code below, instead do yourself a favor and use a package # designed for the task such as diagram, DiagrammeR, shape or Gmisc. # Survival is a recommended package that is included by lots of others so # I try to limit dependencies in the survival vignettes. # par(mar=c(.1, .1, .1, .1)) frame() oldpar <- par(usr=c(0,100,0,100)) # first figure xx <- c(0, 10, 10, 0) yy <- c(0, 0, 10, 10) polygon(xx +10, yy+70) polygon(xx +30, yy+70) arrows( 22, 75, 28, 75, length=.1) text(c(15, 35), c(75,75), c("Alive", "Dead")) # second figure polygon(xx +60, yy+70) for (j in c(55, 70, 85)) { polygon(xx +80, yy+j) arrows(72, (5*75 +j+5)/6, 78, (100+j*5)/6, length=.1) } text(c(65, 85,85,85), c(70,55,70,85)+5, c("A", "D3", "D2", "D1")) # third figure polygon(xx+10, yy+25) for (j in c(15,35)) { polygon(xx +30, yy+j) arrows(22, (5*30 +j+4)/6, 28, (54+j*5)/6, length=.1) } arrows(28, 2+(65 + 35*5)/6, 22, 2+ (160 + 40)/6, length=.1) arrows(35, 33, 35, 27, length=.1) text(c(15, 35,35), c(30, 20, 40), c("Health", "Death", "Illness")) # fourth for (i in c(50, 68)) polygon(xx+i, yy+25) arrows(62, 30, 67, 30, length=.1) arrows(80, 30, 84, 30, length=.1) text(90, 30, "...", cex=2) text(c(55, 73), c(30, 30), c("0", "1")) par(oldpar) ################################################### ### code chunk number 3: crfig2 ################################################### getOption("SweaveHooks")[["fig"]]() par(mar=c(.1, .1, .1, .1)) frame() oldpar <- par(usr=c(0,100,0,100)) # first figure xx <- c(0, 10, 10, 0) yy <- c(0, 0, 10, 10) polygon(xx +10, yy+70) temp <- c(60, 80) for (j in 1:2) { polygon(xx + 30, yy+ temp[j]) arrows(22, 70 + 3*j, 28, temp[j] +5, length=.1) } text(c(15, 35, 35), c(75, 65, 85),c("Entry", "Death", "PCM")) text(25, 55, "Competing Risk") # Second figure polygon(xx +60, yy+70) for (j in 1:2) { polygon(xx + 80, yy+ temp[j]) arrows(72, 70+ 3*j, 78, temp[j] +5, length=.1) } text(50+ c(15, 35, 35), c(75, 65, 85),c("Entry", "Death", "PCM")) arrows(85, 78, 85, 72, length=.1) text(75, 55, "Multi-state 1") # third figure polygon(xx+10, yy+25) temp <- c(15, 35) for (j in 1:2) { polygon(2*xx +30, yy + temp[j]) arrows(22, 25 + 3*j, 28, temp[j] +5, length=.1) } text(c(15, 40, 40), c(30, 20, 40),c("Entry", "Death w/o PCM", "PCM")) polygon(2*xx + 60, yy+temp[2]) arrows(52, 40, 58, 40, length=.1) text(70, 40, "Death after PCM") text(40, 10, "Multi-state 2") ################################################### ### code chunk number 4: mgus1 ################################################### getOption("SweaveHooks")[["fig"]]() oldpar <- par(mfrow=c(1,2)) hist(mgus2$age, nclass=30, main='', xlab="Age") with(mgus2, tapply(age, sex, mean)) mfit1 <- survfit(Surv(futime, death) ~ sex, data=mgus2) mfit1 plot(mfit1, col=c(1,2), xscale=12, mark.time=FALSE, lwd=2, xlab="Years post diagnosis", ylab="Survival") legend("topright", c("female", "male"), col=1:2, lwd=2, bty='n') par(oldpar) ################################################### ### code chunk number 5: mgus2 ################################################### getOption("SweaveHooks")[["fig"]]() etime <- with(mgus2, ifelse(pstat==0, futime, ptime)) event <- with(mgus2, ifelse(pstat==0, 2*death, 1)) event <- factor(event, 0:2, labels=c("censor", "pcm", "death")) table(event) mfit2 <- survfit(Surv(etime, event) ~ sex, data=mgus2) print(mfit2, rmean=240, scale=12) mfit2$transitions plot(mfit2, col=c(1,2,1,2), lty=c(2,2,1,1), mark.time=FALSE, lwd=2, xscale=12, xlab="Years post diagnosis", ylab="Probability in State") legend(240, .6, c("death:female", "death:male", "pcm:female", "pcm:male"), col=c(1,2,1,2), lty=c(1,1,2,2), lwd=2, bty='n') ################################################### ### code chunk number 6: mgus3 ################################################### getOption("SweaveHooks")[["fig"]]() pcmbad <- survfit(Surv(etime, pstat) ~ sex, data=mgus2) plot(pcmbad[2], mark.time=FALSE, lwd=2, fun="event", conf.int=FALSE, xscale=12, xlab="Years post diagnosis", ylab="Fraction with PCM") lines(mfit2[2,1], lty=2, lwd=2, mark.time=FALSE, conf.int=FALSE) legend(0, .25, c("Males, PCM, incorrect curve", "Males, PCM, competing risk"), col=1, lwd=2, lty=c(1,2), bty='n') ################################################### ### code chunk number 7: mgus4 ################################################### ptemp <- with(mgus2, ifelse(ptime==futime & pstat==1, ptime-.1, ptime)) newdata <- tmerge(mgus2, mgus2, id=id, death=event(futime, death), pcm = event(ptemp, pstat)) newdata <- tmerge(newdata, newdata, id, enum=cumtdc(tstart)) with(newdata, table(death, pcm)) ################################################### ### code chunk number 8: mgus4g ################################################### getOption("SweaveHooks")[["fig"]]() temp <- with(newdata, ifelse(death==1, 2, pcm)) newdata$event <- factor(temp, 0:2, labels=c("censor", "pcm", "death")) mfit3 <- survfit(Surv(tstart, tstop, event) ~ sex, data=newdata, id=id) print(mfit3, rmean=240, digits=2) mfit3$transitions plot(mfit3[,1], mark.time=FALSE, col=1:2, lty=1:2, lwd=2, xscale=12, xlab="Years post MGUS diagnosis", ylab="Fraction in the PCM state") legend(48, .04, c("female", "male"), lty=1:2, col=1:2, lwd=2, bty='n') ################################################### ### code chunk number 9: mgus5 ################################################### getOption("SweaveHooks")[["fig"]]() # Death after PCM will correspond to data rows with # enum = 2 and event = death d2 <- with(newdata, ifelse(enum==2 & event=='death', 4, as.numeric(event))) e2 <- factor(d2, labels=c("censor", "pcm", "death w/o pcm", "death after pcm")) mfit4 <- survfit(Surv(tstart, tstop, e2) ~ sex, data=newdata, id=id) plot(mfit2[2,], lty=c(1,2), xscale=12, mark.time=FALSE, lwd=2, xlab="Years post diagnosis", ylab="Probability in State") lines(mfit4[2,3], mark.time=FALSE, col=2, lty=1, lwd=2, conf.int=FALSE) legend(200, .5, c("Death w/o PCM", "ever PCM", "Death after PCM"), col=c(1,1,2), lty=c(2,1,1), lwd=2, bty='n', cex=.82) ################################################### ### code chunk number 10: cfit1 ################################################### options(show.signif.stars = FALSE) # display intelligence cfit2 <- coxph(Surv(etime, event=="death") ~ age + sex + mspike, mgus2) summary(cfit2, scale=c(10, 1, 1)) # scale age in decades ################################################### ### code chunk number 11: cfit2 ################################################### cfit1 <- coxph(Surv(etime, event=="pcm") ~ age + sex + mspike, mgus2) cfit1 quantile(mgus2$mspike, na.rm=TRUE) ################################################### ### code chunk number 12: mpyears ################################################### pfit1 <- pyears(Surv(ptime, pstat) ~ sex, mgus2, scale=12) round(100* pfit1$event/pfit1$pyears, 1) # PCM rate per year temp <- summary(mfit1, rmean="common") #print the mean survival time round(temp$table[,1:6], 1) ################################################### ### code chunk number 13: PCMcurve ################################################### getOption("SweaveHooks")[["fig"]]() newdata <- expand.grid(sex=c("F", "M"), age=c(60, 80), mspike=1.2) newdata temp <- matrix(list(), 3,3) dimnames(temp) <- list(from=c("Entry", "PCM", "Death"), to =c("Entry", "PCM", "Death")) temp[1,2] <- list(survfit(cfit1, newdata, std.err=FALSE)) temp[1,3] <- list(survfit(cfit2, newdata, std.err=FALSE)) csurv <- survfit(temp, p0 =c(1,0,0)) plot(csurv[,2], xmax=25*12, xscale=12, xlab="Years after MGUS diagnosis", ylab="PCM", col=1:2, lty=c(1,1,2,2), lwd=2) legend(10, .14, outer(c("female", "male "), c("diagnosis at age 60", "diagnosis at age 80"), paste, sep=", "), col=1:2, lty=c(1,1,2,2), bty='n', lwd=2) ################################################### ### code chunk number 14: year20 ################################################### # Print out a M/F results at 20 years temp <- summary(csurv, time=20*12)$pstate cbind(newdata, PCM= round(100*temp[,2], 1)) ################################################### ### code chunk number 15: fg1 ################################################### # (first three lines are identical to an earlier section) etime <- with(mgus2, ifelse(pstat==0, futime, ptime)) event <- with(mgus2, ifelse(pstat==0, 2*death, 1)) event <- factor(event, 0:2, labels=c("censor", "pcm", "death")) pcmdat <- finegray(Surv(etime, event) ~ ., data=mgus2, etype="pcm") pcmdat[1:4, c(1:3, 11:14)] deathdat <- finegray(Surv(etime, event) ~ ., data=mgus2, etype="death") dim(pcmdat) dim(deathdat) dim(mgus2) ################################################### ### code chunk number 16: pfit2 ################################################### # The PCM curves of the multi-state model pfit2 <- survfit(Surv(fgstart, fgstop, fgstatus) ~ sex, data=pcmdat, weight=fgwt) # The death curves of the multi-state model dfit2 <- survfit(Surv(fgstart, fgstop, fgstatus) ~ sex, data=deathdat, weight=fgwt) ################################################### ### code chunk number 17: fg2 ################################################### getOption("SweaveHooks")[["fig"]]() fgfit1 <- coxph(Surv(fgstart, fgstop, fgstatus) ~ sex, data=pcmdat, weight= fgwt) summary(fgfit1) fgfit2 <- coxph(Surv(fgstart, fgstop, fgstatus) ~ sex, data=deathdat, weight= fgwt) fgfit2 mfit2 <- survfit(Surv(etime, event) ~ sex, data=mgus2) #reprise the AJ plot(mfit2[,1], col=1:2, lwd=2, xscale=12, conf.times=c(5, 15, 25)*12, xlab="Years post diagnosis", ylab="Fraction with PCM") ndata <- data.frame(sex=c("F", "M")) fgsurv1 <- survfit(fgfit1, ndata) lines(fgsurv1, fun="event", lty=2, lwd=2, col=1:2) legend("topleft", c("Female, Aalen-Johansen", "Male, Aalen-Johansen", "Female, Fine-Gray", "Male, Fine-Gray"), col=1:2, lty=c(1,1,2,2), bty='n') # rate models with only sex pfitr <- coxph(Surv(etime, event=="pcm") ~ sex, mgus2) dfitr <- coxph(Surv(etime, event=="death") ~ sex, mgus2) temp <- matrix(list(), 3,3) temp[1,2] <- list(survfit(pfitr, ndata, std.err=FALSE)) temp[1,3] <- list(survfit(dfitr, ndata, std.err=FALSE)) rcurve <- survfit(temp, p0=c(entry=1, pcm=0, death=0)) ################################################### ### code chunk number 18: fg3 ################################################### fgfit2a <- coxph(Surv(fgstart, fgstop, fgstatus) ~ age + sex + mspike, data=pcmdat, weight=fgwt) fgfit2b <- coxph(Surv(fgstart, fgstop, fgstatus) ~ age + sex + mspike, data=deathdat, weight=fgwt) round(rbind(PCM= coef(fgfit2a), death=coef(fgfit2b)), 3) ################################################### ### code chunk number 19: finegray2 ################################################### getOption("SweaveHooks")[["fig"]]() oldpar <- par(mfrow=c(1,2)) newdata <- expand.grid(sex= c("F", "M"), age=c(60, 80), mspike=1.2) fsurv1 <- survfit(fgfit2a, newdata) # time to progression curves plot(fsurv1, xscale=12, col=1:2, lty=c(1,1,2,2), lwd=2, fun='event', xlab="Years", ylab="Fine-Gray predicted", xmax=12*25, ylim=c(0, .15)) legend(1, .15, c("Female, 60", "Male, 60","Female: 80", "Male, 80"), col=c(1,2,1,2), lty=c(1,1,2,2), lwd=2, bty='n') plot(csurv[,2], xscale=12, col=1:2, lty=c(1,1,2,2), lwd=2, xlab="Years", ylab="Multi-state predicted", xmax=12*25, ylim=c(0, .15)) legend(1, .15, c("Female, 60", "Male, 60","Female: 80", "Male, 80"), col=c(1,2,1,2), lty=c(1,1,2,2), lwd=2, bty='n') par(oldpar) ################################################### ### code chunk number 20: finegray-check ################################################### getOption("SweaveHooks")[["fig"]]() zph.fgfit2a <- cox.zph(fgfit2a) zph.fgfit2a plot(zph.fgfit2a[1]) abline(h=coef(fgfit2a)[1], lty=2, col=2) ################################################### ### code chunk number 21: finegray3 ################################################### getOption("SweaveHooks")[["fig"]]() fsurv2 <- survfit(fgfit2b, newdata) # time to progression curves xtime <- 0:(30*12) #30 years y1a <- 1 - summary(fsurv1, times=xtime)$surv #predicted pcm y1b <- 1 - summary(fsurv2, times=xtime)$surv #predicted deaths before pcm y1 <- (y1a + y1b) #either matplot(xtime/12, y1, col=1:2, lty=c(1,1,2,2), type='l', xlab="Years post diagnosis", ylab="FG: either endpoint") abline(h=1, col=3) legend("bottomright", c("Female, 60", "Male, 60","Female: 80", "Male, 80"), col=c(1,2,1,2), lty=c(1,1,2,2), lwd=2, bty='n') ################################################### ### code chunk number 22: pcmstack ################################################### temp1 <- data.frame(mgus2, time=etime, status=(event=="pcm"), group='pcm') temp2 <- data.frame(mgus2, time=etime, status=(event=="death"), group="death") stacked <- rbind(temp1, temp2) allfit <- coxph(Surv(time, status) ~ hgb + (age + sex)*strata(group), data=stacked) survival/inst/doc/tests.pdf0000644000175100001440000126310113070713776015541 0ustar hornikusers%PDF-1.4 %ÐÔÅØ 3 0 obj << /Length 1153 /Filter /FlateDecode >> stream 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/Size 164 /Root 162 0 R /Info 163 0 R /ID [ ] >> startxref 236084 %%EOF survival/inst/doc/multi.Rnw0000644000175100001440000010314213017617770015521 0ustar hornikusers\documentclass{article} \usepackage{Sweave} \usepackage{amsmath} \title{Multi-state models as a data exploration tool} \author{Terry Therneau} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} \newcommand{\code}[1]{\texttt{#1}} \newcommand{\myfig}[1]{\includegraphics{multi-#1.pdf}} \SweaveOpts{keep.source=TRUE, fig=FALSE} % Ross Ihaka suggestions \DefineVerbatimEnvironment{Sinput}{Verbatim} {xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} % This code floats it's figures in a Latex figure environment. % The echoed R code constantly has fig=TRUE, include=FALSE, which % causes the pdf file to be created but not automatically included % at that point. \SweaveOpts{prefix.string=multi,width=6,height=4} \setkeys{Gin}{width=\textwidth} %\VignetteIndexEntry{Multi-state example} \begin{document} <>= require(survival) #require(Rcolorbrewer) #brewer.pal(5, "Dark2") palette(c("#000000", "#D95F02", "#1B9E77", "#7570B3", "#E7298A", "#66A61E")) options(continue=' ') # These functions are used in the document, but not discussed until the end crisk <- function(what, horizontal = TRUE, ...) { nstate <- length(what) connect <- matrix(0, nstate, nstate, dimnames=list(what, what)) connect[1,-1] <- 1 # an arrow from state 1 to each of the others if (horizontal) statefig(c(1, nstate-1), connect, ...) else statefig(matrix(c(1, nstate-1), ncol=1), connect, ...) } state3 <- function(what, horizontal=TRUE, ...) { if (length(what) != 3) stop("Should be 3 states") connect <- matrix(c(0,0,0, 1,0,0, 1,1,0), 3,3, dimnames=list(what, what)) if (horizontal) statefig(1:2, connect, ...) else statefig(matrix(1:2, ncol=1), connect, ...) } state4 <- function() { sname <- c("Entry", "CR", "Transplant", "Transplant") layout <- cbind(c(1/2, 3/4, 1/4, 3/4), c(5/6, 1/2, 1/2, 1/6)) connect <- matrix(0,4,4, dimnames=list(sname, sname)) connect[1, 2:3] <- 1 connect[2,4] <- 1 statefig(layout, connect) } state5 <- function(what, ...) { sname <- c("Entry", "CR", "Tx", "Rel", "Death") connect <- matrix(0, 5, 5, dimnames=list(sname, sname)) connect[1, -1] <- c(1,1,1, 1.4) connect[2, 3:5] <- c(1, 1.4, 1) connect[3, c(2,4,5)] <- 1 connect[4, c(3,5)] <- 1 statefig(matrix(c(1,3,1)), connect, cex=.8,...) } @ \maketitle \section{Multi-state curves} Consider the simple \code{survfit} call <>= curves <- survfit(Surv(time, status) ~ group, data=mydata) @ In the classic case \code{status} is either a logical or 0/1 numeric variable that represents censoring (0 or false) or an event (1 or true), and the result is a survival curve for each group. If \code{status} is a factor, however, the result is a multi-state estimate. In this case the first level of \code{status} is used to code censoring while the remaining ones are possible states. Here is a simple competing risks example where the three endpoints are labeled as a, b and c. <>= set.seed(1952) crdata <- data.frame(time=1:11, endpoint=factor(c(1,1,2,0,1,1,3,0,2,3,0), labels=c("censor", "a", "b", "c"))) tfit <- survfit(Surv(time, endpoint) ~ 1, data=crdata) dim(tfit) summary(tfit) @ The resulting object \code{tfit} contains an estimate of $P$(state), the probability of being in each state. $P$ is a matrix with one row for each time and one column for each of the four states a--c and the "no event as of yet" state; we will often refer to the latter as the entry state. By definition each row of $P$ sums to 1. The plot of the fit will have 3 curves, by default the curve for an unnamed state is not displayed. (Since they sum to 1 one of the 4 curves is redundant, and the entry state is normally the least interesting of the set.) <>= plot(tfit, col=1:3, lwd=2, ylab="Probability in state") @ The resulting \code{survfms} object appears as a matrix and can be subscripted as such, with a column for each state and rows for each group that was created by any variables on the right hand side of the formula. This makes it simple to display a subset of the curves using plot or lines commands. The unnamed state in the above fit, for instance, can be displayed with \code{plot(tfit[,4])}. The curves are computed using the Aalen-Johansen estimator. The Kaplan-Meier estimate and the cumulative incidence estimate (for competing risks) are each a special case of the AJ estimate. It is more general that that, however; a given subject can have multiple transitions from state to state, including transitions to a state that was visited earlier. In this case the dataset structure is similar to that for time varying covariates in a Cox model: the time variable will be intervals $(t_1, t_2]$ which are open on the left and closed on the right, and the status variable contains the state that was entered at time $t_2$, and a subject will have multiple lines of data. There are a few restrictions. \begin{itemize} \item An identifier variable is required which indicates which rows of the data frame belong to each subject. If the \code{id} argument is missing the code assumes that each row of data is a separate subject, which leads to a nonsense estimate when there are actually multiple rows for each. \item Subjects do not have to enter at time 0 or all at the same time, but each must traverse a connected segment of time. Disjoint intervals such as the pair $(0,5]$, $(8, 10]$ are illegal. \item A subject cannot change groups. Any covariates on the right hand side of the formula must remain constant within subject. (This function is not a way to creat supposed `time-dependent' survival curves.) \item Subjects may have case weights, and these weights may change over time for a subject. \end{itemize} By default every subject is assumed to start in an unnamed common entry state. The \code{istate} argument can instead be used to designate an entry state for each subject; like variables in the formula it is searched for in the \code{data} argument. The distribution of states at the first event time is treated as the initial distribution of states; like ordinary survival an observation which is censored before the first event time has no impact on the results. The extended example below is intended to give more information about the routines. \section{Data set} The \code{myeloid} data set contains simulated data which mimics that from a trial in subjects with acute myeloid leukemia. In this comparison of two conditioning regimens the canonical path for a subject is initial therapy $\rightarrow$ complete response (CR) $\rightarrow$ hematologic stem cell transplant (HSCT) $\rightarrow$ sustained remission, followed by relapse or death. <>= myeloid[1:5,] @ The first few rows of data are shown above. The data set contains the follow-up time and status at last follow-up for each subject, along with the time to transplant (txtime), complete response (crtime) or relapse after CR (rltime). Subject 1 did not receive a transplant, as shown by the NA value, and subject 2 did not achieve CR. \begin{figure} \myfig{sfit0} \caption{Overall survival curves for the two treatments.} \label{sfit0} \end{figure} Overall survival curves for the data are shown in figure \ref{sfit0}. The difference between the treatment arms A and B is substantial. A goal of this analysis is to better understand this difference. Here is the code to generate the simple survival curves: <>= sfit0 <- survfit(Surv(futime, death) ~ trt, myeloid) plot(sfit0, xscale=365.25, xaxs='r', col=1:2, lwd=2, xlab="Years post enrollment", ylab="Survival") legend(20, .4, c("Arm A", "Arm B"), col=1:2, lwd=2, bty='n') @ \section{Competing risks} A first step towards deeper analysis is to look at intermediate states one at a time, e.g., how many subjects ever achieve a CR or ever receive a transplant. Create a working data set that contains variables for simple 2-state competing risks for the pairs CR/death and transplant/death. For competing risks each subject has a single row of data, so this data set simply adds two new variables and redefines two others. At the same time we will convert from days to months. This is the natural time scale for our plots, and forestalls adding the \code{xscale} argument to every plot call. <>= data1 <- myeloid data1$crstat <- factor(with(data1, ifelse(is.na(crtime), death, 2)), labels=c("censor", "death", "CR")) data1$crtime <- with(data1, ifelse(crstat=="CR", crtime, futime)) data1$txstat <- factor(with(data1, ifelse(is.na(txtime), death, 2)), labels=c("censor", "death", "transplant")) data1$txtime <- with(data1, ifelse(txstat=="transplant", txtime, futime)) for (i in c("futime", "crtime", "txtime", "rltime")) data1[[i]] <- data1[[i]] * 12/365.25 #rescale to months @ \begin{figure} \myfig{curve1} \caption{Overall survival curves: time to death, to transplant (Tx), and to complete response (CR). Each shows the estimated fraction of subjects who have ever reached the given state. The vertical line at 2 months is for reference. The curves were limited to the first 48 months to more clearly show early events. The right hand panel shows the state-space model for each pair of curves.} \label{curve1} \end{figure} This data set is the basis for our first set of curves, which are shown in figure \ref{curve1}. The plot overlays three separate \code{survfit} calls: standard survival until death, complete response with death as a competing risk, and transplant with death as a competing risk. For each fit we have shown one selected state: the fraction who have died, fraction ever in CR, and fraction ever to receive transplant, respectively. Most of the CR events happen before 2 months (the green vertical line) and nearly all the additional CRs conferred by treatment B occur between months 2 and 8. Most transplants happen after 2 months, which is consistent with the clinical guide of transplant after CR. The survival advantage for treatment B begins between 4 and 5 months, which argues that it could be at least partially a consequence of the additional CR events. The code to draw figure \ref{curve1} is below. It can be separated into 5 parts: \begin{enumerate} \item Fits for the 3 endpoints are simple and found in the first 3 lines. The \code{crstat} and \code{txstat} variables are factors, which causes a multi-state curve to be generated. \item The \code{layout} and \code{par} commands are used to create a multi-part plot with curves on the left and state space diagrams on the right, and to reduce the amount of white space between them. \item Draw a subset of the curves via subscripting. A multi-state survfit object appears as a matrix of curves, with one row for each group (treatment) and one column for each state. The CR state is the second column in \code{sfit2}, for instance. The CR fit was drawn first simply because it has the greatest y-axis range, then the other curves added using the lines command. \item Decoration of the plots. This includes the line types, colors, legend, choice of x-axis labels, etc. \item Add the state space diagrams. The functions for this are described in the last section of the vignette. \end{enumerate} <>= sfit1 <- survfit(Surv(futime, death) ~ trt, data1) #survival sfit2 <- survfit(Surv(crtime, crstat) ~ trt, data1) # CR sfit3 <- survfit(Surv(txtime, txstat) ~ trt, data1) layout(matrix(c(1,1,1,2,3,4), 3,2), widths=2:1) oldpar <- par(mar=c(5.1, 4.1, 1.1, .1)) plot(sfit2[,2], mark.time=FALSE, fun='event', xmax=48, lty=3, lwd=2, col=1:2, xaxt='n', xlab="Months post enrollment", ylab="Events") lines(sfit1, mark.time=FALSE, xmax=48, fun='event', col=1:2, lwd=2) lines(sfit3[,2], mark.time=FALSE, xmax=48, fun='event', col=1:2, lty=2, lwd=2) xtime <- c(0, 6, 12, 24, 36, 48) axis(1, xtime, xtime) #marks every year rather than 10 months temp <- outer(c("A", "B"), c("death", "transplant", "CR"), paste) temp[7] <- "" legend(25, .3, temp[c(1,2,7,3,4,7,5,6,7)], lty=c(1,1,1, 2,2,2 ,3,3,3), col=c(1,2,0), bty='n', lwd=2) abline(v=2, lty=2, col=3) # add the state space diagrams par(mar=c(4,.1,1,1)) crisk(c("Entry","Death", "CR"), alty=3) crisk(c("Entry","Death", "Tx"), alty=2) crisk(c("Entry","Death")) par(oldpar) @ The association between a particular curve and its corresponding state space diagram is critical. As we will see below, many different models are possible and it is easy to get confused. Attachment of a diagram directly to each curve, as was done above, will not necessarily be day-to-day practice, but the state space should always be foremost. If nothing else, draw it on a scrap of paper and tape it to the side of the terminal when creating a data set and plots. \begin{figure} \myfig{badfit} \caption{Correct (solid) and invalid (dashed) estimates of the number of subjects transplanted.} \label{badfit} \end{figure} Figure \ref{badfit} shows the transplant curves overlaid with the naive KM that censors subjects at death. There is no difference in the initial portion as no deaths have yet intervened, but the final portion overstates the transplant outcome by more than 10\%. \begin{enumerate} \item The key problem with the naive estimate is that subjects who die can never have a transplant. The result of censoring them is an estimate of the ``fraction who would be transplanted, if death before transplant were abolished''. This is not a real world quantity. \item In order to estimate this fictional quantity one needs to assume that death is uninformative with respect to future disease progression. The early deaths in months 0--2, before transplant begins, are however a very different class of patient. Non-informative censoring is untenable. \end{enumerate} We are left with an unreliable estimate of an uninteresting quantity. Mislabeling any true state as censoring is always a mistake, one that will not be repeated here. Here is the code for figure \ref{badfit}. The use of a logical (true/false) as the status variable in the \code{Surv} call leads to ordinary survival calculations. <>= badfit <- survfit(Surv(txtime, txstat=="transplant") ~ trt, data1) layout(matrix(c(1,1,1,2,3,4), 3,2), widths=2:1) oldpar <- par(mar=c(5.1, 4.1, 1.1, .1)) plot(badfit, fun="event", xmax=48, xaxt='n', col=1:2, lty=2, lwd=2, xlab="Months from enrollment", ylab="P(state)") axis(1, xtime, xtime) lines(sfit3[,2], fun='event', xmax=48, col=1:2, lwd=2) legend(24, .3, c("Arm A", "Arm B"), lty=1, lwd=2, col=1:2, bty='n', cex=1.2) par(mar=c(4,.1,1,1)) crisk(c("Entry", "transplant"), alty=2, cex=1.2) crisk(c("Entry","transplant", "Death"), cex=1.2) par(oldpar) @ \section{Multi-state models} The multi-state models are based on a second data set which looks very much like the (start, stop] data sets that are used for time dependent covariates. Consider subject 5 who experienced CR on day 56, relapse on day 112 and death on day 200. In the expanded data set this subject will have 3 lines, one for each of the intervals (0,56], (56, 112] and (112, 200]. The first interval ends with CR and the second with relapse. What if someone has two endpoints on the same day? Creation of a zero length interval will lead to a justifiable complaint from the programs; subjects are not allowed to do instantaneous transitions. For each such observation a decision needs to be made, preferably based on rational scientific argument rather than statistical or programming convenience. It turns out that we do have one such case in the myeloid data: one subject who was declared to be a CR on the day of their transplant. Since complete response will occur before its clinical detection I decided to make the tied CR one day earlier. This issue didn't come up in creating \code{data1} only because it dealt with the pairs CR:death and transplant:death, and neither of these has a tie. We create the data set using the \code{tmerge} function in R, code is shown below. (Because such start-stop data sets are commonly used for Cox models with time-dependent covariates, this is a familiar task to many users and they will have developed their own favorite work flow; tmerge is a useful but not essential tool.) The tmerge function uses a baseline data set, in this case the variables from the starting data that are constant over time, and then adds rows to it. Each \code{event} and \code{tdc} statement sequentially adds either an endpoint or time-dependent covariate as new rows to the data, in much the same way that one would insert new folders into the proper position in a file drawer. Each addition will split a subject's time interval as necessary. <<>= temp <- myeloid id <- which(temp$crtime == temp$txtime) # the one special person temp$crtime[id] <- temp$crtime[id] -1 # move their CR back by 1 day data2 <- tmerge(myeloid[, c('id', 'trt')], temp, id=id, death=event(futime, death), transplant = event(txtime), response = event(crtime), relapse = event(rltime), priortx = tdc(txtime), priorcr = tdc(crtime)) attr(data2, "tcount") data2$event <- with(data2, factor(death + 2*response + 3*transplant + 4*relapse, 0:4, labels=c("censor", "death", "CR", "transplant", "relapse"))) data2[1:10,c(1:4, 11, 9, 10)] @ The tmerge call starts by adding death/censoring time, which appears in the `trailing' column of the tcount table since it defines the right endpoint for each subject, and thus by definition occurs at the trailing end of their interval. Then transplant is added which has 363 within and 1 trailing: there is one subject whose transplant date is also their last follow-up date. Response and relapse times all fall within a prior interval. Looking above at the first 4 subjects in \code{data2}, the fourth follows the canonical path of CR followed by transplant. Subject 1 relapses after CR, without transplant, and subject 2 has transplant without a CR. A critical step in any multi-state model is to print out some portion of the created data set and \emph{read} it. This data set is key, and any errors will invalidate all the analysis which follows. This step has been abbreviated for the vignette; inspection of only the first 4 subjects is a very small sample. Rescale the data set from days to months and look at three more summaries. <>= for (i in c("tstart", "tstop")) data2[[i]] <- data2[[i]] *12/365.25 #scale to months ctab <- table(table(data2$id)) ctab with(data2, table( table(id, event))) etab <- table(data2$event, useNA="ifany") etab @ In the final result there are \Sexpr{ctab[1]} subjects with only a single row of data, \Sexpr{ctab[2]} with 2 rows, etc. The table of \code{id} by \code{event} contains only 0 and 1 as values, i.e., no one has two events of the same type, which is correct for this data set. Overall \Sexpr{etab['CR']} of the \Sexpr{nrow(myeloid)} subjects experience a CR at some point in the study. \begin{figure} \myfig{cr2} \caption{Models for `ever in CR' and `currently in CR'; the only difference is an additional transition. Both models ignore transplant.} \label{cr2} \end{figure} Complete response is a goal of the initial therapy; figure \ref{cr2} looks more closely at this. As was noted before arm B has an increased number of late responses. The duration of response is also increased: the solid curves show the number of subjects still in response, and we see that they spread farther apart than the dotted ``ever in response'' curves. The figure shows only the first eight months in order to better visualize the details, but continuing the curves out to 48 months reveals a similar pattern. Here is the code to create the figure. <>= crstat <- data2$event crstat[crstat=="transplant"] <- "censor" # ignore transplants crsurv <- survfit(Surv(tstart, tstop, crstat) ~ trt, data= data2, id=id, influence=TRUE) layout(matrix(c(1,1,2,3), 2,2), widths=2:1) oldpar <- par(mar=c(5.1, 4.1, 1.1, .1)) plot(sfit2[,2], lty=3, lwd=2, col=1:2, xmax=12, xlab="Months", ylab="CR") lines(crsurv[,2], lty=1, lwd=2, col=1:2, xmax=12) par(mar=c(4, .1, 1, 1)) crisk( c("Entry","CR", "Death"), alty=3) state3(c("Entry", "CR", "Death/Relapse")) par(oldpar) @ Rather than create a new data set, the above code modifies the event variable so as to ignore transitions to the transplant state. They become a non-event, in the same way that extra lines with a status of zero are used to create time-dependent covariates for a Cox model fit. The \code{survfit} call above included the \code{influence=TRUE} argument, which causes the influence array to be calculated and returned. It contains, for each subject, that subject's influence on the time by state matrix of results and allows for calculation of the standard error of the restricted mean. We will return to this in a later section. <>= print(crsurv, rmean=48, digits=2) @ <>= temp <- summary(crsurv, rmean=48)$table delta <- round(temp[4,3] - temp[3,3], 2) @ @ The restricted mean time in the CR state is extended by \Sexpr{round(temp[4,3], 1)} - \Sexpr{round(temp[3,3], 1)} = \Sexpr{delta} months. A question which immediately gets asked is whether this difference is ``significant'', to which there are two answers. The first and more important is to ask whether 5 months is an important gain from either a clinical or patient perspective. The overall restricted mean survival for the study is approximately 30 of the first 48 months post entry (use print(sfit1, rmean=48)); on this backdrop an extra 5 months in CR might or might not be an meaningful advantage from a patient's point of view. The less important answer is to test whether the apparent gain is sufficiently rare from a mathematical point of view, i.e., ``statistical'' significance. The standard errors of the two values are \Sexpr{round(temp[3,4],1)} and \Sexpr{round(temp[4,4],1)}, and since they are based on disjoint subjects the values are independent, leading to a standard error for the difference of $\sqrt{1.1^2 + 1.2^2} = 1.6$. The difference is over 3 standard errors. \begin{figure} \myfig{txsurv} \caption{Transplant status of the subjects, broken down by whether it occurred before or after CR.} \label{txsurv} \end{figure} In summary \begin{itemize} \item Arm B adds late complete responses (about 4\%); there are 212/310 in arm B vs. 244/338 in arm B. \item The difference in 4 year survival is about 6\%. \item There is approximately 2 months longer average duration of CR (of 48). \end{itemize} CR $\rightarrow$ transplant is the target treatment path for a patient; given the improvements listed above why does figure \ref{curve1} show no change in the number transplanted? Figure \ref{txsurv} shows the transplants broken down by whether this happened before or after complete response. Most of the non-CR transplants happen by 10 months. One possible explanation is that once it is apparent to the patient/physician pair that CR is not going to occur, they proceed forward with other treatment options. The extra CR events on arm B, which occur between 2 and 8 months, lead to a consequent increase in transplant as well, but at a later time of 12--24 months: for a subject in CR we can perhaps afford to defer the transplant date. Computation is again based on a manipulation of the event variable: in this case dividing the transplant state into two sub-states based on the presence of a prior CR. The code makes use of the time-dependent covariate \code{priorcr}. (Because of scheduling constraints within a hospital it is unlikely that a CR that is within a few days prior to transplant could have effected the decision to schedule a transplant, however. An alternate breakdown that might be useful would be ``transplant without CR or within 7 days after CR'' versus those that are more than a week later. There are many sensible questions that can be asked.) <>= event2 <- with(data2, ifelse(event=="transplant" & priorcr==1, 6, as.numeric(event))) event2 <- factor(event2, 1:6, c(levels(data2$event), "tx after CR")) txsurv <- survfit(Surv(tstart, tstop, event2) ~ trt, data2, id=id, subset=(priortx ==0)) layout(matrix(c(1,1,1,2,2,0),3,2), widths=2:1) oldpar <- par(mar=c(5.1, 4.1, 1,.1)) plot(txsurv[,c(3,5)], col=1:2, lty=c(1,1,2,2), lwd=2, xmax=48, xaxt='n', xlab="Months", ylab="Transplanted") axis(1, xtime, xtime) legend(15, .13, c("A, transplant without CR", "B, transplant without CR", "A, transplant after CR", "B, transplant after CR"), col=1:2, lty=c(1,1,2,2), lwd=2, bty='n') state4() # add the state figure par(oldpar) @ \begin{figure} \myfig{sfit4} \caption{The full multi-state curves for the two treatment arms.} \label{sfit4} \end{figure} Figure \ref{sfit4} shows the full set of state occupancy probabilities for the cohort over the first 4 years. At each point in time the curves estimate the fraction of subjects currently in that state. The total who are in the transplant state peaks at about 9 months and then decreases as subjects relapse or die; the curve rises whenever someone receives a transplant and goes down whenever someone leaves the state. At 36 months treatment arm B (dashed) has a lower fraction who have died, the survivors are about evenly split between those who have received a transplant and those whose last state is a complete response (only a few of the latter are post transplant). The fraction currently in relapse -- a transient state -- is about 5\% for each arm. The figure omits the curve for ``still in the entry state''. The reason is that at any point in time the sum of the 5 possible states is 1 --- everyone has to be somewhere. Thus one of the curves is redundant, and the fraction still in the entry state is the least interesting of them. (A multi-state \code{survfit} call that does not include the \code{istate} argument will assume that everyone starts in an unnamed entry state. The default plot behavior is to omit the curves for any unnamed states.) <>= sfit4 <- survfit(Surv(tstart, tstop, event) ~ trt, data2, id=id) sfit4$transitions layout(matrix(1:2,1,2), widths=2:1) oldpar <- par(mar=c(5.1, 4.1, 1,.1)) plot(sfit4, col=rep(1:4,each=2), lwd=2, lty=1:2, xmax=48, xaxt='n', xlab="Months", ylab="Current state") axis(1, xtime, xtime) text(c(40, 40, 40, 40), c(.51, .13, .32, .01), c("Death", "CR", "Transplant", "Recurrence"), col=1:4) par(mar=c(5.1, .1, 1, .1)) state5() par(oldpar) @ The transitions table above shows \Sexpr{sfit4$transitions[5,1]} %$ direct transitions from entry to death, i.e., subjects who die without experiencing any of the other intermediate points, \Sexpr{sfit4$transitions[2,3]} who go from CR to transplant (as expected), \Sexpr{sfit4$transitions[3,2]} who go from transplant to CR, etc. %$ No one was observed to go from relapse to CR in the data set, this serves as a data check since it should not be possible per the data entry plan. \section{Influence matrix} For one of the curves above we returned the influence array. For each value in the matrix $P$ = probability in state and each subject $i$ in the data set, this contains the effect of that subject on each value in $P$. Formally, \begin{equation*} I_{ij}(t) = \left . \frac{\partial p_j(t)}{\partial w_i} \right|_w \end{equation*} where $I_{ij}(t)$ is the influence of subject $i$ on $p_j(t)$, and $p_j(t)$ is the estimated probability for state $j$ at time $t$. This is known as the infinitesimal jackknife (among other labels). <>= crsurv <- survfit(Surv(tstart, tstop, crstat) ~ trt, data= data2, id=id, influence=TRUE) curveA <- crsurv[1,] # select treatment A dim(curveA$pstate) # P matrix for treatement A dim(curveA$influence) # influence matrix for treatment A table(data1$trt) curveA$p0 # state distribution at time 0 @ For treatment arm A there are \Sexpr{table(data1$trt)[1]} subjects and \Sexpr{dim(curveA$pstate)[1]} time points in the $P$ matrix. The influence array has subject as the first dimension, and for each subject it has an image of the $P$ matrix containing that subject's influence on each value in $P$, i.e., \code{influence[1,,]} is the influence of subject 1 on $P$. The influence has one extra row, however; the first row for each subjects is the influence of that subject on $p_0$, the initial state probabilities. For this data set everyone starts in the entry state, $p_0$ will always be (0, 0, 0, 1), and so this first influence row will be zero; this does not hold if not all subjects start in the same state. As an exercise we will calculate the mean time in state out to 48 weeks. This is the area under the individual curves from time 0 to 48. Since the curves are step functions this is simple sum of rectangles, treating any intervals after 48 months as having 0 width. <>= t48 <- pmin(48, curveA$time) delta <- diff(c(0, t48, 48)) # width of intervals rfun <- function(pmat, delta) colSums(pmat * delta) #area under the curve rmean <- rfun(rbind(curveA$p0, curveA$pstate), delta) round(rmean, 2) # Apply the same calculation to each subject's influence slice inf <- apply(curveA$influence, 1, rfun, delta=delta) # inf is now a 5 state by 310 subject matrix, containing the IJ estimates # on the AUC or mean time. The sum of squares is a variance. se.rmean <- sqrt(rowSums(inf^2)) round(se.rmean, 2) @ In general, let $U_i$ be the influence of subject $i$. For some function $f(P)$ of the prevalence matrix, the influence of subject $i$ will be $\delta_i = f(P + U_i) - f(P)$ and the infinitesimal jackknife estimate of variance will be $\sum_i \delta^2$. For the simple case of adding up rectangles $f(P +U_i) - f(P) = f(U_i)$ leading to particularly simple code, but this will not always be the case. \section{State space figures} The state space figures in this document were drawn with a simple utility function \code{statefig}. It has two primary arguments along with standard graphical options of color, line type, etc. \begin{enumerate} \item A layout vector or matrix. A vector with values of (1, 3, 1) for instance will allocate one state, then a column with 3 states, then one more state, proceeding from left to right. A matrix with a single row will do the same, whereas a matrix with one column will proceed from top to bottom. \item A $k$ by $k$ connection matrix $C$ where $k$ is the number of states. If $C_{ij} \ne 0$ then an arrow is drawn from state $i$ to state $j$. The row or column names of the matrix are used to label the states. The lines connecting the states can be straight or curved, see the help file for the function for an example. \end{enumerate} The first few state space diagrams were competing risk models, which use the following derived function. It accepts a vector of state names, where the first name is the starting state and the remainder are the possible outcomes. <>= crisk <- function(what, horizontal = TRUE, ...) { nstate <- length(what) connect <- matrix(0, nstate, nstate, dimnames=list(what, what)) connect[1,-1] <- 1 # an arrow from state 1 to each of the others if (horizontal) statefig(c(1, nstate-1), connect, ...) else statefig(matrix(c(1, nstate-1), ncol=1), connect, ...) } @ This next function draws a variation of the illness-death model. It has an initial state, an absorbing state (normally death), and an optional intermediate state. <>= state3 <- function(what, horizontal=TRUE, ...) { if (length(what) != 3) stop("Should be 3 states") connect <- matrix(c(0,0,0, 1,0,0, 1,1,0), 3,3, dimnames=list(what, what)) if (horizontal) statefig(1:2, connect, ...) else statefig(matrix(1:2, ncol=1), connect, ...) } @ The most complex of the state space figures has all 5 states. <>= state5 <- function(what, ...) { sname <- c("Entry", "CR", "Tx", "Rel", "Death") connect <- matrix(0, 5, 5, dimnames=list(sname, sname)) connect[1, -1] <- c(1,1,1, 1.4) connect[2, 3:5] <- c(1, 1.4, 1) connect[3, c(2,4,5)] <- 1 connect[4, c(3,5)] <- 1 statefig(matrix(c(1,3,1)), connect, cex=.8, ...) } @ For figure \ref{txsurv} I want a third row with a single state, but don't want that state centered. For this I need to create my own (x,y) coordinate list as the layout parameter. Coordinates must be between 0 and 1. <>= state4 <- function() { sname <- c("Entry", "CR", "Transplant", "Transplant") layout <- cbind(x =c(1/2, 3/4, 1/4, 3/4), y =c(5/6, 1/2, 1/2, 1/6)) connect <- matrix(0,4,4, dimnames=list(sname, sname)) connect[1, 2:3] <- 1 connect[2,4] <- 1 statefig(layout, connect) } @ The statefig function was written to do ``good enough'' state space figures quickly and easily, in the hope that users will find it simple enough that diagrams are drawn early and often. Other packages such as diagram, DiagrammeR, or dagR are far more flexible and can create more nuanced and well decorated results. \section{Conclusion} With a data set such as this we can fit many different multi-state models. These fits are easy to do, and can give substantial further insight into a data set. \end{document} survival/inst/doc/timedep.R0000644000175100001440000002525213070714002015437 0ustar hornikusers### R code from vignette source 'timedep.Rnw' ################################################### ### code chunk number 1: preamble ################################################### options(width=60, continue=" ") makefig <- function(file, top=1, right=1, left=4) { pdf(file, width=9.5, height=7, pointsize=18) par(mar=c(4, left, top, right) +.1) } library(survival) ################################################### ### code chunk number 2: testdata ################################################### tdata <- data.frame(subject=c(5,5,5), time1=c(0,90, 120), time2 = c(90, 120, 185), death=c(0,0,1), creatinine=c(0.9, 1.5, 1.2)) tdata ################################################### ### code chunk number 3: fake ################################################### getOption("SweaveHooks")[["fig"]]() set.seed(1953) # a good year nvisit <- floor(pmin(lung$time/30.5, 12)) response <- rbinom(nrow(lung), nvisit, .05) > 0 badfit <- survfit(Surv(time/365.25, status) ~ response, data=lung) plot(badfit, mark.time=FALSE, lty=1:2, xlab="Years post diagnosis", ylab="Survival") legend(1.5, .85, c("Responders", "Non-responders"), lty=2:1, bty='n') ################################################### ### code chunk number 4: timedep.Rnw:200-202 (eval = FALSE) ################################################### ## fit <- coxph(Surv(time1, time2, status) ~ age + creatinine, ## data=mydata) ################################################### ### code chunk number 5: timedep.Rnw:273-274 (eval = FALSE) ################################################### ## newdata <- tmerge(data1, data2, id, newvar=tdc(time, value), ...) ################################################### ### code chunk number 6: timedep.Rnw:319-320 ################################################### cgd0[1:4,] ################################################### ### code chunk number 7: cgd1 ################################################### dim(cgd0) newcgd <- tmerge(data1=cgd0[, 1:13], data2=cgd0, id=id, tstop=futime) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime1)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime2)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime3)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime4)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime5)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime6)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime7)) newcgd <- tmerge(newcgd, newcgd, id, enum=cumtdc(tstart)) dim(newcgd) newcgd[1:5,c(1, 4:6, 13:17)] attr(newcgd, "tcount") coxph(Surv(tstart, tstop, infect) ~ treat + inherit + steroids + + cluster(id), newcgd) ################################################### ### code chunk number 8: cgd1b ################################################### test <- tmerge(cgd0[, 1:13], cgd0, id=id, tstop=futime, infect = event(etime1), infect= event(etime2), infect = event(etime3), infect= event(etime4), infect = event(etime5), infect= event(etime6), infect = event(etime7)) test <- tmerge(test, test, id= id, enum = cumtdc(tstart)) all.equal(newcgd, test) ################################################### ### code chunk number 9: stanford ################################################### jasa$subject <- 1:nrow(jasa) #we need an identifier variable tdata <- with(jasa, data.frame(subject = subject, futime= pmax(.5, fu.date - accept.dt), txtime= ifelse(tx.date== fu.date, (tx.date -accept.dt) -.5, (tx.date - accept.dt)), fustat = fustat )) sdata <- tmerge(jasa, tdata, id=subject, death = event(futime, fustat), trt = tdc(txtime), options= list(idname="subject")) attr(sdata, "tcount") sdata$age <- sdata$age -48 sdata$year <- as.numeric(sdata$accept.dt - as.Date("1967-10-01"))/365.25 # model 6 of the table in K&P coxph(Surv(tstart, tstop, death) ~ age*trt + surgery + year, data= sdata, ties="breslow") ################################################### ### code chunk number 10: pbc ################################################### temp <- subset(pbc, id <= 312, select=c(id:sex, stage)) # baseline pbc2 <- tmerge(temp, temp, id=id, death = event(time, status)) #set range pbc2 <- tmerge(pbc2, pbcseq, id=id, ascites = tdc(day, ascites), bili = tdc(day, bili), albumin = tdc(day, albumin), protime = tdc(day, protime), alk.phos = tdc(day, alk.phos)) fit1 <- coxph(Surv(time, status==2) ~ log(bili) + log(protime), pbc) fit2 <- coxph(Surv(tstart, tstop, death==2) ~ log(bili) + log(protime), pbc2) rbind('baseline fit' = coef(fit1), 'time dependent' = coef(fit2)) ################################################### ### code chunk number 11: timedep.Rnw:582-583 ################################################### attr(pbc2, "tcount") ################################################### ### code chunk number 12: timedep.Rnw:585-587 ################################################### #grab a couple of numbers for the paragraph below atemp <- attr(pbc2, "tcount")[2:3,] ################################################### ### code chunk number 13: timedep.Rnw:668-674 (eval = FALSE) ################################################### ## temp <- subset(pbc, id <= 312, select=c(id:sex, stage)) ## pbc2 <- tmerge(temp, temp, id=id, death = event(time, status)) ## pbc2a <- tmerge(pbc2, pbcseq, id=id, ascites = tdc(day, ascites), ## bili = tdc(day, bili), options= list(delay=14)) ## pbc2b <- tmerge(pbc2, pbcseq, id=id, ascites = tdc(day+14, ascites), ## bili = tdc(day+14, bili)) ################################################### ### code chunk number 14: rep (eval = FALSE) ################################################### ## newd <- tmerge(data1=base, data2=timeline, id=repid, tstart=age1, ## tstop=age2, options(id="repid")) ## newd <- tmerge(newd, outcome, id=repid, mcount = cumtdc(age)) ## newd <- tmerge(newd, subset(outcome, event='diabetes'), ## diabetes= tdc(age)) ## newd <- tmerge(newd, subset(outcome, event='arthritis'), ## arthritis= tdc(age)) ################################################### ### code chunk number 15: veteran1 ################################################### getOption("SweaveHooks")[["fig"]]() options(show.signif.stars = FALSE) # display user intelligence vfit <- coxph(Surv(time, status) ~ trt + prior + karno, veteran) vfit quantile(veteran$karno) zp <- cox.zph(vfit, transform= function(time) log(time +20)) zp plot(zp[3]) # a plot for the 3rd variable in the fit abline(0,0, col=2) abline(h= vfit$coef[3], col=3, lwd=2, lty=2) ################################################### ### code chunk number 16: split ################################################### vet2 <- survSplit(Surv(time, status) ~ ., data= veteran, cut=c(90, 180), episode= "tgroup", id="id") vet2[1:7, c("id", "tstart", "time", "status", "tgroup", "age", "karno")] ################################################### ### code chunk number 17: split2 ################################################### vfit2 <- coxph(Surv(tstart, time, status) ~ trt + prior + karno:strata(tgroup), data=vet2) vfit2 cox.zph(vfit2) ################################################### ### code chunk number 18: split3 ################################################### vfit2$means ################################################### ### code chunk number 19: split4 ################################################### quantile(veteran$karno) cdata <- data.frame(tstart= rep(c(0,30,60), 2), time = rep(c(30,60, 100), 2), status= rep(0,6), #necessary, but ignored tgroup= rep(1:3, 2), trt = rep(1,6), prior= rep(0,6), karno= rep(c(40, 75), each=3), curve= rep(1:2, each=3)) cdata sfit <- survfit(vfit2, newdata=cdata, id=curve) km <- survfit(Surv(time, status) ~ I(karno>60), veteran) plot(km, xmax=120, col=1:2, lwd=2, xlab="Days from enrollment", ylab="Survival") lines(sfit, col=1:2, lty=2, lwd=2) ################################################### ### code chunk number 20: vfit3 (eval = FALSE) ################################################### ## vfit3 <- coxph(Surv(time, status) ~ trt + prior + karno + ## I(karno * log(time + 20)), data=veteran) ################################################### ### code chunk number 21: vet3 ################################################### vfit3 <- coxph(Surv(time, status) ~ trt + prior + karno + tt(karno), data=veteran, tt = function(x, t, ...) x * log(t+20)) vfit3 ################################################### ### code chunk number 22: vet3b ################################################### getOption("SweaveHooks")[["fig"]]() plot(zp[3]) abline(coef(vfit3)[3:4], col=2) ################################################### ### code chunk number 23: pbctime ################################################### pfit1 <- coxph(Surv(time, status==2) ~ log(bili) + ascites + age, pbc) pfit2 <- coxph(Surv(time, status==2) ~ log(bili) + ascites + tt(age), data=pbc, tt=function(x, t, ...) { age <- x + t/365.25 cbind(age=age, age2= (age-50)^2, age3= (age-50)^3) }) pfit2 anova(pfit2) # anova(pfit1, pfit2) #this fails 2*(pfit2$loglik - pfit1$loglik)[2] ################################################### ### code chunk number 24: expand ################################################### dtimes <- sort(unique(with(pbc, time[status==2]))) tdata <- survSplit(Surv(time, status==2) ~., pbc, cut=dtimes) tdata$c.age <- tdata$age + tdata$time/365.25 -50 #current age, centered at 50 pfit3 <- coxph(Surv(tstart, time, event) ~ log(bili) + ascites + c.age + I(c.age^2) + I(c.age^3), data=tdata) rbind(coef(pfit2), coef(pfit3)) ################################################### ### code chunk number 25: timedep.Rnw:1078-1085 ################################################### function(x, t, riskset, weights){ obrien <- function(x) { r <- rank(x) (r-.5)/(.5+length(r)-r) } unlist(tapply(x, riskset, obrien)) } ################################################### ### code chunk number 26: timedep.Rnw:1095-1097 ################################################### function(x, t, riskset, weights) unlist(tapply(x, riskset, rank)) survival/inst/doc/adjcurve.pdf0000644000175100001440000171764213070713757016217 0ustar hornikusers%PDF-1.4 %ÐÔÅØ 3 0 obj << /Length 3286 /Filter /FlateDecode >> stream xÚ…ZIÛʾ¿_!ä °h.Í-7çáxrzAœERK,‰ IÍx‚üøÔÚÝ”(û0£f/ÕÕÕµ|Uä__~ùø9-Vq&qfV/»Uíábìþ&Ó‘ÄØSŽ¸ŠÓ,Ìò •†i‘ñ¡¾Ô4Nt’ÚqÆò0f›059Ë#.³02«I²¬xm¼ÞÄ1¬ûH¤1m>ô(è ½5øt´Ûü\®ª°Ê“éEÀE–QÉ”è®ðï ‡+‚%Ð* ÞPl®]µr“–íØóàQeüŠ³èf'ľžA]«ßµÐÁéß×|‚Îß`ìÏ·v(|:T?píø5‰÷HáÒàòQVÞDST sTBºTBŽÌN}pûúŒ28³xe &VJÓŸl“š8À™ÇýAY5QÐôga=ÈY çÐñ0mÀòE^‡#MS¦y~¿ãßVUtkç“,&u­U²Õê‘W¾D¼&™qB6ªJ¹çq<éñŽ„z¶jK+^éâ‘IrôNdõá,HŠè oè½Uð &ö ‰žÜ–8†w‚¿j¥Ý‘®ú®*³3Éø{Y™Iäܱ¢Òð¹'ù¡8ëÓ‘8C½¯K„ëM^”žãèÂèžëï^…×–ÅM7綞øyI¬‹B¢E(WTGü1¤9ØßQo|­ÁÓž¨<:ª¨½¼uJ¸Nâ0£Y¡ß¦æ3Ћ¯‹ª`‹„'žbµ—Í…N âÆîZ¯ñ쬉Ëiò t~dâÒŠàœ-ÞÏûãjß 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00000 n 0000320396 00000 n 0000332908 00000 n 0000333167 00000 n 0000346791 00000 n 0000347108 00000 n 0000357405 00000 n 0000357678 00000 n 0000365303 00000 n 0000365527 00000 n 0000390668 00000 n 0000391240 00000 n 0000403126 00000 n 0000403412 00000 n 0000412678 00000 n 0000412922 00000 n 0000419917 00000 n 0000420137 00000 n 0000427327 00000 n 0000427553 00000 n 0000439354 00000 n 0000439634 00000 n 0000447349 00000 n 0000447625 00000 n 0000454753 00000 n 0000454985 00000 n 0000470421 00000 n 0000470722 00000 n 0000491708 00000 n 0000494784 00000 n 0000494875 00000 n 0000494928 00000 n trailer << /Size 213 /Root 211 0 R /Info 212 0 R /ID [<902D32622D0089D66D7BE19AA0B2ED10> <902D32622D0089D66D7BE19AA0B2ED10>] >> startxref 495196 %%EOF survival/inst/doc/tiedtimes.R0000644000175100001440000000354413070713777016021 0ustar hornikusers### R code from vignette source 'tiedtimes.Rnw' ################################################### ### code chunk number 1: init ################################################### options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text library(survival, quietly=TRUE) ################################################### ### code chunk number 2: interval1 ################################################### birth <- as.Date("1973/03/10") start <- as.Date("1998/09/13") + 1:40 end <- as.Date("1998/12/03") + rep(1:10, 4) interval <- (end-start) table(interval) ################################################### ### code chunk number 3: interval2 ################################################### start.age <- as.numeric(start-birth)/365.25 end.age <- as.numeric(end -birth)/365.25 age.interval <- end.age - start.age length(unique(age.interval)) table(match(age.interval, sort(unique(age.interval)))) ################################################### ### code chunk number 4: tiedtimes.Rnw:81-95 ################################################### ndata <- data.frame(id=1:30, birth.dt = rep(as.Date("1953/03/10"), 30), enroll.dt= as.Date("1993/03/10") + 1:30, end.dt = as.Date("1996/10/21") + 1:30 + rep(1:10, 3), status= rep(0:1, length=30), x = 1:30) ndata$enroll.age <- with(ndata, as.numeric(enroll.dt - birth.dt))/365.25 ndata$end.age <- with(ndata, as.numeric(end.dt - birth.dt))/365.25 fudays <- with(ndata, as.numeric(end.dt - enroll.dt)) fuyrs <- with(ndata, as.numeric(end.age- enroll.age)) cox1 <- coxph(Surv(fudays, status) ~ x, data=ndata) cox2 <- coxph(Surv(fuyrs, status) ~ x, data=ndata) survival/inst/doc/compete.Rnw0000644000175100001440000014726013055122145016021 0ustar hornikusers\documentclass{article}[11pt] \usepackage{Sweave} \usepackage{amsmath} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} %\VignetteIndexEntry{Multi-state models and competing risks} \SweaveOpts{keep.source=TRUE, fig=FALSE} % Ross Ihaka suggestions \DefineVerbatimEnvironment{Sinput}{Verbatim} {xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} % I had been putting figures in the figures/ directory, but the standard % R build script does not copy it and then R CMD check fails \SweaveOpts{prefix.string=compete,width=6,height=4} \newcommand{\myfig}[1]{\includegraphics[height=!, width=\textwidth] {compete-#1.pdf}} \setkeys{Gin}{width=\textwidth} <>= options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=10) #text in graph about the same as regular text options(contrasts=c("contr.treatment", "contr.poly")) #ensure default require("survival") @ \title{Multi-state models and competing risks} \author{Terry Therneau \and Cynthia Crowson \and Elizabeth Atkinson} \newcommand{\code}[1]{\texttt{#1}} \begin{document} \maketitle \section{Multi-state models} \begin{figure} <>= # A note to readers of this code: drawing multi-state figures in this # way via polygon and arrows statements is a major PITA. Don't mimic # the code below, instead do yourself a favor and use a package # designed for the task such as diagram, DiagrammeR, shape or Gmisc. # Survival is a recommended package that is included by lots of others so # I try to limit dependencies in the survival vignettes. # par(mar=c(.1, .1, .1, .1)) frame() oldpar <- par(usr=c(0,100,0,100)) # first figure xx <- c(0, 10, 10, 0) yy <- c(0, 0, 10, 10) polygon(xx +10, yy+70) polygon(xx +30, yy+70) arrows( 22, 75, 28, 75, length=.1) text(c(15, 35), c(75,75), c("Alive", "Dead")) # second figure polygon(xx +60, yy+70) for (j in c(55, 70, 85)) { polygon(xx +80, yy+j) arrows(72, (5*75 +j+5)/6, 78, (100+j*5)/6, length=.1) } text(c(65, 85,85,85), c(70,55,70,85)+5, c("A", "D3", "D2", "D1")) # third figure polygon(xx+10, yy+25) for (j in c(15,35)) { polygon(xx +30, yy+j) arrows(22, (5*30 +j+4)/6, 28, (54+j*5)/6, length=.1) } arrows(28, 2+(65 + 35*5)/6, 22, 2+ (160 + 40)/6, length=.1) arrows(35, 33, 35, 27, length=.1) text(c(15, 35,35), c(30, 20, 40), c("Health", "Death", "Illness")) # fourth for (i in c(50, 68)) polygon(xx+i, yy+25) arrows(62, 30, 67, 30, length=.1) arrows(80, 30, 84, 30, length=.1) text(90, 30, "...", cex=2) text(c(55, 73), c(30, 30), c("0", "1")) par(oldpar) @ \caption{Four multi-state models. The upper left panel depicts simple survival, the upper right is an example of competing risks, the lower left panel is a multi-state illness-death model, and the lower right panel depicts sequential events.} \label{mfig1} \end{figure} A multi-state model is used to model a process where subjects transition from one state to the next. For instance, a standard survival curve can be thought of as a simple multi-state model with two states (alive and dead) and one transition between those two states. A diagram illustrating this process is shown in the top left corner of figure \ref{mfig1}. In these types of diagrams, each box is a state and each arrow is a possible transition. The top right diagram depicts a classic competing risk analysis, where all subjects start on the left and each subject can make a single transition to one of 3 terminal states. The bottom left diagram shows a common multi-state situation known as the illness-death model with recovery. Finally, the lower right diagram represents sequential events, such as repeated infections in the CGD study. In that case one subject had 8 events so there are 9 states corresponding to entry into the study (0 infections) and the first, second, \ldots, eighth events. As will be shown below, there are often multiple choices for the state and transition diagram, and for some data sets it is revealing to look at a problem from multiple views. In addition to deciding the diagram that best matches the research questions, the two other primary decisions are the choice of time scale for the fits, e.g., time from entry in the study vs. time from entry in the state, and what covariates will be used. \section{Multi-state curves} \subsection{Aalen-Johansen estimate} As a starting point for the analysis, it is important to compute and plot estimates of $p(t)$, which is a vector containing the probability of being in each of the states at time $t$. If there is no censoring then $p$ becomes a simple tabulation at time $t$ of all the states. For the general case, we compute this using the Aalen-Johansen estimate via the \code{survfit} function. Mathematically the estimate is simple. For each unique time where an event occurs, form the transition matrix $T(t)$ with elements or rates of $\lambda_{ij}(t) =$ the fraction of subjects who transition from state $i$ to $j$ at time $t$, among those in state $i$ just prior to time $t$. ($T$ is equal to the identity matrix at any time point without an observed transition.) Then \begin{equation} p(t) = p(0) \prod_{s \le t} T(s) \label{AJ} \end{equation} where $p(0)$ is the initial distribution of subjects. Let's work this out for the simple two-state alive $\rightarrow$ {death} model. Let $n(t)$ be the number of subjects still at risk at time $t$ and $d(t)$ the number of deaths at that time point. All subjects start in the alive state and thus $p(0) = (1,0)$ and the transition matrix is \begin{equation*} T(s) = \left( \begin{array}{cc} \frac{n(s)- d(s)}{n(s)} & \frac{d(s)}{n(s)} \\\\ 0 & 1 \end{array} \right) \end{equation*} The second row corresponds to the fact that death is an absorbing state. Writing out the matrices for the first few transitions and multiplying them leads to \begin{equation} p_1(t) = \prod_{s \le t} \left[n(s) - d(s)\right] /n(s) \label{km} \end{equation} which we recognize as the Kaplan-Meier estimate of survival. For the two state alive-dead model the Aalen-Johansen (AJ) estimate has reprised the KM. In the competing risks case $p(t)$ has an alternate form known as the \emph{cumulative incidence} (CI) function \begin{equation} CI_k(t) = \int_0^t \lambda_k(u) S(u) du \label{cuminc} \end{equation} where $\lambda_k$ is the incidence function for outcome $k$, and $S$ is the overall survival curve for ``time to any endpoint''. (The label ``cumulative incidence'' is one of the more unfortunate ones in the survival lexicon, since we normally use `incidence' and `hazard' as interchangeable synonyms but the CI is \emph{not} a cumulative hazard.) Repeating the same matrix exercise for the competing risks, i.e. writing out the Aalen-Johansen computation, exactly recovers the CI formula. The CI is also a special case of the Aalen-Johansen. The AJ estimate is very flexible; subjects can visit multiple states during the course of a study, subjects can start after time 0 (delayed entry), and they can start in any of the states. The \code{survfit} function implements the AJ estimate and will handle all these cases. The standard error of the estimates is computed using an infinitesimal jackknife. Let $D(t)$ be a matrix with one row per subject and one column per state. Each row contains the \emph{change} in $p(t)$ corresponding to subject $i$, i.e., the derivative of $p$ with respect to the $i$th subject's case weight $dp(t)/dw_i$. Then $V(t) = D'WD$ is the estimated variance-covariance matrix of the estimates at time $t$, where $W$ is a diagonal matrix of observation weights. If a single subject is represented by multiple rows in the data set, then $D$ is first collapsed to have one row per subject, the new row for subject $i$ is the sum of the rows for the observations that represented the subject. This is essentially the same algorithm as the robust variance for a Cox model. For simple two state alive -> dead model, the AJ estimate of variance is identical to the traditional Greenwood estimate for the variance of the survival curve $S$. (This was a surprise when we first observed it; proving the equivalence was not straightforward.) The $p(t)$ vector obeys the obvious constraint that its sum at any time is equal to one; each person has to be somewhere. I originally chose to label this as the \emph{current prevalence} estimate, since it estimates what fraction of the subjects are in any given state across time. However the word ``prevalence'' is certain to generate confusion whenever death is one of the states, due to its traditional use as the fraction of living subjects who have a particular condition. We will use the phrase \emph{probability in state} or simply $p$ from this point forward. In the simple two state model Pr(alive) is the usual KM survival estimate, and we have $p_1(t) = 1- p_2(t)$, Pr(alive) = 1 - Pr(dead). Plots for the 2 state case sometimes choose to show Pr(alive) and sometimes Pr(dead). Which one is used often depends on a historical whim of the disease specialty; cardiology journals for instance quite often use Pr(event) resulting in curves that rise starting from zero, while oncology journals invariably use Pr(alive) giving curves that fall downhill from 1. The \code{survfit} routine's historical default for the 2 state case is to print and plot Pr(alive)= $p_1(t)$, which reflects that the author of the routine was working primarily in cancer trials at the time said default was chosen. For simple survival we have gotten used to the idea of using Pr(dead) and Pr(alive) interchangeably, but that habit needs to be left behind for multi-state models, as curves of $1-p_k(t)$ = probability(any other state than $k$) are not useful. In the multi-state case, individual curves can go both up and down. For competing risks the curve for the initial state (leftmost in the diagram) is rarely included in the final plot. Since the curves sum to 1, the full set is redundant. Pr(nothing yet) is usually the least interesting of the set and so it is left off to make the plot less busy. The remaining curves in the competing risks case rise from 0. (This bothers some researchers as it `just looks wrong' to them.) \subsection{Examples} \begin{figure} <>= par(mar=c(.1, .1, .1, .1)) frame() oldpar <- par(usr=c(0,100,0,100)) # first figure xx <- c(0, 10, 10, 0) yy <- c(0, 0, 10, 10) polygon(xx +10, yy+70) temp <- c(60, 80) for (j in 1:2) { polygon(xx + 30, yy+ temp[j]) arrows(22, 70 + 3*j, 28, temp[j] +5, length=.1) } text(c(15, 35, 35), c(75, 65, 85),c("Entry", "Death", "PCM")) text(25, 55, "Competing Risk") # Second figure polygon(xx +60, yy+70) for (j in 1:2) { polygon(xx + 80, yy+ temp[j]) arrows(72, 70+ 3*j, 78, temp[j] +5, length=.1) } text(50+ c(15, 35, 35), c(75, 65, 85),c("Entry", "Death", "PCM")) arrows(85, 78, 85, 72, length=.1) text(75, 55, "Multi-state 1") # third figure polygon(xx+10, yy+25) temp <- c(15, 35) for (j in 1:2) { polygon(2*xx +30, yy + temp[j]) arrows(22, 25 + 3*j, 28, temp[j] +5, length=.1) } text(c(15, 40, 40), c(30, 20, 40),c("Entry", "Death w/o PCM", "PCM")) polygon(2*xx + 60, yy+temp[2]) arrows(52, 40, 58, 40, length=.1) text(70, 40, "Death after PCM") text(40, 10, "Multi-state 2") @ \caption{Three models for the MGUS data.} \label{mfig2} \end{figure} Start with a simple competing risks problem as illustrated in the first diagram of figure \ref{mfig2}. The \code{mgus2} data set contains the time to plasma cell malignancy (PCM) and/or death for 1384 subjects diagnosed with monoclonal gammopathy of undetermined significance (MGUS). Survival and progression time are in months. The code below creates an ordinary Kaplan-Meier curve of post-diagnosis survival for these subjects, along with a histogram of age at diagnosis. The mean age at diagnosis is just over 70 years. <>= oldpar <- par(mfrow=c(1,2)) hist(mgus2$age, nclass=30, main='', xlab="Age") with(mgus2, tapply(age, sex, mean)) mfit1 <- survfit(Surv(futime, death) ~ sex, data=mgus2) mfit1 plot(mfit1, col=c(1,2), xscale=12, mark.time=FALSE, lwd=2, xlab="Years post diagnosis", ylab="Survival") legend("topright", c("female", "male"), col=1:2, lwd=2, bty='n') par(oldpar) @ The xscale and yscale arguments to \code{plot.survfit} affect only the axis labels, not the data. Further additions to the plot region such as \code{legend}, \code{lines}, or \code{text} remain in the original scale. This simplifies programmatic additions such as adding another curve to the plot, while making interactive additions such as a legend somewhat less simple. As a second model for these subjects we will use competing risks with PCM and death without malignancy as the two terminal states, as shown in the upper left of figure \ref{mfig2}. For this model we are only interested in the first event for each subject. Formally we are treating progression to a PCM as an \emph{absorbing state}, i.e., one that subjects never exit. We create a variable \code{etime} containing the time to the first of progression, death, or last follow-up along with an event variable that contains the outcome. The starting data set \code{mgus2} has two pairs of variables \code{(ptime, pstat)} that contain the time to progression and \code{(futime, status)} that contain the time to death or last known alive. The code below creates the necessary \code{etime} and \code{event} variables, then computes and plots the competing risks estimate. <>= etime <- with(mgus2, ifelse(pstat==0, futime, ptime)) event <- with(mgus2, ifelse(pstat==0, 2*death, 1)) event <- factor(event, 0:2, labels=c("censor", "pcm", "death")) table(event) mfit2 <- survfit(Surv(etime, event) ~ sex, data=mgus2) print(mfit2, rmean=240, scale=12) mfit2$transitions plot(mfit2, col=c(1,2,1,2), lty=c(2,2,1,1), mark.time=FALSE, lwd=2, xscale=12, xlab="Years post diagnosis", ylab="Probability in State") legend(240, .6, c("death:female", "death:male", "pcm:female", "pcm:male"), col=c(1,2,1,2), lty=c(1,1,2,2), lwd=2, bty='n') @ The \code{mfit2} call is nearly identical to that for an ordinary Kaplan-Meier, with the exception of the \code{event} variable. \begin{enumerate} \item The event variable was created as a \emph{factor}, whereas for ordinary single state survival the status is either 0/1 or TRUE/FALSE. The first level of the factor must be censoring, which is the status code for those whose follow-up terminated without reaching a new endpoint. Codes for the remaining states can be in any order. The labels for the states are unrestricted, e.g., the first one does not have to be ``censor''. (It will however be treated as censoring, whatever the name.) \item A simple print of the \code{mfit2} object shows the order in which the curves will be displayed. This information was used to choose the line types and colors for the curves. \item The \code{mfit2} object contains curves for all the states, but by default the entry state will not be plotted. The remaining curves all start at 0. \item The transitions component of the result is useful as a data check, e.g., if it showed a transition from death to PCM. \item Each subject's initial state is specified by the \code{istate} argument. When this is omitted all subjects are assumed to start from an entry state named `` '' (the empty string), as seen in the printout above. \end{enumerate} The printout shows that a male subject will spend, on average, 8.7 of his first 20 years post diagnosis in the entry state, 1.1 years in the PCM state and 10.3 of those 20 in the death state. If a cutoff time is not given the default is to use the maximum observed time for all curves, which is 424 months in this case. The result of a multi-state \code{survfit} is a matrix of probabilities with one row per time and one column per state. First are the states found in the event variable (excluding censoring) and then the states found in the \code{istate} variable, removing any duplicates. By default any unnamed state is not plotted -- point 3 above -- for the simple reason that multiple event curves can very quickly get overcrowded with all the multiple lines. Since the three MGUS states of entry/pcm/death must sum to 1 at any given time (everyone has to be somewhere), one of the three curves is redundant and the ``fraction still in the entry state'' curve is normally the least interesting. One can easily add this last state to the plot if desired, e.g., \code{lines(mfit2[,3], col=4, lty=1:2)}, since entry is the third state in the printout. (One can use, e.g., \code{mfit2[, 'pcm']} to select a state as well, but an empty string does not work as the subscript.) A common mistake with competing risks is to use the Kaplan-Meier separately on each event type while treating other event types as censored. The next plot is an example of this for the PCM endpoint. <>= pcmbad <- survfit(Surv(etime, pstat) ~ sex, data=mgus2) plot(pcmbad[2], mark.time=FALSE, lwd=2, fun="event", conf.int=FALSE, xscale=12, xlab="Years post diagnosis", ylab="Fraction with PCM") lines(mfit2[2,1], lty=2, lwd=2, mark.time=FALSE, conf.int=FALSE) legend(0, .25, c("Males, PCM, incorrect curve", "Males, PCM, competing risk"), col=1, lwd=2, lty=c(1,2), bty='n') @ There are two problems with the \code{pcmbad} fit. The first is that it attempts to estimate the expected occurrence of plasma cell malignancy (PCM) if all other causes of death were to be disallowed. In this hypothetical world it is indeed true that many more subjects would progress to PCM (the incorrect curve is higher), but it is also not a world that any of us will ever inhabit. This author views the result in much the same light as discussions of survival after the zombie apocalypse. The second problem is that the computation for this hypothetical case is only correct if all of the competing endpoints are independent, a situation which is almost never true. We thus have an unreliable estimate of an uninteresting quantity. The competing risks curve, on the other hand, estimates the fraction of MGUS subjects who \emph{will experience} PCM, a quantity sometimes known as the lifetime risk, and one which is actually observable. The last example chose to plot only a subset of the curves, something that is often desirable in competing risks problems to avoid a ``tangle of yarn'' plot that simply has too many elements. This is done by subscripting the \code{survfit} object. For subscripting, multi-state curves behave as a matrix with the outcomes as the second subscript. The columns are in order of the levels of \code{event}, i.e., as displayed by our earlier call to \code{table(event)}. The first subscript indexes the groups formed by the right hand side of the model formula, and will be in the same order as simple survival curves. Thus \code{mfit2[2,1]} corresponds to males (2) and the PCM endpoint (1). Curves are listed and plotted in the usual matrix order of R. A third example using the MGUS data treats it as a multi-state model and it shown in the upper right of figure \ref{mfig2}. In this version a subject can have multiple transitions and thus multiple rows in the data set. In this case it is necessary to identify which data rows go with which subject via the \code{id} argument of \code{survfit}; valid estimates of the curves and their standard errors both depend on this. Our model looks like the illness-death model of figure \ref{mfig1} but with ``PCM'' as the upper state and no arrow for a return from that state to health. The necessary data set will have two rows for any subject who has further follow-up after a PCM and a single row for all others. The data set is created below using the \code{tmerge} function, which is discussed in detail in another vignette. We need to decide what to do with the 9 subjects who have PCM and death declared at the same month. (Some of these were cancer cases discovered at autopsy.) They slipped through without comment in the earlier competing risks analysis; only when setting up this second data set did we notice the ties. Looking back at the code, the prior example counted these subjects as a progression. In retrospect this is a defensible choice: even though undetected before death, the disease must have been present for some amount of time previous and so progression did occur first. For the multi-state model we need to be explicit in how this is coded since a sojourn time of 0 within a state is not allowed. Below we push the progression time back by .1 month when there is a tie, but that amount is entirely arbitrary. <>= ptemp <- with(mgus2, ifelse(ptime==futime & pstat==1, ptime-.1, ptime)) newdata <- tmerge(mgus2, mgus2, id=id, death=event(futime, death), pcm = event(ptemp, pstat)) newdata <- tmerge(newdata, newdata, id, enum=cumtdc(tstart)) with(newdata, table(death, pcm)) @ The table above shows that there are no observations in \code{newdata} that have both a PCM and death, i.e., the ties have been resolved. The last \code{tmerge} line above creates a variable \code{enum} which simply counts rows for each person; it will be used later. <>= temp <- with(newdata, ifelse(death==1, 2, pcm)) newdata$event <- factor(temp, 0:2, labels=c("censor", "pcm", "death")) mfit3 <- survfit(Surv(tstart, tstop, event) ~ sex, data=newdata, id=id) print(mfit3, rmean=240, digits=2) mfit3$transitions plot(mfit3[,1], mark.time=FALSE, col=1:2, lty=1:2, lwd=2, xscale=12, xlab="Years post MGUS diagnosis", ylab="Fraction in the PCM state") legend(48, .04, c("female", "male"), lty=1:2, col=1:2, lwd=2, bty='n') @ This plot is quite different in that it shows the fraction of subjects \emph{currently} in the PCM state. Looking at our multi-state diagram this is the fraction of subjects in the upper right PCM box. The curve goes up whenever someone enters the box (progression) and down when they leave (death). Myeloma survival was quite short during the era of this study and the proportion currently in the PCM state rarely rises above 2 percent. The result of \code{print(mfit3)} reveals, as expected, less time spent in the PCM state. In the prior \code{mfit2} model, subjects who enter that state remain there for the duration; in this one they quickly pass through. It is worthwhile to check the \code{transitions} table in the output simply as a data check. In this case it shows subjects going from the entry (unnamed) state to PCM and death along with transitions from PCM to death. This is as expected. An error in creating the input data can lead to surprising counts and an even more surprising curve. We have often found the three curve display below useful in the case of a transient state. It combines the results from competing risk model used above along with a second fit that treats death after PCM as a separate state from death before progression, the \emph{multi-state 2} model of figure \ref{mfig2}. In this plot the fraction of subjects currently in the PCM state is shown by the distance between the two curves. Only males are shown in the plot to minimize overlap. <>= # Death after PCM will correspond to data rows with # enum = 2 and event = death d2 <- with(newdata, ifelse(enum==2 & event=='death', 4, as.numeric(event))) e2 <- factor(d2, labels=c("censor", "pcm", "death w/o pcm", "death after pcm")) mfit4 <- survfit(Surv(tstart, tstop, e2) ~ sex, data=newdata, id=id) plot(mfit2[2,], lty=c(1,2), xscale=12, mark.time=FALSE, lwd=2, xlab="Years post diagnosis", ylab="Probability in State") lines(mfit4[2,3], mark.time=FALSE, col=2, lty=1, lwd=2, conf.int=FALSE) legend(200, .5, c("Death w/o PCM", "ever PCM", "Death after PCM"), col=c(1,1,2), lty=c(2,1,1), lwd=2, bty='n', cex=.82) @ \subsection{Further notes} The Aalen-Johansen method used by \code{survfit} does not account for interval censoring, also known as panel data, where a subject's current state is recorded at some fixed time such as a medical center visit but the actual times of transitions are unknown. Such data requires further assumptions about the transition process in order to model the outcomes and has a more complex likelihood. The \code{msm} package, for instance, deals with data of this type. If subjects reliably come in at regular intervals then the difference between the two results can be small, e.g., the \code{msm} routine estimates time until progression \emph{occurred} whereas \code{survfit} estimates time until progression was \emph{observed}. \begin{itemize} \item When using multi-state data to create Aalen-Johansen estimates, individuals are not allowed to have gaps in the middle of their time line. An example of this would be a data set with (0, 30, pcm] and (50,70, death] as the two observations for a subject where the time from 30-70 is not accounted for. \item Subjects must stay in the same group over their entire observation time, i.e., variables on the right hand side of the equation cannot be time-dependent. \item A transition to the same state is allowed, e.g., observations of (0,50, 1], (50, 75, 3], (75, 89, 4], (89, 93, 4] and (93, 100, 4] for a subject who goes from entry to state 1, then to state 3, and finally to state 4. However, a warning message is issued for the data set in this case, since stuttering may instead be the result of a coding mistake. The same result is obtained if the last three observations were collapsed to a single row of (75, 100, 4]. \end{itemize} \section{Rate models} For simple two-state survival, the Cox model leads to three relationships \begin{align} \lambda(t) &= \lambda_0(t) e^{X\beta} \label{hazard} \\ \Lambda(t) &= \Lambda_0(t) e^{X\beta} \label{cumhaz}\\ S(t) &= \exp(-\Lambda(t)) \label{surv} \end{align} where $\lambda$, $\Lambda$ and $S$ are the hazard, cumulative hazard and survival functions, respectively. There is a single linear predictor which governs both the rate $\lambda$ (the arrow in figure \ref{mfig1}) and probability of residing in the left hand box of the figure. For multi-state models this simplicity no longer holds; proportional hazards does not lead to proportional $p(t)$ curves. The task before us is more complex. The analysis of multi-state data has four key steps. In order of importance: \begin{enumerate} \item Draw a box and arrow figure describing the model. \item Think through the rates (arrows). \begin{enumerate} \item Which covariates should be attached to each rate? Sometimes a covariate is important for one transition, but not for another. \item For which transitions should one or more of the covariates be constrained to have the same coefficient? Sometimes there will be a biologic rationale for this. For other studies an equivalence is forced simply because we have too many unknowns and cannot accommodate them all. (This is the often the same reason that models contain very few interaction terms). \item Which, if any, of the transitions should share the same baseline hazard? Most of the time the baseline rates are all assumed to be different. \item Should there be random effects, and if so what is an appropriate correlation structure? Do some pairs of transitions have a shared effect, some pairs separate effects and others no random effect? Mixed effects Cox models tend to need larger sample size --- does the data set have enough events? \end{enumerate} \item Build an appropriate data set. \item Fit the data. Examine multiple summaries of the model fit, including the predicted occupancy curves. \end{enumerate} Step 1 is key to the entire endeavor. We saw in figure \ref{mfig2} and the examples above that multiple views of a multi-state process can be useful, and this will hold for modeling as well. Step 3 will often be the one that demands the most attention to detail. \subsection{MGUS example} Start with the simplest model for the MGUS data: a competing risks model (upper left diagram of figure \ref{mfig2}), distinct baseline hazards for the two rates, no shared coefficients, and three covariates. <>= options(show.signif.stars = FALSE) # display intelligence cfit2 <- coxph(Surv(etime, event=="death") ~ age + sex + mspike, mgus2) summary(cfit2, scale=c(10, 1, 1)) # scale age in decades @ The effect of age and sex on non-PCM mortality is profound, which is not a surprise given the median starting age of \Sexpr{median(mgus2$age)}. Risk rises \Sexpr{round(exp(10*coef(cfit2)[1]),1)} fold per decade of age and the death rate for males is \Sexpr{round(exp(coef(cfit2)[2]),1)} times as great as that for females. The size of the serum monoclonal spike has almost no impact on non-PCM mortality. A 1 unit increase changes mortality by only 6\%. <>= cfit1 <- coxph(Surv(etime, event=="pcm") ~ age + sex + mspike, mgus2) cfit1 quantile(mgus2$mspike, na.rm=TRUE) @ The mspike size has a major impact on progression, however; each 1 gram change increases risk by \Sexpr{round(exp(coef(cfit1)[3]) ,1)} fold. The interquartile range of \code{mspike} is 0.9 gram so this risk increase is clinically important. The effect of age on the progression rate is much less pronounced, with a coefficient only 1/4 that for mortality, while the effect of sex on progression is completely negligible. The effect of sex on the \emph{lifetime} probability of PCM is not zero, however. Because of a longer lifetime, a female with MGUS will on average spend more total years at risk for PCM than the average male, and so has a larger lifetime risk of PCM. The average rate of progression is about 1\% per year, as shown below, while the mean post diagnosis lifetime is 19 months longer for females. The overall effect is a 1.6\% increase in lifetime risk. <>= pfit1 <- pyears(Surv(ptime, pstat) ~ sex, mgus2, scale=12) round(100* pfit1$event/pfit1$pyears, 1) # PCM rate per year temp <- summary(mfit1, rmean="common") #print the mean survival time round(temp$table[,1:6], 1) @ Notice that each \code{coxph} fit essentially ignores the other event type(s). In the figure, each rate (arrow) depends only on the box from which it originates and the events which it enumerates. Rates are instantaneous quantities, and depend only on the set of subjects who are at risk at at a given moment; if someone is not at risk it really does not matter why. When computing $p(t)$, on the other hand, all the rates must be considered at once. The Aalen-Johansen estimate applies as before, but now the individual entries $\lambda_{ij}(t)$ in each cell of the transition matrix are taken from the relevant fit. As is also the case with predicted survival curves from a simple Cox model, predicted probability-in-state curves correspond to a set of prespecified covariate values. As an example we will generate the curves for four hypothetical subjects: male and female, age 60 and 80, and serum m-spike of 1.2 grams. These are the approximate quartiles of age, and the median mspike. The Aalen-Johansen estimate for this simple 3-state competing risks setup works with a matrix of this form: \begin{equation*} \left( \begin{array}{ccc} & \lambda_{12}{t} & \lambda_{13}(t) \\ 0 & & 0 \\ 0 & 0 & \end{array} \right) \end{equation*} As before, the diagonal elements are chosen so that each row sums to 1. Standard survival curve calculations for a Cox model can be used to obtain $\lambda_{12}$, the rate of transition to the PCM state for our four subjects, and $\lambda_{13}$ = the rate of transition to the ``death before PCM'' state. These are placed into a matrix and combined using a third call. The standard errors from the individual curves won't be used and the survfit routine is a bit faster if we skip them. <>= newdata <- expand.grid(sex=c("F", "M"), age=c(60, 80), mspike=1.2) newdata temp <- matrix(list(), 3,3) dimnames(temp) <- list(from=c("Entry", "PCM", "Death"), to =c("Entry", "PCM", "Death")) temp[1,2] <- list(survfit(cfit1, newdata, std.err=FALSE)) temp[1,3] <- list(survfit(cfit2, newdata, std.err=FALSE)) csurv <- survfit(temp, p0 =c(1,0,0)) plot(csurv[,2], xmax=25*12, xscale=12, xlab="Years after MGUS diagnosis", ylab="PCM", col=1:2, lty=c(1,1,2,2), lwd=2) legend(10, .14, outer(c("female", "male "), c("diagnosis at age 60", "diagnosis at age 80"), paste, sep=", "), col=1:2, lty=c(1,1,2,2), bty='n', lwd=2) @ The individual survival curves that result from \code{survfit(cfit1)} and \code{survfit(cfit2)} are not actually of interest, since each is a Cox model analog of the pcmbad curve we criticized earlier. The cumulative hazard portion of the results is what is used to build an Aalen-Johansen estimate. (Calling \code{survfit} on a set of \code{survfit} objects is, I admit, a bit confusing. It would perhaps have been better to name the second routine ``AalenJohansen'', but we use this often and didn't want to type that long a name.) Sex has nearly no effect on the hazard of PCM, i.e., on any given day the risk of conversion for a male is essentially the same as for a female of the same age. Yet we see above that the fitted Cox models predict a higher lifetime risk for females, and an age effect on lifetime risk that is far from proportional. Very few subjects acquire PCM more than 15 years after a MGUS diagnosis at age 80 for the obvious reason: very few of them will still be alive. Creating the `list' form matrix above is quite easy, in particular we do not need to fill in elements on the diagonal, nor those for which no transitions occur, e.g., from death back to the entry state. The resulting \code{survfit} object is easy to plot or print using standard calls. The approach has a number of caveats, however. \begin{itemize} \item It does not produce standard errors for the curves, as a consequence of being two steps removed from the data. \item It is easy to ``fool'' the program. For instance if you were to get curves for females and males from \code{cfit1}, but the curves from \code{cfit2} were in the reverse order of male then female, results will still be produced but they would not be valid. The user is responsible for setting the problem up correctly. \item The R syntax for a matrix of lists is rather fussy, e.g., you can't leave the \code{list} function out of the lines that assign elements to \code{temp} above. \end{itemize} The \code{mstate} package addresses these issues, at the price of a somewhat more complex syntax. <>= # Print out a M/F results at 20 years temp <- summary(csurv, time=20*12)$pstate cbind(newdata, PCM= round(100*temp[,2], 1)) @ The above table shows that females are modeled to have a higher risk of 20 year progression, even though their hazard at any given moment is nearly identical to males. The difference at 20 years is on the order of our ``back of the napkin'' person-years estimate of 1\% progression per year * 1.7 more years of life for the females, but the progression fraction varies substantially by group. \section{Fine-Gray model} For the competing risk case the Fine-Gray model provides an alternate way of looking at the data. As we saw above, the impact of a particular covariate on the final values $P$ can be complex, even if the models for the hazards are relatively simple. The primary idea of the Fine-Gray approach is to turn the multi-state problem into a collection of two-state ones. In the upper right diagram of figure 1, draw a circle around all of the states except the chosen endpoint and collapse them into a single meta-state. For the MGUS data these are \begin{itemize} \item Model 1 \begin{itemize} \item left box: All subjects in the entry or ``death first'' state \item right box: PCM \end{itemize} \item Model 2 \begin{itemize} \item left box: All subjects in the entry or ``PCM first'' state \item right box: Death (without PCM) \end{itemize} \end{itemize} An interesting aspect of this is that the fit can be done as a two stage process: the first stage creates a special data set while the second fits a weighted \code{coxph} or \code{survfit} model to the data. The data set can be created using the \code{finegray} command. <>= # (first three lines are identical to an earlier section) etime <- with(mgus2, ifelse(pstat==0, futime, ptime)) event <- with(mgus2, ifelse(pstat==0, 2*death, 1)) event <- factor(event, 0:2, labels=c("censor", "pcm", "death")) pcmdat <- finegray(Surv(etime, event) ~ ., data=mgus2, etype="pcm") pcmdat[1:4, c(1:3, 11:14)] deathdat <- finegray(Surv(etime, event) ~ ., data=mgus2, etype="death") dim(pcmdat) dim(deathdat) dim(mgus2) @ The \code{finegray} command has been used to create two data sets: one for the PCM endpoint and one for the death endpoint. In each, four new variables have been added containing a survival time \code{(fgstart, fgstop, fgstatus)} with an `ordinary' status of 0/1, along with a case weight and a large number of new rows. We can use this new data set as yet another way to compute multi-state survival curves, though there is no good reason to use this rather roundabout approach instead of the simpler \code{survfit(Surv(etime, event) \textasciitilde sex)}. <>= # The PCM curves of the multi-state model pfit2 <- survfit(Surv(fgstart, fgstop, fgstatus) ~ sex, data=pcmdat, weight=fgwt) # The death curves of the multi-state model dfit2 <- survfit(Surv(fgstart, fgstop, fgstatus) ~ sex, data=deathdat, weight=fgwt) @ The two new curves are almost identical to the prior estimates, and in fact would be identical if we had accounted for the slightly different censoring patterns in males and females (by adding \code{strata(sex)} to the right hand side of the \code{finegray} formulas). A Cox model fit to the constructed data set yields the Fine-Gray models for PCM and for death. <>= fgfit1 <- coxph(Surv(fgstart, fgstop, fgstatus) ~ sex, data=pcmdat, weight= fgwt) summary(fgfit1) fgfit2 <- coxph(Surv(fgstart, fgstop, fgstatus) ~ sex, data=deathdat, weight= fgwt) fgfit2 mfit2 <- survfit(Surv(etime, event) ~ sex, data=mgus2) #reprise the AJ plot(mfit2[,1], col=1:2, lwd=2, xscale=12, conf.times=c(5, 15, 25)*12, xlab="Years post diagnosis", ylab="Fraction with PCM") ndata <- data.frame(sex=c("F", "M")) fgsurv1 <- survfit(fgfit1, ndata) lines(fgsurv1, fun="event", lty=2, lwd=2, col=1:2) legend("topleft", c("Female, Aalen-Johansen", "Male, Aalen-Johansen", "Female, Fine-Gray", "Male, Fine-Gray"), col=1:2, lty=c(1,1,2,2), bty='n') # rate models with only sex pfitr <- coxph(Surv(etime, event=="pcm") ~ sex, mgus2) dfitr <- coxph(Surv(etime, event=="death") ~ sex, mgus2) temp <- matrix(list(), 3,3) temp[1,2] <- list(survfit(pfitr, ndata, std.err=FALSE)) temp[1,3] <- list(survfit(dfitr, ndata, std.err=FALSE)) rcurve <- survfit(temp, p0=c(entry=1, pcm=0, death=0)) @ The FG model states that males have a less \emph{observed} PCM, by a factor of \Sexpr{round(exp(coef(fgfit1)), 2)}, and that this hazard ratio is constant over time. An overlaid plot of the non-parametric Aalen-Johansen estimates for the PCM state (from \code{survfit}) along with predicted curves from the Fine-Gray model show that proportional hazards is not unreasonable for this particular fit. The predicted values from the rate model, computed just above but not plotted on the curve, also fit well with the data. When there is only a single categorical 0/1 covariate the Fine-Gray model reduces to Gray's test of the subdistribution function, in the same way that a \code{coxph} fit with a single categorical predictor is equivalent to the log-rank test. The mathematics behind the Fine-Gray estimate starts with the functions $F_k(t) = p_k(t)$, where $p$ is the probability in state function estimated by the AJ estimate. This can be thought of as the distribution function for the improper random variable $T^*= I(\mbox{event type}=k)T + I(\mbox{event type}\ne k)\infty$. Fine and Gray refer to $F_k$ as a subdistribution function. In analogy to the survival probability in the two state model define \begin{equation} \gamma_k(t) = - d \log[1-F_k(t)]/dt \label{FG}I \end{equation} and assume that $\gamma_k(t;x) = \gamma_{k0}(t) \exp(X\beta)$. In a 2 state alive $\longrightarrow$ death model, $\gamma$ becomes the usual hazard function $\lambda$. In the same way that our multivariate Cox model \code{cfit2} made the simplifying assumption that the impact of male sex is to increase the hazard for death by a factor of \Sexpr{round(exp(coef(cfit2)['sexM']), 2)}, independent of the subject's age or serum mspike value, the Fine-Gray model assumes that each covariate's effect on $\log(1-F)$ is a constant, independent of other variables. Both model's assumptions are wonderfully simplifying with respect to understanding a covariate, since we can think about each one separately from the others. This is, of course, under the assumption that the model is correct: additivity across covariates, linearity, and proportional hazards all hold. In a multi-state model, however, these assumptions cannot hold for both the per-transition and Fine-Gray models formulations at the same time; if it is true for one, it will not be true for the other. Now consider a multivariate fit on age, sex, and serum m-spike. <>= fgfit2a <- coxph(Surv(fgstart, fgstop, fgstatus) ~ age + sex + mspike, data=pcmdat, weight=fgwt) fgfit2b <- coxph(Surv(fgstart, fgstop, fgstatus) ~ age + sex + mspike, data=deathdat, weight=fgwt) round(rbind(PCM= coef(fgfit2a), death=coef(fgfit2b)), 3) @ The Fine-Gray fits show an effect of all three variables on the subdistribution rates. Males have a lower lifetime risk of PCM before death and a higher risk of death before PCM, while a high serum m-spike works in the opposite direction. The Cox models showed no effect of sex on the instantaneous hazard of PCM and none for serum m-spike on the death rate. However, as shown in the last section, the Cox models do predict a greater lifetime risk for females. We had also seen that older subjects are less likely to experience PCM due to the competing risk of death; this is reflected in the FG model as a negative coefficient for age. Now compute predicted survival curves for the model, and show them alongside the predictions from the multi-state model. <>= oldpar <- par(mfrow=c(1,2)) newdata <- expand.grid(sex= c("F", "M"), age=c(60, 80), mspike=1.2) fsurv1 <- survfit(fgfit2a, newdata) # time to progression curves plot(fsurv1, xscale=12, col=1:2, lty=c(1,1,2,2), lwd=2, fun='event', xlab="Years", ylab="Fine-Gray predicted", xmax=12*25, ylim=c(0, .15)) legend(1, .15, c("Female, 60", "Male, 60","Female: 80", "Male, 80"), col=c(1,2,1,2), lty=c(1,1,2,2), lwd=2, bty='n') plot(csurv[,2], xscale=12, col=1:2, lty=c(1,1,2,2), lwd=2, xlab="Years", ylab="Multi-state predicted", xmax=12*25, ylim=c(0, .15)) legend(1, .15, c("Female, 60", "Male, 60","Female: 80", "Male, 80"), col=c(1,2,1,2), lty=c(1,1,2,2), lwd=2, bty='n') par(oldpar) @ The predictions as a function of age group are quite different for the Fine-Gray model: new PCM cases are predicted 20+ years after diagnosis in both the old and young age groups, while they are predicted to cease in the multi-state fit. The average of the curves is nearly the same at each age, but the global proportional hazards assumption of the FG model forces the curves to remain parallel. We can check the proportional hazards assumption of the models using the \code{cox.zph} function, linearity of the continuous variables age and mspike by using non-linear terms such as \code{pspline} or \code{ns}, and additivity by exploring interactions. All are obvious and important next steps. For instance, the proportional hazards assumption for age shows clear violations. <>= zph.fgfit2a <- cox.zph(fgfit2a) zph.fgfit2a plot(zph.fgfit2a[1]) abline(h=coef(fgfit2a)[1], lty=2, col=2) @ A weakness of the Fine-Gray approach is that since the two endpoints are modeled separately, the results do not have to be consistent. Below is a graph of the predicted fraction who have experienced neither endpoint. For subjects diagnosed at age 80 the Fine-Gray models predict that more than 100\% will either progress or die by 30 years. Predictions based on the Aalen-Johansen approach do not have this issue. <>= fsurv2 <- survfit(fgfit2b, newdata) # time to progression curves xtime <- 0:(30*12) #30 years y1a <- 1 - summary(fsurv1, times=xtime)$surv #predicted pcm y1b <- 1 - summary(fsurv2, times=xtime)$surv #predicted deaths before pcm y1 <- (y1a + y1b) #either matplot(xtime/12, y1, col=1:2, lty=c(1,1,2,2), type='l', xlab="Years post diagnosis", ylab="FG: either endpoint") abline(h=1, col=3) legend("bottomright", c("Female, 60", "Male, 60","Female: 80", "Male, 80"), col=c(1,2,1,2), lty=c(1,1,2,2), lwd=2, bty='n') @ The primary strength of the Fine-Gray model with respect to the Cox model approach is that if lifetime risk is a primary question, then the model has given us a simple and digestible answer to that question: ``females have a 1.2 fold higher lifetime risk of PCM, after adjustment for age and serum m-spike''. This simplicity is not without a price, however, and these authors are not proponents of the approach. There are five issues. \begin{enumerate} \item The attempt to capture a complex process as a single value is grasping for a simplicity that does not exist for many (perhaps most) data sets. The necessary assumptions in a multivariate Cox model of proportional hazards, linearity of continuous variables, and no interactions are strong ones. For the FG model these need to hold for a combined process --- the mixture of transition rates to each endpoint --- which turns out to be a more difficult barrier. \item The sum of predictions need not be consistent. \item From the per-transition models one can work forward and compute $p(t)$, the occupancy probabilities for each state over time; both the hazard ratios and $p$ are useful summaries of the data. We don't have tools to work backwards from a Fine-Gray fit to the per transition hazards. \item The approach is viable only for competing risks and not for other multi-state models. \item The risk sets are odd. \end{enumerate} The last of these is perhaps the most frequently listed issue with the Fine-Gray model, but it is actually a minor complaint. The state probabilities $p(t)$ in a multi-state model are implicitly fractions of the total population we started with: someone who dies in month 1 is still a part of the denominator for the fraction of subjects with PCM at 20 years. In the Fine-Gray formulas this subject explicitly appears in risk set denominators at a later time, which looks odd but is more of an artifact. The first issue is substantial, however, and checking the model assumptions of a Fine-Gray fit is mandatory. The second point is alarming, but it does not have a practical impact unless there is long follow-up. \section{Stacked data sets} How does one fit risk models that have shared coefficients or baseline hazards? One approach is to fit the set of Cox models for the rates `all at once' on a combined data set. For the simple competing risks MGUS fit above, assume that we wanted to add hemoglobin to the fit, with a common coefficient for both the PCM and death endpoint. (Anemia is a feature of both PCM and old age.) Create a stacked data set with $2n$ observations. The first $n$ rows are the data set we would use for a time to PCM analysis, with a simple 0/1 status variable encoding the PCM outcome. The second $n$ rows are the data set we would have used for the `death before PCM' fits, with status encoding the death-before-PCM endpoint. A last variable, \code{group}, is `pcm' for the first $n$ observations and `death' for the remainder. Then fit a model <>= temp1 <- data.frame(mgus2, time=etime, status=(event=="pcm"), group='pcm') temp2 <- data.frame(mgus2, time=etime, status=(event=="death"), group="death") stacked <- rbind(temp1, temp2) allfit <- coxph(Surv(time, status) ~ hgb + (age + sex)*strata(group), data=stacked) @ This fits a common effect for hemoglobin (hgb) but separate age and sex effects for the two endpoints, along with separate baseline hazards. \section{Other software} \subsection{The mstate package} As the number of states + transitions (arrows + boxes) gets larger then the `by hand' approach used above for creating a stacked data set, labeling coefficients, and producing multi-state curves becomes a challenge. (It is still fairly easy to do, just not as easy to ensure it has been done \emph{correctly}.) The \code{mstate} package starts with a definition of the matrix of possible transitions and uses that to drive tools that build and analyze the stacked data set in a more automated fashion. We recommend it for more complex models. (The tutorial above is about at our personal threshold.) A second advantage of \code{mstate} is that all the Cox model fits are now in one well indexed object, which allows for calculation of proper confidence intervals for the state probabilities $p(t)$. (Since all of the steps used the same transition matrix template, the necessary computations are scripted and reliable.) \subsection{The \code{msm} package} There are two broad classes of multi-state data: \begin{itemize} \item Panel data arises when subjects have regular visits, with the current state assessed at each visit. We don't know when the transitions between states occur, or if other states may have been visited in the interim --- only the subject's state at specific times. \item Survival data arises when we observe the transition times; death, for example. \end{itemize} The overall model (boxes and arrows), the quantities of interest (transition rates and $p(t)$), and the desired printout and graphs are identical for the two cases. Much of the work in creating a data set is also nearly the same. The underlying likelihood equations and resulting analytical methods for solving the problem are, however, completely different. The \code{msm} package addresses panel data, while \code{survival}, \code{mstate}, and a host of others are devoted to survival data. \section{Conclusions} When working with acute diseases, such as advanced cancer or end-stage liver disease, there is often a single dominating endpoint. Ordinary single event Kaplan-Meier curves and Cox models are then efficient and sufficient tools for much of the analysis. Such data was the primary use case for survival analysis earlier in the authors' careers. Data with multiple important endpoints is now common, and multi-state methods are an important addition to the statistical toolbox. As shown above, they are now readily available and easy to use. It is sometimes assumed that the presence of competing risks \emph{requires} the use of a Fine-Gray model (we have seen it in referee reports), but this is not correct. The model may often be useful, but is one available option among many. Grasping the big picture for a multi-state data set is always a challenge and we should make use of as many tools as possible. We are often reminded of the story of a centenarian on his 100th birthday proclaiming that he was looking forward to many more years ahead because ``I read the obituaries every day, and you almost never see someone over 100 listed there''. 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hornikusers\documentclass{article}[11pt] \usepackage{Sweave} \usepackage{amsmath} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} %\VignetteIndexEntry{Cox models and ``type 3'' Tests} \SweaveOpts{prefix.string=tests,width=6,height=4, keep.source=TRUE, fig=FALSE} % Ross Ihaka suggestions \DefineVerbatimEnvironment{Sinput}{Verbatim} {xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} \SweaveOpts{width=6,height=4} \setkeys{Gin}{width=\textwidth} <>= options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text options(contrasts=c("contr.treatment", "contr.poly")) #reset default @ \title{Contrasts, populations, and ``type III'' tests} \author{Terry M Therneau \\ \emph{Mayo Clinic}} \newcommand{\code}[1]{\texttt{#1}} \newcommand{\myfig}[1]{\includegraphics[height=!, width=\textwidth] {tests-#1.pdf}} \newcommand{\ybar}{\overline{y}} \begin{document} \maketitle \tableofcontents \section{Introduction} \begin{table} \centering \begin{tabular} {crrrrr} & \multicolumn{5}{c}{Group} \\ &A & B & C & D & E \\ <>= library(survival) age2 <- cut(flchain$age, c(49, 59, 69, 79, 89, 120), labels=c("50-59", "60-69", "70-79", "80-89", "90+")) flchain$flc <- flchain$kappa + flchain$lambda tab1 <- with(flchain, tapply(flc, list(sex, age2), mean)) cat("female&" , paste(round(tab1[1,], 1), collapse=" & "), "\\\\ \n") cat("male &" , paste(round(tab1[2,], 1), collapse=" & "), "\n") @ \end{tabular} \caption{Fitted values from a linear model with two factors.} \label{tab1} \end{table} One of the annoying design shortfalls of R, inherited from S, is how modeling functions deal with categorical predictors. For a simple model such as \code{y ~ age + treatment} where the latter is a categorical, we will normally want to compare pairs of treatments. One way to do this is to set up the columns of 0/1 dummy variables that represent treatment so that the comparisons of interest appear directly as coefficients in the fit. If for instance there were three treatments, a control and two active agents then the two natural comparisons are control vs. agent1 and control vs. agent2. R does this for us without a hitch and nearly automatically, with several options to help control exactly how said 0/1 variables are created. But what if there were 4 treatments and we want to look at all 6 pairwise comparisons? This cannot be set up so that all 6 will appear as one coefficient in the fit, one needs a mechanism to compute these 6 estimates or \emph{contrasts} after the fit. As a more complex case consider the simple data shown in table \ref{tab1}, which are fitted values from a linear model on two factors along with their interaction. There are any number of comparisons that we might want to make in the data set: a trend test across the groups, overall or separately for each sex, all pairwise comparisons between groups, etc. A standard mechanism for this after-the-fit estimates has been lacking. There are several addons that address parts of the question such as \code{pairwise.t.tests} or \code{TukeyHSD}, but they are not applicable to coxph models. The \code{yates} function was motivated by the more perplexing problem of population contrasts, which it also addresses. This note started with an interchange on the R-help. A user asked ``how do I do a type III test using the Cox model'', and I replied that this was not a well defined question. If he/she could define exactly what it was that they were after, then I would look into it. To which the response was that ``SAS does it''. A grant deadline was looming so the discussion did not get any further at that point, but it eventually led to a much longer investigation on my part, which is summarized in this note. There are three central ideas as it turns out: populations, computation, and the mapping linear models ideas onto the Cox model. The first idea, and perhaps the central one, is using the model fit from a current data set to predict for a new population. This plays an important role in predicted survival curves, see for instance the vignette on that topic or chapter 10 of our book \cite{Therneau00}; recognizing that ``type 3'' tests are simply another variant on that theme was a pivotal step in my understanding. This immediately leads to the important subtopic of ``prediction for \emph{which} population''. The SAS type 3 computations corresponds to a very particular and inflexible choice. The second theme is computational: given some summary measure and a population for which you wish to predict it, the result will be some sort of weighted average. There are two primary ways to set up this computation. In a linear model one of them can be reduced to a particular contrast $C \hat\beta$ in the fitted coefficients $\hat\beta$, which is an appealing choice since follow-up computations such as the variance of the estimate become particularly simple. A common, simple, but unreliable algorithm for creating $C$ has been a major source of confusion (hereafter referred to as the NSTT: not safe type three). The last theme is how the linear models formulae map to the Cox model case. In particular, there is a strong temptation to use $C \hat\beta$ with $C$ taken from linear models machinery and $\hat\beta$ from a fitted Cox model. The problem is that this implicitly requires a replacement of $E[\exp(X)]$ with $\exp(E[X])$. For a Cox model $C \beta$ is certainly a valid statistic for any $C$, we just have no clear idea of what it is testing. For the impatient readers among you I'll list the main conclusions of this report at the start. \begin{itemize} \item SAS type 3 predicts for a population with a uniform distribution across all categorical predictors. Scholarly papers discussing fundamental issues with using such an approach as a default analysis method have appeared almost biannually in the statistics literature, with little apparent effect on the usage of the method. SAS documentation of type 3 is almost entirely focused on the algorithm they use for computing $C$ and ignores the population issue. \item Population predictions very often make sense, including the question the type 3 approach is attempting to address. There are valid ways to compute these estimates for a Cox model, they are closely related the inverse probability weight (IPW) methods used in propensity scores and marginal structural models. \item The algorithm used to compute $C$ by the SAS glm procedure is sophisticated and reliable. The SAS phreg procedure uses the linear models approach of $C \hat\beta$ to compute a ``type 3'' contrast, with $C$ computed via the NSTT. The combination is a statistical disaster. (This is true for SAS version 9.4; I will update this note if things change.) \end{itemize} \section{Linear approximations and the Cox model} \label{sect:transfer} One foundation of my concern has to do with the relationship between linear models and coxph. The solution to the Cox model equations can be represented as an iteratively reweighted least-squares problem, with an updated weight matrix and adjusted dependent variable at each iteration, rather like a GLM model. This fact has been rediscovered multiple times, and leads to the notion that since the last iteration of the fit \emph{looks} just like a set of least-squares equations, then various least squares ideas could be carried over to the proportional hazards model by simply writing them out using these final terms. In practice, sometimes this works and sometimes it doesn't. The Wald statistic is one example of the former type, which is completely reliable as long as the coefficients $\beta$ are not too large\footnote{ In practice failure only occurs in the rare case that one of the coefficients is tending to infinity. However, in that case the failure is complete: the likelihood ratio and score tests behave perfectly well but the Wald test is worthless.}. A counter example is found in two ideas used to examine model adequacy: adjusted variable plots and constructed variable plots, each of which was carried over to the Cox model case by reprising the linear-model equations. After a fair bit of exploring I found neither is worth doing \cite{Therneau00}. Copying over a linear models formula simply did not work in this case. \begin{figure} \myfig{data} \caption{Average free light chain for males and females. The figure shows both a smooth and the means within deciles of age.} \label{fig:data} \end{figure} \section{Data set} We will motivate our discussion with the simple case of a two-way analysis. The \code{flchain} data frame contains the results of a small number of laboratory tests done on a large fraction of the 1995 population of Olmsted County, Minnesota aged 50 or older \cite{Kyle06, Dispenzieri12}. The R data set contains a 50\% random sample of this larger study and is included as a part of the survival package. The primary purpose of the study was to measure the amount of plasma immunoglobulins and its components. Intact immunoglobulins are composed of a heavy chain and light chain portion. In normal subjects there is overproduction of the light chain component by the immune cells leading to a small amount of \emph{free light chain} in the circulation. Excessive amounts of free light chain (FLC) are thought to be a marker of disregulation in the immune system. Free light chains have two major forms denoted as kappa and lambda, we will use the sum of the two. An important medical question is whether high levels of FLC have an impact on survival, which will be explored using a Cox model. To explore linear models we will compare FLC values between males and females. A confounding factor is that free light chain values rise with age, in part because it is eliminated by the kidneys and renal function declines with age. The age distribution of males and females differs, so we will need to adjust our simple comparison between the sexes for age effects. The impact of age on mortality is of course even greater and so correction for the age imbalance is is critical when exploring the impact of FLC on survival. Figure \ref{fig:data} shows the trend in free light chain values as a function of age. For illustration of linear models using factors, we have also created a categorical age value using deciles of age. The table of counts shows that the sex distribution becomes increasingly unbalanced at the older ages, from about 1/2 females in the youngest group to a 4:1 ratio in the oldest. <>= library(survival) library(splines) age2 <- cut(flchain$age, c(49, 59, 69, 79, 89, 120), labels=c("50-59", "60-69", "70-79", "80-89", "90+")) counts <- with(flchain, table(sex, age2)) counts # flchain$flc <- flchain$kappa + flchain$lambda male <- (flchain$sex=='M') mlow <- with(flchain[male,], smooth.spline(age, flc)) flow <- with(flchain[!male,], smooth.spline(age, flc)) plot(flow, type='l', ylim=range(flow$y, mlow$y), xlab="Age", ylab="FLC") lines(mlow, col=2) cellmean <- with(flchain, tapply(flc, list(sex, age2), mean, na.rm=T)) matpoints(c(55,65,75, 85, 95), t(cellmean), pch='fm', col=1:2) round(cellmean, 2) @ Notice that the male/female difference in FLC varies with age, \Sexpr{round(cellmean[1,1],1)} versus \Sexpr{round(cellmean[2,1],1)} at age 50--59 and \Sexpr{round(cellmean[1,5],1)} versus \Sexpr{round(cellmean[2,5],1)} at age 90. The data does not fit a simple additive model; there are ``interactions'' to use statistical parlance. An excess of free light chain is thought to be at least partly a reflection of immune senescence, and due to our hormonal backgrounds men and women simply do not age in quite the same way. \section{Population averages} The question of how to test for a main effect in the presence of interaction is an old one. At one time this author considered the phrase ``main effect in the presence of interaction'' to be an oxymoron, but long experience with clinical data sets has led me to the opposite conclusion. Real data always has interactions. The treatment effect of a drug will not be exactly the same for old and young, thin and obese, physically active and sedentary, etc. Explicit recognition of this is an underlying rationale of the current drive towards ``personalized medicine'', though that buzzword often focuses only on genetic differences. Any given data set may often be too small to explore these variations and our statistical models will of necessity smooth over the complexity, but interactions are nevertheless still present. Consider the data shown in figure \ref{fig:data} above, which shows a particular laboratory test value by age and sex. We see that the sex effect varies by age. Given this, what could be meant by a ``main effect'' of sex? One sensible approach is to select a fixed \emph{population} for the ages, and then compute the average sex effect over that population. Indeed this is precisely what many computations do behind the scenes, e.g. the ``type 3'' estimates found in linear models. There are three essential components to the calculation: a reference population for the confounders, a summary measure of interest, and a computational algorithm. To understand how linear models methods may (or may not) extend to the proportional hazards model it is useful consider all three facets; each is revealing. Four possible choices for a target population of ages are given below. \begin{enumerate} \item Empirical: the age distribution of the sample at hand, also called the data distribution. In our sample this would be the age distribution of all \Sexpr{nrow(flchain)} subjects, ignoring sex. \item SAS: a uniform distribution is assumed over all categorical adjusters, and the data distribution for continuous ones. \item External reference: a fixed external population, e.g. the age distribution of the US 2010 census. \item MVUE: minimum variance unbiased; the implicit population corresponding to a multivariate least squares fit. \end{enumerate} Method 3 is common in epidemiology, method 1 is found in traditional survey sampling and in other common cases as we will see below. The type 3 estimates of SAS correspond to population 2. If there an interaction between two categorical variables x1 and x2, then the uniform distribution is taken to be over all combinations formed by the pair, and similarly for higher order interactions. \section{Linear models and populations} If we ignore the age effect, then everyone agrees on the best estimate of mean FLC: the simple average of FLC values within each sex. The male-female difference is estimated as the difference of these means. This is what is obtained from a simple linear regression of FLC on sex. Once we step beyond this and adjust for age, the relevant linear models can be looked at in several ways; we will explore three of them below: contrasts, case weights, and nesting. This ``all roads lead to Rome'' property of linear models is one of their fascinating aspects, at least mathematically. \subsection{Case weights} \begin{figure} \myfig{pop} \caption{Three possible adjusting populations for the FLC data set, a empirical reference in black, least squares based one in red, and the US 2000 reference population as `u'.} \label{fig:pop} \end{figure} How do we form a single number summary of ``the effect of sex on FLC''? Here are four common choices. \begin{enumerate} \item Unadjusted. The mean for males minus the mean for females. The major problem with this is that a difference in age distributions will bias the result. Looking at figure \ref{fig:data} imagine that this were two treatments A and B rather than male/female, and that the upper one had been given to predominantly 50-65 year olds and the lower predominantly to subjects over 80. An unadjusted difference would actually reverse the true ordering of the curves. \item Population adjusted. An average difference between the curves, weighted by age. Three common weightings are \begin{enumerate} \item External reference. It is common practice in epidemiology to use an external population as the reference age distribution, for instance the US 2000 census distribution. This aids in comparing results between studies. \item Empirical population. The overall population structure of the observed data. \item Least squares. The population structure that minimizes the variance of the estimated female-male difference. \end{enumerate} \end{enumerate} The principle idea behind case weights is to reweight the data such that confounders become balanced, i.e., ages are balanced when examining the sex effect and sex is balanced when examining age. Any fitted least squares estimate can be rewritten as a weighted sum of the data points with weight matrix $W= (X'X)^{-1}X'$. $W$ has $p$ rows, one per coefficient, each row is the weight vector for the corresponding element of $\hat\beta$. So we can backtrack and see what population assumption was underneath any given fit by looking at the weights for the relevant coefficient(s). Consider the two fits below. In both the second coefficient is an estimate of the overall difference in FLC values between the sexes. (The relationship in figure \ref{fig:data} is clearly curved so we have foregone the use of a simple linear term for age; there is no point in fitting an obviously incorrect model.) Since $\beta_2$ is a contrast the underlying weight vectors have negative values for the females and positive for the males. <<>>= us2000 <- rowSums(uspop2[51:101,,'2000']) fit1 <- lm(flc ~ sex, flchain, x=TRUE) fit2 <- lm(flc ~ sex + ns(age,4), flchain, x=TRUE) c(fit1$coef[2], fit2$coef[2]) wt1 <- solve(t(fit1$x)%*%fit1$x, t(fit1$x))[2,] # unadjusted wt2 <- solve(t(fit2$x)%*%fit2$x, t(fit2$x))[2,] # age-adjusted table(wt1, flchain$sex) @ To reconstruct the implied population density, one can use the density function with \code{wt1} or \code{wt2} as the case weights. Examination of \code{wt1} immediately shows that the values are $-1/n_f$ for females and $1/n_m$ for males where $n_f$ and $n_m$ are number of males and females, respectively. The linear model \code{fit1} is the simple difference in male and female means; the implied population structure for males and females is the unweighted density of each. Because this data set is very large and age is coded in years we can get a density estimate for fit2 by simple counting. The result is coded below and shown in figure \ref{fig:pop}. The empirical reference and least squares reference are nearly identical. This is not a surprise. Least squares fits produce minimum variance unbiased estimates (MVUE), and the variance of a weighted average is minimized by using weights proportional to the sample size, thus the MVUE estimate will give highest weights to those ages with a lot of people. The weights are not \emph{exactly} proportional to sample size for each age. As we all know, for a given sample size $n$ a study comparing two groups will have the most power with equal allocation between the groups. Because the M/F ratio is more unbalanced at the right edge of the age distribution the MVUE estimate gives just a little less weight there, but the difference between it and the overall data set population will be slight for all but those pathological cases where there is minimal overlap between M/F age distributions. (And in that case the entire discussion about what ``adjustment'' can or should mean is much more difficult.) <>= us2000 <- rowSums(uspop2[51:101,,'2000']) tab0 <- table(flchain$age) tab2 <- tapply(abs(wt2), flchain$age, sum) matplot(50:100, cbind(tab0/sum(tab0), tab2/sum(tab2)), type='l', lty=1, xlab="Age", ylab="Density") us2000 <- rowSums(uspop2[51:101,,'2000']) matpoints(50:100, us2000/sum(us2000), pch='u') legend(60, .02, c("Empirical reference", "LS reference"), lty=1, col=1:2, bty='n') @ The LS calculation does a population adjustment automatically for us behind the scenes via the matrix algebra of linear models. If we try to apply population reference adjustment directly a problem immediately arises: in the US reference \Sexpr{round(100*us2000[46]/sum(us2000),2)}\% of the population is aged 95 years, and our sample has no 95 year old males; it is not possible to re weight the sample so as to exactly match the US population reference. This occurs in any data set that is divided into small strata. The traditional epidemiology approach to this is to use wider age intervals of 5 or 10 years. Weights are chosen for each age/sex strata such that the sum of weights for females = sum of weights for males within each age group (balance), and the total sum of weights in an age group is equal to the reference population. The next section goes into this further. An increasingly popular approach for producing results that are standardized to the empirical reference population (i.e. the data distribution) is to use a smoothed age effect, obtained through inverse probability weights which are based on logistic regression, e.g. in the causal models literature and propensity score literature. This approach is illustrated in a vignette on adjusted survival curves which is also in the survival package. \subsection{Categorical predictors and contrasts} When the adjusting variable or variables are categorical --- a factor in R or a class variable in SAS --- then two more aspects come into play. The first is that any estimate of interest can be written in terms of the cell means. Formally, the cell means are a \emph{sufficient statistic} for the data. For our data set and using the categorized variable \code{age2} let $\theta_{ij}$ parameterize these means. $$ \begin{tabular}{cccccc} &50--59 & 60--69 & 70-79 & 80-89 & 90+ \\ \hline Female & $\theta_{11}$ & $\theta_{12}$ & $\theta_{13}$& $\theta_{14}$& $\theta_{15}$ \\ Male & $\theta_{21}$ & $\theta_{22}$ & $\theta_{23}$& $\theta_{24}$ & $\theta_{25}$ \\ \end{tabular} $$ For a design with three factors we will have $\theta_{ijk}$, etc. Because it is a sufficient statistic, any estimate or contrast of interest can be written as a weighted sum of the $\theta$s. Formulas for the resulting estimates along with their variances and tests were worked out by Yates in 1934 \cite{Yates34} and are often referred to as a Yates weighted means estimates. For higher order designs the computations can be rearranged in a form that is manageable on a desk calculator, and this is in fact the primary point of that paper. (Interestingly, his computational process turns out to be closely related to the fast Fourier transform.) The second facet of categorical variables is that another adjustment is added to the list of common estimates: \begin{enumerate} \item Unadjusted \item Population adjusted \begin{enumerate} \item External reference \item Empirical (data set) reference \item Least squares \item Uniform. A population in which each combination of the factors has the same frequency of occurrence. \end{enumerate} \end{enumerate} The uniform population plays a special role in the case of designed experiments, where equal allocation corresponds to the optimal study design. The Yates estimates are particularly simple in this case. For a hypothetical population with equal numbers in each age category the estimated average FLC for females turns out to be $\mu_f = \sum_j \theta_{1j} /5$ and the male - female contrast is $\sum_j(\theta_{2j}-\theta_{1j})/5$. We will refer to these as the ``Yates'' estimates and contrast for an effect. Conversely, the estimated age effects, treating sex as a confounding effect and assuming an equal distribution of females and males as the reference population, gives an estimated average FLC for the 60-69 year olds of $\mu_{60-69}= (\theta_{12} + \theta_{22})/2$, and etc for the other age groups. We can obtain the building blocks for Yates estimates by using the interaction function and omitting the intercept. <>= yatesfit <- lm(flc ~ interaction(sex, age2) -1, data=flchain) theta <- matrix(coef(yatesfit), nrow=2) dimnames(theta) <- dimnames(counts) round(theta,2) @ For a linear model fit, any particular weighted average of the coefficients along with its variance and the corresponding sums of squares can be computed using the \code{contrast} function given below. Let $C$ be a contrast matrix with $k$ rows, each containing one column per coefficient. Then $C\theta$ is a vector of length $k$ containing the weighted averages and $V = \hat\sigma^2 C (X'X)^{-1}C'$ is its variance matrix. The sums of squares is the increase in the sum of squared residuals if the fit were restricted to the subspace $C\theta =0$. Formulas are from chapter 5 of Searle \cite{Searle71}. Some authors reserve the word \emph{contrast} for the case where each row of $C$ sums to zero and use \emph{estimate} for all others; I am being less restrictive since the same computation serves for both. <<>>= qform <- function(beta, var) # quadratic form b' (V-inverse) b sum(beta * solve(var, beta)) contrast <- function(cmat, fit) { varmat <- vcov(fit) if (class(fit) == "lm") sigma2 <- summary(fit)$sigma^2 else sigma2 <- 1 # for the Cox model case beta <- coef(fit) if (!is.matrix(cmat)) cmat <- matrix(cmat, nrow=1) if (ncol(cmat) != length(beta)) stop("wrong dimension for contrast") estimate <- drop(cmat %*% beta) #vector of contrasts ss <- qform(estimate, cmat %*% varmat %*% t(cmat)) *sigma2 list(estimate=estimate, ss=ss, var=drop(cmat %*% varmat %*% t(cmat))) } yates.sex <- matrix(0, 2, 10) yates.sex[1, c(1,3,5,7,9)] <- 1/5 #females yates.sex[2, c(2,4,6,8,10)] <- 1/5 #males contrast(yates.sex, yatesfit)$estimate # the estimated "average" FLC for F/M contrast(yates.sex[2,]-yates.sex[,1], yatesfit) # male - female contrast @ <>= # Create the estimates table -- lots of fits emat <- matrix(0., 6, 3) dimnames(emat) <- list(c("Unadjusted", "MVUE: continuous age", "MVUE: categorical age", "Empirical (data) reference", "US200 reference", "Uniform (Yates)"), c("est", "se", "SS")) #unadjusted emat[1,] <- c(summary(fit1)$coef[2,1:2], anova(fit1)["sex", "Sum Sq"]) # MVUE -- do the two fits fit2 <- lm(flc ~ ns(age,4) + sex, flchain) emat[2,] <- c(summary(fit2)$coef[6, 1:2], anova(fit2)["sex", "Sum Sq"]) fit2 <- lm(flc ~ age2 + sex, flchain) emat[3,] <- c(summary(fit2)$coef[6, 1:2], anova(fit2)["sex", "Sum Sq"]) #Remainder, use contrasts tfun <- function(wt) { cvec <- c(matrix(c(-wt, wt), nrow=2, byrow=TRUE)) temp <- contrast(cvec, yatesfit) c(temp$est, sqrt(temp$var), temp$ss) } emat[4,] <- tfun(colSums(counts)/sum(counts)) usgroup <- tapply(us2000, rep(1:5, c(10,10,10,10,11)), sum)/sum(us2000) emat[5,]<- tfun(usgroup) emat[6,] <- tfun(rep(1/5,5)) @ \begin{table} \centering \begin{tabular}{l|ccc} & estimate & sd & SS \\ \hline <>= temp <- dimnames(emat)[[1]] for (i in 1:nrow(emat)) cat(temp[i], sprintf(" &%5.3f", emat[i,1]),sprintf(" &%6.5f", emat[i,2]), sprintf(" & %6.1f", emat[i,3]), "\\\\ \n") @ \end{tabular} \caption{Estimates of the male-female difference along with their standard errors. The last 4 rows are based on categorized age.} \label{tab:allest} \end{table} Table \ref{tab:est} shows all of the estimates of the male/female difference we have considered so far along with their standard errors. Because it gives a much larger weight to the 90+ age group than any of the other estimates, and that group has the largest M-F difference, the projected difference for a uniform population (Yates estimate) yields the largest contrast. It pays a large price for this in terms of standard error, however, and is over twice the value of the other approaches. As stated earlier, any least squares parameter estimate can be written as a weighted sum of the y values. Weighted averages have minimal variance when all of the weights are close to 1. The unadjusted estimate adheres to this precisely and the data-reference and MVUE stay as close as possible to constant weights, subject to balancing the population. The Yates estimate, by treating every cell equally, implicitly gives much larger weights to the oldest ages. Table \ref{tab:est} shows the effective observation weights used for each of the age categories. <>= casewt <- array(1, dim=c(2,5,4)) # case weights by sex, age group, estimator csum <- colSums(counts) casewt[,,2] <- counts[2:1,] / rep(csum, each=2) casewt[,,3] <- rep(csum, each=2)/counts casewt[,,4] <- 1/counts #renorm each so that the mean weight is 1 for (i in 1:4) { for (j in 1:2) { meanwt <- sum(casewt[j,,i]*counts[j,])/ sum(counts[j,]) casewt[j,,i] <- casewt[j,,i]/ meanwt } } @ \begin{table} \centering \begin{tabular}{rlrrrrr} &&50--59& 60--69 & 70--79 & 80--89 & 90+ \\ \hline <>= tname <- c("Unadjusted", "Min var", "Empirical", "Yates") for (i in 1:2) { for (j in 1:4) { cat("&",tname[j], " & ", paste(sprintf("%4.2f", casewt[i,,j]), collapse= " & "), "\\\\\n") if (j==1) cat(c("Female", "Male")[i]) } if (i==1) cat("\\hline ") } @ \end{tabular} \caption{Observation weights for each data point corresponding to four basic approaches. All weights are normed so as to have an average value of 1.} \label{tab:est} \end{table} Looking at table \ref{tab:est} notice the per observation weights for the $\ge 90$ age group, which is the one with the greatest female/male imbalance in the population. For all but the unbalanced estimate (which ignores age) the males are given a weight that is approximately 3 times that for females in order to re balance the shortage of males in that category. However, the absolute values of the weights differ considerably. \subsection{Different codings} Because the cell means are a sufficient statistic, all of the estimates based on categorical age can be written in terms of the cell means $\hat\theta$. The Yates contrast is the simplest to write down: $$ \begin{tabular} {rrrrrr} & 50--59 & 60--69 & 70--79 & 80--89 & 90+ \\ \hline Female & -1/5 & -1/5 & -1/5 & -1/5 & -1/5 \\ Male & 1/5 & 1/5 & 1/5 & 1/5 & 1/5 \end{tabular} $$ %(Note that for calculating a sum of squares we will get the exact same %result from a matrix using $\pm 1$ rather than $\pm 1/5$; %the Yates contrast is often written this way.) For the data set weighting the values of 1/5 are replaced by $n_{+j}/n_{++}$, the overall frequency of each age group, where a $+$ in the subscript stands for addition over that subscript in the table of counts. The US population weights use the population frequency of each age group. The MVUE contrast has weights of $w_j/\sum w_j$ where $w_j = 1/(1/n_{1j} + 1/n_{2j})$, which are admittedly not very intuitive. $$ \begin{tabular}{rrrrrr} & 50--59 & 60--69 & 70--79 & 80--89 & 90+ \\ \hline <>= temp <- 1/colSums(1/counts) temp <- temp/sum(temp) cat("Female", sprintf(" & %5.3f", -temp), "\\\\ \n") cat("Male", sprintf(" & %5.3f", temp), "\\\\ \n") @ \end{tabular} $$ In the alternate model \code{y \textasciitilde sex + age2} the MVUE contrast is much simpler, namely (0, 1, 0,0,0,0,0), and can be read directly off the printout as $\beta/se(\beta)$. The computer's calculation of $(X'X)^{-1}$ has derived the ``complex'' MVUE weights for us without needing to lift a pencil. The Yates contrast, however, cannot be created from the coefficients of the simpler model at all. This observation holds in general: a contrast that is simple to write down in one coding may appear complicated in another, or not even be possible. The usual and more familiar coding for a two way model is \begin{equation} y_{ij} = \mu + \alpha_i + \beta_j + \gamma_{ij} \label{std} \end{equation} What do the Yates' estimates look like in this form? Let $e_i$ be the Yates estimate for row $i$ and $k$ the number of columns in the two way table of $\theta$ values. Then \begin{align*} e_i &= (1/k)\sum_{j=1}^k \theta_{ij} \\ &= \mu + \alpha_i + \sum_j \left(\beta_j + \gamma_{ij}\right)/k \end{align*} and the Yates test for row effect is \begin{align} 0 &= e_i - e_{i'} \quad \forall i,i' \nonumber \\ &= (\alpha_i - \alpha_{i'}) + (1/k)\sum_j(\gamma_{ij} - \gamma_{i'j}) \label{ycont} \end{align} Equation \eqref{std} is over determined and all computer programs add constraints in order to guarantee a unique solution. However those constraints are applied, however, equation \eqref{ycont} holds. The default in R is treatment contrasts, which use the first level of any factor as a reference level. Under this constraint the reference coefficients are set to zero, i.e., all coefficients of equations \eqref{std} and \eqref{ycont} above where $i=1$ or $j=1$. We have been computing the male - female contrast, corresponding to $i=2$ and $i'=1$ in equation \eqref{ycont}, and the Yates contrast for sex becomes $\alpha_2 + 1/5(\gamma_{22} +\gamma_{23} +\gamma_{24} +\gamma_{25})$. The code below verifies that this contrast plus the usual R fit replicates the results in table \ref{tab:allest}. <>= fit3 <- lm(flc ~ sex * age2, flchain) coef(fit3) contrast(c(0,1, 0,0,0,0, .2,.2,.2,.2), fit3) #Yates @ The usual constraint is SAS is to use the last level of any class variable as the reference group, i.e., all coefficients with $i=2$ or $j=5$ in equations \eqref{std} and \eqref{ycont} are set to zero. <>= options(contrasts=c("contr.SAS", "contr.poly")) sfit1 <- lm(flc ~ sex, flchain) sfit2 <- lm(flc ~ sex + age2, flchain) sfit3 <- lm(flc ~ sex * age2, flchain) contrast(c(0,-1, 0,0,0,0, -.2,-.2,-.2,-.2), sfit3) # Yates for SAS coding @ The appendix contains SAS code and output for the three models \code{sfit1, sfit2} and \code{sfit3} above. The \code{E3} option was added to the SAS model statements, which causes a symbolic form of the contrasts that were used for ``type III'' results to be included in the printout. Look down the column labeled ``SEX'' and you will see exactly the coefficients used just above, after a bit of SAS to English translation. \begin{itemize} \item The SAS printout is labeled per equation \eqref{std}, so L1= column 1 of the full $X$ matrix = intercept. L2 = column 2 = females, L3 = column 3 = males, L4= column 4 = age 50--59, etc. \item In the symbolic printout they act as though sum constraints were in force: the last column of age is labeled with a symbolic value that would cause the age coefficients to sum to zero. However, in actuality these coefficients are set to zero. The table of parameter estimates at the end of the printout reveals this; forced zeros have a blank for their standard error. \item When calculating the contrast one can of course skip over the zero coefficients, and the R functions do not include them in the coefficient vector. Remove all of these aliased rows from the SAS symbolic printout to get the actual contrast that is used; this will agree with my notation. \item The SAS printout corresponds to a female-male contrast and I have been using male-female for illustration. This changes the signs of the contrast coefficients but not the result. \end{itemize} The \code{estimate} statement in the SAS code required that all of the coefficients be listed, even the aliased ones (someone more proficient in SAS may know a way to avoid this and enter only the non-aliased values.) %A general principle is that a given hypothesis may be represented as %a simple contrast in one coding but be complex in another. %The unadjusted test is a trivial contrast in the sfit1 coding, but a %complex one in the sfit3 coding. %The Yates test cannot be expressed as a contrast using the sfit1 or sfit2 %coding, is simple and obvious in the cell means coding, and has %simple but non obvious coefficients in the sfit3 coding. %Que sera sera. So, how do we actually compute the Yates contrast in a computer program? We will take it as a give that no one wants to memorize contrast formulas. Appendix \ref{sect:coding} describes three algorithms for the computation. One of these three (NSTT) is completely unreliable, but is included because it is so often found in code. If one uses the sum constraints commonly found in textbooks, which corresponds to the \code{contr.sum} constraint in R and to \code{effect} constraints in SAS, and there are no missing cells, then the last term in equation \eqref{ycont} is zero and the simple contrast $\alpha_i =0$ will be equal to the Yates contrast for sex. I often see this method recommended on R help in response to the question of ``how to obtain type III'', computed either by use of the \code{drop1} command or the \code{Anova} function found within the car package, but said advice almost never mentions the need for this particular non-default setting of the contrasts option\footnote{The Companion to Applied Regression (car) package is designed to be used with the book of the same name by John Fox, and the book does clarify the need for sum constraints.}. When applied to other codings the results of this procedure can be surprising. <>= options(contrasts = c("contr.treatment", "contr.poly")) #R default fit3a <- lm(flc ~ sex * age2, flchain) options(contrasts = c("contr.SAS", "contr.poly")) fit3b <- lm(flc~ sex * age2, flchain) options(contrasts=c("contr.sum", "contr.poly")) fit3c <- lm(flc ~ sex * age2, flchain) # nstt <- c(0,1, rep(0,8)) #test only the sex coef = the NSTT method temp <- rbind(unlist(contrast(nstt, fit3a)), unlist(contrast(nstt, fit3b)), unlist(contrast(nstt, fit3c)))[,1:2] dimnames(temp) <- list(c("R", "SAS", "sum"), c("effect", "SS")) print(temp) # drop1(fit3a, .~.) @ For the case of a two level effect such as sex, the NSTT contrast under the default R coding is a comparison of males to females in the first age group \textbf{only}, and under the default SAS coding it is a comparison of males to females within the \textbf{last} age group. Due to this easy creation of a test statistic which has no relation to the global comparison one expects from the ``type 3'' label the acronym \emph{not safe type three}(NSTT) was chosen, ``not SAS'' and ``nonsense'' are alternate mnemonics. \subsection{Sums of squares and projections} \label{sect:anova} The most classic exposition of least squares is as a set of projections, each on to a smaller space. Computationally we represent this as a series of model fits, each fit summarized by the change from the prior fit in terms of residual sum of squares. <>= options(show.signif.stars = FALSE) #exhibit intelligence sfit0 <- lm(flc ~ 1, flchain) sfit1b <- lm(flc ~ age2, flchain) anova(sfit0, sfit1b, sfit2, sfit3) @ The second row is a test for the age effect. The third row of the above table summarizes the improvement in fit for the model with sex + age2 over the model with just age2, a test of ``sex, adjusted for age''. This test is completely identical to the minimum variance contrast, and is in fact the way in which that SS is normally obtained. The test for a sex effect, unadjusted for age, is identical to an anova table that compares the intercept-only fit to one with sex, i.e., the second line from a call to \code{anova(sfit0, sfit1)}. The anova table for a nested sequence of models $A$, $A+B$, $A + B +C$, \ldots has a simple interpretation, outside of contrasts or populations, as an improvement in fit. Did the variable(s) $B$ add significantly to the goodness of fit for a model with just $A$, was $C$ an important addition to a model that already includes $A$ and $B$? The assessment of improvement is based on the likelihood ratio test (LRT), and extends naturally to all other models based on likelihoods. The tests based on a target population (external, data population, or Yates) do not fit naturally into this approach, however. %Obtaining the Yates contrast using a sequential sums of squares approach %is possible but a bit contrived. %Our final fit in the table will be \code{sfit3}, but %the one prior to it needs to be from a constrained version of \code{sfit3}, %whose solution lies in the space spanned by the Yates contrast %$\beta_2 + \beta_7/5 + \beta_8/5 + \beta_9/5 + \beta_{10}/5 = 0$. %There is no simple way to write down an ordinary LS model equation that %will do this, and instead one must use one a program for constrained %linear regression; these are far less familiar. %There are many algorithms to fit a constrained linear regression, one is %to transform the problem as $X\beta = (XQ)(Q'\beta) = Z \phi$ %where $Q$ is an orthogonal transformation matrix. %If the first column of $Q$ is chosen as a scaled version of the Yates %contrast, then setting that contrast equal to zero is the same as %the constraint $\phi_1 =0$; it suffices to fit a model using all but the %first column of $Z$. \subsection{What is SAS type 3?} We are now in a position to fully describe the SAS sums of squares. \begin{itemize} \item Type 1 is the output of the ANOVA table, where terms are entered in the order specified in the model. \item Type 2 is the result of a two stage process \begin{enumerate} \item Order the terms by level: 0= intercept, 1= main effects, 2= 2 way interactions, \ldots. \item For terms of level k, print the MVUE contrast from a model that includes all terms of levels $0-k$. Each of these will be equivalent to the corresponding line of a sequential ANOVA table where the term in question was entered as the last one of its level. \end{enumerate} \item Type 3 and 4 are also a 2 stage process \begin{enumerate} \item Segregate the terms into those for which a Yates contrast can be formed versus those for which it can not. The second group includes the intercept, any continuous variables, and any factor (class) variables that do not participate in interactions with other class variables. \item For variables in the first group compute Yates contrasts. For those in the second group compute the type 2 results. \end{enumerate} \end{itemize} SAS has two different algorithms for computing the Yates contrast, which correspond to the \code{ATT} and \code{STT} options of the \code{yates} function. SAS describes the two contrast algorithms in their document ``The four types of estimable functions'' \cite{SASguide}, one of which defines type 3 and the other type 4. I found it very challenging to recreate their algorithm from this document. Historical knowledge of the underlying linear model algorithms used by SAS is a useful and almost necessary adjunct, as many of the steps in the document are side effects of their calculation. When there are missing cells, then it is not possible to compute a contrast that corresponds to a uniform distribution over the cells, and thus the standard Yates contrast is also not defined. The SAS type 3 and 4 algorithms still produce a value, however. What exactly this result ``means'' and whether it is a good idea has been the subject of lengthy debates which I will not explore here. Sometimes the type 3 and type 4 algorithms will agree but often do not when there are missing cells, which further muddies the waters. Thus we have 3 different tests: the MVUE comparison which will be close but not exactly equal to the data set population, Yates comparisons which correspond to a uniform reference population, and the SAS type 3 (STT) which prints out a chimeric blend of uniform population weighting for those factor variables that participate in interactions and the MVUE weighting for all the other terms. \subsection{Which estimate is best?} Deciding which estimate is the best is complicated. Unfortunately a lot of statistical textbooks emphasize the peculiar situation of balanced data with exactly the same number of subjects in each cell. Such data is \emph{extremely} peculiar if you work in medicine; in 30 years work and several hundred studies I have seen 2 instances. In this peculiar case the unadjusted, MVUE, empirical reference and Yates populations are all correspond to a uniform population and so give identical results. No thinking about which estimate is best is required. This has led many to avoid the above question, instead pining for that distant Eden where the meaning of ``row effect'' is perfectly unambiguous. But we are faced with real data and need to make a choice. The question has long been debated in depth by wiser heads than mine. In a companion paper to his presentation at the joint statistical meetings in 1992, Macnaughton \cite{Macnaughton92} lists 54 references to the topic between 1952 and 1991. Several discussion points recur: \begin{enumerate} \item Many take the sequential ANOVA table as primary, i.e., a set of nested models along with likelihood ratio tests (LRT), and decry all comparisons of ``main effects in the presence of interaction.'' Population weightings other than the LS one do not fit nicely into the nested framework. \item Others are distressed by the fact that the MVUE adjusting population is data dependent, so that one is ``never sure exactly what hypothesis being tested''. \item A few look at the contrast coefficients themselves, with a preference for simple patterns since they ``are interpretable''. \item No one approach works for all problems. Any author who proposes a uniform rule is quickly presented with counterexamples. \end{enumerate} Those in group 1 argue strongly against the Yates weighting and those in group 2 argue for the Yates contrast. Group 3 is somewhat inexplicable to me since any change in the choice of constraint type will change all the patterns. I fear that an opening phrase from the 1986 overview/review of Herr \cite{Herr86} is still apropos, ``In an attempt to understand how we have arrived at our present state of ignorance \ldots''. There are some cases where the Yates approach is clearly sensible, for instance a designed experiment which has become unbalanced due to a failed assay or other misadventure that has caused a few data points to be missing. There are cases such as the FLC data where the Yates contrast makes little sense at all --- the hypothetical population with equal numbers of 50 and 90 year olds is one that will never be seen--- so it is rather like speculating on the the potential covariate effect in dryads and centaurs. The most raucous debate has circled around the case of testing for a treatment effect in the presence of multiple enrolling centers. Do we give each patient equal weight (MVUE) or each center equal weight (Yates). A tongue-in-cheek but nevertheless excellent commentary on the subject is given by the old curmudgeon, aka Guernsey McPearson \cite{Senn1, Senn2}. A modern summary with focus on the clinical trials arena is found in chapter 14 of the textbook by Senn \cite{Senn07} I have found two papers particularly useful in thinking about this. Senn \cite{Senn00} points out the strong parallels between tests for main effects when there may be interactions and meta analyses, cross connecting these two approaches is illuminating. A classic reference is the 1978 paper by Aitkin \cite{Aitkin78}. This was read before the Royal Statistical Society and includes remarks by 10 discussants forming a who's who of statistical theory (F Yates, J Nelder, DR Cox, DF Andrews, KR Gabriel, \ldots). The summary of the paper states that ``It is shown that a standard method of analysis used in many ANOVA programs, equivalent to Yates method of weighted squares of means, may lead to inappropriate models''; the paper goes on to carefully show why no one method can work in all cases. Despite the long tradition among RSS discussants of first congratulating the speaker and then skewering every one their conclusions, not one defense of the always-Yates approach is raised! This includes the discussion by Yates himself, who protests that his original paper advocated the proposed approach with reservations, it's primary advantage being that the computations could be performed on a desk calculator. I have two primary problems with the SAS type 3 approach. The first and greatest is that their documentation recommends the method with no reference to this substantial and sophisticated literature discussing strengths and weaknesses of the Yates contrast. This represents a level of narcissism which is completely unprofessional. %Recommending the type III approach as best for all cases, as they do, has %caused actual harm. The second is that their documentation explains the method is a way that is almost impenetrably opaque. If this is the only documentation one has, there will not be 1 statistician in 20 who would be able to explain the actual biological hypothesis which is being addressed by a type 3 test. \section{Cox models} \subsection{Tests and contrasts} Adapting the Yates test to a Cox model is problematic from the start. First, what do we mean by a ``balanced population''? In survival data, the variance of the hazard ratio for each particular sex/age combination is proportional to the number of deaths in that cell rather than the number of subjects. Carrying this forward to the canonical problem of adjusting a treatment effect for enrolling center, does this lead to equal numbers of subjects or equal numbers of events? Two centers might have equal numbers of patients but different number of events because one initiated the study at a later time (less follow up per subject), or it might have the same follow up time but a lower death rate. Should we reweight in one case (which one), both, or neither? The second issue is that the per-cell hazard ratio estimates are no longer a minimally sufficient statistic, so underlying arguments about a reference population no longer directly translate into a contrast of the parameters. A third but more minor issue is that the three common forms of the test statistic --- Wald, score, and LRT --- are identical in a linear model but not for the Cox model, so which should we choose? To start, take a look at the overall data and compute the relative death rates for each age/sex cell. <>= options(contrasts= c("contr.treatment", "contr.poly")) # R default cfit0 <- coxph(Surv(futime, death) ~ interaction(sex, age2), flchain) cmean <- matrix(c(0, coef(cfit0)), nrow=2) cmean <- rbind(cmean, cmean[2,] - cmean[1,]) dimnames(cmean) <- list(c("F", "M", "M/F ratio"), dimnames(counts)[[2]]) signif(exp(cmean),3) @ Since the Cox model is a relative risk model all of the death rates are relative to one of the cells, in this case the 50--59 year old females has been arbitrarily chosen as the reference cell and so has a defined rate of 1.00. Death rates rise dramatically with age for both males and females (no surprise), with males always slightly ahead in the race to a coffin. The size of the disadvantage for males decreases in the last 2 decades, however. The possible ways to adjust for age in comparing the two sexes are \begin{enumerate} \item The likelihood ratio test. This is analogous to the sequential ANOVA table in a linear model, and has the strongest theoretical justification. \item A stratified Cox model, with age group as the stratification factor. This gives a more general and rigorous adjustment for age. Stratification on institution is a common approach in clinical trials. \item The Wald or score test for the sex coefficient, in a model that adjusts for age. This is analogous to Wald tests in the linear model, and is asymptotically equivalent the the LRT. \item The test from a reweighted model, using case weights. Results using this approach have been central to causal model literature, particularly adjustment for covariate imbalances in observational studies. (Also known as \emph{marginal structural models}). Adjustment to a uniform population is also possible. \item A Yates-like contrast in the Cox model coefficients. \begin{itemize} \item A reliable algorithm such as cell means coding. \item Unreliable approach such as the NSTT \end{itemize} \end{enumerate} I have listed these in order from the most to the least available justification, both in terms of practical experience and available theory. The two standard models are for sex alone, and sex after age. Likelihood ratio tests for these models are the natural analog to anova tables for the linear model, and are produced by the same R command. Here are results for the first three, along with the unadjusted model that contains sex only. <>= options(contrasts=c("contr.SAS", "contr.poly")) cfit1 <- coxph(Surv(futime, death) ~ sex, flchain) cfit2 <- coxph(Surv(futime, death) ~ age2 + sex, flchain) cfit3 <- coxph(Surv(futime, death) ~ sex + strata(age2), flchain) # Unadjusted summary(cfit1) # # LRT anova(cfit2) # # Stratified anova(cfit3) summary(cfit3) # # Wald test signif(summary(cfit2)$coefficients, 3) # anova(cfit1, cfit2) @ Without adjustment for age the LRT for sex is only \Sexpr{round(2*diff(cfit1$loglik),1)}, and after adjustment for %$ a it increases to \Sexpr{round(anova(cfit2)[3,2],2)}. Since females are older, not adjusting for age almost completely erases the evidence of their actual survival advantage. Results of the LRT are unchanged if we change to any of the other possible codings for the factor variables (not shown). Adjusting for age group using a stratified model gives almost identical results to the sequential LRT, in this case. The Wald tests for sex are equal to $[\beta/ se(\beta)]^2$ using the sex coefficient from the fits, \Sexpr{round(summary(cfit1)$coef[1,4]^2,2)} and \Sexpr{round(summary(cfit2)$coef[5,4]^2,2)} for the unadjusted and adjusted models, respectively. Unlike a linear model they are not exactly equal to the anova table results based on the log-likelihood, but tell the same story. Now consider weighted models, with both empirical and uniform distributions as the target age distribution. The fits require use of a robust variance, since we are approaching it via a survey sampling computation. The tapply function creates a per-subject index into the case weight table created earlier. <>= wtindx <- with(flchain, tapply(death, list(sex, age2))) cfitpop <- coxph(Surv(futime, death) ~ sex, flchain, robust=TRUE, weight = (casewt[,,3])[wtindx]) cfityates <- coxph(Surv(futime, death) ~ sex, flchain, robust=TRUE, weight = (casewt[,,4])[wtindx]) # # Glue it into a table for viewing # tfun <- function(fit, indx=1) { c(fit$coef[indx], sqrt(fit$var[indx,indx])) } coxp <- rbind(tfun(cfit1), tfun(cfit2,5), tfun(cfitpop), tfun(cfityates)) dimnames(coxp) <- list(c("Unadjusted", "Additive", "Empirical Population", "Uniform Population"), c("Effect", "se(effect)")) signif(coxp,3) @ The population estimates based on reweighting lie somewhere between the unadjusted and the sequential results. We expect that balancing to the empirical population will give a solution that is similar to the age + sex model, in the same way that the close but not identical to the MVUE estimate in a linear model. Balancing to a hypothetical population with equal numbers in each age group yields a substantially smaller estimate of effect. since it gives large weights to the oldest age group, where in this data set the male/female difference is smallest. Last, look at constructed contrasts from a cell means model. We can either fit this using the interaction, or apply the previous contrast matrix to the coefficients found above. Since the ``intercept'' of a Cox model is absorbed into the baseline hazard our contrast matrix will have one less column. <<>>= cfit4 <- coxph(Surv(futime, death) ~ sex * age2, flchain) # Uniform population contrast ysex <- c(0,-1, 0,0,0,0, -.2,-.2,-.2,-.2) #Yates for sex, SAS coding contrast(ysex[-1], cfit4) # Verify using cell means coding cfit4b <- coxph(Surv(futime, death) ~ interaction(sex, age2), flchain) temp <- matrix(c(0, coef(cfit4b)),2) # the female 50-59 is reference diff(rowMeans(temp)) #direct estimate of the Yates # temp2 <- rbind(temp, temp[2,] - temp[1,]) dimnames(temp2) <- list(c('female', 'male', 'difference'), levels(age2)) round(temp2, 3) # # # NSTT contrast contrast(c(1,0,0,0,0,0,0,0,0), cfit4) @ In the case of a two level covariate such as sex, the NSTT algorithm plus the SAS coding yields an estimate and test for a difference in sex for the \emph{first} age group; the proper contrast is an average. Since it gives more weight to the larger ages, where the sex effect is smallest, the Yates-like contrast is smaller than the result from an additive model \code{cfit2}. Nevertheless, this contrast and the sequential test are more similar for the survival outcome than for the linear models. This is due to the fact that the variances of the individual hazards for each sex/age combination are proportional to the number of deaths in that cell rather than the number of subjects per cell. A table of the number of deaths is not as imbalanced as the table of subject counts, and so the Yates and MLE ``populations'' are not as far apart as they were for the linear regression. There are fewer subjects at the higher ages but they die more frequently. Why is the Yates-like contrast so different than the result of creating a uniform age distribution using case weights followed by an MLE estimate? Again, the MLE estimate has death counts as the effective weights; the case-weighted uniform population has smaller weights for the youngest age group and that group also has the lowest death rate, resulting in lower influence for that group and an estimate shrunken towards the 90+ difference of \Sexpr{round(temp2[3,5], 3)}. All told, for survival models adjustment to a uniform population is a slippery target. \subsection{SAS phreg results} Now for the main event: what does SAS do? First, for the simple case of an additive model the SAS results are identical to those shown above. The coefficients, variances and log-likelihoods for cfit2 are identical to the phreg output for an additive model, as found in the appendix. As would be expected from the linear models case, the ``type III'' results for the additive model are simply the Wald tests for the fit, repackaged with a new label. Now look at the model that contains interactions. We originally surmised that a contrast calculation would be the most likely way in which the phreg code would implement type 3, as it is the easiest to integrate with existing code. Results are shown in the last SAS fit of the appendix. Comparing these results of the SAS printout labeled as ``Type III Wald'' to the contrasts calculated above shows that phreg is using the NSTT method. This is a bit of a shock. All of the SAS literature on type III emphasizes the care with which they form the calculation so as to always produce a Yates contrast (or in the case of missing cells a Yates-like one), and there was no hint in the documentation that phreg does anything different. As a double check direct contrast statements corresponding to the Yates and NSTT contrasts were added to the SAS code, and give confirmatory results. A further run which forced sum constraints by adding \code{'/ effect'} to the SAS class statement (not shown) restored the correct Yates contrast, as expected. As a final check, look at the NSTT version of the LRT, which corresponds to simply dropping the sex column from the $X$ matrix. <>= xmat4 <- model.matrix(cfit4) cfit4b <- coxph(Surv(futime, death) ~ xmat4[,-1], flchain) anova(cfit4b, cfit4) @ This agrees with the LR ``type 3'' test of the phreg printout. \subsection{Conclusion} Overall, both rebalanced estimates and coefficient contrasts are interesting exercises for the Cox model, but their actual utility is unclear. It is difficult to make a global optimality argument for either one, particularly in comparison to the sequential tests which have the entire weight of likelihood theory as a justification. Case reweighted estimates do play a key role when attempting to adjust for non-random treatment assignment, as found in the literature for causal analysis and marginal structural models; a topic and literature far too extensive and nuanced for discussion in this note. No special role is apparent, at least to this author, for regular or even sporadic use of a Yates contrast in survival models. The addition of such a feature and label to the SAS phreg package is a statistical calamity, one that knowledgeable and conscientious statistical practitioners will likely have to fight for the rest of their careers. In the common case of a treatment comparison, adjusted for enrolling center, the default ``type III'' printout from phreg corresponds to a comparison of treatments within the last center; the only contribution of the remainder of the data set is to help define the baseline hazard function and the effect of any continuous adjusters that happen to be in the model. The quadruple whammy of a third rate implementation (the NSTT), defaults that lead to a useless and misleading result, no documentation of the actual computation that is being done, and irrational reverence for the type III label conspire to make this a particularly unfortunate event. \appendix \section{Computing the Yates estimate} \label{sect:coding} We will take it as a given that no one wants to memorize contrast formulas, and so we need a way to compute Yates contrasts automatically in a computer program. The most direct method is to encode the original fit in terms of the cell means, as has been done throughout this report. The Yates contrast is then simply an average of estimates across the appropriate margin. However, we normally will want to solve the linear or Cox model fit in a more standard coding and then compute the Yates contrast after the fact. Note that any population re norming requires estimates of the cell means, whether they were explicit parameters or not, i.e., the model fit must include interaction terms. Here are three algorithms for this post-hoc computation. All of them depend, directly or indirectly, on the breakdown found earlier in equation \eqref{std}. \begin{align} y_{ij} &= \mu + \alpha_i + \beta_j + \gamma_{ij} + \epsilon \label{a1} \\ &= \theta_{ij} + \epsilon \label{a2}\\ \theta_{ij} &= \mu + \alpha_i + \beta_j + \gamma_{ij} \label{a3} \\ \end{align} Equation \eqref{a1} is the standard form from our linear models textbooks, equation \eqref{a2} is the cell means form, and \eqref{a3} is the result of matching them together. Using this equivalence a Yates test for row effects will be \begin{align} 0 &= e_i - e_{i'} \quad \forall i,i' \nonumber \\ &= (\alpha_i - \alpha_{i'}) + (1/k)\sum_j(\gamma_{ij} - \gamma_{i'j}) \label{ycont2} \end{align} where the subscripts $i$ and $i'$ range over the rows and $k$ is the number of columns. To illustrate the methods we will use 3 small data sets defined below. All are unbalanced. The second data set removes the aD observation and so has a zero cell, the third removes the diagonal and has 3 missing cells. <>= data1 <- data.frame(y = rep(1:6, length=20), x1 = factor(letters[rep(1:3, length=20)]), x2 = factor(LETTERS[rep(1:4, length=10)]), x3 = 1:20) data1$x1[19] <- 'c' data1 <- data1[order(data1$x1, data1$x2),] row.names(data1) <- NULL with(data1, table(x1,x2)) # data2 -- single missing cell indx <- with(data1, x1=='a' & x2=='D') data2 <- data1[!indx,] #data3 -- missing the diagonal data3 <- data1[as.numeric(data1$x1) != as.numeric(data1$x2),] @ \subsection{NSTT method} The first calculation method is based on a simple observation. If we impose the standard sums constraint on equation \eqref{a1} which is often found in textbooks (but nowhere else) of $\sum_i \alpha_i = \sum_j \beta_j = 0$, $\sum_i\gamma_{ij} =0 \; \forall j$ and $\sum_j \gamma_{ij} = 0 \; \forall i$, then the last term in equation \eqref{ycont2} is identically 0. Thus the Yates contrast corresponds exactly to a test of $\alpha=0$. In R we can choose this coding by using the \code{contr.sum} option. This approach has the appearance of simplicity: we can do an ordinary test for row effects within an interaction model. Here is R code that is often proposed for ``type III'' computation, which is based on the same process. <<>>= options(contrasts=c("contr.sum", "contr.poly")) fit1 <- lm(y ~ x1*x2, data1) drop1(fit1, .~.) @ The problem with this approach is that it depends critically on use of the sum constraints. If we apply the same code after fitting the data set under the more usual constraints a completely different value ensues. <<>>= options(contrasts=c("contr.SAS", "contr.poly")) fit2 <- lm(y ~ x1*x2, data1) drop1(fit2, .~.) options(contrasts=c("contr.treatment", "contr.poly")) fit3 <- lm(y ~ x1*x2, data1) drop1(fit3, .~.) @ Both common choices of contrasts give a different answer than contr.sum, and both are useless. I thus refer to this as the Not Safe Type Three (NSTT) algorithm, ``not SAS type three'' and ``nonsense type three'' are two other sensible expansions. This approach should NEVER be used in practice. \subsection{ATT} The key idea of the averaging approach (Averaged Type Three) is to directly evaluate equation \eqref{ycont2}. The first step of the computation is shown below <>= X <- model.matrix(fit2) ux <- unique(X) ux indx <- rep(1:3, c(4,4,4)) effects <- t(rowsum(ux, indx)/4) # turn sideways to fit the paper better effects yates <- effects[,-1] - effects[,1] yates @ The data set ux has 12 rows, one for each of the 12 unique x*x2 combinations. Because data1 was sorted, the first 4 rows correspond to x=1, the next 4 to x=2 and the next to x=3 which is useful for illustration but has no impact on the computation. The average of rows 1-4 (column 1 of \code{effects} above) is the estimated average response for subjects with x1=a, assuming a uniform distribution over the 12 cells. Any two differences between the three effects is an equivalent basis for computing the Yates contrast. We can verify that the resulting estimates correspond to a uniform target population by directly examining the case weights for the estimate. Each of them gives a total weight of 1/4 to each level of x2. Each element of $\beta\beta$ is a weighted average of the data, revealed by the rows of the matrix $(X'X)^{-1}X'$. The estimate are a weighted sum of the coefficients, so are also a weighted average of the $y$ values. <<>>= wt <- solve(t(X) %*% X, t(X)) # twelve rows (one per coef), n columns casewt <- t(effects) %*% wt # case weights for the three "row efffects" for (i in 1:3) print(tapply(casewt[i,], data1$x2, sum)) @ \subsection{STT} The SAS type III method takes a different approach, based on a a dependency matrix $D$. Start by writing the $X$ matrix for the problem using all of the parameters in equation \eqref{a1}. For our flc example this will have columns for intercept (1), sex (2), age group (5) and the age group by sex interaction (10) = 18 columns. Now define the lower triangular square matrix $D$ such that \begin{itemize} \item If the $i$th column of $X$ can be written as a linear combination of columns 1 through $i-1$, then row $i$ of $D$ contains that linear combination and $D_{ii}=0$. \item If the $i$th column is not linearly dependent on earlier ones then $D_{ii}=1$ and $D_{ij}=0$ for all $j \ne i$. \end{itemize} Columns of $D$ that correspond to linearly dependent columns of $X$ will be identically zero and can be discarded (or not) at this point. The result of this operation replicates table 12.2 in the SAS reference \cite{SASguide} labeled ``the form of estimable functions''. To obtain the Yates contrasts for an effect replace the appropriate columns of $D$ with the residuals from a regression on all columns to the right of it. Simple inspection shows that the columns of $D$ corresponding to any given effect will already be orthogonal to other effects in $D$ \emph{except} those for interactions that contain it; so the regression does not have to include all columns to the right. It is easy to demonstrate that this gives the uniform population contrast (Yates) for a large number of data sets, but I have not yet constructed a proof. (I suspect it could be approached using the Rao-Blackwell theorem.) \subsection{Bystanders} What about a model that has a extra predictor, such as \code{x3} in our example data and in the fit below? <<>>= fit4 <- lm(y ~ x1*x2 + x3, data=data1) @ The standard approach is to ignore this variable when setting up ``type III'' tests: the contrast for \code{x1} will be the same as it was in the prior model, with a 0 row in the middle for the x3 coefficient. \subsection{Missing cells} When there are combinations of factors with 0 subjects in that group, it is not possible to create a uniform population via reweighting of either subjects or parameters. There is thus no Yates contrast corresponding to the hypothetical population of interest. For that matter, adjustment to any fixed population is no longer possible, such as the US 2000 reference, unless groups are pooled so as to remove any counts of zero, and even then the estimate could be problematic due to extreme weights. This fact does not stop each of the above 3 algorithms from executing and producing a number. This raises two further issues. First, what does that number \emph{mean}? Much ink has been spilled on this subject, but I personally have never been able to come to grips with a satisfactory explanation and so have nothing to offer on the topic. I am reluctant to use such estimates. The second issue is that the computational algorithms become more fragile. \begin{itemize} \item The NSTT algorithm is a disaster in waiting, so no more needs to be said about situations where its behavior may be even worse. \item When fitting the original model, there will be one or more NA coefficients due to the linear dependencies that arise. A natural extension of the ATT method is to leave these out of the sums when computing each average. However, there are data sets for which the particular set of coefficients returned as missing will depend on the order in which variables were listed in the model statement, which in turn will change the ATT result. \item For the STT method, our statement that certain other columns in $D$ will be orthogonal to the chosen effect is no longer true. To match SAS, the orthogonalization step above should include only those effects further to the right that contain the chosen effect (the one we are constructing a contrast vector for). As a side effect, this makes the STT result invariant to the order of the variables in the model statement. \end{itemize} \section{SAS computations} The following code was executed in version 9.3 of SAS. \begin{verbatim} options ls=70; libname save "sasdata"; title "Sex only"; proc glm data=save.flc; class sex; model flc = sex; title "Sex only"; proc glm data=save.flc; class sex age2; model flc = age2 sex /solution E1 E2 E3; title "Second fit, no interaction"; proc glm data=save.flc; class sex age2; model flc = sex age2 sex*age2/solution E1 E2 E3; estimate 'yates' sex 1 -1 sex*age2 .2 .2 .2 .2 .2 -.2 -.2 -.2 -.2 -.2; title "Third fit, interaction"; proc phreg data=save.flc; class sex age2; model futime * death(0) = sex age2/ ties=efron; title "Phreg fit, sex and age, additive"; proc phreg data=save.flc; class sex age2; model futime * death(0) = sex age2 sex*age2 / ties=efron type3(all); estimate 'Yates sex' sex 1 sex*age2 .2 .2 .2 .2; contrast 'NSTT sex ' sex 1 ; contrast 'NSTT age' age2 1 0 0 0 , age2 0 1 0 0 , age2 0 0 1 0 , age2 0 0 0 1; title "Phreg fit, sex and age with interaction"; proc phreg data=save.flc; class sex age2/ param=effect; model futime * death(0) = sex age2 sex*age2 / ties=efron; title "Phreg, using effect coding"; \end{verbatim} The SAS output is voluminous, covering over a dozen pages. A subset is extracted below, leaving out portions that are unimportant to our comparison. First the GLM model for sex only. There are no differences between type 1 and type 3 output for this model. \small \begin{verbatim} ... Number of Observations Read 7874 Number of Observations Used 7874 ... Dependent Variable: flc Sum of Source DF Squares Mean Square F Value Model 1 142.19306 142.19306 42.27 Error 7872 26481.86345 3.36406 Corrected Total 7873 26624.05652 \end{verbatim} \normalsize The second fit with sex and then age. \small \begin{verbatim} Type I Estimable Functions -----------------Coefficients------------------ Effect age2 sex Intercept 0 0 age2 1 L2 0 age2 2 L3 0 age2 3 L4 0 age2 4 L5 0 age2 5 -L2-L3-L4-L5 0 sex F -0.2571*L2-0.2576*L3-0.1941*L4-0.0844*L5 L7 sex M 0.2571*L2+0.2576*L3+0.1941*L4+0.0844*L5 -L7 Type II Estimable Functions ---Coefficients---- Effect age2 sex Intercept 0 0 age2 1 L2 0 age2 2 L3 0 age2 3 L4 0 age2 4 L5 0 age2 5 -L2-L3-L4-L5 0 sex F 0 L7 sex M 0 -L7 Type III Estimable Functions ---Coefficients---- Effect age2 sex Intercept 0 0 age2 1 L2 0 age2 2 L3 0 age2 3 L4 0 age2 4 L5 0 age2 5 -L2-L3-L4-L5 0 sex F 0 L7 sex M 0 -L7 Dependent Variable: flc Sum of Source DF Squares Mean Square F Value Model 5 2212.13649 442.42730 142.60 Error 7868 24411.92003 3.10268 Corrected Total 7873 26624.05652 Source DF Type I SS Mean Square F Value age2 4 1929.642183 482.410546 155.48 sex 1 282.494304 282.494304 91.05 Source DF Type II SS Mean Square F Value age2 4 2069.943424 517.485856 166.79 sex 1 282.494304 282.494304 91.05 Source DF Type III SS Mean Square F Value age2 4 2069.943424 517.485856 166.79 sex 1 282.494304 282.494304 91.05 Standard Parameter Estimate Error t Value Pr > |t| Intercept 5.503757546 B 0.17553667 31.35 <.0001 age2 1 -2.587424744 B 0.17584961 -14.71 <.0001 age2 2 -2.249164537 B 0.17684133 -12.72 <.0001 age2 3 -1.770342603 B 0.17834253 -9.93 <.0001 age2 4 -1.082104827 B 0.18584656 -5.82 <.0001 age2 5 0.000000000 B sex F -0.383454133 B 0.04018624 -9.54 <.0001 sex M 0.000000000 B \end{verbatim} \normalsize The third linear models fit, containing interactions. For first portion I have trimmed off long printout on the right, i.e. the estimable functions for the age2*sex effect since they are not of interest. \small \begin{verbatim} Type I Estimable Functions --------------------Coefficients-------- Effect sex age2 Intercept 0 0 sex F L2 0 sex M -L2 0 age2 1 -0.0499*L2 L4 age2 2 -0.0373*L2 L5 age2 3 0.0269*L2 L6 age2 4 0.0482*L2 L7 age2 5 0.0121*L2 -L4-L5-L6-L7 sex*age2 F 1 0.3786*L2 0.6271*L4+0.1056*L5+0.0796*L6+0.0346*L7 sex*age2 F 2 0.2791*L2 0.0778*L4+0.5992*L5+0.0587*L6+0.0255*L7 sex*age2 F 3 0.2182*L2 0.0527*L4+0.0528*L5+0.6245*L6+0.0173*L7 sex*age2 F 4 0.1055*L2 0.0188*L4+0.0188*L5+0.0142*L6+0.7006*L7 sex*age2 F 5 0.0186*L2 -0.7764*L4-0.7764*L5-0.777*L6-0.7781*L7 sex*age2 M 1 -0.4285*L2 0.3729*L4-0.1056*L5-0.0796*L6-0.0346*L7 sex*age2 M 2 -0.3164*L2 -0.0778*L4+0.4008*L5-0.0587*L6-0.0255*L7 sex*age2 M 3 -0.1913*L2 -0.0527*L4-0.0528*L5+0.3755*L6-0.0173*L7 sex*age2 M 4 -0.0573*L2 -0.0188*L4-0.0188*L5-0.0142*L6+0.2994*L7 sex*age2 M 5 -0.0065*L2 -0.2236*L4-0.2236*L5-0.223*L6-0.2219*L7 Type II Estimable Functions --------------------Coefficients--------------------- Effect sex age2 Intercept 0 0 sex F L2 0 sex M -L2 0 age2 1 0 L4 age2 2 0 L5 age2 3 0 L6 age2 4 0 L7 age2 5 0 -L4-L5-L6-L7 sex*age2 F 1 0.41*L2 0.6271*L4+0.1056*L5+0.0796*L6+0.0346*L7 sex*age2 F 2 0.3025*L2 0.0778*L4+0.5992*L5+0.0587*L6+0.0255*L7 sex*age2 F 3 0.2051*L2 0.0527*L4+0.0528*L5+0.6245*L6+0.0173*L7 sex*age2 F 4 0.073*L2 0.0188*L4+0.0188*L5+0.0142*L6+0.7006*L7 sex*age2 F 5 0.0093*L2 -0.7764*L4-0.7764*L5-0.777*L6-0.7781*L7 sex*age2 M 1 -0.41*L2 0.3729*L4-0.1056*L5-0.0796*L6-0.0346*L7 sex*age2 M 2 -0.3025*L2 -0.0778*L4+0.4008*L5-0.0587*L6-0.0255*L7 sex*age2 M 3 -0.2051*L2 -0.0527*L4-0.0528*L5+0.3755*L6-0.0173*L7 sex*age2 M 4 -0.073*L2 -0.0188*L4-0.0188*L5-0.0142*L6+0.2994*L7 sex*age2 M 5 -0.0093*L2 -0.2236*L4-0.2236*L5-0.223*L6-0.2219*L7 Type III Estimable Functions ---------------------Coefficients--------------------- Effect sex age2 sex*age2 Intercept 0 0 0 sex F L2 0 0 sex M -L2 0 0 age2 1 0 L4 0 age2 2 0 L5 0 age2 3 0 L6 0 age2 4 0 L7 0 age2 5 0 -L4-L5-L6-L7 0 sex*age2 F 1 0.2*L2 0.5*L4 L9 sex*age2 F 2 0.2*L2 0.5*L5 L10 sex*age2 F 3 0.2*L2 0.5*L6 L11 sex*age2 F 4 0.2*L2 0.5*L7 L12 sex*age2 F 5 0.2*L2 -0.5*L4-0.5*L5-0.5*L6-0.5*L7 -L9-L10-L11-L12 sex*age2 M 1 -0.2*L2 0.5*L4 -L9 sex*age2 M 2 -0.2*L2 0.5*L5 -L10 sex*age2 M 3 -0.2*L2 0.5*L6 -L11 sex*age2 M 4 -0.2*L2 0.5*L7 -L12 sex*age2 M 5 -0.2*L2 -0.5*L4-0.5*L5-0.5*L6-0.5*L7 L9+L10+L11+L12 Source DF Type I SS Mean Square F Value sex 1 142.193063 142.193063 45.97 age2 4 2069.943424 517.485856 167.30 sex*age2 4 87.218363 21.804591 7.05 Source DF Type II SS Mean Square F Value sex 1 282.494304 282.494304 91.33 age2 4 2069.943424 517.485856 167.30 sex*age2 4 87.218363 21.804591 7.05 Source DF Type III SS Mean Square F Value sex 1 126.961986 126.961986 41.05 age2 4 1999.446491 499.861623 161.60 sex*age2 4 87.218363 21.804591 7.05 Standard Parameter Estimate Error t Value Pr > |t| yates -0.58972607 0.09204824 -6.41 <.0001 Standard Parameter Estimate Error t Value Pr > |t| Intercept 6.003043478 B 0.36672295 16.37 <.0001 sex F -1.024512614 B 0.41553944 -2.47 0.0137 sex M 0.000000000 B age2 1 -3.176876326 B 0.36950532 -8.60 <.0001 age2 2 -2.787597918 B 0.37048599 -7.52 <.0001 age2 3 -2.088127335 B 0.37292760 -5.60 <.0001 age2 4 -1.353746449 B 0.38703805 -3.50 0.0005 age2 5 0.000000000 B sex*age2 F 1 0.813889663 B 0.42023749 1.94 0.0528 sex*age2 F 2 0.716160958 B 0.42189464 1.70 0.0896 sex*age2 F 3 0.330651265 B 0.42487846 0.78 0.4365 sex*age2 F 4 0.313230835 B 0.44127621 0.71 0.4778 sex*age2 F 5 0.000000000 B sex*age2 M 1 0.000000000 B sex*age2 M 2 0.000000000 B sex*age2 M 3 0.000000000 B sex*age2 M 4 0.000000000 B sex*age2 M 5 0.000000000 B \end{verbatim} \normalsize The phreg printout for the additive model with age and sex. \small \begin{verbatim} Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 2357.5239 5 <.0001 Score 3823.3905 5 <.0001 Wald 2374.5250 5 <.0001 Type 3 Tests Wald Effect DF Chi-Square Pr > ChiSq sex 1 69.9646 <.0001 age2 4 2374.5211 <.0001 Analysis of Maximum Likelihood Estimates Parameter Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq sex F 1 -0.36617 0.04378 69.9646 <.0001 age2 1 1 -4.18209 0.12180 1179.0289 <.0001 age2 2 1 -3.23859 0.11418 804.5068 <.0001 age2 3 1 -2.17521 0.10963 393.6524 <.0001 age2 4 1 -1.15226 0.11072 108.3077 <.0001 \end{verbatim} \normalsize The model with age*sex interaction. \small \begin{verbatim} Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 37736.900 35374.050 AIC 37736.900 35392.050 SBC 37736.900 35443.188 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 2362.8497 9 <.0001 Score 3873.5113 9 <.0001 Wald 2357.9498 9 <.0001 Type 3 Tests LR Statistics Effect DF Chi-Square Pr > ChiSq sex 1 0.4607 0.4973 age2 4 932.1371 <.0001 sex*age2 4 5.3258 0.2555 Score Statistics Effect DF Chi-Square Pr > ChiSq sex 1 0.4757 0.4904 age2 4 1506.8699 <.0001 sex*age2 4 5.2516 0.2624 Wald Statistics Effect DF Chi-Square Pr > ChiSq sex 1 0.4833 0.4869 age2 4 964.6007 <.0001 sex*age2 4 5.2322 0.2643 Analysis of Maximum Likelihood Estimates Parameter Standard Parameter DF Estimate Error Chi-Square sex F 1 -0.16537 0.23789 0.4833 age2 1 1 -4.02699 0.22585 317.9171 age2 2 1 -3.04796 0.21843 194.7187 age2 3 1 -1.99577 0.21577 85.5504 age2 4 1 -1.10659 0.22256 24.7216 sex*age2 F 1 1 -0.21121 0.26896 0.6167 sex*age2 F 2 1 -0.29334 0.25518 1.3214 sex*age2 F 3 1 -0.25663 0.24829 1.0684 sex*age2 F 4 1 -0.04339 0.25527 0.0289 Contrast DF Chi-Square Pr > ChiSq NSTT sex 1 0.4833 0.4869 NSTT age 4 964.6007 <.0001 Likelihood Ratio Statistics for Type 1 Analysis LR Source -2 Log L DF Chi-Square Pr > ChiSq (Without Covariates) 37736.8997 sex 37733.0932 1 3.8066 0.0511 age2 35379.3758 4 2353.7173 <.0001 sex*age2 35374.0501 4 5.3258 0.2555 Standard Label Estimate Error z Value Pr > |z| Yates -0.3263 0.06149 -5.31 <.0001 \end{verbatim} \normalsize \begin{thebibliography}{9} \bibitem{Aitkin78} M. Aitkin (1978). The analysis of unbalanced cross classifications (with discussion). \emph{J Royal Stat Soc A} 141:195-223. \bibitem{Dispenzieri12} A. Dispenzieri, J. Katzmann, R. Kyle, D. Larson, T. Therneau, C. Colby, R. Clark, .G Mead, S. Kumar, L..J Melton III and S.V. Rajkumar (2012). Use of monoclonal serum immunoglobulin free light chains to predict overall survival in the general population, \emph{Mayo Clinic Proc} 87:512--523. \bibitem{Herr86} D. G. Herr (1986). On the History of ANOVA in Unbalanced, Factorial Designs: The First 30 Years. \emph{Amer Statistician} 40:265-270. \bibitem{Kyle06} R. Kyle, T. Therneau, S.V. Rajkumar, D. Larson, M. Plevak, J. Offord, A. Dispenzieri, J. Katzmann, and L.J. Melton, III (2006), Prevalence of monoclonal gammopathy of undetermined significance, \emph{New England J Medicine} 354:1362--1369. \bibitem{Macnaughton92} D. B. Macnaughton (1992). Which sum of squares are best in an unbalanced analysis of variance. www.matstat.com/ss. \bibitem{Nelder77} J. Nelder (1977). A reformulation of linear models (with discussion). \emph{J Royal Stat Soc A} 140:48--76. \bibitem{SASguide} SAS Institute Inc. (2008), The four types of estimable functions. SAS/STAT 9.2 User's Guide, chapter 15. \bibitem{Searle71} S. R. Searle, \emph{Linear Models}, Wiley, New York, 1971. \bibitem{Senn1} S. Senn. Multi-centre trials and the finally decisive argument. www.senns.demon.co.uk/wprose.html\#FDA. \bibitem{Senn2} S. Senn. Good mixed centre practice. www.senns.demon.co.uk/wprose.html\#Mixed. \bibitem{Senn07} S. Senn. Statistical Issues in Drug Development, Wiley, New York, 2007. \bibitem{Senn00} S. Senn. The many modes of meta. Drug Information J 34:535-549, 2000. \bibitem{Therneau00} T. M. Therneau and P. M. Grambsch, \emph{Modeling Survival Data: Extending the Cox Model}, Springer-Verlag, New York, 2000. \bibitem{Yates34} F. Yates (1934). The analysis of multiple classifications with unequal numbers in the different classes. \emph{J Am Stat Assoc}, 29:51--66. \end{thebibliography} \end{document} survival/inst/doc/adjcurve.R0000644000175100001440000004156313070713757015636 0ustar hornikusers### R code from vignette source 'adjcurve.Rnw' ################################################### ### code chunk number 1: init ################################################### options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text require(survival, quietly=TRUE) fdata <- flchain[flchain$futime > 7,] fdata$age2 <- cut(fdata$age, c(0,54, 59,64, 69,74,79, 89, 110), labels = c(paste(c(50,55,60,65,70,75,80), c(54,59,64,69,74,79,89), sep='-'), "90+")) ################################################### ### code chunk number 2: adjcurve.Rnw:181-195 ################################################### group3 <- factor(1+ 1*(fdata$flc.grp >7) + 1*(fdata$flc.grp >9), levels=1:3, labels=c("FLC < 3.38", "3.38 - 4.71", "FLC > 4.71")) age1 <- cut(fdata$age, c(49,59,69,79, 110)) levels(age1) <- c(paste(c(50,60,70), c(59,69,79), sep='-'), '80+') temp1 <- table(group3, age1) temp2 <- round(100* temp1/rowSums(temp1)) pfun <- function(x,y) { paste(ifelse(x<1000, "\\phantom{0}", ""), x, " (", ifelse(y<10, "\\phantom{0}", ""), y, ") ", sep="") } cat(paste(c("FLC $<$ 3.38", pfun(temp1[1,], temp2[1,])), collapse=" & "), "\\\\\n") cat(paste(c("FLC 3.38--4.71", pfun(temp1[2,], temp2[2,])), collapse=" & "), "\\\\\n") cat(paste(c("FLC $>$ 4.71", pfun(temp1[3,], temp2[3,])), collapse=" & "), "\n") ################################################### ### code chunk number 3: flc1 ################################################### getOption("SweaveHooks")[["fig"]]() fdata <- flchain[flchain$futime >=7,] fdata$age2 <- cut(fdata$age, c(0,54, 59,64, 69,74,79, 89, 110), labels = c(paste(c(50,55,60,65,70,75,80), c(54,59,64,69,74,79,89), sep='-'), "90+")) fdata$group <- factor(1+ 1*(fdata$flc.grp >7) + 1*(fdata$flc.grp >9), levels=1:3, labels=c("FLC < 3.38", "3.38 - 4.71", "FLC > 4.71")) sfit1 <- survfit(Surv(futime, death) ~ group, fdata) plot(sfit1, mark.time=F, col=c(1,2,4), lty=1, lwd=2, xscale=365.25, xlab="Years from Sample", ylab="Survival") text(c(11.1, 10.5, 7.5)*365.25, c(.88, .57, .4), c("FLC < 3.38", "3.38 - 4.71", "FLC > 4.71"), col=c(1,2,4)) ################################################### ### code chunk number 4: adjcurve.Rnw:271-276 ################################################### tab1 <- with(fdata, table(group, age2, sex)) cat("Low&", paste(tab1[1,,1], collapse=" &"), "\\\\\n") cat("Med&", paste(tab1[2,,1], collapse=" &"), "\\\\\n") cat("High&", paste(tab1[3,,1], collapse=" &"), "\\\\\n") ################################################### ### code chunk number 5: adjcurve.Rnw:281-284 ################################################### cat("Low&", paste(tab1[1,,2], collapse=" &"), "\\\\\n") cat("Med&", paste(tab1[2,,2], collapse=" &"), "\\\\\n") cat("High&", paste(tab1[3,,2], collapse=" &"), "\n") ################################################### ### code chunk number 6: flc2 ################################################### getOption("SweaveHooks")[["fig"]]() temp <- with(fdata, table(group, age2, sex)) dd <- dim(temp) # Select subjects set.seed(1978) select <- array(vector('list', length=prod(dd)), dim=dd) for (j in 1:dd[2]) { for (k in 1:dd[3]) { n <- temp[3,j,k] # how many to select for (i in 1:2) { indx <- which(as.numeric(fdata$group)==i & as.numeric(fdata$age2) ==j & as.numeric(fdata$sex) ==k) select[i,j,k] <- list(sample(indx, n, replace=(n> temp[i,j,k]))) } indx <- which(as.numeric(fdata$group)==3 & as.numeric(fdata$age2) ==j & as.numeric(fdata$sex) ==k) select[3,j,k] <- list(indx) #keep all the group 3 = high } } data2 <- fdata[unlist(select),] sfit2 <- survfit(Surv(futime, death) ~ group, data2) plot(sfit2,col=c(1,2,4), lty=1, lwd=2, xscale=365.25, xlab="Years from Sample", ylab="Survival") lines(sfit1, col=c(1,2,4), lty=2, lwd=1, xscale=365.25) legend(730, .4, levels(fdata$group), lty=1, col=c(1,2,4), bty='n', lwd=2) ################################################### ### code chunk number 7: adjcurve.Rnw:390-396 ################################################### # I can't seem to put this all into an Sexpr z1 <- with(fdata,table(age, sex, group)) z2<- apply(z1, 1:2, min) ztemp <- 3*sum(z2) z1b <- with(fdata, table(age>64, sex, group)) ztemp2 <- sum(apply(z1b, 1:2, min)) ################################################### ### code chunk number 8: adjcurve.Rnw:414-415 ################################################### survdiff(Surv(futime, death) ~ group, data=data2) ################################################### ### code chunk number 9: adjcurve.Rnw:443-449 ################################################### refpop <- uspop2[as.character(50:100),c("female", "male"), "2000"] pi.us <- refpop/sum(refpop) age100 <- factor(ifelse(fdata$age >100, 100, fdata$age), levels=50:100) tab100 <- with(fdata, table(age100, sex, group))/ nrow(fdata) us.wt <- rep(pi.us, 3)/ tab100 #new weights by age,sex, group range(us.wt) ################################################### ### code chunk number 10: adjcurve.Rnw:460-469 ################################################### temp <- as.numeric(cut(50:100, c(49, 54, 59, 64, 69, 74, 79, 89, 110)+.5)) pi.us<- tapply(refpop, list(temp[row(refpop)], col(refpop)), sum)/sum(refpop) tab2 <- with(fdata, table(age2, sex, group))/ nrow(fdata) us.wt <- rep(pi.us, 3)/ tab2 range(us.wt) index <- with(fdata, cbind(as.numeric(age2), as.numeric(sex), as.numeric(group))) fdata$uswt <- us.wt[index] sfit3a <-survfit(Surv(futime, death) ~ group, data=fdata, weight=uswt) ################################################### ### code chunk number 11: flc3a ################################################### getOption("SweaveHooks")[["fig"]]() tab1 <- with(fdata, table(age2, sex))/ nrow(fdata) matplot(1:8, cbind(pi.us, tab1), pch="fmfm", col=c(2,2,1,1), xlab="Age group", ylab="Fraction of population", xaxt='n') axis(1, 1:8, levels(fdata$age2)) tab2 <- with(fdata, table(age2, sex, group))/nrow(fdata) tab3 <- with(fdata, table(group)) / nrow(fdata) rwt <- rep(tab1,3)/tab2 fdata$rwt <- rwt[index] # add per subject weights to the data set sfit3 <- survfit(Surv(futime, death) ~ group, data=fdata, weight=rwt) temp <- rwt[,1,] #show female data temp <- temp %*% diag(1/apply(temp,2,min)) round(temp, 1) #show female data ################################################### ### code chunk number 12: flc3 ################################################### getOption("SweaveHooks")[["fig"]]() plot(sfit3, mark.time=F, col=c(1,2,4), lty=1, lwd=2, xscale=365.25, xlab="Years from Sample", ylab="Survival") lines(sfit3a, mark.time=F, col=c(1,2,4), lty=1, lwd=1, xscale=365.25) lines(sfit1, mark.time=F, col=c(1,2,4), lty=2, lwd=1, xscale=365.25) legend(730, .4, levels(fdata$group), lty=1, col=c(1,2,4), bty='n', lwd=2) ################################################### ### code chunk number 13: adjcurve.Rnw:553-562 ################################################### id <- 1:nrow(fdata) cfit <- coxph(Surv(futime, death) ~ group + cluster(id), data=fdata, weight=rwt) summary(cfit)$robscore if (exists("svykm")) { #true if the survey package is loaded sdes <- svydesign(id = ~0, weights=~rwt, data=fdata) dfit <- svykm(Surv(futime, death) ~ group, design=sdes, se=TRUE) } ################################################### ### code chunk number 14: ipw ################################################### options(na.action="na.exclude") gg <- as.numeric(fdata$group) lfit1 <- glm(I(gg==1) ~ factor(age2) * sex, data=fdata, family="binomial") lfit2 <- glm(I(gg==2) ~ factor(age2) * sex, data=fdata, family="binomial") lfit3 <- glm(I(gg==3) ~ factor(age2) * sex, data=fdata, family="binomial") temp <- ifelse(gg==1, predict(lfit1, type='response'), ifelse(gg==2, predict(lfit2, type='response'), predict(lfit3, type='response'))) all.equal(1/temp, fdata$rwt) ################################################### ### code chunk number 15: flc4 ################################################### getOption("SweaveHooks")[["fig"]]() lfit1b <-glm(I(gg==1) ~ age + sex, data=fdata, family="binomial") lfit2b <- glm(I(gg==2) ~ age +sex, data=fdata, family="binomial") lfit3b <- glm(I(gg==3) ~ age + sex, data=fdata, family="binomial") # weights for each group using simple logistic twt <- ifelse(gg==1, 1/predict(lfit1b, type="response"), ifelse(gg==2, 1/predict(lfit2b, type="response"), 1/predict(lfit3b, type="response"))) tdata <- data.frame(fdata, lwt=twt) #grouped plot for the females temp <- tdata[tdata$sex=='F',] temp$gg <- as.numeric(temp$group) c1 <- with(temp[temp$gg==1,], tapply(lwt, age2, sum)) c2 <- with(temp[temp$gg==2,], tapply(lwt, age2, sum)) c3 <- with(temp[temp$gg==3,], tapply(lwt, age2, sum)) xtemp <- outer(1:8, c(-.1, 0, .1), "+") #avoid overplotting ytemp <- 100* cbind(c1/sum(c1), c2/sum(c2), c3/sum(c3)) matplot(xtemp, ytemp, col=c(1,2,4), xlab="Age group", ylab="Weighted frequency (%)", xaxt='n') ztab <- table(fdata$age2) points(1:8, 100*ztab/sum(ztab), pch='+', cex=1.5, lty=2) # Add the unadjusted temp <- tab2[,1,] temp <- scale(temp, center=F, scale=colSums(temp)) matlines(1:8, 100*temp, pch='o', col=c(1,2,4), lty=2) axis(1, 1:8, levels(fdata$age2)) ################################################### ### code chunk number 16: adjcurve.Rnw:694-704 ################################################### # compute new weights wtscale <- table(fdata$group)/ tapply(fdata$rwt, fdata$group, sum) wt2 <- c(fdata$rwt * wtscale[fdata$group]) c("rescaled cv"= sd(wt2)/mean(wt2), "rwt cv"=sd(fdata$rwt)/mean(fdata$rwt)) cfit2a <- coxph(Surv(futime, death) ~ group + cluster(id), data=fdata, weight= rwt) cfit2b <- coxph(Surv(futime, death) ~ group + cluster(id), data=fdata, weight=wt2) round(c(cfit2a$rscore, cfit2b$rscore),1) ################################################### ### code chunk number 17: strata ################################################### allfit <- survfit(Surv(futime, death) ~ group + age2 + sex, fdata) temp <- summary(allfit)$table temp[1:6, c(1,4)] #abbrev printout to fit page ################################################### ### code chunk number 18: flc5 ################################################### getOption("SweaveHooks")[["fig"]]() xtime <- seq(0, 14, length=57)*365.25 #four points/year for 14 years smat <- matrix(0, nrow=57, ncol=3) # survival curves serr <- smat #matrix of standard errors pi <- with(fdata, table(age2, sex))/nrow(fdata) #overall dist for (i in 1:3) { temp <- allfit[1:16 + (i-1)*16] #curves for group i for (j in 1:16) { stemp <- summary(temp[j], times=xtime, extend=T) smat[,i] <- smat[,i] + pi[j]*stemp$surv serr[,i] <- serr[,i] + pi[i]*stemp$std.err^2 } } serr <- sqrt(serr) plot(sfit1, lty=2, col=c(1,2,4), xscale=365.25, xlab="Years from sample", ylab="Survival") matlines(xtime, smat, type='l', lwd=2, col=c(1,2,4),lty=1) ################################################### ### code chunk number 19: adjcurve.Rnw:829-830 ################################################### survdiff(Surv(futime, death) ~ group + strata(age2, sex), fdata) ################################################### ### code chunk number 20: flc8 ################################################### getOption("SweaveHooks")[["fig"]]() cfit4a <- coxph(Surv(futime, death) ~ age + sex + strata(group), data=fdata) surv4a <- survfit(cfit4a) plot(surv4a, col=c(1,2,4), mark.time=F, xscale=365.25, xlab="Years post sample", ylab="Survival") ################################################### ### code chunk number 21: flc6 ################################################### getOption("SweaveHooks")[["fig"]]() tab4a <- with(fdata, table(age, sex)) uage <- as.numeric(dimnames(tab4a)[[1]]) tdata <- data.frame(age = uage[row(tab4a)], sex = c("F","M")[col(tab4a)], count= c(tab4a)) tdata3 <- tdata[rep(1:nrow(tdata), 3),] #three copies tdata3$group <- factor(rep(1:3, each=nrow(tdata)), labels=levels(fdata$group)) sfit4a <- survexp(~group, data=tdata3, weight = count, ratetable=cfit4a) plot(sfit4a, mark.time=F, col=c(1,2,4), lty=1, lwd=2, xscale=365.25, xlab="Years from Sample", ylab="Survival") lines(sfit3, mark.time=F, col=c(1,2,4), lty=2, lwd=1, xscale=365.25) legend(730,.4, c("FLC low", "FLC med", "FLC high"), lty=1, col=c(1,2,4), bty='n', lwd=2) ################################################### ### code chunk number 22: adjcurve.Rnw:941-948 ################################################### tfit <- survfit(cfit4a, newdata=tdata, se.fit=FALSE) curves <- vector('list', 3) twt <- c(tab4a)/sum(tab4a) for (i in 1:3) { temp <- tfit[i,] curves[[i]] <- list(time=temp$time, surv= c(temp$surv %*% twt)) } ################################################### ### code chunk number 23: flc6b ################################################### getOption("SweaveHooks")[["fig"]]() par(mfrow=c(1,2)) cfit4b <- coxph(Surv(futime, death) ~ age*sex + strata(group), fdata) sfit4b <- survexp(~group, data=tdata3, ratetable=cfit4b, weights=count) plot(sfit4b, fun='event', xscale=365.25, xlab="Years from sample", ylab="Deaths") lines(sfit3, mark.time=FALSE, fun='event', xscale=365.25, lty=2) lines(sfit4a, fun='event', xscale=365.25, col=2) temp <- median(fdata$sample.yr) mrate <- survexp.mn[as.character(uage),, as.character(temp)] crate <- predict(cfit4b, newdata=tdata, reference='sample', type='lp') crate <- matrix(crate, ncol=2)[,2:1] # mrate has males then females, match it # crate contains estimated log(hazards) relative to a baseline, # and mrate absolute hazards, make both relative to a 70 year old for (i in 1:2) { mrate[,i] <- log(mrate[,i]/ mrate[21,2]) crate[,i] <- crate[,i] - crate[21,2] } matplot(mrate, crate, col=2:1, type='l') abline(0, 1, lty=2, col=4) ################################################### ### code chunk number 24: adjcurve.Rnw:1019-1027 ################################################### getOption("SweaveHooks")[["fig"]]() obs <- with(fdata, tapply(death, list(age2, sex, group), sum)) pred<- with(fdata, tapply(predict(cfit4b, type='expected'), list(age2, sex, group), sum)) excess <- matrix(obs/pred, nrow=8) #collapse 3 way array to 2 dimnames(excess) <- list(dimnames(obs)[[1]], c("low F", "low M", "med F", "med M", "high F", "high M")) round(excess, 1) ################################################### ### code chunk number 25: adjcurve.Rnw:1043-1052 ################################################### cfit5a <- coxph(Surv(futime, death) ~ strata(group):age +sex, fdata) cfit5b <- coxph(Surv(futime, death) ~ strata(group):(age +sex), fdata) cfit5c <- coxph(Surv(futime, death) ~ strata(group):(age *sex), fdata) options(show.signif.stars=FALSE) # see footnote anova(cfit4a, cfit5a, cfit5b, cfit5c) temp <- coef(cfit5a) names(temp) <- c("sex", "ageL", "ageM", "ageH") round(temp,3) ################################################### ### code chunk number 26: flc7 ################################################### getOption("SweaveHooks")[["fig"]]() pred5a <- with(fdata, tapply(predict(cfit5a, type='expected'), list(age2, sex, group), sum)) excess5a <- matrix(obs/pred5a, nrow=8, dimnames=dimnames(excess)) round(excess5a, 1) sfit5 <- survexp(~group, data=tdata3, ratetable=cfit5a, weights=count) plot(sfit3, fun='event', xscale=365.25, mark.time=FALSE, lty=2, col=c(1,2,4), xlab="Years from sample", ylab="Deaths") lines(sfit5, fun='event', xscale=365.25, col=c(1,2,4)) ################################################### ### code chunk number 27: flc8 ################################################### getOption("SweaveHooks")[["fig"]]() # there is a spurious warning from the model below: R creates 3 unneeded # columns in the X matrix cfit6 <- coxph(Surv(futime, death) ~ strata(group):age2 + sex, fdata) saspop <- with(fdata, expand.grid(age2= levels(age2), sex= levels(sex), group = levels(group))) sfit6 <- survexp(~group, data=saspop, ratetable=cfit6) plot(sfit6, fun='event', xscale=365.25, mark.time=FALSE, lty=1, col=c(1,2,4), xlab="Years from sample", ylab="Deaths") lines(sfit5, fun='event', xscale=365.25, lty=2, col=c(1,2,4)) survival/inst/doc/multi.R0000644000175100001440000003066413070713772015162 0ustar hornikusers### R code from vignette source 'multi.Rnw' ################################################### ### code chunk number 1: multi.Rnw:32-75 ################################################### require(survival) #require(Rcolorbrewer) #brewer.pal(5, "Dark2") palette(c("#000000", "#D95F02", "#1B9E77", "#7570B3", "#E7298A", "#66A61E")) options(continue=' ') # These functions are used in the document, but not discussed until the end crisk <- function(what, horizontal = TRUE, ...) { nstate <- length(what) connect <- matrix(0, nstate, nstate, dimnames=list(what, what)) connect[1,-1] <- 1 # an arrow from state 1 to each of the others if (horizontal) statefig(c(1, nstate-1), connect, ...) else statefig(matrix(c(1, nstate-1), ncol=1), connect, ...) } state3 <- function(what, horizontal=TRUE, ...) { if (length(what) != 3) stop("Should be 3 states") connect <- matrix(c(0,0,0, 1,0,0, 1,1,0), 3,3, dimnames=list(what, what)) if (horizontal) statefig(1:2, connect, ...) else statefig(matrix(1:2, ncol=1), connect, ...) } state4 <- function() { sname <- c("Entry", "CR", "Transplant", "Transplant") layout <- cbind(c(1/2, 3/4, 1/4, 3/4), c(5/6, 1/2, 1/2, 1/6)) connect <- matrix(0,4,4, dimnames=list(sname, sname)) connect[1, 2:3] <- 1 connect[2,4] <- 1 statefig(layout, connect) } state5 <- function(what, ...) { sname <- c("Entry", "CR", "Tx", "Rel", "Death") connect <- matrix(0, 5, 5, dimnames=list(sname, sname)) connect[1, -1] <- c(1,1,1, 1.4) connect[2, 3:5] <- c(1, 1.4, 1) connect[3, c(2,4,5)] <- 1 connect[4, c(3,5)] <- 1 statefig(matrix(c(1,3,1)), connect, cex=.8,...) } ################################################### ### code chunk number 2: multi.Rnw:81-82 (eval = FALSE) ################################################### ## curves <- survfit(Surv(time, status) ~ group, data=mydata) ################################################### ### code chunk number 3: simple1 ################################################### set.seed(1952) crdata <- data.frame(time=1:11, endpoint=factor(c(1,1,2,0,1,1,3,0,2,3,0), labels=c("censor", "a", "b", "c"))) tfit <- survfit(Surv(time, endpoint) ~ 1, data=crdata) dim(tfit) summary(tfit) ################################################### ### code chunk number 4: multi.Rnw:112-113 ################################################### getOption("SweaveHooks")[["fig"]]() plot(tfit, col=1:3, lwd=2, ylab="Probability in state") ################################################### ### code chunk number 5: overall ################################################### myeloid[1:5,] ################################################### ### code chunk number 6: sfit0 ################################################### getOption("SweaveHooks")[["fig"]]() sfit0 <- survfit(Surv(futime, death) ~ trt, myeloid) plot(sfit0, xscale=365.25, xaxs='r', col=1:2, lwd=2, xlab="Years post enrollment", ylab="Survival") legend(20, .4, c("Arm A", "Arm B"), col=1:2, lwd=2, bty='n') ################################################### ### code chunk number 7: data1 ################################################### data1 <- myeloid data1$crstat <- factor(with(data1, ifelse(is.na(crtime), death, 2)), labels=c("censor", "death", "CR")) data1$crtime <- with(data1, ifelse(crstat=="CR", crtime, futime)) data1$txstat <- factor(with(data1, ifelse(is.na(txtime), death, 2)), labels=c("censor", "death", "transplant")) data1$txtime <- with(data1, ifelse(txstat=="transplant", txtime, futime)) for (i in c("futime", "crtime", "txtime", "rltime")) data1[[i]] <- data1[[i]] * 12/365.25 #rescale to months ################################################### ### code chunk number 8: curve1 ################################################### getOption("SweaveHooks")[["fig"]]() sfit1 <- survfit(Surv(futime, death) ~ trt, data1) #survival sfit2 <- survfit(Surv(crtime, crstat) ~ trt, data1) # CR sfit3 <- survfit(Surv(txtime, txstat) ~ trt, data1) layout(matrix(c(1,1,1,2,3,4), 3,2), widths=2:1) oldpar <- par(mar=c(5.1, 4.1, 1.1, .1)) plot(sfit2[,2], mark.time=FALSE, fun='event', xmax=48, lty=3, lwd=2, col=1:2, xaxt='n', xlab="Months post enrollment", ylab="Events") lines(sfit1, mark.time=FALSE, xmax=48, fun='event', col=1:2, lwd=2) lines(sfit3[,2], mark.time=FALSE, xmax=48, fun='event', col=1:2, lty=2, lwd=2) xtime <- c(0, 6, 12, 24, 36, 48) axis(1, xtime, xtime) #marks every year rather than 10 months temp <- outer(c("A", "B"), c("death", "transplant", "CR"), paste) temp[7] <- "" legend(25, .3, temp[c(1,2,7,3,4,7,5,6,7)], lty=c(1,1,1, 2,2,2 ,3,3,3), col=c(1,2,0), bty='n', lwd=2) abline(v=2, lty=2, col=3) # add the state space diagrams par(mar=c(4,.1,1,1)) crisk(c("Entry","Death", "CR"), alty=3) crisk(c("Entry","Death", "Tx"), alty=2) crisk(c("Entry","Death")) par(oldpar) ################################################### ### code chunk number 9: badfit ################################################### getOption("SweaveHooks")[["fig"]]() badfit <- survfit(Surv(txtime, txstat=="transplant") ~ trt, data1) layout(matrix(c(1,1,1,2,3,4), 3,2), widths=2:1) oldpar <- par(mar=c(5.1, 4.1, 1.1, .1)) plot(badfit, fun="event", xmax=48, xaxt='n', col=1:2, lty=2, lwd=2, xlab="Months from enrollment", ylab="P(state)") axis(1, xtime, xtime) lines(sfit3[,2], fun='event', xmax=48, col=1:2, lwd=2) legend(24, .3, c("Arm A", "Arm B"), lty=1, lwd=2, col=1:2, bty='n', cex=1.2) par(mar=c(4,.1,1,1)) crisk(c("Entry", "transplant"), alty=2, cex=1.2) crisk(c("Entry","transplant", "Death"), cex=1.2) par(oldpar) ################################################### ### code chunk number 10: >= options(width=60, continue=" ") makefig <- function(file, top=1, right=1, left=4) { pdf(file, width=9.5, height=7, pointsize=18) par(mar=c(4, left, top, right) +.1) } library(survival) @ \section{Introduction} This vignette covers 3 different but interrelated concepts: \begin{itemize} \item An introduction to time dependent covariates, along with some of the most common mistakes. \item Tools for creating time-dependent covariates, or rather the data sets used to encode them. \item Time dependent coefficients. \end{itemize} \section{Time dependent covariates} One of the strengths of the Cox model is its ability to encompass covariates that change over time. The practical reason that time-dependent covariates work is based on the underlying way in which the Cox model works: at each event time the program compares the current covariate values of the subject who had the event to the current values of all others who were at risk at that time. One can think of it as a lottery model, where at each death time there is a drawing to decide which subject ``wins'' the event. Each subject's risk score $\exp(X\beta)$ determines how likely they are to win, e.g., how many ``tickets'' they have purchased for the drawing. The model tries to assign a risk score to each subject that best predicts the outcome of each drawing based on \begin{itemize} \item The risk set: which subjects are present for each event; the set of those able to ``win the prize''. \item The covariate values of each subject just prior to the event time. \end{itemize} The model has a theoretical foundation in martingale theory, a mathematical construct which arose out of the study of games of chance. A key underlying condition for a martingale like game is that present actions depend only on the past. The decision of whether to play (is one in the risk set or not) and the size of a bet (covariates) can depend in any way on prior bets and patterns of won/lost, but cannot look into the future. If this holds then multiple properties can be proven about the resulting process. A simple way to code time-dependent covariates uses intervals of time. Consider a subject with follow-up from time 0 to death at 185 days, and assume that we have a time dependent covariate (creatinine) that was measured at day 0, 90 and 120 with values of .9, 1.5, and 1.2 mg/dl. A way to encode that data for the computer is to break the subject's time into 3 time intervals 0-90, 90-120, 120-185, with one row of data for each interval. The data might look like the following <>= tdata <- data.frame(subject=c(5,5,5), time1=c(0,90, 120), time2 = c(90, 120, 185), death=c(0,0,1), creatinine=c(0.9, 1.5, 1.2)) tdata @ We read this as stating that over the interval from 0 to 90 the creatinine for subject ``5'' was 0.9 (last known level), and that this interval did not end in a death. The underlying code treats intervals as open on the left and closed on the right, e.g. the creatinine on exactly day 90 is 0.9. One way to think of this is that all changes for a given day (covariates or status) are recorded at the end of the day. The key rule for time dependent covariates in a Cox model is simple and essentially the same as that for gambling: \emph{you cannot look into the future}. A covariate may change in any way based on past data or outcomes, but it may not reach forward in time. In the above simple data set this means that we cannot add a linear interpolation between the creatinine values 0.9 and 1.5 to get a predicted value of 1.1 on day 100; on day 100 the later value of 1.5 has not yet been seen. A an example consider a recent analysis from the Mayo Clinic study of aging (MCSA), a study which enrolled a stratified random sample from the population of Olmsted County and then has followed them forward in time. The occurrence of mild cognitive impairment (MCI), dementia, and death are all of interest. The paper starts out with a table comparing baseline covariates for those who never progress to MCI versus those who ever did, there is also a table of baseline covariates versus survival. Both of these are fine: if you think in terms of an R formula they could be written with future outcomes on the left hand side of the formula and past information on the right. A table that compared the survival of those who did or did not progress to MCI, however, would be invalid. It corresponds to a model with a future occurrence on both sides of the equation. One of the more well known examples of this error is analysis by treatment response: at the end of a trial a survival curve is made comparing those who had an early response to treatment (shrinkage of tumor, lowering of cholesterol, or whatever) to those who did not, and it discovered that responders have a better curve. A Cox model fit to the same data will demonstrate a strong ``significant'' effect. The problem arises because any early deaths, those that occur before response can be assessed, will all be assigned to the non-responder group, even deaths that have nothing to do with the condition under study. Below is a simple example based on the advanced lung cancer data set. Assume that subjects came in monthly for 12 cycles of treatment, and randomly declare a ``response'' for 5\% of the subjects at each visit. <>= set.seed(1953) # a good year nvisit <- floor(pmin(lung$time/30.5, 12)) response <- rbinom(nrow(lung), nvisit, .05) > 0 badfit <- survfit(Surv(time/365.25, status) ~ response, data=lung) plot(badfit, mark.time=FALSE, lty=1:2, xlab="Years post diagnosis", ylab="Survival") legend(1.5, .85, c("Responders", "Non-responders"), lty=2:1, bty='n') @ What is most surprising about this error is the \emph{size} of the false effect that is produced. A Cox model using the above data reports a hazard ratio of 1.9 fold with a p-value of less than 1 in 1000. The alarm about this incorrect approach has been sounded often \cite{Anderson83, Buyse96, Suissa08} but the analysis is routinely re-discovered. A slightly subtler form of the error is discussed in Redmond et al \cite{Redmond83}. The exploration was motivated by a flawed analysis presented in Bonadonna et. al \cite{Bref} which looked at the effect of total dose. breast cancer chemotherapy patients were divided into three groups based on whether the patient eventually received $>85$\%, 65--85\% or $<65$\% of the dose planned at the start of their treatment. Per the above, this approach leads to a severe bias since early deaths do not finish all their cycles of chemotherapy and hence by definition get a lower dose. A proportional hazards model using total dose received shows a very strong effect for dose, so much so that it could encourage a treating physician to defer necessary dose reductions in response to treatment toxicity. Redmond looked at a variant of this: create a variable $p$ for each subject which is the fraction of the target dose \emph{up to} the last entry for that subject. A subject who died after recieving only 6 weeks of a planned 12 week regimen could still score 100\%. This looks like it should cure the bias issue, but as it turns out it leads to bias in the other direction. The reason is that dose reductions due to toxicity occur more often in the later cycles of treatment, and thus living longer leads to smaller values of $p$. A proportional hazards regression fit to $p$ implies that a smaller dose is protective! The proper approach is to code the predictor as a time-dependent covariate. For treatment response this will be a variable that starts at 0 for all subjects and is recoded to 1 only when the response occurs. For dose it would measure cumulative dose to date. There are many variations on the error: interpolation of the values of a laboratory test linearly between observation times, removing subjects who do not finish the treatment plan, imputing the date of an adverse event as midway between observation times, etc. Using future data will often generate large positive or negative bias in the coefficients, but sometimes it generates little bias at all. It is nearly impossible to predict a priori which of these will occur in any given data set. Using such a covariate is similar to jogging across a Los Angeles freeway: disaster is not guaranteed --- but it is likely. The most common way to encode time-dependent covariates is to use the (start, stop] form of the model. <>= fit <- coxph(Surv(time1, time2, status) ~ age + creatinine, data=mydata) @ In data set \code{mydata} a patient might have the following observations \begin{center} \begin{tabular}{ccccccc} subject & time1 & time2 & status & age & creatinine & \ldots \\ \hline 1 & 0 & 15 & 0 & 25 & 1.3 \\ 1 & 15& 46 & 0 & 25 & 1.5 \\ 1 & 46& 73 & 0 & 25 & 1.4 \\ 1 & 73& 100& 1 & 25 & 1.6 \\ \end{tabular} \end{center} In this case the variable \code{age} = age at entry to the study stays the same from line to line, while the value of creatinine varies and is treated as 1.3 over the interval $(0, 15]$, 1.5 over $(15, 46]$, etc. The intervals are open on the left and closed on the right, which means that the creatinine is taken to be 1.3 on day 15. The status variable describes whether or not each interval ends in an event. One common question with this data setup is whether we need to worry about correlated data, since a given subject has multiple observations. The answer is no, we do not. The reason is that this representation is simply a programming trick. The likelihood equations at any time point use only one copy of any subject, the program picks out the correct row of data at each time. There two exceptions to this rule: \begin{itemize} \item When subjects have multiple events, then the rows for the events are correlated within subject and a cluster variance is needed. \item When a subject appears in overlapping intervals. This however is almost always a data error, since it corresponds to two copies of the subject being present in the same strata at the same time, e.g., she could meet herself at a party. \end{itemize} A subject can be at risk in multiple strata at the same time, however. This corresponds to being simultaneously at risk for two distinct outcomes. \section{Building time-dependent sets with tmerge} \subsection{The function} A useful function for building data sets is \code{tmerge}, which is part of the survival library. The idea is to build up a time dependent data set one endpoint at at time. The primary arguments are \begin{itemize} \item data1: the base data set that will be added onto \item data2: the source for new information \item id: the subject identifier in the new data \item \ldots: additional arguments that add variables to the data set \item tstart, tstop: used to set the time range for each subject \item options \end{itemize} The created data set has three new variables (at least), which are \code{id}, \code{tstart} and \code{tstop}. The key part of the call are the ``\ldots'' arguments which each can be one of four types: tdc() and cumtdc() add a time dependent variable, event() and cumevent() add a new endpoint. In the survival routines time intervals are open on the left and closed on the right, i.e., (tstart, tstop]. Time dependent covariates apply from the start of an interval and events occur at the end of an interval. If a data set already had intervals of (0,10] and (10, 14] a new time dependent covariate or event at time 8 would lead to three intervals of (0,8], (8,10], and (10,14]; the new time-dependent covariate value would be added to the second interval, a new event would be added to the first one. The basic form of the function is <>= newdata <- tmerge(data1, data2, id, newvar=tdc(time, value), ...) @ Where \code{data1} is the starting data set and additions to the data are taken from \code{data2}. The idea behind the function is that each addition will be ``slipped in'' to the original data in the same way that one would slide a new card into an existing deck of cards. It is a complex function, and we illustrate it below with a set of examples that sequentially reveal its features. \subsection{CGD data set} Chronic granulomatous disease (CGD) is a heterogeneous group of uncommon inherited disorders characterized by recurrent pyogenic infections that usually begin early in life and may lead to death in childhood. In 1986, Genentech, Inc. conducted a randomized, double-blind, placebo-controlled trial in 128 CGD patients who received Genentech's humanized interferon gamma (rIFN-g) or placebo three %' times daily for a year. Data were collected on all serious infections until the end of followup, which occurred before day 400 for most patients. One patient was taken off on the day of his last infection; all others have some followup after their last episode. Below are the first 10 observations, see the help page for \texttt{cgd0} for the full list of variable names. The last few columns contain the duration of follow-up for the subject followed by infection times. Subject 1 was followed for 414 days and had infections on days 219 and 373, subject 2 had 7 infections and subject 3 had none. \small \begin{verbatim} 1 204 082888 1 2 12 147.0 62.0 2 2 2 2 414 219 373 2 204 082888 0 1 15 159.0 47.5 2 2 1 2 439 8 26 152 241 249 322 350 3 204 082988 1 1 19 171.0 72.7 1 2 1 2 382 4 204 091388 1 1 12 142.0 34.0 1 2 1 2 388 5 238 092888 0 1 17 162.5 52.7 1 2 1 1 383 246 253 6 245 093088 1 2 44 153.3 45.0 2 2 2 2 364 7 245 093088 0 1 22 175.0 59.7 1 2 1 2 364 292 8 245 093088 1 1 7 111.0 17.4 1 2 1 2 363 9 238 100488 0 1 27 176.0 82.8 2 2 1 1 349 294 10 238 100488 1 1 5 113.0 19.5 1 2 1 1 371 \end{verbatim} \normalsize The data set is included as \code{cgd0} in the survival library. Here is the R printout of the first four subjects. <<>>= cgd0[1:4,] @ We want to turn this into a data set that has survival in a counting process form. \begin{itemize} \item Each row of the resulting data set represents a time interval (time1, time2] which is open on the left and closed on the right. Covariate values for that row are the covariate values that apply over that interval. \item The event variable for each row $i$ is 1 if the time interval ends with an event and 0 otherwise. \end{itemize} We don't need variables etime1--etime7 in the final data set, so they are left out of the data1 argument in the first call. <>= dim(cgd0) newcgd <- tmerge(data1=cgd0[, 1:13], data2=cgd0, id=id, tstop=futime) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime1)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime2)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime3)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime4)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime5)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime6)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime7)) newcgd <- tmerge(newcgd, newcgd, id, enum=cumtdc(tstart)) dim(newcgd) newcgd[1:5,c(1, 4:6, 13:17)] attr(newcgd, "tcount") coxph(Surv(tstart, tstop, infect) ~ treat + inherit + steroids + + cluster(id), newcgd) @ These lines show the canonical way to use tmerge: each call adds one more bit of information to the data set. \begin{itemize} \item The first call sets the \emph{time range} for each subject to be from 0 (default) to last follow-up. If a later call tried to add an event outside that range, at time = -2 say, that addition would be ignored. The range can be set explicitly by using the tstop and (optional) tstart arguments, or implicitly as will be done in the heart transplant example below. This first result has \Sexpr{nrow(cgd0)} rows, the same number as \code{cgd0}. \item Each additional call then adds either an endpoint or a covariate, splitting individual rows of the input in two as necessary. An \code{event} or \code{cumevent} directive adds events, while a \code{tdc} or \code{cumtdc} one adds a time dependent covariate. Events happen at the ends of intervals and time-dependent covariates change at the start of an interval. \item Additions from \code{data2} with a missing time value are ignored. \item The result of \code{tmerge} is a data frame with a few extra attributes. One of these, tcount, is designed to help visualize the process and was printed out after the last step above. Assume that a subject already had 3 intervals of (2,5), (5,10) and (14,40). A new event added at time 1 would be ``early'' while one at time 50 is after any interval and would be recorded as ``late''. An event at time 3 is within an interval, one at 5 is on the border of two intervals, one at 14 is at the leading edge of an interval, one at time 10 in on the trailing edge and at time 11 is in a gap. In this data set all new additions fell strictly within prior intervals. We also see that etime6 and etime7 each added only a single event to the data. \item If two observations in data2 for a single person share exactly the same time, the created value will be the later contribution for tdc() or event() calls, cumtdc() and cumevent() will add. The ``tied'' column tells how often this happened; in some data sets this behavior might not be desired and one would need to break the ties before calling tmerge. \item The last tmerge call adds a simple time-dependent variable \code{enum} which is a running observation count for each subject. This can often be a useful variable in later models or processing, e.g. \code{enum==1} selects off the first row for each subject. \item The extra attributes of the data frame are ephemeral: they will be lost as soon as any further manipulation is done. This is intentional. \item One can verify that the resulting data set is equivalent to \code{cgd}, a (start, stop] version of the CGD data in the survival library which had been created by hand several years earlier. \end{itemize} The \code{tmerge} function processes arguments sequentially, and the above example can be rewritten as below. There is no computational advantage of one form versus the other. <>= test <- tmerge(cgd0[, 1:13], cgd0, id=id, tstop=futime, infect = event(etime1), infect= event(etime2), infect = event(etime3), infect= event(etime4), infect = event(etime5), infect= event(etime6), infect = event(etime7)) test <- tmerge(test, test, id= id, enum = cumtdc(tstart)) all.equal(newcgd, test) @ \subsection{Stanford heart transplant} The \code{jasa} data set contains information from the Stanford heart transplant study, in the form that it appeared in the paper of Crowley and Hu \cite{Crowley77}. The data set has one line per subject which contains the baseline covariates along with dates of enrollment, transplant, and death or last follow-up. We want to create \code{transplant} as a time dependent covariate. As is often the case with real data, this data set contains a few anomalies that need to be dealt with when setting up an analysis data set. \begin{enumerate} \item One subject died on the day of entry. However (0,0) is an illegal time interval for the \code{coxph} routine. It suffices to have them die on day 0.5. An alternative is to add 1 day to everyone's follow-up, e.g., subject 2 who enrolled on Jan 2 1968 and died on Jan 7 would be credited with 6 days. (This is what Kalbfleisch and Prentice do in their textbook.) The result of the final \code{coxph} call is the same from either strategy. \item A subject transplanted on day 10 is considered to have been on medical treatment for days 1--10 and as transplanted starting on day 11. That is, except for patient 38 who died on the same day as their procedure. They should be treated as a transplant death; the problem is resolved by moving this transplant back .5 day. \item The treatment coefficients in table 6.1 of the definitive analysis found in Kalbfleisch and Prentice \cite{Kalbfleisch02} will only be obtained if covariates are defined in precisely the same way, since their models include interactions. (Table 5.2 in the original edition of the book). For age this is (age in days)/ 365.25 - 48 years, and for year of enrollment it is the number of years since the start of the study: (entry date - 1967/10/1)/365.25. (Until I figured this out I would get occasional ``why is coxph giving the wrong answers'' emails.) \end{enumerate} Since time is in days the fractional time of 0.5 could be any value between 0 and 1, our choice will not affect the results. <>= jasa$subject <- 1:nrow(jasa) #we need an identifier variable tdata <- with(jasa, data.frame(subject = subject, futime= pmax(.5, fu.date - accept.dt), txtime= ifelse(tx.date== fu.date, (tx.date -accept.dt) -.5, (tx.date - accept.dt)), fustat = fustat )) sdata <- tmerge(jasa, tdata, id=subject, death = event(futime, fustat), trt = tdc(txtime), options= list(idname="subject")) attr(sdata, "tcount") sdata$age <- sdata$age -48 sdata$year <- as.numeric(sdata$accept.dt - as.Date("1967-10-01"))/365.25 # model 6 of the table in K&P coxph(Surv(tstart, tstop, death) ~ age*trt + surgery + year, data= sdata, ties="breslow") @ This example shows a special case for the \code{tmerge} function that is quite common: if the first created variable is an event then the time range for each subject is inferred to be from 0 to the event time: explicit \code{tstop} and \code{tstart} arguments are not required. It also makes use of a two argument form of \code{event}. Each of the \code{event}, \code{cumevent}, \code{tdc} and \code{cumtdc} functions may have a second argument, which if present will be used as the value for the event code or time dependent covariate. If this second argument is not present a value of 1 is used. If a created variable is not already in data1, the starting value \emph{before} the first definition of that variable is a NA for a \code{tdc} or \code{cumtdc} call that has two arguments and 0 in all other cases. If the variable being created is already a part of data1, then our updates make changes to that variable. Be careful of this. This feature is what allowed for the \code{infection} indicator to be build up incrementally in the cgd example above, but quite surprising results can occur when you think a new variable is being created de novo but its name is already in use. For example, if we name the new variable `transplant' in the third line of \code{sdata} above it collides with an existing variable in the \code{jasa} data set; the result is to not create a time-dependent transplant variable at all. (The author made this mistake himself when creating this vignette, and then spent several hours searching the tmerge code for an error that wasn't there.) The \code{tcount} table for the above fit shows all the deaths at the trailing edge of their interval, which is expected since the time of death or last follow-up was used to define each subject's interval of risk. Two of the transplants happened on day 0 and are listed as occurring on the leading edge of the first follow-up interval for the subject. The other 67 transplants were strictly within the (0, last follow up) interval of each subject. \subsection{PBC data} The \code{pbc} data set contains baseline data and follow-up status for a set of subjects with primary biliary cirrhosis, while the \code{pbcseq} data set contains repeated laboratory values for those subjects. The first data set contains data on 312 subjects in a clinical trial plus 106 that agreed to be followed off protocol, the second data set has data only on the trial subjects. <>= temp <- subset(pbc, id <= 312, select=c(id:sex, stage)) # baseline pbc2 <- tmerge(temp, temp, id=id, death = event(time, status)) #set range pbc2 <- tmerge(pbc2, pbcseq, id=id, ascites = tdc(day, ascites), bili = tdc(day, bili), albumin = tdc(day, albumin), protime = tdc(day, protime), alk.phos = tdc(day, alk.phos)) fit1 <- coxph(Surv(time, status==2) ~ log(bili) + log(protime), pbc) fit2 <- coxph(Surv(tstart, tstop, death==2) ~ log(bili) + log(protime), pbc2) rbind('baseline fit' = coef(fit1), 'time dependent' = coef(fit2)) @ We start the build with a baseline data set that has a subset of the variables. This is due to my own frugality --- I happen to like data sets that are more trim. It is not a requirement of the tmerge function, however, and a user is certainly free to skip the first step above and build \code{pbc2} directly from data set \code{pbc}. The coefficients of bilirubin and prothrombin time are somewhat larger in the time-dependent analysis than the fit using only baseline values. In this autoimmune disease there is steady progression of liver damage, accompanied by a steady rise in these two markers of dysfunction. The baseline analysis captures patients' disease status at the start, the time-dependent analysis is able to account for those who progress more quickly. In the pbc data set the status variable is 0= censored, 1= liver transplant and 2= death; the above analyses were models of time to death, censoring at transplant. (At the time of the PBC study liver transplantation was still in its infancy and it is fair to view the 19/312 subjects who received the procedure as a random sample. In the modern era there are far more waiting recipients than organs and available livers are directed to those patients who illness is most dire; censoring at transplant would not lead to an interpretable result.) By default \code{tmerge} ignores any updates from \code{data2} that have a missing value for either the time or the value. In the pbcseq data set there are several observations with a missing alkaline phosphotase value. A consequence of this behavior is that the pbc2 data set effectively uses ``last value carried forward'' values for alk.phos, replacing those missing values. Subject 6 for instance has a total follow-up of 2503, and alk.phos values of 682 and NA on days 1492 and 2453, respectively; in the final data set it is coded 682 from day 1492 until last follow up. One can change this default by adding \code{options=list(na.rm=FALSE)} to the second call above, in which case the alkaline phosphotase value over the interval (2453, 2503] will become missing. Any \code{tdc} calls with a missing time are still ignored, independent of the na.rm value, since we would not know where to insert them. <<>>= attr(pbc2, "tcount") @ <>= #grab a couple of numbers for the paragraph below atemp <- attr(pbc2, "tcount")[2:3,] @ The tcount results are interesting. For the first addition of ascites we have \Sexpr{atemp[1, 'leading']} observations on a leading edge of follow up, which is all of the baseline lab values at time 0, and \Sexpr{atemp[1, 'within']} further additions within the subjects' follow-up interval. The latter cause a new break point to be added at each of these intermediate laboratory dates, for subsequent additions these \Sexpr{atemp[1, 'within']} times lie on a boundary of two intervals. Another \Sexpr{atemp[1, 'late']} non-missing alkaline phosphotase values occurred after the last follow-up date of the pbc data set and are ignored. Bilirubin is missing on no subjects, so it's addition creates a few more unique break points in the follow-up, namely those clinical visits for which the ascites value was missing. The data for the pbcseq data set was assembled at a later calendar time than the primary data set. Since having lab test results is a certain marker that the patient is still alive, would a better analysis have used this test information to extend the last follow-up date for these \Sexpr{atemp[2,'late']} ``late'' subjects with a later laboratory date? Not necessarily. Odd things happen in survival analysis when risk sets are extended piecemeal. A basic tenet of the Cox model is that if someone is marked as being ``at risk'' over some interval $(s, t)$, this means that ``if they had had an event over that interval, we would have recorded it.'' Say someone ended their initial follow-up time at 3000 days and then had a lab test at 3350 days (subjects returned about once a year). If we only extend the time of those who had a test, then saying that this subject was at risk during the interval (3000, 3350) is false: if they had died in that interval, they would not have had the lab test and would not obtained the extension, nor would their death have been updated in the original \code{pbc} data set. The cutoff rule of \code{tmerge} is purposefully conservative to avoid creating such anomalies. In the case of the PBC data set this author happens to know that active follow-up \emph{was} continued for all subjects, both those that did and did not return for further laboratory tests. This updated follow-up information is included in the pbcseq data and could have been used to set a wider time range. Such is not always the case, however. Automatic additions to a data set via electronic systems can be particularly troublesome. One case from the author's experience involved a study of patient outcomes after organ transplant. Cases were actively followed up for 3 years, at which time priorities shifted and the clerical staff responsible for the active follow-up were reassigned. Automatic updates from a state death index continued to accumulate, however. A Kaplan-Meier curve computed at 5 years showed the remarkable result of a 3 year survival of .9 followed by a precipitous drop to 0 at 5 years! This is because there was, by definition, 100\% mortality in all those subjects with more than 3 years of supposed follow-up. \subsection{Time delay and other options} The \code{options} argument to the tmerge routine is a list with one or more of the following five elements, listed below along with their default values. \begin{itemize} \item idname = 'id' \item tstartname = 'tstart' \item tstopname = 'tstop' \item na.rm = TRUE \item delay = 0 \end{itemize} The first three of these are the variable names that will be used for the identifier, start, and stop variables which are added to the output data set. They only need to be specified one time within a series of tmerge calls in order to effect a change. The na.rm option has been discussed above; it affects tdc() and cumtdc() directives within a single tmerge call. The delay option causes any tdc or cumtdc action in the tmerge call to be delayed by a fixed amount. The final two tmerge calls below are \emph{almost} identical in their action: <>= temp <- subset(pbc, id <= 312, select=c(id:sex, stage)) pbc2 <- tmerge(temp, temp, id=id, death = event(time, status)) pbc2a <- tmerge(pbc2, pbcseq, id=id, ascites = tdc(day, ascites), bili = tdc(day, bili), options= list(delay=14)) pbc2b <- tmerge(pbc2, pbcseq, id=id, ascites = tdc(day+14, ascites), bili = tdc(day+14, bili)) @ The difference between \code{pbc2a} and \code{pbc2b} is that the first call does not defer baseline values for each subject, i.e., any value with a time that is on or before the the subject's first time point, as that will introduce intervals with a missing value into the result. The more important question is \emph{why} one would wish to delay or lag a time dependent covariate. One reason is to check for cases of reverse causality. It is sometimes the case that a covariate measured soon before death is not a predictor of death but rather is simply a marker for an event that is already in progress. A simple example would the the time dependent covariate ``have called the family for a final visit''. A less obvious one from the author's experience occurs when a clinical visit spans more than one day, the endpoint is progression, and one or more laboratory results that were used to define ``progression'' get recorded in the data set 1-2 days before the progression event. (They were perhaps pulled automatically from a laboratory information system). One then ends up with the tautology of a test value predicting its own result. Even more subtle biases can occur via coding errors. For any data set containing constructed time-dependent covariates, it has become the author's practice to re-run the analyses after adding a 7-14 day lag to key variables. When the results show a substantial change, and this is not infrequent, understanding why this occurred is an critical step. Even if there is not an actual error, one has to question the value of a covariate that can predict death within the next week but fails for a longer horizon. \subsection{Cumulative events} The action of the \code{cumevent} operator is different than \code{cumtdc} in several ways. Say that we have a subject with outcomes of one type at times 5, 10, and 15 and another type at times 6 and 15, with a follow-up interval of 0 to 20. For illustration I'll call the first event 'asthma' and the second 'IBD' (a disease flare in inflammatory bowel disease). A resulting data set would have the following form: \begin{center} \begin{tabular}{rcccc} &\multicolumn{2}{c}{cumtdc} & \multicolumn{2}{c}{cumevent} \\ interval & asthma & IBD & asthma & IBD \\ \hline (0, 5] & 0 &0 & 1 & 0 \\ (5, 6] & 1 &0 & 0 & 1 \\ (6, 10]& 1 &1 & 2 & 0 \\ (10, 15] & 2& 1& 3 & 2 \\ (15, 20] & 3& 2& 0 & 0 \end{tabular} \end{center} Events happen at the ends of an interval and time-dependent covariates change the following intervals. More importantly, time-dependent covariates persist while events do not, a \code{cumevent} action simply changes the label attached to an event. \subsubsection{REP} The motivating case for \code{tmerge} came from a particular problem: the Rochester Epidemiology Project has tracked all subjects living in Olmsted County, Minnesota, from 1965 to the present. For an investigation of cumulative comorbidity we had three data sets \begin{itemize} \item base: demographic data such as sex and birth date \item timeline: one or more rows for each subject containing age intervals during which they were a resident of the county. The important variables are id, age1 and age2; each (age1, age2) pair marks an interval of residence. Disjoint intervals are not uncommon. \item outcome: one row for the first occurrence of each outcome of interest. The outcomes were 20 comorbid conditions as defined by a particular research initiative from the National Institutes of Health. \end{itemize} The structure for building the data is shown below. (The data for this example unfortunately cannot be included with the survival library so the code is shown but not executed.) <>= newd <- tmerge(data1=base, data2=timeline, id=repid, tstart=age1, tstop=age2, options(id="repid")) newd <- tmerge(newd, outcome, id=repid, mcount = cumtdc(age)) newd <- tmerge(newd, subset(outcome, event='diabetes'), diabetes= tdc(age)) newd <- tmerge(newd, subset(outcome, event='arthritis'), arthritis= tdc(age)) @ The first call to tmerge adds the time line for each observation to the baseline data. For this first call both data1 and data2 must contain a copy of the id variable (here \code{repid}), and data1 is constrained to have only a single line for each id value. (Subjects have a single baseline.) Each subsequent call adds a new variable to the data set. The second line creates a covariate which is a cumulative count of the number of comorbidities thus far for each subject. The third line creates a time dependent covariate (tdc) which will be 0 until the age of diabetes and is 1 thereafter, the fourth line creates a time dependent variable for the presence of arthritis. Time dependent covariates that occur before the start of a subject's follow-up interval or during a gap in time do not generate a new time point, but they do set the value of that covariate for future times. Events that occur in a gap are not counted. The rationale is that during a subject's time within the county we would like the variable ``prior diagnosis of diabetes'' to be accurate, even if that diagnosis occurred during a prior period when the subject was not a resident. For events outside of the time line, we have no way to know who the appropriate comparison group is, and so must ignore those events. (Formally, the risk set would be the set of all non-residents who, if they were to have had an event at the same age, we would find out about it because they will later move to the county, have a medical encounter here, and have that event written into the ``prior conditions'' section of their medical record.) \section{Time dependent coefficients} Time dependent covariates and time dependent coefficients are two different extensions of a Cox model, as shown in the two equations below. \begin{align} \lambda(t) &= \lambda_0(t) e^{\beta X(t)} \label{tdcovar} \\ \lambda(t) &= \lambda_0(t) e^{\beta(t) X} \label{tdbeta} \end{align} Equation \eqref{tdcovar} is a time dependent covariate, a commonly used and well understood usage. Equation \eqref{tdbeta} has a time dependent coefficient. These models are much less common, but represent one way to deal with non-proportional hazards -- the proportional hazard assumption is precisely that the coefficient does not change over time: $\beta(t) = c$. The \code{cox.zph} function will plot an estimate of $\beta(t)$ for a study and is used to diagnose and understand non-proportional hazards. Here for example is a test case using the veterans cancer data. <>= options(show.signif.stars = FALSE) # display user intelligence vfit <- coxph(Surv(time, status) ~ trt + prior + karno, veteran) vfit quantile(veteran$karno) zp <- cox.zph(vfit, transform= function(time) log(time +20)) zp plot(zp[3]) # a plot for the 3rd variable in the fit abline(0,0, col=2) abline(h= vfit$coef[3], col=3, lwd=2, lty=2) @ Karnofsky score is a very important predictor, but its effect is not constant over time as shown by both the test and the plot. Early on it has a large negative effect: the risk of someone at the first quartile is approximately exp(35*.03377) = 3.2 fold times that of someone at the third quartile, but by 200 days this has waned and is not much different from zero. One explanation is that, in this very acute illness, any measure that is over 6 months old is no longer relevant. The proportional hazards model estimates an average hazard over time, the value of which is shown by the dashed horizontal line. The use of an average hazard is often reasonable, the proportional hazards assumption is after all never precisely true. In this case, however, the departure is quite large and a time dependent coefficient is a more useful summary of the actual state. The cox.zph plot is excellent for diagnosis but does not, however, produce a formal fit of $\beta(t)$. What if we want to fit the model? \subsection{Step functions} One of the simplest extensions is a step function for $\beta(t)$, i.e., different coefficients over different time intervals. An easy way to do this is to use the \code{survSplit} function to break the data set into time dependent parts. We will arbitrarily divide the veteran's data into 3 epochs of the first 3 months, 3-6 months, and greater than 6 months. <>= vet2 <- survSplit(Surv(time, status) ~ ., data= veteran, cut=c(90, 180), episode= "tgroup", id="id") vet2[1:7, c("id", "tstart", "time", "status", "tgroup", "age", "karno")] @ The first subject died at 72 days, his data is unchanged. The second and third subjects contribute time to each of the three intervals. <>= vfit2 <- coxph(Surv(tstart, time, status) ~ trt + prior + karno:strata(tgroup), data=vet2) vfit2 cox.zph(vfit2) @ A fit to the revised data shows that the effect of baseline Karnofsky score is essentially limited to the first two months. The \code{cox.zph} function shows no further time dependent effect of Karnofsky score. This last is of course no surprise, since we used the original graph to pick the cut points. A ``test'' that the coefficients for the three intervals are different will be biased by this sequential process and should be viewed with caution. Survival curves post fit require a little more care. The default curve uses the mean covariate values, which is always problematic and completely useless in this case. Look at the set of saved means for the model: <>= vfit2$means @ The default curve will be for someone on treatment arm \Sexpr{round(vfit2$means[1], 2)}, %$ which applies to no one, and a single set of ``blended'' values of the Karnofsky score, each times the three Karnofsky coefficients. This is easily rectified by creating a new data set with time intervals. <>= quantile(veteran$karno) cdata <- data.frame(tstart= rep(c(0,30,60), 2), time = rep(c(30,60, 100), 2), status= rep(0,6), #necessary, but ignored tgroup= rep(1:3, 2), trt = rep(1,6), prior= rep(0,6), karno= rep(c(40, 75), each=3), curve= rep(1:2, each=3)) cdata sfit <- survfit(vfit2, newdata=cdata, id=curve) km <- survfit(Surv(time, status) ~ I(karno>60), veteran) plot(km, xmax=120, col=1:2, lwd=2, xlab="Days from enrollment", ylab="Survival") lines(sfit, col=1:2, lty=2, lwd=2) @ In the new data set the \code{tgroup} variable correctly tracks time intervals. The default behavior for survival curves based on a coxph model is to create one curve for each line in the input data; the \code{id} option causes it to use a set of lines for each curve. Karnofsky scores at the 25th and 75th percentiles roughly represent the average score for the lower half of the subjects and that for the upper half, respectively, and are plotted over the top of the Kaplan-Meier curves for those below and above the median. At 30 days the Cox model curves essentially become parallel. \subsection{Continuous time-dependent coefficients} If $\beta(t)$ is assumed to have a simple functional form we can fool an ordinary Cox model program in to doing the fit. The particular form $\beta(t) = a + b\log(t)$ has for instance often been assumed. Then $\beta(t) x = ax + b \log(t) x = ax + b z$ for the special time dependent covariate $z = \log(t) x$. The time scale for the \code{cox.zph} plot used further above of $\log(t + 20)$ was chosen to make the first 200 days of the plot roughly linear. Per the figure this simple linear model does not fit over the entire range, but we will forge ahead and use it as an example anyway. (After all, most who fit the log(t) form have not bothered to even look at a plot.) An obvious but incorrect approach is <>= vfit3 <- coxph(Surv(time, status) ~ trt + prior + karno + I(karno * log(time + 20)), data=veteran) @ This mistake has been made often enough the the \code{coxph} routine has been updated to print an error message for such attempts. The issue is that the above code does not actually create a time dependent covariate, rather it creates a time-static value for each subject based on their value for the covariate \code{time}; no differently than if we had constructed the variable outside of a \code{coxph} call. This variable most definitely breaks the rule about not looking into the future, and one would quickly find the circularity: large values of \code{time} predict long survival, because long survival leads to large values for \code{time}. A true time-dependent covariate can be constructed using the \emph{time-transform} functionality of coxph. <>= vfit3 <- coxph(Surv(time, status) ~ trt + prior + karno + tt(karno), data=veteran, tt = function(x, t, ...) x * log(t+20)) vfit3 @ The time dependent coefficient is estimated to be $\beta(t) =$ \Sexpr{round(coef(vfit3)[3], 3)} + \Sexpr{round(coef(vfit3)[4], 3)} * log(t + 20). We can add said line to the \code{cox.zph} plot. Not surprisingly, the result is rather too high for time $>$ 200 and underestimates the initial slope. Still the fit is better than a horizontal line, as confirmed by the p-value for the slope term in \code{vfit3}. (The p-value for that term from cox.zph is nearly identical, as it must be, since the tests in cox.zph are for a linear effect on the chosen time scale.) <>= plot(zp[3]) abline(coef(vfit3)[3:4], col=2) @ This same coding dichotomy exists in SAS phreg, by the way. Adding \code{time} to the right hand side of the model statement will create the time-fixed (incorrect) variable, while a programming statement within phreg that uses \code{time} as a variable will generate time-dependent objects. The error is less likely there because phreg's model statement has no equivalent to the \code{I()} function, i.e., you cannot simply write ``log(time)'' on the right hand side. \section{Predictable time-dependent covariates} Occasionally one has a time-dependent covariate whose values in the future are predictable. The most obvious of these is patient age, occasionally this may also be true for the cumulative dose of a drug. If age is entered as a linear term in the model, then the effect of changing age can be ignored in a Cox model, due to the structure of the partial likelihood. Assume that subject $i$ has an event at time $t_i$, with other subject $j \in R_i$ at risk at that time, with $a$ denoting age. The partial likelihood term is \begin{equation*} \frac{e^{\beta * a_i}}{\sum_{j \in R_i} e^{\beta* a_j}} = \frac{e^{\beta * (a_i + t_i)}}{\sum_{j \in R_i} e^{\beta* (a_j + t_i)}} \end{equation*} We see that using time-dependent age (the right hand version) or age at baseline (left hand), the partial likelihood term is identical since $\exp(\beta t_i)$ cancels out of the fraction. However, if the effect of age on risk is \emph{non-linear}, this cancellation does not occur. Since age changes continuously, we would in theory need a very large data set to completely capture the effect, an interval per day to match the usual resolution for death times. In practice this level of resolution is not necessary; though we all grow older, risk does not increase so rapidly that we need to know our age to the day! One method to create a time-changing covariate is to use the \emph{time-transform} feature of coxph. Below is an example using the pbc data set. The longest follow-up time in that data set is over 13 years, follow-up time is in days, and we might worry that the intermediate data set would be huge. The program only needs the value of the time dependent covariate(s) for each subject at the times of events, however, so the maximum number of rows in the intermediate data set is the number of subjects times the number of unique event times. <>= pfit1 <- coxph(Surv(time, status==2) ~ log(bili) + ascites + age, pbc) pfit2 <- coxph(Surv(time, status==2) ~ log(bili) + ascites + tt(age), data=pbc, tt=function(x, t, ...) { age <- x + t/365.25 cbind(age=age, age2= (age-50)^2, age3= (age-50)^3) }) pfit2 anova(pfit2) # anova(pfit1, pfit2) #this fails 2*(pfit2$loglik - pfit1$loglik)[2] @ Since initial age is in years and time is in days, it was important to scale within the pspline function. The likelihood ratio of 10.8 on 2 degrees of freedom shows that the additional terms are mildly significant. When there are one or more terms on the right hand side of the equation marked with the tt() operator, the program will pre-compute the values of that variable for each unique event time. A user-defined function is called with arguments of \begin{itemize} \item the covariate: whatever is inside the tt() call \item the event time \item the event number: if there are multiple strata and the same event time occurs in two of them, they can be treated separately \item the weight for the observation, if the call used weights \end{itemize} There is a single call to the function with a large $x$ vector, it contains an element for each subject at risk at each event time. If there are multiple tt() terms in the formula, then the tt argument should be a list of functions with the requisite number of elements. An alternate way to fit the above model is to create the expanded data set directly and then do an ordinary \code{coxph} call on the expanded data. The disadvantage of this is the very large data set, of course, but an advantage is that further processing of the model is available, such as residuals or survival curves. A reasonable strategy is to use \code{tt()} expressions for initial analysis and then expanded data sets to follow up on selected models. <>= dtimes <- sort(unique(with(pbc, time[status==2]))) tdata <- survSplit(Surv(time, status==2) ~., pbc, cut=dtimes) tdata$c.age <- tdata$age + tdata$time/365.25 -50 #current age, centered at 50 pfit3 <- coxph(Surv(tstart, time, event) ~ log(bili) + ascites + c.age + I(c.age^2) + I(c.age^3), data=tdata) rbind(coef(pfit2), coef(pfit3)) @ There are other interesting uses for the time-transform capability. One example is O'Brien's logit-rank test procedure \cite{obrien78}. He proposed replacing the covariate at each event time with a logit transform of its ranks. This removes the influence of any outliers in the predictor $x$. For this case we ignore the event time argument and concentrate on the groupings. <<>>= function(x, t, riskset, weights){ obrien <- function(x) { r <- rank(x) (r-.5)/(.5+length(r)-r) } unlist(tapply(x, riskset, obrien)) } @ This relies on the fact that the input arguments to tt() are ordered by the event number or risk set. This function is used as a default if no tt argument is present in the coxph call, but there are tt terms in the model formula. (Doing so allowed me to depreciate the survobrien function). Another interesting usage is to replace the data by simple ranks, not rescaled to 0--1. <<>>= function(x, t, riskset, weights) unlist(tapply(x, riskset, rank)) @ The score statistic for this model is $(C-D)/2$, where $C$ and $D$ are the number of concordant and discordant pairs, see the survConcordance function. The score statistic from this fit is then a test for significance of the concordance statistics, and is in fact the basis for the standard error reported by survConcordance. The O'Brien test can be viewed as concordance statistic that gives equal %' weight to each event time, whereas the standard concordance weights each event proportionally to the size of the risk set. (The Cox score statistic depends on the mean $x$ at each event time; since ranks go from 1 to number at risk the mean also scales.) Although handy, the computational impact of the tt argument should be considered before using it. The Cox model requires computation of a weighted mean and variance of the covariates at each event time, a process that is inherently $O(ndp^2)$ where $n$ = the sample size, $d$ = the number of events and $p$= the number of covariates. Much of the algorithmic effort in coxph() is to use updating methods for the mean and variance matrices, reducing the compute time to $O((n+d) p^2)$. When a tt term appears updating is not possible; for even moderate size data sets the impact of $nd$ versus $n+d$ can be surprising. The time-transform is a newer addition and still has some rough edges. At this moment the $x=TRUE$ argument is needed to get proper residuals and predicted values, and termplot is unable to properly reconstruct the data to plot a fit. Please communicate any concerns or interesting examples to the author. \begin{thebibliography}{9} \bibitem{Anderson83} Anderson JR, Cain KC, and Gelber RD. Analysis of survival by tumor response. J Clinical Oncology 1:710--719, 1983. \bibitem{Buyse96} M Buyse and P Piedbois. The relationship between response to treatment and survival time. Stat in Med 15:2797--2812, 1996. \bibitem{Crowley77} J Crowley and M Hu. Covariance analysis of heart transplant survival data. J American Statistical Assoc, 72:27--36, 1977. \bibitem{Gail72} M H Gail. Does cardiac transplantation prolong life? A reassessment. Annals Int Medicine 76:815-17, 1972. \bibitem{Kalbfleisch02} J Kalbfleisch and R Prentice. The statistical analysis of failure time data, second edition. Wiley, 2002. \bibitem{obrien78} O'Brien, Peter. A non-parametric test for association with censored data, Biometrics 34:243--250, 1978. \bibitem{Redmond83} Redmond C, Fisher B, Wieand HS. The methodologic dilemma in retrospectively correlating the amount of chemotherapy received in adjuvant therapy protocols with disease free survival: a commentary. Cancer Treatment Reports 67:519--526, 1983. \bibitem{Suissa08} S Suissa. Immortal time bias in pharmacoepidemiology. Am J Epi, 167:492-499, 2008. \end{thebibliography} \end{document} survival/inst/doc/splines.Rnw0000644000175100001440000003233513017617770016051 0ustar hornikusers\documentclass{article} \usepackage{amsmath} \usepackage{Sweave} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} \SweaveOpts{keep.source=TRUE, fig=FALSE} %\VignetteIndexEntry{Splines, plots, and interactions} % Ross Ihaka suggestions \DefineVerbatimEnvironment{Sinput}{Verbatim} {xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} \SweaveOpts{prefix.string=splines,width=6,height=4} \setkeys{Gin}{width=\textwidth} \newcommand{\code}[1]{\texttt{#1}} <>= options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text options(contrasts=c("contr.treatment", "contr.poly")) #reset default @ \title{Spline terms in a Cox model} \author{Terry Therneau} \begin{document} \maketitle This is a trio of topics that comes up just often enough in my work that I end up re-discovering how to do it correctly about once a year. A note showing how may be useful to others, it is certainly a useful reference for me. \section{Plotting smooth terms} Here is a simple example using the MGUS data. I prefer a simpler color palette than the default found in termplot. <>= require(survival) mfit <- coxph(Surv(futime, death) ~ sex + pspline(age, df=4), data=mgus) mfit termplot(mfit, term=2, se=TRUE, col.term=1, col.se=1) @ Note that the \code{term=2} option is passed directly from the \code{termplot} routine to a \code{predict(fit, type='terms')} call. For coxph models, the \code{predict} function allows terms to be specified either by position or name. Other routines, e.g. \code{gam}, respond only to a name. (This can be a bit of a pain since it must exactly match the \emph{printed} call in both spelling and spacing; and the printed spacing may not match what the user typed.) Three questions are whether the curve is significantly non-linear, how the curve is centered and whether we can easily plot it on the hazard as opposed to the log hazard scale. The first question is answered by the printout, the solution to the others is to use the plot=FALSE option of termplot, which returns the data points that would be plotted back to the user. <>= ptemp <- termplot(mfit, se=TRUE, plot=FALSE) attributes(ptemp) ptemp$age[1:4,] @ The termplot function depends on a call to predict with type='terms', which returns a centered set of predictions. Like a simple linear model fit, the intercept is a separate term, which is found in the ``constant'' attribute above, and each column of the result is centered so that the average predicted value is zero. Since any given $x$ value may appear multiple times in the data and thus in the result of predict, and the termplot function removes duplicates, the data returned by \code{termplot} may not be precisely centered at zero. Now suppose we want to redraw this on log scale with age 50 as the reference, i.e., the risk is 1 for a 50 year old. Since the Cox model is a relative hazards model we can choose whatever center we like. (If there were no one of exactly age 50 in the data set the first line below would need to do an interpolation, e.g. by using the approx function.) <>= ageterm <- ptemp$age # this will be a data frame center <- with(ageterm, y[x==50]) ytemp <- ageterm$y + outer(ageterm$se, c(0, -1.96, 1.96), '*') matplot(ageterm$x, exp(ytemp - center), log='y', type='l', lty=c(1,2,2), col=1, xlab="Age at diagnosis", ylab="Relative death rate") @ Voila! We now have a plot that is interpretable with respect to a fixed reference. The approach is appropriate for any term, not just psplines. The above plot uses log scale for the y axis which is appropriate for the question of whether a non-linear age effect was even necessary for this model (it is not), one could remove the log argument to emphasize the Gomperzian effect of age on mortality. \section{Monotone splines} Consider the following model using the \code{mgus2} data set. <>= fit <- coxph(Surv(futime, death) ~ age + pspline(hgb, 4), mgus2) fit termplot(fit, se=TRUE, term=2, col.term=1, col.se=1, xlab="Hemoglobin level") @ Low hemoglobin or anemia is a recognized marker of frailty in older age, so the rise in risk for low levels is not surprising. The rise on the right hand portion of the curve is less believable --- the normal range of HGB is 12-15.5 for women and 13.5 to 17.5 for men, why would we expect a rise there? A monotone fit that forces the curve to be horizontal from 14 onward fits well within the confidence bands, so we might want to force monotonicity. There are two tools for this within the pspline function. The first is to decrease the overall degrees of freedom and the second is to use \code{combine} option to force equality of selected coefficients. Start by decreasing the degrees of freedom. The pspline function automatically picks the number of basis (nterms) to be ``sufficiently large'' for the given degrees of freedom. We fix it at a single value for the rest of this example to better isolate the effects of degrees of freedom and of constraints. <>= termplot(fit, se=TRUE, col.term=1, col.se=1, term=2, xlab="Hemoglobin level", ylim=c(-.4, 1.3)) df <- c(3, 2.5, 2) for (i in 1:3) { tfit <- coxph(Surv(futime, death) ~ age + pspline(hgb, df[i], nterm=8), mgus2) temp <- termplot(tfit, se=FALSE, plot=FALSE, term=2) lines(temp$hgb$x, temp$hgb$y, col=i+1, lwd=2) } legend(14, 1, paste("df=", c(4, df)), lty=1, col=1:4, lwd=2) @ This has reduced, but not eliminated, the right hand rise at the expense of a less sharp transition at the value of 14. The \code{combine} option makes use of a property of the P-spline basis, which is that the curve will be monotone if and only if the coefficients are monotone. We can then use a pool adjacent violators algorithm to sequentially force equality for those coefficients which go the wrong way. Look at the coefficients for the fit with 2.5 degrees of freedom. <>= fit2a <- coxph(Surv(futime, death) ~ age + pspline(hgb, 2.5, nterm=8), mgus2) coef(fit2a) plot(1:10, coef(fit2a)[-1]) @ Now force the last 3 to be equal, then the last 4, and see how this changes the fit. <>= temp <- c(1:7, 8,8,8) fit2b <- coxph(Surv(futime, death) ~ age + pspline(hgb, 2.5, nterm=8, combine=temp), data= mgus2) temp2 <- c(1:6, 7,7,7,7) fit2c <- coxph(Surv(futime, death) ~ age + pspline(hgb, 2.5, nterm=8, combine=temp2), data= mgus2) matplot(1:10, cbind(coef(fit2a)[-1], coef(fit2b)[temp+1], coef(fit2c)[temp2+1]), type='b', pch='abc', xlab="Term", ylab="Pspline coef") @ We see that constraining the last four terms along with a degrees of freedom of is almost enough to force monotonicity; it may be sufficient if our goal is a simple plot for display. This dance between degrees of freedom, number of terms, and constraints has a component of artistry. When all three values become large the result will begin to approach a step function, reminiscent of non-parametric isotonic regression, whereas small values begin to approach a linear fit. The best compromise of smoothness and constraints will be problem specific. \section{Splines in an interaction} As an example we will use the effect of age on survival in the \texttt{flchain} data set, a population based sample of subjects from Olmsted County, Minnesota. If we look at a simple model using age and sex we see that both are very significant. <>= options(show.signif.stars=FALSE) # display intelligence fit1 <- coxph(Surv(futime, death) ~ sex + pspline(age, 3), data=flchain) fit1 termplot(fit1, term=2, se=TRUE, col.term=1, col.se=1, ylab="log hazard") @ We used a \code{pspline} term rather than \code{ns}, say, because the printout for a pspline nicely segregates the linear and non-linear age effects. The non-linearity is not very large, as compared to the linear portion, but still may be important. We would like to go forward and fit separate age curves for the males and the females, since the above fit makes an untested assumption that the male/female ratio of death rates will be the same at all ages. The primary problem is that a formula of \texttt{sex * pspline(age)} does not work; the coxph routine is not clever enough to do the right thing automatically for \code{pspline} interactions. (Perhaps some future version will be sufficiently intelligent, but don't hold your breath). As a first solution we will use regression splines, i.e., splines that can be represented using a basis matrix. <>= options(show.signif.stars=FALSE) # display statistical intellegence require(splines, quietly=TRUE) nfit1 <- coxph(Surv(futime, death) ~ sex + age, flchain) nfit2 <- coxph(Surv(futime, death) ~ sex + ns(age, df=3), flchain) nfit3 <- coxph(Surv(futime, death) ~ sex * ns(age, df=3), flchain) anova(nfit1, nfit2, nfit3) @ The nonlinear term is significant but the interaction is not. Nevertheless we would like to plot the two estimated curves for \code{nfit3}, expecting that they will be approximately parallel. The \code{termplot} routine is not able to deal with models that have an interaction and will bow out with a warning message; we use explicit prediction instead, which is nearly as easy. <>= pdata <- expand.grid(age= 50:99, sex=c("F", "M")) pdata[1:5,] ypred <- predict(nfit3, newdata=pdata, se=TRUE) yy <- ypred$fit + outer(ypred$se, c(0, -1.96, 1.96), '*') matplot(50:99, exp(matrix(yy, ncol=6)), type='l', lty=c(1,1,2,2,2,2), lwd=2, col=1:2, log='y', xlab="Age", ylab="Relative risk") legend(55, 20, c("Female", "Male"), lty=1, lwd=2, col=1:2, bty='n') abline(h=1) @ The \code{ns} function generates a basis of dummy variables to represent the spline, which will work automatically in interactions. The coefficients that result are not very interpretable, but the result of predict is invariant to this. The issues as compared to using \code{termplot} are \begin{enumerate} \item We need to provide our own set of predictor values for the plot, whereas \code{termplot} would automatically use the set of unique age and sex values. \item Keeping track of the indexing. The predict function produces two vectors each of length \code{nrow(pdata)} with a predicted value and its standard error, one value for each row of \code{pdata}. The data set is in order of females, then males. We fold it into an appropriate matrix for use with matplot. \item The vertical centering of the curves corresponds to an average population predictor of$\eta = X\beta =0$; i.e., the average over the subjects in the data set. This is a consequence of the variable centering that \code{coxph} does for numerical stability. To center at some particular (age, sex) pair obtain the predicted value for that fictional subject and subtract the resulting value from \code{yy}. \end{enumerate} To create the same figure with \code{pspline} curves it is necessary to code the males and females as two separate terms. To do this create our own dummy variables to handle the interaction. <>= agem <- with(flchain, ifelse(sex=="M", age, 60)) agef <- with(flchain, ifelse(sex=="F", age, 60)) fit2 <- coxph(Surv(futime, death) ~ sex + pspline(agef, df=3) + pspline(agem, df=3), data=flchain) anova(fit2, fit1) @ You might well ask why we used 60 as a dummy value of \texttt{agem} for the females instead of 0? If a value of 0 is used it forces the pspline function to create a basis set that includes all the empty space between 0 and 50, and do predictions at 0; these last can become numerically unstable leading to errors or incorrect values. Best is to pick a value close to the mean, though any value within the range will do. For this plot we will use a 65 year old female as the reference. <>= # predictions pdata2 <- pdata pdata2$agem <- with(pdata2, ifelse(sex=="M", age, 60)) pdata2$agef <- with(pdata2, ifelse(sex=="F", age, 60)) ypred2 <- predict(fit2, pdata2, se=TRUE) yy <- ypred2$fit + outer(ypred2$se, c(0, -1.96, 1.96), '*') # reference refdata <- data.frame(sex='F', agef=65, agem=60) ref <- predict(fit2, newdata=refdata, type="lp") # plot matplot(50:99, exp(matrix(yy-ref, ncol=6)), type='l', lty=c(1,1,2,2,2,2), lwd=2, col=1:2, log='y', xlab="Age", ylab="Relative risk") legend(55, 20, c("Female", "Male"), lty=1, lwd=2, col=1:2, bty='n') abline(h=1) @ The final curves for males and female are not quite parallel, most of the difference is at the highest ages, however, where there are very few subjects. One thing the plot does not display is that the spacing between the male and female points also has a standard error. This moves the entire bundle of three red curves up and down. It is not clear how best to add this information into the plot. For questions of parallelism and shape, as here, it seemed best to ignore it, which is what the termplot function also does. If someone were reading individual male/female differences off the plot a different choice would be appropriate. \end{document} survival/inst/doc/timedep.pdf0000644000175100001440000111721613070714001016011 0ustar hornikusers%PDF-1.4 %ÐÔÅØ 3 0 obj << /Length 2244 /Filter /FlateDecode >> stream xÚ­XIÛ8¾çW}iˆ‘ÚgNéJè¹x€&}P$U•¦,« É©vÿúy+EÙ®äPeñ‘|ËÇ·‘¿ìß¼û5.6&­I“Íþ~cŒ Ó4Ûd& ãÒnöÍæ?Á¿¦­ º#ü{Øîâ( ö|÷->´0xÞîlà.kà¯=nm̸Æw@¶°âë6ƒ Fc‡ÿçvb&ocî(­G¼ù~¢€™®¹ÿ¹ÿ}Sš°°ùfgMXš‚UfªÓçÈdðSwËΉyw¤1‰‘¢oüÅã?O’(ôݯ¦°Â2M-â¶ËL˜¥(Q„EiX‰ý¶€õ#Z g`<ö$f¤ZDá„ÌM܉j 0̸իp_ܬS¼LkM›>dÝßÈê ÛÌûIÞ{ÊO[5×Ópd+’Ô·Â&YXZ°ÂÄa™” g N£àîлú&ÆdaeAÆy›ß?‹õ(ùÀ%où×)‚?“‹.ùÆ$aœdÂ/OÂ4/7»Ä†EQ2?³9°÷72$6dÙˆÊEAsªqÔ1:IJؔa™Ù Fä!E$fí_ô„8ÏäáÃ=f&çÄÔä _z:·‰É1ïk:v°·âø°è ¯áa,øË;Ïhñ+"5*O©¦ÈBúô¶'N<ƒ¬2¼ lÊV}¶&º6¿ ÀG‚þk]BкuHt8YQø;ÉŸOŽ~3C¶È×1„Ñ Æ}:2k[pù®Žüí7ÂÇ'ÞÚão'ü Zù—·È-ã™'{¾ °ŸBI´¥¨FáVÕpå¦H m•ô$ª—º'Ù´f•Söô”jÈS‘ã‹›Êi¸…%ªUÍ’¹®ãˆÿIüŒ6¦,ƒÏ&Nœ¸é'‡×?yÀjåa|W 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################################################### options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text options(contrasts=c("contr.treatment", "contr.poly")) #reset default ################################################### ### code chunk number 2: mplot ################################################### getOption("SweaveHooks")[["fig"]]() require(survival) mfit <- coxph(Surv(futime, death) ~ sex + pspline(age, df=4), data=mgus) mfit termplot(mfit, term=2, se=TRUE, col.term=1, col.se=1) ################################################### ### code chunk number 3: mplot2 ################################################### ptemp <- termplot(mfit, se=TRUE, plot=FALSE) attributes(ptemp) ptemp$age[1:4,] ################################################### ### code chunk number 4: mplot3 ################################################### getOption("SweaveHooks")[["fig"]]() ageterm <- ptemp$age # this will be a data frame center <- with(ageterm, y[x==50]) ytemp <- ageterm$y + outer(ageterm$se, c(0, -1.96, 1.96), '*') matplot(ageterm$x, exp(ytemp - center), log='y', type='l', lty=c(1,2,2), col=1, xlab="Age at diagnosis", ylab="Relative death rate") ################################################### ### code chunk number 5: hgb ################################################### fit <- coxph(Surv(futime, death) ~ age + pspline(hgb, 4), mgus2) fit termplot(fit, se=TRUE, term=2, col.term=1, col.se=1, xlab="Hemoglobin level") ################################################### ### code chunk number 6: df ################################################### termplot(fit, se=TRUE, col.term=1, col.se=1, term=2, xlab="Hemoglobin level", ylim=c(-.4, 1.3)) df <- c(3, 2.5, 2) for (i in 1:3) { tfit <- coxph(Surv(futime, death) ~ age + pspline(hgb, df[i], nterm=8), mgus2) temp <- termplot(tfit, se=FALSE, plot=FALSE, term=2) lines(temp$hgb$x, temp$hgb$y, col=i+1, lwd=2) } legend(14, 1, paste("df=", c(4, df)), lty=1, col=1:4, lwd=2) ################################################### ### code chunk number 7: fit2.5 ################################################### fit2a <- coxph(Surv(futime, death) ~ age + pspline(hgb, 2.5, nterm=8), mgus2) coef(fit2a) plot(1:10, coef(fit2a)[-1]) ################################################### ### code chunk number 8: fit2b ################################################### temp <- c(1:7, 8,8,8) fit2b <- coxph(Surv(futime, death) ~ age + pspline(hgb, 2.5, nterm=8, combine=temp), data= mgus2) temp2 <- c(1:6, 7,7,7,7) fit2c <- coxph(Surv(futime, death) ~ age + pspline(hgb, 2.5, nterm=8, combine=temp2), data= mgus2) matplot(1:10, cbind(coef(fit2a)[-1], coef(fit2b)[temp+1], coef(fit2c)[temp2+1]), type='b', pch='abc', xlab="Term", ylab="Pspline coef") ################################################### ### code chunk number 9: fit1 ################################################### getOption("SweaveHooks")[["fig"]]() options(show.signif.stars=FALSE) # display intelligence fit1 <- coxph(Surv(futime, death) ~ sex + pspline(age, 3), data=flchain) fit1 termplot(fit1, term=2, se=TRUE, col.term=1, col.se=1, ylab="log hazard") ################################################### ### code chunk number 10: nfit ################################################### options(show.signif.stars=FALSE) # display statistical intellegence require(splines, quietly=TRUE) nfit1 <- coxph(Surv(futime, death) ~ sex + age, flchain) nfit2 <- coxph(Surv(futime, death) ~ sex + ns(age, df=3), flchain) nfit3 <- coxph(Surv(futime, death) ~ sex * ns(age, df=3), flchain) anova(nfit1, nfit2, nfit3) ################################################### ### code chunk number 11: nfit2 ################################################### pdata <- expand.grid(age= 50:99, sex=c("F", "M")) pdata[1:5,] ypred <- predict(nfit3, newdata=pdata, se=TRUE) yy <- ypred$fit + outer(ypred$se, c(0, -1.96, 1.96), '*') matplot(50:99, exp(matrix(yy, ncol=6)), type='l', lty=c(1,1,2,2,2,2), lwd=2, col=1:2, log='y', xlab="Age", ylab="Relative risk") legend(55, 20, c("Female", "Male"), lty=1, lwd=2, col=1:2, bty='n') abline(h=1) ################################################### ### code chunk number 12: fit2 ################################################### agem <- with(flchain, ifelse(sex=="M", age, 60)) agef <- with(flchain, ifelse(sex=="F", age, 60)) fit2 <- coxph(Surv(futime, death) ~ sex + pspline(agef, df=3) + pspline(agem, df=3), data=flchain) anova(fit2, fit1) ################################################### ### code chunk number 13: plot2 ################################################### getOption("SweaveHooks")[["fig"]]() # predictions pdata2 <- pdata pdata2$agem <- with(pdata2, ifelse(sex=="M", age, 60)) pdata2$agef <- with(pdata2, ifelse(sex=="F", age, 60)) ypred2 <- predict(fit2, pdata2, se=TRUE) yy <- ypred2$fit + outer(ypred2$se, 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options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text require(survival, quietly=TRUE) ################################################### ### code chunk number 2: breslow1 ################################################### breslow1 <- function(beta) { # first test data set, Breslow approximation r = exp(beta) lpl = 2*beta - (log(3*r +3) + 2*log(r+3)) U = (6+ 3*r - r^2)/((r+1)*(r+3)) H = r/(r+1)^2 + 6*r/(r+3)^2 c(beta=beta, loglik=lpl, U=U, H=H) } beta <- log((3 + sqrt(33))/2) temp <- rbind(breslow1(0), breslow1(beta)) dimnames(temp)[[1]] <- c("beta=0", "beta=solution") temp ################################################### ### code chunk number 3: validate.Rnw:186-209 ################################################### iter <- matrix(0, nrow=6, ncol=4, dimnames=list(paste("iter", 0:5), c("beta", "loglik", "U", "H"))) # Exact Newton-Raphson beta <- 0 for (i in 1:6) { iter[i,] <- breslow1(beta) beta <- beta + iter[i,"U"]/iter[i,"H"] } iter # coxph fits test1 <- data.frame(time= c(1, 1, 6, 6, 8, 9), status=c(1, 0, 1, 1, 0, 1), x= c(1, 1, 1, 0, 0, 0)) temp <- matrix(0, nrow=6, ncol=4, dimnames=list(1:6, c("iter", "beta", "loglik", "H"))) for (i in 0:5) { tfit <- coxph(Surv(time, status) ~ x, data=test1, ties="breslow", iter.max=i) temp[i+1,] <- c(tfit$iter, coef(tfit), tfit$loglik[2], 1/vcov(tfit)) } temp ################################################### ### code chunk number 4: mresid1 ################################################### mresid1 <- function(r) { status <- c(1,0,1,1,0,1) xbeta <- c(r,r,r,1,1,1) temp1 <- 1/(3*r +3) temp2 <- 2/(r+3) + temp1 status - xbeta*c(temp1, temp1, temp2, temp2, temp2, 1+ temp2) } r0 <- mresid1(1) r1 <- round(mresid1((3 + sqrt(33))/2), 6) ################################################### ### code chunk number 5: iter ################################################### temp <- matrix(0, 8, 3) dimnames(temp) <- list(paste0("iteration ", 0:7, ':'), c("beta", "loglik", "H")) bhat <- 0 for (i in 1:8) { r <- exp(bhat) temp[i,] <- c(bhat, 2*(bhat - log(3*r +3)), 2*r/(r+1)^2) bhat <- bhat + (r+1)/r } round(temp,3) ################################################### ### code chunk number 6: breslow2 ################################################### ufun <- function(r) { 4 - (r/(r+1) + r/(r+2) + 3*r/(3*r+2) + 6*r/(3*r+1) + 6*r/(3*r+2)) } rhat <- uniroot(ufun, c(.5, 1.5), tol=1e-8)$root bhat <- log(rhat) c(rhat=rhat, bhat=bhat) ################################################### ### code chunk number 7: temp ################################################### true2 <- function(beta, newx=0) { r <- exp(beta) loglik <- 4*beta - log(r+1) - log(r+2) - 3*log(3*r+2) - 2*log(3*r+1) u <- 1/(r+1) + 1/(3*r+1) + 4/(3*r+2) - ( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1)) imat <- r/(r+1)^2 + 2*r/(r+2)^2 + 6*r/(3*r+2)^2 + 3*r/(3*r+1)^2 + 3*r/(3*r+1)^2 + 12*r/(3*r+2)^2 hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), 2/(3*r+2) ) xbar <- c(r/(r+1), r/(r+2), 3*r/(3*r+2), 3*r/(3*r+1), 3*r/(3*r+1), 3*r/(3*r+2)) # The matrix of weights, one row per obs, one col per time # deaths at 2,3,6,7,8,9 wtmat <- matrix(c(1,0,0,0,1,0,0,0,0,0, 0,1,0,1,1,0,0,0,0,0, 0,0,1,1,1,0,1,1,0,0, 0,0,0,1,1,0,1,1,0,0, 0,0,0,0,1,1,1,1,0,0, 0,0,0,0,0,1,1,1,1,1), ncol=6) wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat x <- c(1,0,0,1,0,1,1,1,0,0) status <- c(1,1,1,1,1,1,1,0,0,0) xbar <- colSums(wtmat*x)/ colSums(wtmat) n <- length(x) # Table of sums for score and Schoenfeld resids hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time dM <- -hazmat #Expected part for (i in 1:6) dM[i,i] <- dM[i,i] +1 #observed dM[7,6] <- dM[7,6] +1 # observed mart <- rowSums(dM) # Table of sums for score and Schoenfeld resids # Looks like the last table of appendix E.2.1 of the book resid <- dM * outer(x, xbar, '-') score <- rowSums(resid) scho <- colSums(resid) # We need to split the two tied times up, to match coxph scho <- c(scho[1:5], scho[6]/2, scho[6]/2) var.g <- cumsum(hazard*hazard /c(1,1,1,1,1,2)) var.d <- cumsum( (xbar-newx)*hazard) surv <- exp(-cumsum(hazard) * exp(beta*newx)) varhaz <- (var.g + var.d^2/imat)* exp(2*beta*newx) list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard, mart=mart, score=score, rmat=resid, scho=scho, surv=surv, var=varhaz) } val2 <- true2(bhat) rtemp <- round(val2$mart, 6) ################################################### ### code chunk number 8: wt1 ################################################### ufun <- function(r) { xbar <- c( (2*r^2 + 11*r)/(r^2 + 11*r +7), 11*r/(11*r + 5), 2*r/(2*r +1)) 11- (xbar[1] + 10* xbar[2] + 2* xbar[3]) } rhat <- uniroot(ufun, c(1,3), tol= 1e-9)$root bhat <- log(rhat) c(rhat=rhat, bhat=bhat) ################################################### ### code chunk number 9: wt2 ################################################### wfun <- function(r) { beta <- log(r) pl <- 11*beta - (log(r^2 + 11*r + 7) + 10*log(11*r +5) + 2*log(2*r +1)) xbar <- c((2*r^2 + 11*r)/(r^2 + 11*r +7), 11*r/(11*r +5), 2*r/(2*r +1)) U <- 11 - (xbar[1] + 10*xbar[2] + 2*xbar[3]) H <- ((4*r^2 + 11*r)/(r^2 + 11*r +7)- xbar[1]^2) + 10*(xbar[2] - xbar[2]^2) + 2*(xbar[3]- xbar[3]^2) c(loglik=pl, U=U, H=H) } temp <- matrix(c(wfun(1), wfun(rhat)), ncol=2, dimnames=list(c("loglik", "U", "H"), c("beta=0", "beta-hat"))) round(temp, 6) survival/inst/doc/tiedtimes.Rnw0000644000175100001440000001233713026507356016361 0ustar hornikusers\documentclass{article}[11pt] \usepackage{Sweave} \usepackage{amsmath} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} \newcommand{\code}[1]{\texttt{#1}} \SweaveOpts{keep.source=TRUE, fig=FALSE} % Ross Ihaka suggestions \DefineVerbatimEnvironment{Sinput}{Verbatim} {xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} \SweaveOpts{prefix.string=adjcurve,width=6,height=4} \setkeys{Gin}{width=\textwidth} %\VignetteIndexEntry{Roundoff error and tied times} <>= options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text library(survival, quietly=TRUE) @ \title{Roundoff error and Tied Times} \author{Terry M Therneau} \begin{document} \maketitle \section{Round off error} The heart of the issue can be shown with a simple example. Calculate the following set of intervals for subjects with the same birth date who were enrolled in a study from September 14 through October 23, and then followed for 2--3 months. <>= birth <- as.Date("1973/03/10") start <- as.Date("1998/09/13") + 1:40 end <- as.Date("1998/12/03") + rep(1:10, 4) interval <- (end-start) table(interval) @ Each interval has a different start and end date, but there are only 4 unique interval lengths, each of which appears 10 times. Now convert this to an age scale. <>= start.age <- as.numeric(start-birth)/365.25 end.age <- as.numeric(end -birth)/365.25 age.interval <- end.age - start.age length(unique(age.interval)) table(match(age.interval, sort(unique(age.interval)))) @ There are now eight different age intervals instead of 4, and the 8 unique values appear between 1 and 9 times each. We have become a victim of floating point precision. The exact results above, i.e. how many 'unique' time intervals are found, may depend on your computer system. Some users prefer to use time in days and some prefer time in years, and those users reasonably expect survival analysis results to be identical on the two scales. Both the coxph and survfit routines treat tied event times in a special way, however, and this roundoff can make actual ties appear as non-tied values. In that case results will differ. Parametric survival routines such as \code{survreg} are not affected by the problem since they do not treat ties differently than other values. In survival version 2.40 this issue has been addressed for the coxph and survfit routines; input times are subjected to the same logic found in the all.equal routine in order to determine actual ties. This may change the results for some data sets. For the following test case cox1 and cox2 have identical results in in version 2.40 but different results in prior versions of the survival package. <<>>= ndata <- data.frame(id=1:30, birth.dt = rep(as.Date("1953/03/10"), 30), enroll.dt= as.Date("1993/03/10") + 1:30, end.dt = as.Date("1996/10/21") + 1:30 + rep(1:10, 3), status= rep(0:1, length=30), x = 1:30) ndata$enroll.age <- with(ndata, as.numeric(enroll.dt - birth.dt))/365.25 ndata$end.age <- with(ndata, as.numeric(end.dt - birth.dt))/365.25 fudays <- with(ndata, as.numeric(end.dt - enroll.dt)) fuyrs <- with(ndata, as.numeric(end.age- enroll.age)) cox1 <- coxph(Surv(fudays, status) ~ x, data=ndata) cox2 <- coxph(Surv(fuyrs, status) ~ x, data=ndata) @ A downside to the new procedure is that the code will now give an error message for some constructed data sets. An example sent by one user had several time intervals of length 1e-9, which is less than the roundoff precision used by the \code{all.equal} routine and consequently turned them into illegal intervals of zero length. The \code{timefix} argument of \code{coxph.control} can be used to address this. This general issue of floating point precision arises often enough in R that it is part of the frequently asked questions, see FAQ 7.31 on CRAN. The author of the survival routines (me) has always used days as the scale for analysis -- just by habit, not for any particluarly scientific reason -- so the issue had never appeared in my work nor in the survival package's test suite. Due to user input, near ties had been addressed earlier in the survfit routine, but only when the status variable was 0/1, not when it is a factor. The new code uses a single routine \code{aeqSurv} to deal with ties in a uniform way for all the affected functions. As a final footnote, the simple data set above also gives different results when using the SAS phreg procedure and I suspect the problem exists in other software as well --- the R routines are not alone.\footnote{I have reported this to SAS as of November 2016 and was told that they plan to address the problem.} As a consequence, the maintainer expects to get new emails that ``we have found a bug in your code: it gives a different answer than SAS''. (This is an actual quote.) \end{document} survival/inst/doc/tests.R0000644000175100001440000003242613070713777015175 0ustar hornikusers### R code from vignette source 'tests.Rnw' ################################################### ### code chunk number 1: tests.Rnw:20-24 ################################################### options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text options(contrasts=c("contr.treatment", "contr.poly")) #reset default ################################################### ### code chunk number 2: tests.Rnw:44-52 ################################################### library(survival) age2 <- cut(flchain$age, c(49, 59, 69, 79, 89, 120), labels=c("50-59", "60-69", "70-79", "80-89", "90+")) flchain$flc <- flchain$kappa + flchain$lambda tab1 <- with(flchain, tapply(flc, list(sex, age2), mean)) cat("female&" , paste(round(tab1[1,], 1), collapse=" & "), "\\\\ \n") cat("male &" , paste(round(tab1[2,], 1), collapse=" & "), "\n") ################################################### ### code chunk number 3: data ################################################### getOption("SweaveHooks")[["fig"]]() library(survival) library(splines) age2 <- cut(flchain$age, c(49, 59, 69, 79, 89, 120), labels=c("50-59", "60-69", "70-79", "80-89", "90+")) counts <- with(flchain, table(sex, age2)) counts # flchain$flc <- flchain$kappa + flchain$lambda male <- (flchain$sex=='M') mlow <- with(flchain[male,], smooth.spline(age, flc)) flow <- with(flchain[!male,], smooth.spline(age, flc)) plot(flow, type='l', ylim=range(flow$y, mlow$y), xlab="Age", ylab="FLC") lines(mlow, col=2) cellmean <- with(flchain, tapply(flc, list(sex, age2), mean, na.rm=T)) matpoints(c(55,65,75, 85, 95), t(cellmean), pch='fm', col=1:2) round(cellmean, 2) ################################################### ### code chunk number 4: tests.Rnw:384-393 ################################################### us2000 <- rowSums(uspop2[51:101,,'2000']) fit1 <- lm(flc ~ sex, flchain, x=TRUE) fit2 <- lm(flc ~ sex + ns(age,4), flchain, x=TRUE) c(fit1$coef[2], fit2$coef[2]) wt1 <- solve(t(fit1$x)%*%fit1$x, t(fit1$x))[2,] # unadjusted wt2 <- solve(t(fit2$x)%*%fit2$x, t(fit2$x))[2,] # age-adjusted table(wt1, flchain$sex) ################################################### ### code chunk number 5: pop ################################################### getOption("SweaveHooks")[["fig"]]() us2000 <- rowSums(uspop2[51:101,,'2000']) tab0 <- table(flchain$age) tab2 <- tapply(abs(wt2), flchain$age, sum) matplot(50:100, cbind(tab0/sum(tab0), tab2/sum(tab2)), type='l', lty=1, xlab="Age", ylab="Density") us2000 <- rowSums(uspop2[51:101,,'2000']) matpoints(50:100, us2000/sum(us2000), pch='u') legend(60, .02, c("Empirical reference", "LS reference"), lty=1, col=1:2, bty='n') ################################################### ### code chunk number 6: yfit ################################################### yatesfit <- lm(flc ~ interaction(sex, age2) -1, data=flchain) theta <- matrix(coef(yatesfit), nrow=2) dimnames(theta) <- dimnames(counts) round(theta,2) ################################################### ### code chunk number 7: tests.Rnw:548-570 ################################################### qform <- function(beta, var) # quadratic form b' (V-inverse) b sum(beta * solve(var, beta)) contrast <- function(cmat, fit) { varmat <- vcov(fit) if (class(fit) == "lm") sigma2 <- summary(fit)$sigma^2 else sigma2 <- 1 # for the Cox model case beta <- coef(fit) if (!is.matrix(cmat)) cmat <- matrix(cmat, nrow=1) if (ncol(cmat) != length(beta)) stop("wrong dimension for contrast") estimate <- drop(cmat %*% beta) #vector of contrasts ss <- qform(estimate, cmat %*% varmat %*% t(cmat)) *sigma2 list(estimate=estimate, ss=ss, var=drop(cmat %*% varmat %*% t(cmat))) } yates.sex <- matrix(0, 2, 10) yates.sex[1, c(1,3,5,7,9)] <- 1/5 #females yates.sex[2, c(2,4,6,8,10)] <- 1/5 #males contrast(yates.sex, yatesfit)$estimate # the estimated "average" FLC for F/M contrast(yates.sex[2,]-yates.sex[,1], yatesfit) # male - female contrast ################################################### ### code chunk number 8: tests.Rnw:573-599 ################################################### # Create the estimates table -- lots of fits emat <- matrix(0., 6, 3) dimnames(emat) <- list(c("Unadjusted", "MVUE: continuous age", "MVUE: categorical age", "Empirical (data) reference", "US200 reference", "Uniform (Yates)"), c("est", "se", "SS")) #unadjusted emat[1,] <- c(summary(fit1)$coef[2,1:2], anova(fit1)["sex", "Sum Sq"]) # MVUE -- do the two fits fit2 <- lm(flc ~ ns(age,4) + sex, flchain) emat[2,] <- c(summary(fit2)$coef[6, 1:2], anova(fit2)["sex", "Sum Sq"]) fit2 <- lm(flc ~ age2 + sex, flchain) emat[3,] <- c(summary(fit2)$coef[6, 1:2], anova(fit2)["sex", "Sum Sq"]) #Remainder, use contrasts tfun <- function(wt) { cvec <- c(matrix(c(-wt, wt), nrow=2, byrow=TRUE)) temp <- contrast(cvec, yatesfit) c(temp$est, sqrt(temp$var), temp$ss) } emat[4,] <- tfun(colSums(counts)/sum(counts)) usgroup <- tapply(us2000, rep(1:5, c(10,10,10,10,11)), sum)/sum(us2000) emat[5,]<- tfun(usgroup) emat[6,] <- tfun(rep(1/5,5)) ################################################### ### code chunk number 9: tests.Rnw:604-608 ################################################### temp <- dimnames(emat)[[1]] for (i in 1:nrow(emat)) cat(temp[i], sprintf(" &%5.3f", emat[i,1]),sprintf(" &%6.5f", emat[i,2]), sprintf(" & %6.1f", emat[i,3]), "\\\\ \n") ################################################### ### code chunk number 10: weights ################################################### casewt <- array(1, dim=c(2,5,4)) # case weights by sex, age group, estimator csum <- colSums(counts) casewt[,,2] <- counts[2:1,] / rep(csum, each=2) casewt[,,3] <- rep(csum, each=2)/counts casewt[,,4] <- 1/counts #renorm each so that the mean weight is 1 for (i in 1:4) { for (j in 1:2) { meanwt <- sum(casewt[j,,i]*counts[j,])/ sum(counts[j,]) casewt[j,,i] <- casewt[j,,i]/ meanwt } } ################################################### ### code chunk number 11: tests.Rnw:652-662 ################################################### tname <- c("Unadjusted", "Min var", "Empirical", "Yates") for (i in 1:2) { for (j in 1:4) { cat("&",tname[j], " & ", paste(sprintf("%4.2f", casewt[i,,j]), collapse= " & "), "\\\\\n") if (j==1) cat(c("Female", "Male")[i]) } if (i==1) cat("\\hline ") } ################################################### ### code chunk number 12: tests.Rnw:705-709 ################################################### temp <- 1/colSums(1/counts) temp <- temp/sum(temp) cat("Female", sprintf(" & %5.3f", -temp), "\\\\ \n") cat("Male", sprintf(" & %5.3f", temp), "\\\\ \n") ################################################### ### code chunk number 13: treatment ################################################### fit3 <- lm(flc ~ sex * age2, flchain) coef(fit3) contrast(c(0,1, 0,0,0,0, .2,.2,.2,.2), fit3) #Yates ################################################### ### code chunk number 14: SAS ################################################### options(contrasts=c("contr.SAS", "contr.poly")) sfit1 <- lm(flc ~ sex, flchain) sfit2 <- lm(flc ~ sex + age2, flchain) sfit3 <- lm(flc ~ sex * age2, flchain) contrast(c(0,-1, 0,0,0,0, -.2,-.2,-.2,-.2), sfit3) # Yates for SAS coding ################################################### ### code chunk number 15: nstt ################################################### options(contrasts = c("contr.treatment", "contr.poly")) #R default fit3a <- lm(flc ~ sex * age2, flchain) options(contrasts = c("contr.SAS", "contr.poly")) fit3b <- lm(flc~ sex * age2, flchain) options(contrasts=c("contr.sum", "contr.poly")) fit3c <- lm(flc ~ sex * age2, flchain) # nstt <- c(0,1, rep(0,8)) #test only the sex coef = the NSTT method temp <- rbind(unlist(contrast(nstt, fit3a)), unlist(contrast(nstt, fit3b)), unlist(contrast(nstt, fit3c)))[,1:2] dimnames(temp) <- list(c("R", "SAS", "sum"), c("effect", "SS")) print(temp) # drop1(fit3a, .~.) ################################################### ### code chunk number 16: anova ################################################### options(show.signif.stars = FALSE) #exhibit intelligence sfit0 <- lm(flc ~ 1, flchain) sfit1b <- lm(flc ~ age2, flchain) anova(sfit0, sfit1b, sfit2, sfit3) ################################################### ### code chunk number 17: relrate ################################################### options(contrasts= c("contr.treatment", "contr.poly")) # R default cfit0 <- coxph(Surv(futime, death) ~ interaction(sex, age2), flchain) cmean <- matrix(c(0, coef(cfit0)), nrow=2) cmean <- rbind(cmean, cmean[2,] - cmean[1,]) dimnames(cmean) <- list(c("F", "M", "M/F ratio"), dimnames(counts)[[2]]) signif(exp(cmean),3) ################################################### ### code chunk number 18: cox anova ################################################### options(contrasts=c("contr.SAS", "contr.poly")) cfit1 <- coxph(Surv(futime, death) ~ sex, flchain) cfit2 <- coxph(Surv(futime, death) ~ age2 + sex, flchain) cfit3 <- coxph(Surv(futime, death) ~ sex + strata(age2), flchain) # Unadjusted summary(cfit1) # # LRT anova(cfit2) # # Stratified anova(cfit3) summary(cfit3) # # Wald test signif(summary(cfit2)$coefficients, 3) # anova(cfit1, cfit2) ################################################### ### code chunk number 19: coxfit ################################################### wtindx <- with(flchain, tapply(death, list(sex, age2))) cfitpop <- coxph(Surv(futime, death) ~ sex, flchain, robust=TRUE, weight = (casewt[,,3])[wtindx]) cfityates <- coxph(Surv(futime, death) ~ sex, flchain, robust=TRUE, weight = (casewt[,,4])[wtindx]) # # Glue it into a table for viewing # tfun <- function(fit, indx=1) { c(fit$coef[indx], sqrt(fit$var[indx,indx])) } coxp <- rbind(tfun(cfit1), tfun(cfit2,5), tfun(cfitpop), tfun(cfityates)) dimnames(coxp) <- list(c("Unadjusted", "Additive", "Empirical Population", "Uniform Population"), c("Effect", "se(effect)")) signif(coxp,3) ################################################### ### code chunk number 20: tests.Rnw:1219-1235 ################################################### cfit4 <- coxph(Surv(futime, death) ~ sex * age2, flchain) # Uniform population contrast ysex <- c(0,-1, 0,0,0,0, -.2,-.2,-.2,-.2) #Yates for sex, SAS coding contrast(ysex[-1], cfit4) # Verify using cell means coding cfit4b <- coxph(Surv(futime, death) ~ interaction(sex, age2), flchain) temp <- matrix(c(0, coef(cfit4b)),2) # the female 50-59 is reference diff(rowMeans(temp)) #direct estimate of the Yates # temp2 <- rbind(temp, temp[2,] - temp[1,]) dimnames(temp2) <- list(c('female', 'male', 'difference'), levels(age2)) round(temp2, 3) # # # NSTT contrast contrast(c(1,0,0,0,0,0,0,0,0), cfit4) ################################################### ### code chunk number 21: nstt-lrt ################################################### xmat4 <- model.matrix(cfit4) cfit4b <- coxph(Surv(futime, death) ~ xmat4[,-1], flchain) anova(cfit4b, cfit4) ################################################### ### code chunk number 22: ydata ################################################### data1 <- data.frame(y = rep(1:6, length=20), x1 = factor(letters[rep(1:3, length=20)]), x2 = factor(LETTERS[rep(1:4, length=10)]), x3 = 1:20) data1$x1[19] <- 'c' data1 <- data1[order(data1$x1, data1$x2),] row.names(data1) <- NULL with(data1, table(x1,x2)) # data2 -- single missing cell indx <- with(data1, x1=='a' & x2=='D') data2 <- data1[!indx,] #data3 -- missing the diagonal data3 <- data1[as.numeric(data1$x1) != as.numeric(data1$x2),] ################################################### ### code chunk number 23: tests.Rnw:1411-1414 ################################################### options(contrasts=c("contr.sum", "contr.poly")) fit1 <- lm(y ~ x1*x2, data1) drop1(fit1, .~.) ################################################### ### code chunk number 24: tests.Rnw:1421-1427 ################################################### options(contrasts=c("contr.SAS", "contr.poly")) fit2 <- lm(y ~ x1*x2, data1) drop1(fit2, .~.) options(contrasts=c("contr.treatment", "contr.poly")) fit3 <- lm(y ~ x1*x2, data1) drop1(fit3, .~.) ################################################### ### code chunk number 25: att ################################################### X <- model.matrix(fit2) ux <- unique(X) ux indx <- rep(1:3, c(4,4,4)) effects <- t(rowsum(ux, indx)/4) # turn sideways to fit the paper better effects yates <- effects[,-1] - effects[,1] yates ################################################### ### code chunk number 26: tests.Rnw:1467-1470 ################################################### wt <- solve(t(X) %*% X, t(X)) # twelve rows (one per coef), n columns casewt <- t(effects) %*% wt # case weights for the three "row efffects" for (i in 1:3) print(tapply(casewt[i,], data1$x2, sum)) ################################################### ### code chunk number 27: tests.Rnw:1507-1508 ################################################### fit4 <- lm(y ~ x1*x2 + x3, data=data1) survival/inst/doc/validate.Rnw0000644000175100001440000013372613017617770016173 0ustar hornikusers\documentclass{article}[11pt] \usepackage{Sweave} \usepackage{amsmath} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} \SweaveOpts{keep.source=TRUE, fig=FALSE} % Ross Ihaka suggestions \DefineVerbatimEnvironment{Sinput}{Verbatim} {xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} \SweaveOpts{prefix.string=adjcurve,width=6,height=4} \setkeys{Gin}{width=\textwidth} %\VignetteIndexEntry{Validation} <>= options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text require(survival, quietly=TRUE) @ \newcommand{\imat}{H} % use H for the hessian rather than script I \newcommand{\Cvar}{H^{-1}} % use H for the hessian rather than script I \newcommand{\splus}{R} % ``the survival package'' would be an alternate \newcommand{\xbar}{\overline x} \newcommand{\lhat}{\hat \Lambda} \def\bhat{\hat\beta} %define "bhat" to mean "beta hat" \def\Mhat{\widehat M} %define "Mhat" to mean M-hat \newcommand{\code}[1]{\texttt{#1}} \title{Validation} \author{Terry M Therneau} \date{Dec 2015} \begin{document} \maketitle \section{Introduction} \begin{quotation} `When I use a word,' Humpty Dumpty said, in rather a scornful tone, `it means just what I choose it to mean - neither more nor less.' `The question is,' said Alice, `whether you can make words mean so many different things.' `The question is,' said Humpty Dumpty, `which is to be master - that's all.' -Lewis Caroll, \emph{Through the Looking Glass} \end{quotation} ``Validatation'' is a label which is used for many different things in scientific research, so much so that the word is essentially meaningless without further clarification. One of the more common meanings assigned to it in the software realm is ``repeatability'', i.e. that a new release of a given package or routine will give the same results as it did the week before. Users of the software often assume the word implies a more rigorous criterion, namely that the routine gives \emph{correct} answers. Validation of the latter type is rare, however; and I surmise that a primary reason for this is that working out correct answers is boring, tedious work. This note contains a set of examples, often very simple, that have evolved over multiple decades. They have proven extremely useful in debugging the methods, not least because all the intermediate steps of each calculation are transparent, and have been incorporated into the formal test suite for the survival package as the files \code{book1.R}, \code{book2.R}, etc. They also continue to be a resource for package's defence: I have been told multiple times that some person or group cannot use R in their work because ``SAS is validated'' while R is not. The survival package passes all of the tests below and SAS passes many but not all of them. It is my hope that the formal test cases will be a resource for developers on multiple platforms. Portions of this work were included as an appendix in the textbook of Therneau and Grambsch \cite{Therneau2000} precisely for this reason. \section{Basic formulas} All these examples have a single covariate. Let $x_i$ be the covariate for each subject, $r_i= exp(x_i \beta)$ the risk score for the subject, and $w_i$ the case weight, if any. Let $Y_i(t)$ be 1 if subject $i$ is at risk at time $t$ and 0 otherwise, and $\delta_i(t)$ be the death indicator which is 1 if subject $i$ has an event at time $t$. At each death time we have the following quantities: \begin{align} d(t) &= \sum_i Y_i(t) w_i r_i \\ LPL(t) &= \left( \sum_i \delta_i(t) \log(r_i) \right) / \log(d(t)) \\ \xbar(t) &= \left( \sum_i Y_i(t) w_i r_i x_i \right) /d(t) \\ U(t) &= \sum_i \delta_i(t) (x_i - \xbar(t)) \label{U1} \\ H(t) &= \sum_i Y_i(t) (x_i - \xbar(t))^2 / d(t) \\ &= \left(\sum_i Y_i(t) x_i^2/d(t) \right)- \xbar(t)^2 \label{H2} \\ \lambda(t) &= \sum_i \delta_i(t)/ d(t) \end{align} The denominator $d$ is the weighted number of subjects at the time, $LPL$ is the contribution to the log partial likelihood at time $t$, and $\xbar$ and $H$ are the weighted mean and variance of the covariate $x$ at each time. The sum of $H(t)$ over the death times is the second derivative of the LPL, also known as the Hessian matrix. $U$ is the contribution to the first derivative of the LPL at time $t$ and $\lambda$ is the increment in the baseline hazard function. \section{Test data 1} This data set of $n=6$ subjects has a single 0/1 covariate $x$. There is one tied death time, one time with both a death and a censored observation, one with only a death, and one with only censoring. (This is as small as a data set can be and still cover these four important cases.) Let $r = \exp(\beta)$ be the risk score for a subject with $x=1$; the risk score is $\exp(0) =1$ for those with $x=0$. Table \ref{tab:val1} shows the data set along with the mean and increment to the hazard at each time point. \begin{table}[b] \centering \begin{tabular}{ccc|cc|cc} &&& \multicolumn{2}{c|}{$\xbar(t)$} & \multicolumn{2}{c}{$d\lhat_0(t)$} \\ Time& Status& $x$& Breslow& Efron& Breslow& Efron \\ \hline 1&1&1&$r/(r+1)$ & $r/(r+1)$& $1/(3r+3)$ & $1/(3r+3)$ \\ 1&0&1&&&&\\ 6&1&1& $r/(r+3)$ & $r/(r+3)$ & $1/(r+3)$& $1/(r+3)$ \\ 6&1&0& $r/(r+3)$ & $r/(r+5)$ & $1/(r+3)$& $1/(r+5)$ \\ 8&0&0&&&& \\ 9&1&0&0&0& 1& 1\\ \end{tabular} \caption{Test data 1} \label{tab:val1} \end{table} \subsection{Breslow estimates} \label{sect:valbreslow} The log partial likelihood (LPL) has a term for each event; each term is the log of the ratio of the score for the subject who had an event over the sum of scores for those who did not. The LPL, first derivative $U$ of the LPL and second derivative (or Hession) $\imat$ are: \begin{eqnarray*} LPL &=& \{\beta- \log(3r+3)\} + \{\beta - \log(r+3)\} + \{0-\log(r+3)\} + \{0-0\} \\ &=& 2\beta - \log(3r+3) - 2\log(r+3). \\ \\ U &=& \left(1-\frac{r}{r+1}\right) + \left(1-\frac{r}{r+3}\right) + \left(0-\frac{r}{r+3} \right) + (0-0) \\ &=& \frac{-r^2 + 3r + 6}{(r+1)(r+3)} .\\ \\ -\imat&=& \left\{\frac{r}{r+1} - \left( \frac{r}{r+1} \right )^2\right\} +2 \left\{\frac{r}{r+3} - \left( \frac{r}{r+3} \right )^2\right\} + (0-0) \\ &=& \frac{r}{(r+1)^2} + \frac{6r}{(r+3)^2}. \end{eqnarray*} (For a 0/1 covariate the variance formula \eqref{H2} simplifies to $\xbar - \xbar^2$, but only in that case. We used this fact above.) The following function computes these quantities. <>= breslow1 <- function(beta) { # first test data set, Breslow approximation r = exp(beta) lpl = 2*beta - (log(3*r +3) + 2*log(r+3)) U = (6+ 3*r - r^2)/((r+1)*(r+3)) H = r/(r+1)^2 + 6*r/(r+3)^2 c(beta=beta, loglik=lpl, U=U, H=H) } beta <- log((3 + sqrt(33))/2) temp <- rbind(breslow1(0), breslow1(beta)) dimnames(temp)[[1]] <- c("beta=0", "beta=solution") temp @ The maximum partial likelihood occurs when $U(\beta)=0$, namely $r^2 -3r -6 =0$. Using the usual formula for a quadratic equation gives $r=(1/2)(3 + \sqrt{33})$ and $\bhat = \log(r) \approx 1.475285$. The above call to \code{breslow1} verifies that the first derivative is zero at this point. Newton--Raphson iteration has increments of $-\Cvar U$. Starting with the usual initial estimate of $\beta=0$, the first iteration is $\beta=8/5$ and further ones are shown below. <<>>= iter <- matrix(0, nrow=6, ncol=4, dimnames=list(paste("iter", 0:5), c("beta", "loglik", "U", "H"))) # Exact Newton-Raphson beta <- 0 for (i in 1:6) { iter[i,] <- breslow1(beta) beta <- beta + iter[i,"U"]/iter[i,"H"] } iter # coxph fits test1 <- data.frame(time= c(1, 1, 6, 6, 8, 9), status=c(1, 0, 1, 1, 0, 1), x= c(1, 1, 1, 0, 0, 0)) temp <- matrix(0, nrow=6, ncol=4, dimnames=list(1:6, c("iter", "beta", "loglik", "H"))) for (i in 0:5) { tfit <- coxph(Surv(time, status) ~ x, data=test1, ties="breslow", iter.max=i) temp[i+1,] <- c(tfit$iter, coef(tfit), tfit$loglik[2], 1/vcov(tfit)) } temp @ The \code{coxph} routine declares convergence after 4 iterations for this data set, so the last two calls with \code{iter.max} of 4 and 5 give identical results. The martingale residuals are defined as $O-E$ = observed - expected, where the observed is the number of events for the subject (0 or 1) and $E$ is the expected number assuming that the model is completely correct. For the first death all 6 subjects are at risk, and the martingale formulation views the outcome as a lottery in which the subjects hold $r$, $r$, $r$, 1, 1 and 1 tickets, respectively. The contribution to $E$ for subject 1 at time 1 is thus $r/(r+3)$. Carrying this forward the residuals can be written as simple function of the cumulative baseline hazard $\Lambda_0(t)$, the Nelson cumulative hazard estimator with case weights of $w_ir_i$; this is shown in the `Breslow' column of table \ref{tab:val1}. (Also known as the Aalen estimate, Breslow estimate, and all possible combinations of the three names.) Then the residual can be written as \begin{equation} M_i = \delta_i - \exp(x_i\beta)\lhat(t_i) \label{mart} \end{equation} Each of the two subjects who die at time 6 are credited with the full hazard increment at time 6. Residuals at $\beta=0$ and $\bhat$ are shown in the table below. <>= mresid1 <- function(r) { status <- c(1,0,1,1,0,1) xbeta <- c(r,r,r,1,1,1) temp1 <- 1/(3*r +3) temp2 <- 2/(r+3) + temp1 status - xbeta*c(temp1, temp1, temp2, temp2, temp2, 1+ temp2) } r0 <- mresid1(1) r1 <- round(mresid1((3 + sqrt(33))/2), 6) @ \begin{center} \begin{tabular}{c|lrr} Subject &\multicolumn{1}{c}{$\Lambda_0$} & $\Mhat(0)$ & $\Mhat(\bhat)$ \\ \hline 1& $1/(3r+3)$ & $5/6$ & \Sexpr{r1[1]} \\ 2& $1/(3r+3)$ & $-1/6$ & \Sexpr{r1[2]} \\ 3& $1/(3r+3) + 2/(r+3)$ &$1/3$ & \Sexpr{r1[3]} \\ 4& $1/(3r+3) + 2/(r+3)$ &$1/3$ & \Sexpr{r1[4]} \\ 5& $1/(3r+3) + 2/(r+3)$ & $-2/3$ & \Sexpr{r1[5]} \\ 6 & $1/(3r+3) + 2/(r+3) +1$ & $-2/3$ & \Sexpr{r1[6]} \end{tabular} \end{center} The score statistic $U$ can be written as a two way sum involving the covariate(s) and the martingale residuals \begin{equation} U = \sum_{i=1}^n \int [x_i - \xbar(t)] dM_i(t) \label{score} \end{equation} The martingale residual $M$ has jumps at the observed deaths, leading to the table below with 6 rows and 3 columns. The score residuals $L_i$ are defined as the per-patient contributions to this total, i.e., the row sums, and the Schoenfeld residuals are the per-time point contributions, i.e., the column sums. \begin{center} \begin{tabular}{cccc} &\multicolumn{3}{c}{Time} \\ Subject & 1 & 6 & 9 \\ \hline 1&$ \left(1- \frac{r}{r+1} \right) \left(1- \frac{r}{3r+3} \right)$ &0&0 \\ 2& $\left(1- \frac{r}{r+1} \right) \left(0- \frac{r}{3r+3} \right)$ &0&0 \\ 3& $\left(1- \frac{r}{r+1} \right) \left(0- \frac{r}{3r+3} \right)$ & $\left(1- \frac{r}{r+3} \right) \left(1- \frac{2r}{r+3} \right)$ & 0\\ 4& $\left(0- \frac{r}{r+1} \right) \left(0- \frac{1}{3r+3} \right)$ & $\left(0- \frac{r}{r+3} \right) \left(1- \frac{2}{r+3} \right)$ & 0\\ 5& $\left(0- \frac{r}{r+1} \right) \left(0- \frac{1}{3r+3} \right)$ & $\left(0- \frac{r}{r+3} \right) \left(0- \frac{2}{r+3} \right)$ & 0\\ 6& $\left(0- \frac{r}{r+1} \right) \left(0- \frac{1}{3r+3} \right)$ & $\left(0- \frac{r}{r+3} \right) \left(0- \frac{2}{r+3} \right)$ & (0 - 0) (1-1) \end{tabular} \end{center} At $\beta=0$ the score residuals are 5/12, -1/12, 7/24, -1/24, 5/24 and 5/24. Showing that the three column sums are identical to the three terms of equation \eqref{U1} is left as an exercise for the reader, namely $1- \xbar(1)$, $(1- \xbar(6)) + (0- \xbar(6))$ and $1 - \xbar(9)$. The computer program returns 4 residuals, one per event, rather than one per death time as this has proven to be more useful for plots and other downstream computations. In the multivariate case there will be a matrix like the above for each covariate. Let $L$ be the $n$ by $p$ matrix made up of the collection of row sums where $n$ is the number of subjects and $p$ is the number of covariates, this is the matrix of score residuals. The dfbeta residuals are the $n$ by $p$ matrix $D = L \Cvar$; $\imat$ has been defined above for this data set. $D$ is an approximate measure of the influence of each observation on the solution vector. Similarly, the scaled Schoenfeld residuals are the (number of events) by $p$ matrix obtained by multiplying the Schoenfeld residuals by $\Cvar$. As stated above there is a close connection between the Nelson--Aalen estimate estimate of cumulative hazard and the Breslow approximation for ties. The baseline hazard is shown as the column $\Lambda_0$ in table \ref{tab:val1}. The estimated hazard for a subject with covariate $x_i$ is $\Lambda_i(t) = \exp(x_i \beta) \Lambda_0(t)$ and the survival estimate for the subject is $S_i(t)= \exp(-\Lambda_i(t))$. The variance of the cumulative hazard is the sum of two terms. Term 1 is a natural extension of the Nelson--Aalen estimator to the case where there are weights. It is a running sum, with an increment at each death of $1/(\sum Y_i(t)r_i(t))^2$. For a subject with covariate $x_i$ this term is multiplied by $[\exp(x_i \beta)]^2$. The second term is $c\Cvar c'$, where $\imat$ is the information matrix of the Cox model and $c$ is a vector. The second term accounts for the fact that the weights themselves have a variance; $c$ is the derivative of $S(t)$ with respect to $\beta$ and can be formally written as $$ \exp(x\beta) \int_0^t (\bar x(s) - x_i) d\hat\Lambda_0 (s)\,. $$ This can be recognized as $-1$ times the score residual process for a subject with $x_i$ as covariates and no events; it measures leverage of a particular observation on the estimate of $\beta$. It is intuitive that a small score residual --- an observation whose covariates has little influence on $\beta$ --- results in a small added variance; that is, $\beta$ has little influence on the estimated survival. \begin{center} \begin{tabular}{c|l} Time & Term 1 \\ \hline 1& $1/(3r+3)^2$ \\ 6& $1/(3r+3)^2 + 2/(r+3)^2$ \\ 9& $1/(3r+3)^2 + 2/(r+3)^2 + 1/1^2$ \\ \multicolumn{2}{c}{} \\ Time & $c$ \\ \hline 1& $(r/(r+1))* 1/(3r+3)$ \\ 6& $(r/(r+1))* 1/(3r+3) + (r/(r+3))* 2/(r+3)$ \\ 9& $(r/(r+1))* 1/(3r+3) + (r/(r+3))* 2/(r+3) + 0*1$\\ \end{tabular} \end{center} For $\beta=0$, $x=0$: \begin{center} \begin{tabular}{c|lll} Time & \multicolumn{2}{c}{Variance}&\\ \hline 1 & 1/36 &+ $1.6*(1/12)^2 $ &= 7/180\\ 6 & (1/36 + 2/16) &+ $1.6*(1/12 + 2/16)^2 $ &= 2/9\\ 9 & (1/36 + 2/16 + 1)&+ $1.6*(1/12 + 2/16 + 0)^2$&= 11/9\\ \end{tabular} \end{center} For $\beta=1.4752849$, $ x=0$ \begin{center} \begin{tabular}{c|lll} Time & \multicolumn{2}{c}{Variance}&\\ \hline 1 & 0.0038498 &+ .004021 &= 0.007871\\ 2 & 0.040648 &+ .0704631 &= 0.111111\\ 4 & 1.040648 &+ .0704631 &= 1.111111\\ \end{tabular} \end{center} \subsection{Efron approximation} The Efron approximation \cite{Efron77} differs from the Breslow only at day 6, where two deaths occur. A useful way to view the approximation is to recast the problem as a lottery model. On day 1 there were 6 subjects in the lottery and 1 ticket was drawn, at which time the winner became ineligible for further drawings and withdrew. On day 6 there were 4 subjects in the drawing (at risk) and two tickets (deaths) were drawn. The Breslow approximation considers all four subjects to be eligible for both drawings, which implies that one of them could in theory have won both, that is, died twice. This is of clearly impossible. The Efron approximation treats the two drawings on day 6 as sequential. All four living subjects are at risk for the first of them, then the winner is withdrawn. Three subjects are eligible for the second drawing, either subjects 3, 5, and 6 or subjects 2, 5, and 6, but we do not know which. In some sense then, subjects 3 and 4 each have ``.5 probability" of being at risk for the second event at time 6. In the computation, we treat the two deaths at time 6 as two separate times (two terms in the loglik), with subjects 3 and 4 each having a case weight of 1/2 for the second one. The mean covariate for the second event is then $$ \frac{1*r/2 + 0*1/2 + 0*1 + 0*1 } {r/2 + 1/2 + 1+1} = \frac{r}{r+5} $$ and the main quantities are \begin{eqnarray*} LL &=& \{\beta- \log(3r+3)\} + \{\beta - \log(r+3)\} + \{0-\log(r/2 +5/2)\} + \{0-0\} \\ &=& 2\beta - \log(3r+3) - \log(r+3) - \log(r/2 +5/2)\\ \\ U &=& \left(1-\frac{r}{r+1}\right) + \left(1-\frac{r}{r+3}\right) + \left(0-\frac{r}{r+5}\right) + (0-0) \\ &=& \frac{-r^3 + 23r + 30}{(r+1)(r+3)(r+5)} \\ \\ I&=& \left\{\frac{r}{r+1} - \left( \frac{r}{r+1} \right )^2\right\} + \left\{\frac{r}{r+3} - \left( \frac{r}{r+3} \right )^2\right\} \\ && + \left\{\frac{r}{r+5} - \left( \frac{r}{r+5} \right )^2\right\}. \end{eqnarray*} The solution corresponds to the one positive root of $U(\beta)=0$, which is $r=2\sqrt{23/3}\cos(\phi/3)$ where $\phi=\arccos\{(45/23)\sqrt{3/23}\}$ via the standard formula for the roots of a cubic equation. This yields $r \approx 5.348721$ or $\bhat = \log(r) \approx 1.676857$. Plugging this value into the formulas above yields $$ \begin{array}{ll} LL(0)=-4.276666 & LL(\bhat)=-3.358979 \\ U(0) = 52/48 & U(\bhat) = 0 \\ \imat(0) = 83/144 & \imat(\bhat) = 0.652077. \end{array} $$ The martingale residuals are again $O-E$, but the expected part of the calculation changes. For the first drawing at time 6 the total number of ``tickets'' in the drawing is $r+1+1+1$; subject 4 has an increment of $r/(r+3)$ and the others $1/(r+3)$ to their expected value. For the second event at time 6 subjects 3 and 4 have a weight of 1/2, the total number of tickets is $(r+5)/2$ and the consequent increment in the cumulative hazard is $2/(r+5)$. This $\beta=0$ this calculation is equivalent to the Fleming-Harrington \cite{Fleming84} estimate of cumulative hazard. Subjects 3 and 4 receive 1/2 of this second increment to $E$ and subjects 5 and 6 the full increment. Efron \cite{Efron77} did not discuss residuals so did not investigate this aspect of the approximation, we nevertheless sometime refer to this using combinations of Fleming, Harrington, Efron in the same way as the Nelson-Aalen-Breslow estimate. The martingale residuals are \begin{center} \begin{tabular}{cl} Subject & $M_i$ \\ \hline 1 & $1 - r/(3r+3)$ \\ 2 & $0 - r/(3r+3)$ \\ 3 & $1 - r/(3r+3) - r/(r+3) - r/(r+5)$ \\ 4 & $1 - 1/(3r+3) - 1/(r+3) - 1/(r+5)$ \\ 5 & $0 - 1/(3r+3) - 1/(r+3) - 2/(r+5)$ \\ 6 & $0 - 1/(3r+3) - 1/(r+3) - 2/(r+5) - 1$ \\ \end{tabular} \end{center} giving residuals at $\beta=0$ of 5/6, -1/6, 5/12, 5/12, -3/4 and -3/4. The matrix defining the score and Schoenfeld residuals has the same first column (time 1) and last column as before, with the following contributions at time 6. \begin{center} \begin{tabular}{ccc} &\multicolumn{2}{c}{Time} \\ Subject & 6 (first) & 6 (second)\\ \hline 1&0 & 0 \\ 2&0 & 0 \\ 3& $\left(1- \frac{r}{r+3} \right) \left(1- \frac{r}{r+3} \right)$ & $\left(1- \frac{r}{r+5} \right) \left(1- \frac{2r}{r+5} \right)/2$ \\ 4& $\left(0- \frac{r}{r+3} \right) \left(0- \frac{1}{r+3} \right)$ & $\left(0- \frac{r}{r+5} \right) \left(1- \frac{2}{r+5} \right)/2$ \\ 5& $\left(0- \frac{r}{r+3} \right) \left(0- \frac{1}{r+3} \right)$ & $\left(0- \frac{r}{r+5} \right) \left(0- \frac{2}{r+5} \right)$ \\ 6& $\left(0- \frac{r}{r+3} \right) \left(0- \frac{1}{r+3} \right)$ & $\left(0- \frac{r}{r+5} \right) \left(0- \frac{2}{r+5} \right)$ \end{tabular} \end{center} The score residuals at $\beta=0$ are 5/12, -1/12, 55/144, -5/144, 29/144 and 29/144. It is an error to generate residuals for the Efron method by using formula \eqref{mart}, which was derived from the Breslow approximation. It is clear that some packages do exactly this, however, which can be verified using formulas from above. (Statistical forensics is another use for our results.) What are the consequences of this? On a formal level the resulting ``martingale residuals'' no longer have an expected value of 0 and thus are not martingales, so one loses theoretical backing for derived plots or statistics. The score, Schoenfeld, dfbeta and scaled Schoenfeld residuals are based on the martingale residual so suffer the same loss. On a practical level, when the fraction of ties is small it is quite often the case that $\bhat$ is nearly the same when using the Breslow and Efron approach. We have normally found the correct and ad hoc residuals to be similar as well in that case, sufficiently so that explorations of functional form (martingale residuals), leverage and robust variance (dfbeta) and proportional hazards (scaled Schoenfeld) led to the same conclusions. This will not hold when there are a moderate to large number of ties. The variance formula for the baseline hazard function in the Efron case is evaluated the same way as before, as the sum of $(\mbox{hazard increment})^2$, treating a tied death as multiple separate hazard increments. In term 1 of the variance, the variance increment at time 6 is now $1/(r+3)^2 + 4/(r+5)^2$ rather than $2/(r+3)^2$. The increment to $d$ at time 6 is $(r/(r+3))* 1/(r+3) + (r/(r+5))* 2/(r+5)$. (Numerically, the result of this computation is intermediate between the Nelson--Aalen variance and the Greenwood variance used in the Kaplan--Meier.) For $\beta=0$, $x=0$, let $v= \Cvar = 144/83$. \begin{center} \begin{tabular}{c|ll} Time & \multicolumn{2}{c}{Variance}\\ \hline 1 & 1/36 \\ & \quad + $v(1/12)^2 $ &= \phantom{0}119/2988\\ 6 & (1/36 + 1/16 + 4/25)& \\ &\quad + $v(1/12 + 1/16+ 1/18)^2$ &= 1996/6225\\ 9 & (1/36 + 1/16 + 4/25 + 1) \\& \quad + $v(1/12 + 1/16 + 1/18 +0)^2$&= 8221/6225\\ \end{tabular} \end{center} For $\beta=1.676857$, $ x=0$. \begin{center} \begin{tabular}{c|ll} Time & \multicolumn{2}{c}{Variance}\\ \hline 1 & 0.00275667 + .00319386 & = 0.0059505\\ 2 & 0.05445330 + .0796212 & = 0.134075\\ 4 & 1.05445330 + .0796212 &= 1.134075\\ \end{tabular} \end{center} \subsection{Exact partial likelihood} Returning to the lottery analogy, for the two deaths at time 6 the exact partial likelihood computes the direct probability that those two subjects would be selected given that a pair will be chosen. The numerator is $r_3 r_4$, the product of the risk scores of the subjects with an event, and the denominator is the sum over all 6 pairs who could have been chosen: $r_3r_4 + r_3r_5 + r_3r_6 + r_4 r_5 + r_4r_6 + r_5r_6$. (If there were 10 tied deaths from a pool of 60 available the sum will have over 75 billion terms, each a product of 10 values; a truly formidable computation!) In our case, three of the four subjects at risk at time 6 have a risk score of $\exp(0x)=1$ and one a risk score of $r$, and the denominator is $r +r+ r+1 +1 +1$. \begin{eqnarray*} LL &=& \{\beta- \log(3r+3)\} + \{\beta - \log(3r+3)\} + \{0-0\} \\ &=& 2\{\beta - \log(3r+3)\}. \\ \\ U &=& \left(1-\frac{r}{r+1}\right) + \left(1-\frac{r}{r+1}\right) + (0-0)\\ &=& \frac{2}{r+1}. \\ \\ -\imat&=& \frac{2r}{(r+1)^2}. \\ \end{eqnarray*} The solution $U(\beta)=0$ corresponds to $r=\infty$, with a loglikelihood that asymptotes to $-2\log(3)$ = 2.1972. The Newton--Raphson iteration has increments of $(r+1)/r$ leading to the following iteration for $\bhat$: <>= temp <- matrix(0, 8, 3) dimnames(temp) <- list(paste0("iteration ", 0:7, ':'), c("beta", "loglik", "H")) bhat <- 0 for (i in 1:8) { r <- exp(bhat) temp[i,] <- c(bhat, 2*(bhat - log(3*r +3)), 2*r/(r+1)^2) bhat <- bhat + (r+1)/r } round(temp,3) @ The Newton-Raphson iteration quickly settles down to addition of a constant increment to $\bhat$ at each step while the partial likelihood approaches an asymptote: this is a fairly common case when the Cox MLE is infinite. A solution at $\bhat=10$ or 15 is hardly different in likelihood from the true maximum, and most programs will stop iterating around this point. The information matrix, which measures the curvature of the likelihood function at $\beta$, rapidly goes to zero as $\beta$ grows. It is difficult to describe a satisfactory definition of the expected number of events for each subject and thus a definition of the proper martingale residual for the exact calculation. Among other things it should lead to a consistent score residual, i.e., ones that sum to the total score statistic $U$ \begin{align*} L_i &= \int (x_i - \xbar(t)) dM_i(t) \\ \sum L_i &= U \end{align*} The residuals defined above for the Breslow and Efron approximations have this property, for instance. The exact partial likelihood contribution to $U$ for a set of set of $k$ tied deaths, however, is a sum of all subsets of size $k$; how would one partition this term as a simple sum over subjects? The exact partial likelihood is infrequently used and examination of post fit residuals is even rarer. The survival package (and all others that I know of) takes the easy road in this case and uses equation \eqref{mart} along with the Nelson-Aalen-Breslow hazard to form residuals. They are certainly not correct, but the viable options were to use this, the Efron residuals, or print an error message. At $\bhat=\infty$ the Breslow residuals are still well defined. Subjects 1 to 3, those with a covariate of 1, experience a hazard of $r/(3r+3)=1/3$ at time 1. Subject 3 accumulates a hazard of 1/3 at time 1 and a further hazard of 2 at time 6. The remaining subjects are at an infinitely lower risk during days 1 to 6 and accumulate no hazard then, with subject 6 being credited with 1 unit of hazard at the last event. The residuals are thus $1-1/3=2/3$, $0-1/3$, $1-7/3= -4/3$, $1-0$, 0, and 0, respectively, for the six subjects. \section{Test data 2} This data set also has a single covariate, but in this case a (start, stop] style of input is employed. Table \ref{tab:val2} shows the data sorted by the end time of the risk intervals. The columns for $\xbar$ and hazard are the values at the event times; events occur at the end of each interval for which status = 1. \begin{table}\centering \begin{tabular}{ccc|ccc} &&&Number& \\ Time&Status&$x$&at Risk& $\xbar$& $d\lhat$ \\ \hline (1,2] &1 &1 &2 &$r/(r+1)$ & $1/(r+1)$\\ (2,3] &1 &0 &3 & $r/(r+2)$ & $1/(r+2)$ \\ (5,6] &1 &0 &5 & $3r/(3r+2)$ & $1/(3r+2)$ \\ (2,7] &1 &1 &4 & $3r/(3r+1)$ & $1/(3r+1)$ \\ (1,8] &1 &0 &4 & $3r/(3r+1)$ & $1/(3r+1)$ \\ (7,9] &1 &1 &5 & $3r/(3r+2)$ & $2/(3r+2)$ \\ (3,9] &1 &1 && \\ (4,9] &0 &1 && \\ (8,14]&0 &0 &2& 0&0 \\ (8,17]&0 &0 &1& 0&0 \\ \end{tabular} \caption{Test data 2} \label{tab:val2} \end{table} \subsection{Breslow approximation} For the Breslow approximation we have \begin{eqnarray*} LL &=& \log\left(\frac{r}{r+1}\right) +\log\left(\frac{1}{r+2}\right) +\log\left(\frac{1}{3r+2}\right) +\\ && \log\left(\frac{r}{3r+1}\right) +\log\left(\frac{1}{3r+1}\right) +2\log\left(\frac{r}{3r+2}\right) \\ &=& 4\beta - \log(r+1) - \log(r+3)- 3\log(3r+2) -2\log(3r+1). \\ \\ U &=& \left(1-\frac{r}{r+1}\right) + \left(0-\frac{r}{r+2}\right) + \left(0-\frac{3r}{3r+2}\right) + \\ && \left(1-\frac{3r}{3r+1}\right) + \left(0-\frac{3r}{3r+1}\right) + 2\left(1-\frac{3r}{3r+2}\right) \\ \\ \\ \imat &=& \frac{r}{(r+1)^2} + \frac{2r}{(r+2)^2} + \frac{6r}{(3r+2)^2} + \frac{3r}{(3r+1)^2} \\ && \frac{3r}{(3r+1)^2} + \frac{12r}{(3r+2)^2} . \\ \end{eqnarray*} In this case $U$ is a quartic equation and we find the solution numerically. <>= ufun <- function(r) { 4 - (r/(r+1) + r/(r+2) + 3*r/(3*r+2) + 6*r/(3*r+1) + 6*r/(3*r+2)) } rhat <- uniroot(ufun, c(.5, 1.5), tol=1e-8)$root bhat <- log(rhat) c(rhat=rhat, bhat=bhat) @ The solution is at $U(\bhat)=0$ or $r \approx .9189477$; $\bhat = \log(r) \approx -.084526$. Then <>= true2 <- function(beta, newx=0) { r <- exp(beta) loglik <- 4*beta - log(r+1) - log(r+2) - 3*log(3*r+2) - 2*log(3*r+1) u <- 1/(r+1) + 1/(3*r+1) + 4/(3*r+2) - ( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1)) imat <- r/(r+1)^2 + 2*r/(r+2)^2 + 6*r/(3*r+2)^2 + 3*r/(3*r+1)^2 + 3*r/(3*r+1)^2 + 12*r/(3*r+2)^2 hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), 2/(3*r+2) ) xbar <- c(r/(r+1), r/(r+2), 3*r/(3*r+2), 3*r/(3*r+1), 3*r/(3*r+1), 3*r/(3*r+2)) # The matrix of weights, one row per obs, one col per time # deaths at 2,3,6,7,8,9 wtmat <- matrix(c(1,0,0,0,1,0,0,0,0,0, 0,1,0,1,1,0,0,0,0,0, 0,0,1,1,1,0,1,1,0,0, 0,0,0,1,1,0,1,1,0,0, 0,0,0,0,1,1,1,1,0,0, 0,0,0,0,0,1,1,1,1,1), ncol=6) wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat x <- c(1,0,0,1,0,1,1,1,0,0) status <- c(1,1,1,1,1,1,1,0,0,0) xbar <- colSums(wtmat*x)/ colSums(wtmat) n <- length(x) # Table of sums for score and Schoenfeld resids hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time dM <- -hazmat #Expected part for (i in 1:6) dM[i,i] <- dM[i,i] +1 #observed dM[7,6] <- dM[7,6] +1 # observed mart <- rowSums(dM) # Table of sums for score and Schoenfeld resids # Looks like the last table of appendix E.2.1 of the book resid <- dM * outer(x, xbar, '-') score <- rowSums(resid) scho <- colSums(resid) # We need to split the two tied times up, to match coxph scho <- c(scho[1:5], scho[6]/2, scho[6]/2) var.g <- cumsum(hazard*hazard /c(1,1,1,1,1,2)) var.d <- cumsum( (xbar-newx)*hazard) surv <- exp(-cumsum(hazard) * exp(beta*newx)) varhaz <- (var.g + var.d^2/imat)* exp(2*beta*newx) list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard, mart=mart, score=score, rmat=resid, scho=scho, surv=surv, var=varhaz) } val2 <- true2(bhat) rtemp <- round(val2$mart, 6) @ $$ \begin{array}{ll} LL(0)= \Sexpr{round(true2(0)$loglik, 6)} & LL(\bhat)= \Sexpr{round(val2$loglik,6)} \\ U(0) = -2/15 & U(\bhat) = 0 \\ \imat(0) = 2821/1800 & \imat(\bhat) = \Sexpr{round(val2$imat,6)} %$ \end{array} $$ \def\haz{\hat \lambda} The martingale residuals are (status--cumulative hazard) or $O-E = \delta_i - \int Y_i(s) r_i d\lhat(s)$. Let $\haz_1, \ldots, \haz_6$ be the six increments to the cumulative hazard listed in Table \ref{tab:val2}. Then the cumulative hazards and martingale residuals for the subjects are as follows. \begin{center} \begin{tabular}{c|lrr} Subject &$\Lambda_i$ & $\Mhat(0)$ & $\Mhat(\bhat)$ \\ \hline 1& $r\haz_1$ & 1--30/60 & \Sexpr{rtemp[1]} \\ 2& $\haz_2 $ & 1--20/60 & \Sexpr{rtemp[2]}\\ 3& $\haz_3 $ & 1--12/60 & \Sexpr{rtemp[3]} \\ 4& $r(\haz_2 + \haz_3 + \haz_4)$& 1--47/60 & \Sexpr{rtemp[4]}\\ 5& $\haz_1+\haz_2+\haz_3+\haz_4+\haz_5$& 1--92/60 & \Sexpr{rtemp[5]}\\ 6 &$r*(\haz_5 + \haz_6) $& 1--39/60 & \Sexpr{rtemp[6]} \\ 7& $r*(\haz_3+\haz_4+\haz_5+ \haz_6)$& 1--66/60& \Sexpr{rtemp[7]}\\ 8& $r*(\haz_3+\haz_4+\haz_5+ \haz_6)$& 0--66/60&\Sexpr{rtemp[8]} \\ 9& $\haz_6$ & 0--24/60 & \Sexpr{rtemp[9]} \\ 10& $\haz_6$ & 0--24/60 & \Sexpr{rtemp[10]} \end{tabular} \end{center} The score and Schoenfeld residuals can be laid out in a tabular fashion. Each entry in the table is the value of $\{x_i - \xbar(t_j)\} d\Mhat_i(t_j)$ for subject $i$ and event time $t_j$. The row sums of the table are the score residuals for the subject; the column sums are the Schoenfeld residuals at each event time. Below is the table for $\beta= \log(2)$ ($r=2$). This is a slightly more stringent test than the table for $\beta=0$, since in this latter case a program could be missing a factor of $r = \exp(\beta)=1$ and give the correct answer. However, the results are much more compact than those for $\bhat$, since the solutions are exact fractions. %\newcommand{\pf}[2]{$\left(\frac{#1}{#2}\right)$} %positive fraction %\newcommand{\nf}[2]{$\left(\frac{-#1}{#2}\right)$} %negative fraction \newcommand{\pf}[2]{$\phantom{-}\frac{#1}{#2}$} %positive fraction \newcommand{\nf}[2]{$-\frac{#1}{#2}$} %negative fraction \renewcommand{\arraystretch}{1.5} \begin{center} \begin{tabular}{c|cccccc|c} & \multicolumn{6}{c|}{Event Time} & Score\\ Id&2&3&6&7&8&9& Resid \\ \hline 1&\pf{1}{9} &&&&&& $\phantom{-}\frac{1}{9}$ \\ 2&&\nf{3}{8} &&&&& $-\frac{3}{8}$ \\ 3&&&\nf{21}{32}&&&& $-\frac{21}{32}$ \\ 4&&\nf{1}{4} & \nf{1}{16} & \pf{5}{49} &&& $-\frac{165}{784} $\\ 5&\pf{2}{9}& \pf{1}{8} & \pf{3}{32} & \pf{6}{49} & \nf{36}{49}&& $-\frac{2417}{14112} $\\ 6&&&&& \nf{2}{49} & \pf{1}{8} & $\phantom{-}\frac{33}{392}$ \\ 7&&& \nf{1}{16} & \nf{2}{49}& \nf{2}{49} & \pf{1}{8} & $-\frac{15}{784}$ \\ 8&&& \nf{1}{16} & \nf{2}{49}& \nf{2}{49} & \nf{1}{8} & $-\frac{211}{784}$ \\ 9&&&&&& \pf{3}{16} &$ \phantom{-}\frac{3}{16}$ \\ 10&&&&&& \pf{3}{16} & $\phantom{-}\frac{3}{16}$ \\ \hline & \pf{1}{3} &\nf{1}{2} & \nf{3}{4} & \pf{1}{7} & \nf{6}{7} & \pf{1}{2} & \nf{95}{84} \\ &&&&&&& \\ & $\frac{1}{r+1}$ & $\frac{-r}{r+2}$ & $\frac{-3r}{r+2}$ & $\frac{1}{3r+1}$ & $\frac{3r}{3r+1}$ & $\frac{4}{3r+2}$ \end{tabular} \end{center} Both the Schoenfeld and score residuals sum to the score statistic $U(\beta)$. As discussed further above, programs will return two Schoenfeld residuals at time 7, one for each subject who had an event at that time. \subsection{Efron approximation} This example has only one tied death time, so only the term(s) for the event at time 9 change. The main quantities at that time point are as follows. \begin{center} \begin{tabular}{r|cc} &Breslow & Efron \\ \hline $LL$ & $2\log\left(\frac{r}{3r+2}\right)$ & $\log\left(\frac{r}{3r+2}\right) + \log\left(\frac{r}{2r+2}\right)$ \\ $U$ & $\frac{2}{3r+2}$& $\frac{1}{3r+2} + \frac{1}{2r+2}$ \\ $\imat$& $2\frac{6r}{(3r+2)^2} $ &$\frac{6r}{(3r+2)^2} + \frac{4r}{(2r+2)^2}$\\ $d\lhat$ & $\frac{2}{3r+2} $ & $\frac{1}{3r+2} + \frac{1}{2r+2}$ \end{tabular} \end{center} \renewcommand{\arraystretch}{1} \section{Test data 3} This is very similar to test data 1, but with the addition of case weights. There are 9 observations, $x$ is a 0/1/2 covariate, and weights range from 1 to 4. As before, let $r = \exp(\beta)$ be the risk score for a subject with $x=1$. Table \ref{tab:val3} shows the data set along with the mean and increment to the hazard at each point. \begin{table} \centering \begin{tabular}{cccc|cc} Time&Status&$X$ & Wt& $\xbar(t)$ & $d\lhat_0(t)$ \\ \hline 1& 1& 2 & 1& $(2r^2+11r) d\lhat_0 =\xbar_1$ & $1/(r^2 + 11r +7)$ \\ 1& 0& 0 & 2&& \\ 2& 1& 1 & 3& $11r/(11r+5) = \xbar_2$ & $10/(11r+5)$ \\ 2& 1& 1 & 4&& \\ 2& 1& 0 & 3&& \\ 2& 0& 1 & 2&& \\ 3& 0& 0 & 1&& \\ 4& 1& 1 & 2& $2r/(2r+1)= \xbar_3$ & $ 2/(2r+1)$ \\ 5& 0& 0 & 1 & \\ \end{tabular} \caption{Test data 3} \label{tab:val3} \end{table} \subsection{Breslow estimates} The likelihood is a product of terms, one for each death, of the form $$ \left( \frac{e^{X_i \beta}}{\sum_j Y_j(t_i) w_j e^{X_j \beta}} \right) ^{w_i} $$ For integer weights, this gives the same results as would be obtained by replicating each observation the specified number of times, which is in fact one motivation for the definition. The definitions for the score vector $U$ and information matrix $\imat$ simply replace the mean and variance with weighted versions of the same. Let $PL(\beta,w)$ be the log partial liklihood when all the observations are given a common case weight of $w$; it is easy to prove that $PL(\beta,w) = wPL(\beta,1) - d\log(w)$ where $d$ is the number of events. One consequence of this is that $PL$ can be positive for weights that are less than 1, a case which sometimes occurs in survey sampling applications. (This can be a big surprise the first time one encounters it.) \begin{eqnarray*} LL &=& \{2\beta - \log(r^2 + 11r +7)\} + 3\{\beta - \log(11r+5)\} \\ && + 4\{\beta - \log(11r+5)\} +3\{0 - \log(11r+5)\} \\ && + 2\{\beta - \log(2r+1) \} \\ &=& 11\beta - \log(r^2 + 11r +7) -10\log(11r+5) - 2\log(2r+1) \\\\ U &=& (2- \xbar_1) + 3(0-\xbar_2) + 4(1-\xbar_2) + 3(1-\xbar_2) + 2(1-\xbar_3) \\ &=& 11 - [(2r^2+11r)/(r^2+11r+7) + 10(11r/(11r+5)) + 2(2r/(2r+1))] \\ I &=& [(4r^2 + 11r)/(r^2 + 11r +7) - \xbar_1^2] + 10(\xbar_2 - \xbar_2^2) + 2(\xbar_3 - \xbar_3^2) \\ \end{eqnarray*} The solution corresponds to $U(\beta)=0$ and can be computed using a simple search for the zero of the equation. <>= ufun <- function(r) { xbar <- c( (2*r^2 + 11*r)/(r^2 + 11*r +7), 11*r/(11*r + 5), 2*r/(2*r +1)) 11- (xbar[1] + 10* xbar[2] + 2* xbar[3]) } rhat <- uniroot(ufun, c(1,3), tol= 1e-9)$root bhat <- log(rhat) c(rhat=rhat, bhat=bhat) @ From this we have <>= wfun <- function(r) { beta <- log(r) pl <- 11*beta - (log(r^2 + 11*r + 7) + 10*log(11*r +5) + 2*log(2*r +1)) xbar <- c((2*r^2 + 11*r)/(r^2 + 11*r +7), 11*r/(11*r +5), 2*r/(2*r +1)) U <- 11 - (xbar[1] + 10*xbar[2] + 2*xbar[3]) H <- ((4*r^2 + 11*r)/(r^2 + 11*r +7)- xbar[1]^2) + 10*(xbar[2] - xbar[2]^2) + 2*(xbar[3]- xbar[3]^2) c(loglik=pl, U=U, H=H) } temp <- matrix(c(wfun(1), wfun(rhat)), ncol=2, dimnames=list(c("loglik", "U", "H"), c("beta=0", "beta-hat"))) round(temp, 6) @ When $\beta=0$, the three unique values for $\xbar$ at $t=1$, 2, and 4 are 13/19, 11/16 and 2/3, respectively, and the increments to the cumulative hazard are 1/19, 10/16 = 5/8, and 2/3, see table \ref{tab:val3}. The martingale and score residuals at $\beta=0$ and $\bhat$ are \begin{center} \begin{tabular}{cc|lr} Id &Time& \multicolumn{1}{c}{$M(0)$} &\multicolumn{1}{c}{$M(\bhat)$} \\ \hline A&1 & $1-1/19 = 18/19 $&0.85531\\ B&1 & $0-1/19 = -1/19 $&-0.02593\\ C&2 & $1-(1/19 + 5/8)= 49/152 $&0.17636 \\ D&2 & $1-(1/19 + 5/8)= 49/152 $&0.17636\\ E&2 & $1-(1/19 + 5/8)= 49/152 $&0.65131\\ F&2 & $0-(1/19 + 5/8)= -103/152 $&-0.82364\\ G&3 & $0-(1/19 + 5/8)= -103/152 $&-0.34869\\ H&4 & $1-(1/19 + 5/8 +2/3)= -157/456 $&-0.64894\\ I&5 & $0-(1/19 + 5/8 +2/3)= -613/456 $&-0.69808\\ \end{tabular} \end{center} Score residuals at $\beta=0$ are \begin{center} \begin{tabular}{cc|r} Id &Time& Score \\ \hline A&1 &$(2-13/19)(1-1/19)$\\ B&1 &$(0-13/19)(0-1/19)$\\ C&2 &$ (1-13/19)(0-1/19) + (1-11/16)(1-5/8) $ \\ D&2 &$(1-13/19)(0-1/19) + (1-11/16)(1-5/8)$ \\ E&2 &$(0-13/19)(0-1/19) + (0-11/16)(1-5/8)$ \\ F&2 &$(1-13/19)(0-1/19) + (1-11/16)(0-5/8)$ \\ G&3 &$(1-13/19)(0-1/19) + (0-11/16)(0-5/8)$ \\ H&4 &$(1-13/19)(0-1/19) + (1-11/16)(0-5/8) $ \\ && $ + (1-2/3)(1-2/3)$ \\ I&5 &$(1-13/19)(0-1/19) + (1-11/16)(0-5/8)$ \\ & &$+ (0-2/3)(0-2/3) $ \\ \end{tabular} \end{center} {\splus} also returns unweighted residuals by default, with an option to return the weighted version; it is the weighted sum of residuals that totals zero, $\sum w_i \Mhat_i=0$. Whether the weighted or the unweighted form is more useful depends on the intended application, neither is more ``correct'' than the other. {\splus} does differ for the dfbeta residuals, for which the default is to return weighted values. For the third observation in this data set, for instance, the unweighted dfbeta is an approximation to the change in $\bhat$ that will occur if the case weight is changed from 2 to 3, corresponding to deletion of one of the three ``subjects'' that this observation represents, and the weighted form approximates a change in the case weight from 0 to 3, i.e., deletion of the entire observation. The increments of the Nelson-Aalen estimate of the hazard are shown in the rightmost column of table \ref{tab:val3}. The hazard estimate for a hypothetical subject with covariate $X^\dagger$ is $\Lambda_i(t) = \exp(X^\dagger \beta) \Lambda_0(t)$ and the survival estimate is $S_i(t)= \exp(-\Lambda_i(t))$. The two term of the variance, for $X^\dagger=0$, are Term1 + $d'Vd$: \begin{center} \begin{tabular}{c|l} Time & Term 1 \\ \hline 1& $1/(r^2 + 11r+7)^2$ \\ 2& $1/(r^2 + 11r+7)^2 + 10/(11r+5)^2$ \\ 4& $1/(r^2 + 11r+7)^2 + 10/(11r+5)^2 + 2/(2r+1)^2$ \\ \multicolumn{2}{c}{} \\ Time & $d$ \\ \hline 1& $(2r^2+11r)/(r^2+11r+7)^2$ \\ 2& $(2r^2+11r)/(r^2+11r+7)^2 + 110r/(11r+5)^2$ \\ 4& $(2r^2+11r)/(r^2+11r+7)^2 + 110r/(11r+5)^2 + 4r/(2r+1)^2$ \end{tabular} \end{center} For $\beta=\log(2)$ and $X^\dagger =0$, where $k\equiv$ the variance of $\bhat$ = 1/2.153895 this reduces to \begin{center} \begin{tabular}{c|ll} Time & \multicolumn{2}{c}{Variance}\\ \hline 1 & 1/1089 &+ $k(30/1089)^2$ \\ 2 & (1/1089+ 10/729) &+ $k(30/1089+ 220/729)^2 $ \\ 4 & (1/1089+ 10/729 + 2/25)&+ $k(30/1089+ 220/729 + 8/25)^2$\\ \end{tabular} \end{center} giving numeric values of 0.0012706, 0.0649885, and 0.2903805, respectively. \subsection{Efron approximation} For the Efron approximation the combination of tied times and case weights can be approached in at least two ways. One is to treat the case weights as replication counts. There are then 10 tied deaths at time 2 in the data above, and the Efron approximation involves 10 different denominator terms. Let $a= 7r+3$, the sum of risk scores for the 3 observations with an event at time 2 and $b=4r+2$, the sum of risk scores for the other subjects at risk at time 2. For the replication approach, the loglikelihood is \begin{eqnarray*} LL &=& \{2\beta - \log(r^2 + 11r +7)\} + \\ && \{7\beta - \log(a+b) - \log(.9a+b) - \ldots - \log(.1a+b) \} + \\ && \{2\beta - \log(2r+1) - \log(r+1)\}. \end{eqnarray*} A test program can be created by comparing results from the weighted data set (9 observations) to the unweighted replicated data set (19 observations). This is the approach taken by SAS \code{phreg} using the \code{freq} statement. It's advantage is that the appropriate result for all of the weighted computations is perfectly clear the disadvantage is that the only integer case weights are supported. (A secondary advantage is that I did not need to create another algebraic derivation for this appendix.) A second approach, used in {\splus}, allows for non-integer weights. The data is considered to be 3 tied observations, and the log-likelihood at time 2 is the sum of 3 weighted terms. The first term of the three is one of \begin{eqnarray*} && 3 [\beta - \log(a+b)] \\ && 4 [\beta - \log(a+b)] \\ &{\rm or}&3 [0 - \log(a+b)], \end{eqnarray*} depending on whether the event for observation C, D or E actually happened first (had we observed the time scale more exactly); the leading multiplier of 3, 4 or 3 is the case weight. The second term is one of \begin{eqnarray*} && 4 [\beta - \log(4s+3+b)] \\ && 3 [0 - \log(4s+3+b)] \\ && 3 [\beta - \log(3s+3+b)] \\ && 3 [\beta - \log(3s+3+b)] \\ && 3 [0 - \log(4s+3+b)] \\ &{\rm or}&4 [\beta - \log(4s+3+b)]. \end{eqnarray*} The first choice corresponds to an event order of observation C then D (subject D has the event, with D and E still at risk), the second to $C \rightarrow E$, then $D\rightarrow C$, $D\rightarrow E$, $E \rightarrow C$ and $E \rightarrow D$, respectively. For a weighted Efron approximation first replace the argument to the $\log$ function by its average argument, just as in the unweighted case. Once this is done the average term in the above corresponds to using an average weight of 10/3. The final log-likelihood and score statistic are \begin{eqnarray*} LL &=& \{2\beta - \log(r^2 + 11r +7)\} \\ && + \{7\beta - (10/3)[\log(a+b) + \log(2a/3 +b) + \log(a/3+b)] \} \\&& + 2\{\beta - \log(2r+1) \} \\ \\ U &=& (2- \xbar_1) + 2(1-\xbar_3) \\ && + 7 - (10/3)[\xbar_2 + 26r/(26r+12) + 19r/(19r+9)] \\ &=& 11 -(\xbar_1 + (10/3)(\xbar_2 + \xbar_{2b} +\xbar_{2c}) + 2\xbar_3)\\ \\ I &=& [(4s^2+11s)/(s^2+11s+7)- \xbar_1^2] \\ &&+ (10/3)[ (\xbar_2- \xbar_2^2) + (\xbar_{2b}- \xbar_{2b}^2) + (\xbar_{2b}- \xbar_{2b}^2) \\ &&+2(\xbar_3 - \xbar_3^2) \\ \end{eqnarray*} The solution is at $\beta=.87260425$, and $$ \begin{array}{ll} LL(0)=-30.29218 & LL(\bhat)=-29.41678 \\ U(0) = 2.148183 & U(\bhat) = 0 \\ \imat(0) = 2.929182 & \imat(\bhat) = 1.969447 \,. \end{array} $$ The hazard increment and mean at times 1 and 4 are identical to those for the Breslow approximation, as shown in table \ref{tab:val3}. At time 2, the number at risk for the first, second and third portions of the hazard increment are $n_1= 11r+5$, $n_2= (2/3)(7r+3) + 4r+2 = (26r+12)/3$, and $n_3=(1/3)(7r+3) + 4r+2 = (19r+9)/3$. Subjects F--I experience the full hazard at time 2 of $(10/3)(1/n_1 + 1/n_2 + 1/n_3)$, subjects B--D experience $(10/3)(1/n_1 + 2/3n_2 + 1/3n_3)$. Thus, at $\beta=0$ the martingale residuals are \begin{center} \begin{tabular}{cc|ll} Id& Time & \multicolumn{1}{c}{$\Mhat(0)$} \\ \hline A & 1 & 1 - 1/19 & = 18/19 \\ B & 1 & 0 - 1/19 & = -1/19 \\ C & 2 & 1 - (1/19 + 10/48 + 20/114 + 10/84)& =473/1064 \\ D & 2 & 1 - (1/19 + 10/48 + 20/114 + 10/84)& =473/1064 \\ E & 2 & 1 - (1/19 + 10/48 + 20/114 + 10/84) &=473/1064 \\ F & 2 & 0 - (1/19 + 10/48 + 10/38\phantom{4} + 10/28)& =-2813/3192 \\ G & 3 & 0 - (1/19 + 10/48 + 10/38\phantom{4} + 10/28) &=-2813/3192 \\ H & 4 & 1 - (1/19 + 10/48 + 10/38\phantom{4} + 10/28 + 2/3) &=-1749/3192 \\ I & 5 & 0 - (1/19 + 10/48 + 10/38\phantom{4} + 10/28 + 2/3) &=-4941/3192 \end{tabular} \end{center} The hazard estimate for a hypothetical subject with covariate $X^\dagger$ is $\Lambda_i(t) = \exp(X^\dagger \beta) \Lambda_0(t)$, $\Lambda_0$ has increments of $1/(r^2 + 11r +7$, $(10/3)(1/n_1 + 1/n_2 + 1/n_3)$ and $2/(2r+1)$. This increment at time 2 is a little larger than the Breslow jump of $10/d1$. The first term of the variance will have an increment of $[\exp((X^\dagger \beta)(]^2 (10/3)(1/n_1^2 + 1/n_2^2 + 1/n_3^2)$ at time 2. The increment to the cumulative distance from the center $d$ will be \begin{eqnarray*} && [X^\dagger - \frac{11r}{11r+5}] \frac{10}{3 n_1} \\ &+& [X^\dagger -\frac{(2/3)7r + 4r}{n2} ] (10/3)(1/n_2) \\ &+& [X^\dagger -\frac{(1/3)7r + 4r}{n2} ] (10/3)(1/n_3) \end{eqnarray*} For $X^\dagger = 1$ and $\beta=\pi/3$ we get cumulative hazard and variance below. We have $r\equiv e^\pi/3$, $V$= %\begin{tabular}{l$=$l|l$+$l$=$r} %\multicolumn{2}{c}{$\Lambda$} & \multicolumn{3}{c}{Variance} \\ \hline %e/(r^2+ 11r+7) & 0.03272832 & e^2/(r^2+ 11r+7)^2 & \end{document} survival/tests/0000755000175100001440000000000013070714004013301 5ustar hornikuserssurvival/tests/singtest.Rout.save0000644000175100001440000000366712055204303016763 0ustar hornikusers R version 2.15.2 (2012-10-26) -- "Trick or Treat" Copyright (C) 2012 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # A simple test of an overdetermined system > # Should give a set of NA coefficients > # > test1 <- data.frame(time= c(4, 3,1,1,2,2,3), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0)) > > temp <- rep(0:3, rep(7,4)) > > stest <- data.frame(start = 10*temp, + stop = 10*temp + test1$time, + status = rep(test1$status,4), + x = c(test1$x+ 1:7, rep(test1$x,3)), + epoch = rep(1:4, rep(7,4))) > > # Will create a warning about a singular X matrix > fit1 <- coxph(Surv(start, stop, status) ~ x * factor(epoch), stest) Warning message: In coxph(Surv(start, stop, status) ~ x * factor(epoch), stest) : X matrix deemed to be singular; variable 2 3 4 > fit1$coef # elements 2:4 should be NA x factor(epoch)2 factor(epoch)3 factor(epoch)4 0.1041579 NA NA NA x:factor(epoch)2 x:factor(epoch)3 x:factor(epoch)4 1.5726996 1.5726996 1.5726996 > all.equal(is.na(fit1$coef), c(F,T,T,T,F,F,F), check.attributes=FALSE) [1] TRUE > > proc.time() user system elapsed 0.168 0.032 0.193 survival/tests/anova.R0000644000175100001440000000204212164374110014531 0ustar hornikusers# # Test out anova, with strata terms # options(na.action=na.omit) library(survival) fit1 <- coxph(Surv(time, status) ~ ph.ecog + wt.loss + strata(sex) + poly(age,3), lung) ztemp <- anova(fit1) tdata <- na.omit(lung[, c('time', 'status', 'ph.ecog', 'wt.loss', 'sex', 'age')]) fit2 <- coxph(Surv(time, status)~ ph.ecog + wt.loss + poly(age,3) + strata(sex), data=tdata) ztemp2 <- anova(fit2) all.equal(ztemp, ztemp2) fit2 <- coxph(Surv(time, status) ~ ph.ecog + wt.loss + strata(sex), tdata) fit3 <- coxph(Surv(time, status) ~ ph.ecog + strata(sex), tdata) all.equal(ztemp$loglik, c(fit1$loglik[1], fit3$loglik[2], fit2$loglik[2], fit1$loglik[2])) all.equal(ztemp$Chisq[-1], 2* diff(ztemp$loglik)) all.equal(ztemp$Df[-1], c(1,1,3)) ztemp2 <- anova(fit3, fit2, fit1) all.equal(ztemp2$loglik, ztemp$loglik[-1]) all.equal(ztemp2$Chisq[2:3], ztemp$Chisq[3:4]) # Change from ztemp2$P; it's a data frame and in R 3.0.2 abbreviated names # give a warning all.equal(ztemp2[[4]][2:3], ztemp[[4]][3:4]) survival/tests/model.matrix.Rout.save0000644000175100001440000000611012466142446017527 0ustar hornikusers R Under development (unstable) (2014-09-01 r66509) -- "Unsuffered Consequences" Copyright (C) 2014 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # Test out the revised model.matrix code > # > test1 <- data.frame(time= c(9, 3,1,1,6,6,8), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0), + z= factor(c('a', 'a', 'b', 'b', 'c', 'c', 'a'))) > > fit1 <- coxph(Surv(time, status) ~ z, test1, iter=1) > fit2 <- coxph(Surv(time, status) ~z, test1, x=T, iter=1) > all.equal(model.matrix(fit1), fit2$x) [1] TRUE > > # This has no level 'b', make sure dummies recode properly > test2 <- data.frame(time= c(9, 3,1,1,6,6,8), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0), + z= factor(c('a', 'a', 'a', 'a', 'c', 'c', 'a'))) > > ftest <- model.frame(fit1, data=test2) > all.equal(levels(ftest$z), levels(test1$z)) [1] TRUE > > # xtest will have one more row than the others, since it does not delete > # the observation with a missing value for status > xtest <- model.matrix(fit1, data=test2) > dummy <- fit2$x > dummy[,1] <- 0 > all.equal(xtest[-2,], dummy, check.attributes=FALSE) [1] TRUE > > # The case of a strata by factor interaction > # Use iter=0 since there are too many covariates and it won't converge > test1$x2 <- factor(rep(1:2, length=7)) > fit3 <- coxph(Surv(time, status) ~ strata(x2)*z, test1, iter=0) > xx <- model.matrix(fit3) > all.equal(attr(xx, "assign"), c(2,2,3,3)) [1] TRUE > all.equal(colnames(xx), c("zb", "zc", "strata(x2)2:zb", + "strata(x2)2:zc")) [1] TRUE > all.equal(attr(xx, "contrasts"), + list("strata(x2)"= "contr.treatment", z="contr.treatment")) [1] TRUE > > fit3b <- coxph(Surv(time, status) ~ strata(x2)*z, test1, iter=0, x=TRUE) > all.equal(fit3b$x, xx) [1] TRUE > > > # A model with a tt term > fit4 <- coxph(Surv(time, status) ~ tt(x) + x, test1, iter=0, + tt = function(x, t, ...) x*t) > ff <- model.frame(fit4) > # There is 1 subject in the final risk set, 4 at risk at time 6, 6 at time 1 > # The .strata. variable numbers from last time point to first > all.equal(ff$.strata., rep(1:3, c(1, 4,6))) [1] TRUE > all.equal(ff[["tt(x)"]], ff$x* c(9,6,1)[ff$.strata.]) [1] TRUE > > xx <- model.matrix(fit4) > all.equal(xx[,1], ff[[2]], check.attributes=FALSE) [1] TRUE > > > proc.time() user system elapsed 0.196 0.028 0.220 survival/tests/expected.Rout.save0000644000175100001440000002611012257335007016722 0ustar hornikusers R version 3.0.1 (2013-05-16) -- "Good Sport" Copyright (C) 2013 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # Tests of expected survival > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > # > # This makes several scripts easier > # Certain tests depended in the now-depreciated date library > {if (is.R()) mdy.date <- function(m, d, y) { + y <- ifelse(y<100, y+1900, y) + as.Date(paste(m,d,y, sep='/'), "%m/%d/%Y") + } + else mdy.date <- function(m,d,y) { + y <- ifelse(y<100, y+1900, y) + timeDate(paste(y, m, d, sep='/'), in.format="%Y/%m/%d") + } + } > > # This function takes a single subject and walks down the rate table > # Input: the vector of starting points, futime, and a ratetable > # Output: the full history of walking through said table. Let n= #unique > # rates that were used > # cell = n by #dims of the table: index of the table cell > # days = time spent in cell > # hazard= accumulated hazard = days * rate > # This does not do date or factor conversions -- start has to be numeric > # > ratewalk <- function(start, futime, ratetable=survexp.us) { + if (!is.ratetable(ratetable)) stop("Bad rate table") + ratedim <- dim(ratetable) + nvar <- length(ratedim) + if (length(start) != nvar) stop("Wrong length for start") + if (futime <=0) stop("Invalid futime") + + attR <- attributes(ratetable) + discrete <- (attR$type ==1) #discrete categories + + maxn <- sum(!discrete)*prod(ratedim[!discrete]) #most cells you can hit + cell <- matrix(0, nrow=maxn, ncol=nvar) + days <- hazard <- double(maxn) + + eps <- 1e-8 #Avoid round off error + n <- 0 + while (futime >0) { + n <- n+1 + #what cell am I in? + # Note that at the edges of the rate table, we use the edge: if + # it only goes up the the year 2000, year 2000 is used for any + # dates beyond. This effectively eliminates one boundary + cell[n,discrete] <- start[discrete] + edge <- futime #time to nearest edge, or finish + for (j in which(!discrete)) { + indx <- sum(start[j] >= attR$cutpoints[[j]]-eps) + cell[n, j] <- max(1, indx) + if (indx < ratedim[j]) + edge <- min(edge, (attR$cutpoints[[j]])[indx+1] - start[j]) + } + days[n] <- edge #this many days in the cell + # using a matrix as a subscript is so handy sometimes + hazard[n] <- edge * (as.matrix(ratetable))[cell[n,,drop=F]] + futime <- futime - edge #amount of time yet to account for + start[!discrete] <- start[!discrete] + edge #walk forward in time + } + list(cell=cell[1:n,], days=days[1:n], hazard=hazard[1:n]) + } > > # Simple test of ratewalk: 20 years old, start on 7Sep 1960 (day 250) > # 116 days at the 1960, 20 year old male rate, through the end of the day > # on 12/31/1960, then 84 days at the 1961 rate. > # The decennial q for 1960 males is .00169. > zz <- ratewalk(c(20.4*365.25, 1, 250), 200) > all.equal(zz$hazard[1], -(116/365.25)*log(1-.00169)) [1] TRUE > all.equal(zz$days, c(116,84)) [1] TRUE > > > # > # Simple case 1: a single male subject, born 1/1/36 and entered on study 1/2/55 > # > # Compute the 1, 5, 10 and 12 year expected survival > > temp1 <- mdy.date(1,1,36) > temp2 <- mdy.date(1,2,55) > exp1 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=1, race='white'), + ratetable=survexp.usr,times=c(366, 1827, 3653, 4383)) > > tyear <- as.numeric(temp2 - mdy.date(1,1,1960)) > h1 <- ratewalk(c(temp2-temp1, 1, 1, tyear), 366, survexp.usr) > h2 <- ratewalk(c(temp2-temp1, 1, 1, tyear), 1827, survexp.usr) > h3 <- ratewalk(c(temp2-temp1, 1, 1, tyear), 3653, survexp.usr) > h4 <- ratewalk(c(temp2-temp1, 1, 1, tyear), 4383, survexp.usr) > > aeq(-log(exp1$surv), c(sum(h1$hazard), sum(h2$hazard), sum(h3$hazard), + sum(h4$hazard))) [1] TRUE > > > # Just a little harder: > # Born 3/1/25 and entered the study on 6/10/55. The code creates shifted > # dates to align with US rate tables - entry is 59 days earlier (days from > # 1/1/25 to 3/1/25). > # > temp1 <- mdy.date(3,1,25) > temp2 <- mdy.date(6,10,55) > exp1 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=2, race='black'), + ratetable=survexp.usr,times=c(366, 1827, 3653, 4383)) > > tyear <- as.numeric(temp2 - mdy.date(1,1,1960)) - 59 > h1 <- ratewalk(c(temp2-temp1, 2, 2, tyear), 366, survexp.usr) > h2 <- ratewalk(c(temp2-temp1, 2, 2, tyear), 1827, survexp.usr) > h3 <- ratewalk(c(temp2-temp1, 2, 2, tyear), 3653, survexp.usr) > h4 <- ratewalk(c(temp2-temp1, 2, 2, tyear), 4383, survexp.usr) > > aeq(-log(exp1$surv), c(sum(h1$hazard), sum(h2$hazard), sum(h3$hazard), + sum(h4$hazard))) [1] TRUE > > # > # Simple case 2: make sure that the averages are correct, for Ederer method > # > # Compute the 1, 5, 10 and 12 year expected survival > > temp1 <- mdy.date(1:6,6:11,1890:1895) > temp2 <- mdy.date(6:1,11:6,c(55:50)) > temp3 <- c(1,2,1,2,1,2) > age <- temp2 - temp1 > > exp1 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=temp3), + times=c(366, 1827, 3653, 4383)) > exp2 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=temp3) + I(1:6), + times=c(366, 1827, 3653, 4383)) > exp3 <- exp2$surv > for (i in 1:length(temp1)){ + exp3[,i] <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=temp3), + times=c(366, 1827, 3653, 4383), subset=i)$surv + } > > > print(aeq(exp2$surv, exp3)) [1] TRUE > print(all.equal(exp1$surv, apply(exp2$surv, 1, mean))) [1] TRUE > > # They agree, but are they right? > # > for (i in 1:length(temp1)) { + offset <- as.numeric(temp1[i] - mdy.date(1,1, 1889+i)) + tyear = (as.numeric(temp2[i] - mdy.date(1,1,1960))) - offset + haz1 <- ratewalk(c((temp2-temp1)[i], temp3[i], tyear), 366) + haz2 <- ratewalk(c((temp2-temp1)[i], temp3[i], tyear), 1827) + haz3 <- ratewalk(c((temp2-temp1)[i], temp3[i], tyear), 3653) + haz4 <- ratewalk(c((temp2-temp1)[i], temp3[i], tyear), 4383) + print(aeq(-log(exp2$surv[,i]), c(sum(haz1$hazard), sum(haz2$hazard), + sum(haz3$hazard), sum(haz4$hazard)))) + } [1] TRUE [1] TRUE [1] TRUE [1] TRUE [1] TRUE [1] TRUE > > # > # Check that adding more time points doesn't change things > # > exp4 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=temp3) + I(1:6), + times=sort(c(366, 1827, 3653, 4383, 30*(1:100)))) > aeq(exp4$surv[match(exp2$time, exp4$time),], exp2$surv) [1] TRUE > > exp4 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=temp3), + times=sort(c(366, 1827, 3653, 4383, 30*(1:100)))) > aeq(exp1$surv, exp4$surv[match(exp1$time, exp4$time, nomatch=0)]) [1] TRUE > > > # > # Now test Hakulinen's method, assuming an analysis date of 3/1/57 > # > futime <- mdy.date(3,1,57) - temp2 > xtime <- sort(c(futime, 30, 60, 185, 365)) > > exp1 <- survexp(futime ~ ratetable(year=temp2, age=(temp2-temp1), sex=1), + times=xtime, conditional=F) > exp2 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=1) + I(1:6), + times=futime) > > wt <- rep(1,6) > con <- double(6) > for (i in 1:6) { + con[i] <- sum(exp2$surv[i,i:6])/sum(wt[i:6]) + wt <- exp2$surv[i,] + } > > exp1$surv[match(futime, xtime)] [1] 0.9557362 0.9285840 0.9025661 0.8774220 0.8532489 0.8297416 > aeq(exp1$surv[match(futime, xtime)], cumprod(con)) [1] TRUE > > > # > # Now for the conditional method > # > exp1 <- survexp(futime ~ ratetable(year=temp2, age=(temp2-temp1), sex=1), + times=xtime, conditional=T) > > cond <- exp2$surv > for (i in 6:2) cond[i,] <- (cond[i,]/cond[i-1,]) #conditional survival > for (i in 1:6) con[i] <- exp(mean(log(cond[i, i:6]))) > > all.equal(exp1$surv[match(futime, xtime)], cumprod(con)) [1] TRUE > cumprod(con) [1] 0.9556656 0.9284398 0.9023612 0.8771798 0.8529944 0.8294940 > > # > # Test out expected survival, when the parent pop is another Cox model > # > test1 <- data.frame(time= c(4, 3,1,1,2,2,3), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0)) > > fit <- coxph(Surv(time, status) ~x, test1, method='breslow') > > dummy <- data.frame(time=c(.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5), + status=c(1,0,1,0,1,0,1,1,1), x=(-4:4)/2) > > efit <- survexp(time ~ ratetable(x=x), dummy, ratetable=fit, cohort=F) > > # > # Now, compare to the true answer, which is known to us > # > ss <- exp(fit$coef) > haz <- c( 1/(3*ss+3), 2/(ss+3), 1) #truth at time 0,1,2,4+ > chaz <- cumsum(c(0,haz)) > chaz2 <- chaz[c(1,2,2,3,3,3,3,4,4)] > > risk <- exp(fit$coef*dummy$x) > efit2 <- exp(-risk*chaz2) > > all.equal(as.vector(efit), as.vector(efit2)) #ignore mismatched name attrib [1] TRUE > > # > # Now test the direct-adjusted curve (Ederer) > # > efit <- survexp( ~ ratetable(x=x), dummy, ratetable=fit, se=F) > direct <- survfit(fit, newdata=dummy, censor=FALSE)$surv > > chaz <- chaz[-1] #drop time 0 > d2 <- exp(outer(-chaz, risk)) > all.equal(as.vector(direct), as.vector(d2)) #this tests survfit [1] TRUE > > all.equal(as.vector(efit$surv), as.vector(apply(direct,1,mean))) #direct [1] TRUE > > # Check out the "times" arg of survexp > efit2 <- survexp( ~ ratetable(x=x), dummy, ratetable=fit, se=F, + times=c(.5, 2, 3.5,6)) > aeq(efit2$surv, c(1, efit$surv[c(2,2,3)])) [1] TRUE > > # > # Now test out the Hakulinen method (Bonsel's method) > # By construction, we have a large correlation between x and censoring > # > # In theory, hak1 and hak2 would be the same. In practice, like a KM and > # F-H, they differ when n is small. > # > efit <- survexp( time ~ ratetable(x=x), dummy, ratetable=fit, se=F) > > surv <- wt <- rep(1,9) > tt <- c(1,2,4) > hak1 <- hak2 <- NULL > for (i in 1:3) { + wt[dummy$time < tt[i]] <- 0 + hak1 <- c(hak1, exp(-sum(haz[i]*risk*surv*wt)/sum(surv*wt))) + hak2 <- c(hak2, sum(exp(-haz[i]*risk)*surv*wt)/sum(surv*wt)) + surv <- surv * exp(-haz[i]*risk) + } > > all.equal(as.vector(efit$surv), as.vector(cumprod(hak1))) [1] TRUE > > # > # Now do the conditional estimate > # > efit <- survexp( time ~ ratetable(x=x), dummy, ratetable=fit, se=F, + conditional=T) > wt <- rep(1,9) > cond <- NULL > for (i in 1:3) { + wt[dummy$time < tt[i]] <- 0 + cond <- c(cond, exp(-sum(haz[i]*risk*wt)/sum(wt))) + } > > all.equal(as.vector(efit$surv), as.vector(cumprod(cond))) [1] TRUE > > proc.time() user system elapsed 0.692 0.076 0.766 survival/tests/factor2.Rout.save0000644000175100001440000000345111732700061016455 0ustar hornikusers R version 2.14.0 (2011-10-31) Copyright (C) 2011 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > options(na.action=na.exclude) > # > # More tests of factors in prediction, using a new data set > # > fit <- coxph(Surv(time, status) ~ factor(ph.ecog), lung) > > tdata <- data.frame(ph.ecog = factor(0:3)) > p1 <- predict(fit, newdata=tdata, type='lp') > p2 <- predict(fit, type='lp') > aeq(p1, p2[match(0:3, lung$ph.ecog)]) [1] TRUE > > fit2 <- coxph(Surv(time, status) ~ factor(ph.ecog) + factor(sex), lung) > tdata <- expand.grid(ph.ecog = factor(0:3), sex=factor(1:2)) > p1 <- predict(fit2, newdata=tdata, type='risk') > > xdata <- expand.grid(ph.ecog=factor(1:3), sex=factor(1:2)) > p2 <- predict(fit2, newdata=xdata, type='risk') > all.equal(p2, p1[c(2:4, 6:8)], check.attributes=FALSE) [1] TRUE > > > fit3 <- survreg(Surv(time, status) ~ factor(ph.ecog) + age, lung) > tdata <- data.frame(ph.ecog=factor(0:3), age=50) > predict(fit, type='lp', newdata=tdata) 1 2 3 4 -0.39518177 -0.02634168 0.52120527 1.81279848 > predict(fit3, type='lp', newdata=tdata) 1 2 3 4 6.399571 6.142938 5.770523 4.916993 > survival/tests/strata2.Rout.save0000644000175100001440000000334412055204344016500 0ustar hornikusers R version 2.15.2 (2012-10-26) -- "Trick or Treat" Copyright (C) 2012 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # > # New tests 4/2010 to validate strata by covariate interactions > # > library(survival) Loading required package: splines > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > tdata <- lung > tdata$sex <- lung$sex +3 > > # Both of these should produce warning messages about singular X, since there > # are ph.ecog=3 subjects in only 1 of the strata. > # Does not affect the test > fit1 <- coxph(Surv(time, status) ~ age + sex:strata(ph.ecog), lung) Warning message: In coxph(Surv(time, status) ~ age + sex:strata(ph.ecog), lung) : X matrix deemed to be singular; variable 5 > fit2 <- coxph(Surv(time, status) ~ age + sex:strata(ph.ecog), tdata) Warning message: In coxph(Surv(time, status) ~ age + sex:strata(ph.ecog), tdata) : X matrix deemed to be singular; variable 5 > > aeq(fit1$coef, fit2$coef) [1] TRUE > aeq(fit1$var, fit2$var) [1] TRUE > aeq(predict(fit1), predict(fit2)) [1] TRUE > > proc.time() user system elapsed 0.200 0.028 0.224 survival/tests/r_capacitor.R0000644000175100001440000000104111732700061015707 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) capacitor <- read.table('data.capacitor', row.names=1, col.names=c('', 'days', 'event', 'voltage')) fitig <- survreg(Surv(days, event)~voltage, dist = "gaussian", data = capacitor) summary(fitig) fitix <- survreg(Surv(days, event)~voltage, dist = "extreme", data = capacitor) summary(fitix) fitil <- survreg(Surv(days, event)~voltage, dist = "logistic", data = capacitor) summary(fitil) survival/tests/fr_cancer.Rout.save0000644000175100001440000001074212536400614017044 0ustar hornikusers R Under development (unstable) (2015-06-04 r68474) -- "Unsuffered Consequences" Copyright (C) 2015 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # Here is a test case with multiple smoothing terms > # > > fit0 <- coxph(Surv(time, status) ~ ph.ecog + age, lung) > fit1 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,3), lung) > fit2 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,4), lung) > fit3 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,8), lung) > > > > fit4 <- coxph(Surv(time, status) ~ ph.ecog + pspline(wt.loss,3), lung) > > fit5 <-coxph(Surv(time, status) ~ ph.ecog + pspline(age,3) + + pspline(wt.loss,3), lung) > > fit1 Call: coxph(formula = Surv(time, status) ~ ph.ecog + pspline(age, 3), data = lung) coef se(coef) se2 Chisq DF p ph.ecog 0.44802 0.11707 0.11678 14.64453 1.00 0.00013 pspline(age, 3), linear 0.01126 0.00928 0.00928 1.47231 1.00 0.22498 pspline(age, 3), nonlin 2.07924 2.08 0.37143 Iterations: 4 outer, 12 Newton-Raphson Theta= 0.861 Degrees of freedom for terms= 1.0 3.1 Likelihood ratio test=21.9 on 4.08 df, p=0.000227 n=227 (1 observation deleted due to missingness) > fit2 Call: coxph(formula = Surv(time, status) ~ ph.ecog + pspline(age, 4), data = lung) coef se(coef) se2 Chisq DF p ph.ecog 0.45047 0.11766 0.11723 14.65751 1.00 0.00013 pspline(age, 4), linear 0.01117 0.00927 0.00927 1.45195 1.00 0.22822 pspline(age, 4), nonlin 2.95816 3.08 0.41197 Iterations: 4 outer, 11 Newton-Raphson Theta= 0.797 Degrees of freedom for terms= 1.0 4.1 Likelihood ratio test=22.7 on 5.07 df, p=0.000412 n=227 (1 observation deleted due to missingness) > fit3 Call: coxph(formula = Surv(time, status) ~ ph.ecog + pspline(age, 8), data = lung) coef se(coef) se2 Chisq DF p ph.ecog 0.47640 0.12024 0.11925 15.69732 1.00 7.4e-05 pspline(age, 8), linear 0.01172 0.00923 0.00923 1.61161 1.00 0.20 pspline(age, 8), nonlin 6.93188 6.99 0.43 Iterations: 5 outer, 15 Newton-Raphson Theta= 0.691 Degrees of freedom for terms= 1 8 Likelihood ratio test=27.6 on 8.97 df, p=0.00108 n=227 (1 observation deleted due to missingness) > fit4 Call: coxph(formula = Surv(time, status) ~ ph.ecog + pspline(wt.loss, 3), data = lung) coef se(coef) se2 Chisq DF p ph.ecog 0.51545 0.12960 0.12737 15.81939 1.00 7e-05 pspline(wt.loss, 3), line -0.00702 0.00655 0.00655 1.14638 1.00 0.28 pspline(wt.loss, 3), nonl 2.44612 2.09 0.31 Iterations: 3 outer, 10 Newton-Raphson Theta= 0.776 Degrees of freedom for terms= 1.0 3.1 Likelihood ratio test=21.1 on 4.06 df, p=0.000326 n=213 (15 observations deleted due to missingness) > fit5 Call: coxph(formula = Surv(time, status) ~ ph.ecog + pspline(age, 3) + pspline(wt.loss, 3), data = lung) coef se(coef) se2 Chisq DF p ph.ecog 0.47422 0.13495 0.13206 12.34842 1.00 0.00044 pspline(age, 3), linear 0.01368 0.00976 0.00974 1.96406 1.00 0.16108 pspline(age, 3), nonlin 1.90116 2.07 0.40284 pspline(wt.loss, 3), line -0.00717 0.00661 0.00660 1.17529 1.00 0.27832 pspline(wt.loss, 3), nonl 2.07729 2.03 0.35929 Iterations: 4 outer, 12 Newton-Raphson Theta= 0.85 Theta= 0.779 Degrees of freedom for terms= 1.0 3.1 3.0 Likelihood ratio test=25.2 on 7.06 df, p=0.000726 n=213 (15 observations deleted due to missingness) > > rm(fit1, fit2, fit3, fit4, fit5) > > proc.time() user system elapsed 0.276 0.024 0.294 survival/tests/data.rat20000644000175100001440000001001311732700061015000 0ustar hornikusers1 1 1 60 182 1 2 1 1 60 182 0 3 1 1 60 63 1 3 1 2 63 68 1 3 1 3 68 182 0 4 1 1 60 152 1 4 1 2 152 182 0 5 1 1 60 130 1 5 1 2 130 134 1 5 1 3 134 145 1 6 1 1 60 98 1 6 1 2 98 152 1 6 1 1 60 98 1 6 1 2 98 152 1 6 1 3 152 182 1 7 1 1 60 88 1 7 1 2 88 95 1 7 1 3 95 105 1 7 1 4 105 130 1 7 1 5 130 137 1 7 1 6 137 167 1 7 1 7 167 182 0 8 1 1 60 152 1 8 1 2 152 182 0 9 1 1 60 81 1 9 1 2 81 182 0 10 1 1 60 71 1 10 1 2 71 84 1 10 1 3 84 126 1 10 1 4 126 134 1 10 1 5 134 152 1 10 1 6 152 182 0 11 1 1 60 116 1 11 1 2 116 130 1 11 1 3 130 182 0 12 1 1 60 91 1 12 1 2 91 182 0 13 1 1 60 63 1 13 1 2 63 68 1 13 1 3 68 84 1 13 1 4 84 95 1 13 1 5 95 152 1 13 1 6 152 182 0 14 1 1 60 105 1 14 1 2 103 152 1 14 1 3 152 182 0 15 1 1 60 63 1 15 1 2 63 102 1 15 1 3 102 152 1 15 1 4 152 182 0 16 1 1 60 63 1 16 1 2 63 77 1 16 1 3 77 112 1 16 1 4 112 140 1 16 1 5 140 182 0 17 1 1 60 77 1 17 1 2 77 119 1 17 1 3 119 152 1 17 1 4 152 161 1 17 1 5 161 167 1 17 1 6 167 182 0 18 1 1 60 105 1 18 1 2 105 112 1 18 1 3 112 145 1 18 1 4 145 161 1 18 1 5 161 182 1 19 1 1 60 152 1 19 1 2 152 182 1 20 1 1 60 81 1 20 1 2 81 95 1 20 1 3 95 182 0 21 1 1 60 84 1 21 1 2 84 91 1 21 1 3 91 102 1 21 1 4 102 108 1 21 1 5 108 130 1 21 1 6 130 134 1 21 1 7 134 182 0 22 1 1 60 182 0 23 1 1 60 91 1 23 1 2 91 182 0 24 0 1 60 63 1 24 0 2 63 102 1 24 0 3 102 119 1 24 0 4 119 161 1 24 0 5 161 161 1 24 0 6 161 172 1 24 0 7 172 179 1 24 0 8 179 182 0 25 0 1 60 88 1 25 0 2 88 91 1 25 0 3 91 95 1 25 0 4 95 105 1 25 0 5 105 112 1 25 0 6 112 119 1 25 0 7 119 119 1 25 0 8 119 137 1 25 0 9 137 145 1 25 0 10 145 167 1 25 0 11 167 172 1 25 0 12 172 182 0 26 0 1 60 91 1 26 0 2 91 98 1 26 0 3 98 108 1 26 0 4 108 112 1 26 0 5 112 134 1 26 0 6 134 137 1 26 0 7 137 161 1 26 0 8 161 161 1 26 0 9 161 179 1 26 0 10 179 182 0 27 0 1 60 71 1 27 0 2 71 174 1 27 0 2 174 182 0 28 0 1 60 95 1 28 0 2 95 105 1 28 0 3 105 134 1 28 0 4 134 137 1 28 0 5 137 140 1 28 0 6 140 145 1 28 0 7 145 150 1 28 0 8 150 150 1 28 0 9 150 182 0 29 0 1 60 66 1 29 0 2 66 68 1 29 0 3 68 130 1 29 0 4 130 137 1 29 0 5 137 182 0 30 0 1 60 77 1 30 0 2 77 85 1 30 0 3 85 112 1 30 0 4 112 137 1 30 0 5 137 161 1 30 0 6 161 174 1 30 0 7 174 182 0 31 0 1 60 81 1 31 0 2 81 84 1 31 0 3 84 126 1 31 0 4 125 134 1 31 0 5 134 161 1 31 0 6 161 161 1 31 0 7 161 174 1 31 0 8 174 182 0 32 0 1 60 68 1 32 0 2 68 77 1 32 0 3 77 98 1 32 0 4 98 102 1 32 0 5 102 102 1 32 0 6 102 102 1 32 0 7 102 182 0 33 0 1 60 112 1 33 0 2 112 182 0 34 0 1 60 88 1 34 0 2 88 88 1 34 0 3 88 91 1 34 0 4 91 98 1 34 0 5 98 112 1 34 0 6 112 134 1 34 0 7 134 134 1 34 0 8 134 137 1 34 0 9 137 137 1 34 0 10 137 140 1 34 0 11 140 140 1 34 0 12 140 152 1 34 0 13 152 152 1 34 0 14 152 182 0 35 0 1 60 77 1 35 0 2 77 179 1 35 0 3 179 182 0 36 0 1 60 112 1 36 0 2 112 182 0 37 0 1 60 71 1 37 0 2 71 71 1 37 0 3 71 74 1 37 0 4 74 77 1 37 0 5 77 112 1 37 0 6 112 116 1 37 0 7 116 116 1 37 0 8 116 140 1 37 0 9 140 140 1 37 0 10 140 167 1 37 0 11 167 182 0 38 0 1 60 77 1 38 0 2 77 95 1 38 0 3 95 126 1 38 0 4 126 150 1 38 0 5 150 182 0 39 0 1 60 88 1 39 0 2 88 126 1 39 0 3 126 130 1 39 0 4 130 130 1 39 0 5 130 134 1 39 0 6 134 182 0 40 0 1 60 63 1 40 0 2 63 74 1 40 0 3 74 84 1 40 0 4 84 84 1 40 0 5 84 88 1 40 0 6 88 91 1 40 0 7 91 95 1 40 0 8 95 108 1 40 0 9 108 134 1 40 0 10 134 137 1 40 0 11 137 179 1 40 0 12 179 182 0 41 0 1 60 81 1 41 0 2 81 88 1 41 0 3 88 105 1 41 0 4 105 116 1 41 0 5 116 123 1 41 0 6 123 140 1 41 0 7 140 145 1 41 0 8 145 152 1 41 0 9 152 161 1 41 0 10 161 161 1 41 0 11 161 179 1 41 0 12 179 182 0 42 0 1 60 88 1 42 0 2 88 95 1 42 0 3 95 112 1 42 0 4 112 119 1 42 0 5 119 126 1 42 0 6 126 126 1 42 0 7 126 150 1 42 0 8 150 157 1 42 0 9 157 179 1 42 0 10 179 182 0 43 0 1 60 68 1 43 0 2 68 68 1 43 0 3 68 84 1 43 0 4 84 102 1 43 0 5 102 105 1 43 0 6 105 119 1 43 0 7 119 123 1 43 0 8 123 123 1 43 0 9 123 137 1 43 0 10 137 161 1 43 0 11 161 179 1 43 0 12 179 182 0 44 0 1 60 140 1 44 0 2 140 182 0 45 0 1 60 152 1 45 0 2 152 182 1 45 0 3 182 182 1 46 0 1 60 81 1 46 0 2 81 182 0 47 0 1 60 63 1 47 0 2 63 88 1 47 0 3 88 134 1 47 0 4 134 182 0 48 0 1 60 84 1 48 0 2 84 134 1 48 0 3 134 182 1 survival/tests/quantile.R0000644000175100001440000000476112701744412015264 0ustar hornikusers# # Formal test of the quantile routine for survfit library(survival) aeq <- function(x, y, ...) all.equal(as.vector(x), as.vector(y), ...) # There are 8 cases: strata Y/N, ncol(surv) >1, conf.int = T/F # Subcase: the quantile exactly agrees with a horizontal segment of # the curve or not. # First do the 4 cases where fit$surv is a vector # test1 <- data.frame(time= c(9, 3,1,1,6,6,8, 10), status=c(1,NA,1,0,1,1,0, 0), x= c(0, 2,1,1,1,0,0, 0)) # True survival = (6/7) * (3/5) * (1/2) for overall # The q's are chosen to include a point < first jump, mid, after last jump, # and exact intersections with the "flats" of the curve. # qq <- c(13/14, 6/7, 2/3, .5, 9/35, .1) # Nothing on the right hand side, simple survival (no strata) fit1 <- survfit(Surv(time, status) ~ 1, test1, conf.type='none') aeq(quantile(fit1, 1-qq), c(1, 3.5, 6, 9, 9.5, NA)) #without conf.int fit2 <- survfit(Surv(time, status) ~ 1, test1) #with conf.int aeq(quantile(fit2, 1-qq), list(quantile = c(1, 3.5, 6, 9, 9.5, NA), lower = c(1,1,1,6,6,9), upper = rep(as.numeric(NA), 6)), check.attributes=FALSE) aeq(quantile(fit2, 1-qq, FALSE), c(1, 3.5, 6, 9, 9.5, NA)) # Now a variable on the right (strata in the result) # curve 0: (t=6, S=3/4), (t=9, S=3/8) # curve 1: (t=1, S=2/3), (t=6, S= 0) fit1 <- survfit(Surv(time, status) ~ x, test1, conf.type='none') aeq(quantile(fit1, 1-qq), matrix(c(6,6,9,9,NA,NA, 1,1,3.5, 6,6,6), nrow=2, byrow=T)) fit2 <- survfit(Surv(time, status) ~ x, test1) aeq(quantile(fit2, 1-qq, FALSE), matrix(c(6,6,9,9,NA,NA, 1,1,3.5, 6,6,6), nrow=2, byrow=T)) temp <- quantile(fit2, 1-qq) aeq(temp$quantile, matrix(c(6,6,9,9,NA,NA, 1,1,3.5, 6,6,6), nrow=2, byrow=T)) aeq(temp$lower, matrix(c(6,6,6,6,9,9, 1,1,1,1, NA,NA), nrow=2, byrow=T)) aeq(temp$upper, rep(as.numeric(NA), 12)) # Second major case set -- a survfit object where fit$surv is a matrix # This arises from coxph models # There is only 1 subject with ph.ecog=3 which is a nice edge case cfit <- coxph(Surv(time, status) ~ age + strata(ph.ecog), lung) sfit <- survfit(cfit, newdata=data.frame(age=c(50, 70))) qtot <- quantile(sfit, qq) for (i in 1:4) { for (j in 1:2) { temp <- quantile(sfit[i,j], qq) print(c(aeq(qtot$quantile[i,j,], temp$quantile), aeq(qtot$upper[i,j,], temp$upper), aeq(qtot$lower[i,j,], temp$lower))) } } temp <- quantile(sfit, qq, conf.int=FALSE) all.equal(qtot$quantile, temp) survival/tests/fr_ovarian.Rout.save0000644000175100001440000000400112536400664017244 0ustar hornikusers R Under development (unstable) (2015-06-04 r68474) -- "Unsuffered Consequences" Copyright (C) 2015 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # Test on the ovarian data > > fit1 <- coxph(Surv(futime, fustat) ~ rx + age, ovarian) > fit2 <- coxph(Surv(futime, fustat) ~ rx + pspline(age, df=2), + data=ovarian) > fit2$iter [1] 2 8 > > fit2$df [1] 0.9426611 1.9293051 > > fit2$history $`pspline(age, df = 2)` $`pspline(age, df = 2)`$theta [1] 0.4468868 $`pspline(age, df = 2)`$done [1] TRUE $`pspline(age, df = 2)`$history thetas dfs [1,] 1.0000000 1.000000 [2,] 0.0000000 5.000000 [3,] 0.6000000 1.734267 [4,] 0.4845205 1.929305 $`pspline(age, df = 2)`$half [1] 0 > > fit4 <- coxph(Surv(futime, fustat) ~ rx + pspline(age, df=4), + data=ovarian) > fit4 Call: coxph(formula = Surv(futime, fustat) ~ rx + pspline(age, df = 4), data = ovarian) coef se(coef) se2 Chisq DF p rx -0.373 0.761 0.749 0.241 1.00 0.6238 pspline(age, df = 4), lin 0.139 0.044 0.044 9.978 1.00 0.0016 pspline(age, df = 4), non 2.592 2.93 0.4457 Iterations: 3 outer, 14 Newton-Raphson Theta= 0.242 Degrees of freedom for terms= 1.0 3.9 Likelihood ratio test=19.4 on 4.9 df, p=0.00149 n= 26 > > > > proc.time() user system elapsed 0.204 0.020 0.218 survival/tests/difftest.Rout.save0000644000175100001440000000604211732700061016724 0ustar hornikusers R version 2.14.0 Under development (unstable) (2011-04-10 r55401) Copyright (C) 2011 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: x86_64-unknown-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # Test some more features of surv.diff > # > # First, what happens when one group is a dummy > # > > > # > # The AML data, with a third group of early censorings "tacked on" > # > aml3 <- list(time= c( 9, 13, 13, 18, 23, 28, 31, 34, 45, 48, 161, + 5, 5, 8, 8, 12, 16, 23, 27, 30, 33, 43, 45, + 1, 2, 2, 3, 3, 3, 4), + status= c( 1,1,0,1,1,0,1,1,0,1,0, 1,1,1,1,1,0,1,1,1,1,1,1, + 0,0,0,0,0,0,0), + x = as.factor(c(rep("Maintained", 11), + rep("Nonmaintained", 12), rep("Dummy",7) ))) > > aml3 <- data.frame(aml3) > > # These should give the same result (chisq, df), but the second has an > # extra group > survdiff(Surv(time, status) ~x, aml) Call: survdiff(formula = Surv(time, status) ~ x, data = aml) N Observed Expected (O-E)^2/E (O-E)^2/V x=Maintained 11 7 10.69 1.27 3.4 x=Nonmaintained 12 11 7.31 1.86 3.4 Chisq= 3.4 on 1 degrees of freedom, p= 0.0653 > survdiff(Surv(time, status) ~x, aml3) Call: survdiff(formula = Surv(time, status) ~ x, data = aml3) N Observed Expected (O-E)^2/E (O-E)^2/V x=Dummy 7 0 0.00 NaN NaN x=Maintained 11 7 10.69 1.27 3.4 x=Nonmaintained 12 11 7.31 1.86 3.4 Chisq= 3.4 on 1 degrees of freedom, p= 0.0653 > > > # > # Now a test of the stratified log-rank > # There are no tied times within institution, so the coxph program > # can be used to give a complete test > # > fit <- survdiff(Surv(time, status) ~ pat.karno + strata(inst), cancer) > > cfit <- coxph(Surv(time, status) ~ factor(pat.karno) + strata(inst), + cancer, iter=0) > > tdata <- na.omit(cancer[,c('time', 'status', 'pat.karno', 'inst')]) > > temp1 <- tapply(tdata$status-1, list(tdata$pat.karno, tdata$inst), sum) > temp1 <- ifelse(is.na(temp1), 0, temp1) > temp2 <- tapply(cfit$resid, list(tdata$pat.karno, tdata$inst), sum) > temp2 <- ifelse(is.na(temp2), 0, temp2) > > temp2 <- temp1 - temp2 > > #Now temp1=observed, temp2=expected > all.equal(c(temp1), c(fit$obs)) [1] TRUE > all.equal(c(temp2), c(fit$exp)) [1] TRUE > > all.equal(fit$var[-1,-1], solve(cfit$var)) [1] TRUE > > rm(tdata, temp1, temp2) > survival/tests/turnbull.Rout.save0000644000175100001440000001724311732700061016770 0ustar hornikusers R version 2.7.1 (2008-06-23) Copyright (C) 2008 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # The test data set from Turnbull, JASA 1974, 169-73. > # > # status 0=right censored > # 1=exact > # 2=left censored > # > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > > turnbull <- data.frame( time =c( 1,1,1, 2,2,2, 3,3,3, 4,4,4), + status=c( 1,0,2, 1,0,2, 1,0,2, 1,0,2), + n =c(12,3,2, 6,2,4, 2,0,2, 3,3,5)) > # > # Compute the K-M for the Turnbull data > # via a slow EM calculation > # > > emsurv <- function(time, status, wt, verbose=T) { + left.cen <- (status==2) + if (!any(left.cen)) stop("No left censored data!") + if (!any(status==1))stop("Must have some exact death times") + + tempy <- Surv(time[!left.cen], status[!left.cen]) + ww <- wt[!left.cen] + tempx <- factor(rep(1, sum(!left.cen))) + tfit <- survfit(tempy~tempx, weight=ww) + if (verbose) + cat("Iteration 0, survival=", format(round(tfit$surv[tfit$n.event>0],3)), + "\n") + + stimes <- tfit$time[tfit$n.event>0] + ltime <- time[left.cen] + lwt <- wt[left.cen] + tempx <- factor(rep(1, length(stimes) + sum(!left.cen))) + tempy <- Surv(c(time[!left.cen], stimes), + c(status[!left.cen], rep(1, length(stimes)))) + for (iter in 1:4) { + wt2 <- stimes*0 + ssurv <- tfit$surv[tfit$n.event>0] + sjump <- diff(c(1, ssurv)) + for (j in 1:(length(ltime))) { + k <- sum(ltime[j]>=stimes) #index of the death time + if (k==0) + stop("Left censored observation before the first death") + wt2[1:k] <- wt2[1:k] + lwt[j]*sjump[1:k] /(ssurv[k]-1) + } + tfit <- survfit(tempy~tempx, weight=c(ww, wt2)) + if (verbose) { + cat("Iteration", iter, "survival=", + format(round(tfit$surv[tfit$n.event>0],3)), "\n") + cat(" weights=", format(round(wt2,3)), "\n") + } + } + survfit(tempy ~ tempx, weights=c(ww, wt2)) + } > > temp <-emsurv(turnbull$time, turnbull$status, turnbull$n) Iteration 0, survival= 0.613 0.383 0.287 0.144 Iteration 1 survival= 0.549 0.303 0.214 0.094 weights= 7.856 3.477 0.828 0.839 Iteration 2 survival= 0.540 0.296 0.210 0.095 weights= 8.228 3.394 0.714 0.664 Iteration 3 survival= 0.538 0.295 0.210 0.095 weights= 8.315 3.356 0.690 0.638 Iteration 4 survival= 0.538 0.295 0.210 0.095 weights= 8.338 3.342 0.685 0.635 > print(summary(temp)) Call: survfit(formula = tempy ~ tempx, weights = c(ww, wt2)) time n.risk n.event survival std.err lower 95% CI upper 95% CI 1 44.00 20.34 0.5378 0.0752 0.4089 0.707 2 20.66 9.34 0.2946 0.0719 0.1827 0.475 3 9.32 2.68 0.2098 0.0673 0.1119 0.393 4 6.64 3.64 0.0948 0.0507 0.0333 0.270 > # First check, use the data from Turnbull, JASA 1974, 169-173. > > tdata <- data.frame(time =c(1,1,1,2,2,2,3,3,3,4,4,4), + status=rep(c(1,0,2),4), + n =c(12,3,2,6,2,4,2,0,2,3,3,5)) > > tfit <- survfit(Surv(time, time, status, type='interval') ~1, tdata, weight=n) > all.equal(round(tfit$surv,3), c(.538, .295, .210, .095)) [1] TRUE > > > # Second check, compare to a reversed survival curve > # This is not as simple a test as one might think, because left and right > # censored observations are not treated symmetrically by the routine: > # time <= y for left and time> y for right (this is to make the routine > # correct for the common situation of panel data). > # To get equivalence, make the left censoreds happen just a little bit > # earlier. The left-continuous/right-continuous shift is also a bother. > # > test1 <- data.frame(time= c(9, 3,1,1,6,6,8), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0)) > fit1 <- survfit(Surv(time, status) ~1, test1) > temp <- ifelse(test1$status==0, 4.99,5) - test1$time > fit2 <- survfit(Surv(temp, status, type='left') ~1, test1) > > all.equal(round(fit1$surv[1:2],5), round(1-fit2$surv[3:2],5)) [1] TRUE > > rm(tdata, tfit, fit1, temp, fit2) > # > # Create a data set similar to the one provided by Al Zinsmeister > # It is a hard test case for survfit.turnbull > # > time1 <- c(rep(0,100), rep(1,200), 100, 200, 210, 220, + rep(365,100), rep(366,5), 731:741) > > time2 <- c((1:100)*3, 10+1:100, rep(365:366, c(60,40)), NA, 500, NA, 450, + rep(730,90), rep(NA,10), c(528,571,691,730,731), + NA, 1095:1099, NA, 1400, 1200, 772, 1461) > > zfit <- survfit(Surv(time1, time2, type='interval2') ~1) > > # > # There are 100 intervals of the form (0,x) where x is from 3 to 300, > # and 200 more of the form (1,x) where x is from 11 to 366. These > # lead to a mass point in the interval (1,3), which is placed at 2. > # The starting estimate has far too little mass placed here, and it takes > # the EM a long time to realize that most of the weight for the first 300 > # subjects goes here. With acceleration, it takes 16 iterations, without > # it takes >40. (On Al's orginal data, without accel still wasn't there after > # 165 iters!) > # > # The next 4 obs give rise to potential jumps at 100.5, 200.5, 211.5, and > # 221. However, the final estimate has no mass at all on any of these. > # Assume mass of a,b, and c at 2, 100.5 and 365.5, and consider the > # contributions: > # 123 obs that overlap a only > # 137 obs that overlap a and b > # 40 obs that overlap a, b, c > # 1 obs that overlap b, c > # 108 obs that overlap c (200, 210,200, 365, and 366 starting points) > # For some trial values of a,b,c, compare the loglik to that of (a+b),0,c > # First one: a^123 (a+b)^137 (a+b+c)^40 (b+c) c^108 > # Second: (a+b)^123 (a+b)^137 (a+b+c)^40 c c^108 > # Likelhood improves if (1 + b/a)^123 > 1+ b/c, which is true for almost > # all a and c. In particular, at the solution a and c are approx .7 and > # .18, respectively. > # > # The program can't see this coming, of course, and so iterates towards a > # KM with epsilon sized jumps at 100.5, 200.5, and 211.5. Whether these > # intervals should be removed during iteration, as detected, is an open > # question for me. > # > # > # True solution: mass points at 2, 365.5, 408, and 756.5, of sizes a, b, c, d > # Likelihood: a^260 (a+b)^40 (b+c)^92 (b+c+d)^12 c^5 d^11 > # Solution: a=0.6958, b=0.1674, c=0.1079, d=0.0289 > > tfun <- function(x) { + if (length(x) ==3) x <- c(x, .03) + x <- x/sum(x) #make probabilities sum to 1 + loglik <- 260*log(x[1]) + 40*log(x[1]+x[2]) + 92*log(x[2] + x[3]) + + 12*log(x[2]+x[3]+x[4]) + 5*log(x[3]) + 11*log(x[4]) + -loglik #find the max, not the min + } > > nfit <- nlminb(start=c(.7,.15, .1), tfun, lower=0, upper=1) > nparm <- c(nfit$par, .03) > nparm <- nparm / sum(nparm) > zparm <- -diff(c(1, zfit$surv[match(c(2, 365.5, 408, 756.5), zfit$time)])) > aeq(round(tfun(nparm),4), round(tfun(zparm),4)) [1] TRUE > # .0001 is the tolerance in survfit.turnbull > > rm(tfun, nfit, nparm, zparm, time1, time2, zfit) > survival/tests/aareg.R0000644000175100001440000001604511732700061014512 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Test aareg, for some simple data where the answers can be computed # in closed form # aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) test1 <- data.frame(time= c(4, 3,1,1,2,2,3), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0), wt= c(1, 1:6)) tfit <- aareg(Surv(time, status) ~ x, test1) aeq(tfit$times, c(1,2,2)) aeq(tfit$nrisk, c(6,4,4)) aeq(tfit$coefficient, matrix(c(0,0,1/3, 1/3, 1, -1/3), ncol=2)) aeq(tfit$tweight, matrix(c(3,3,3, 3/2, 3/4, 3/4), ncol=2)) aeq(tfit$test.statistic, c(1,1)) aeq(tfit$test.var, c(1, -1/4, -1/4, 1/4 + 9/16 + 1/16)) tfit <- aareg(Surv(time, status) ~ x, test1, test='nrisk') aeq(tfit$tweight, matrix(c(3,3,3, 3/2, 3/4, 3/4), ncol=2)) #should be as before aeq(tfit$test.statistic, c(4/3, 6/3+ 4 - 4/3)) aeq(tfit$test.var, c(16/9, -16/9, -16/9, 36/9 + 16 + 16/9)) # In the 1-variable case, this is the same as the default Aalen weight tfit <- aareg(Surv(time, status) ~ x, test1, test='variance') aeq(tfit$test.statistic, c(1,1)) aeq(tfit$test.var, c(1, -1/4, -1/4, 1/4 + 9/16 + 1/16)) # # Repeat the above, with case weights # tfit <- aareg(Surv(time, status) ~x, test1, weights=wt) aeq(tfit$times, c(1,2,2)) aeq(tfit$nrisk, c(21,16,16)) aeq(tfit$coefficient, matrix(c(0,0,5/12, 2/9, 1, -5/12), ncol=2)) aeq(tfit$tweight, matrix(c(12,12,12, 36/7, 3,3), ncol=2)) aeq(tfit$test.statistic, c(5, 72/63 + 3 - 15/12)) aeq(tfit$test.var, c(25, -25/4, -25/4, (72/63)^2 + 9 + (5/4)^2)) tfit <- aareg(Surv(time, status) ~x, test1, weights=wt, test='nrisk') aeq(tfit$test.statistic, c(20/3, 42/9 + 16 - 16*5/12)) aeq(tfit$test.var, c(400/9, -400/9, -400/9, (42/9)^2 + 16^2 + (16*5/12)^2)) # # Make a test data set with no NAs, in sorted order, no ties, # 15 observations tdata <- lung[15:29, c('time', 'status', 'age', 'sex', 'ph.ecog')] tdata$status <- tdata$status -1 tdata <- tdata[order(tdata$time, tdata$status),] row.names(tdata) <- 1:15 tdata$status[8] <- 0 #for some variety afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, tdata, nmin=6) # # Now, do it "by hand" cfit <- coxph(Surv(time, status) ~ age + sex + ph.ecog, tdata, iter=0, method='breslow') dt1 <- coxph.detail(cfit) sch1 <- resid(cfit, type='schoen') # First estimate of Aalen: from the Cox computations, first 9 # The first and last cols of the ninth are somewhat unstable (approx =0) mine <- rbind(solve(dt1$imat[,,1], sch1[1,]), solve(dt1$imat[,,2], sch1[2,]), solve(dt1$imat[,,3], sch1[3,]), solve(dt1$imat[,,4], sch1[4,]), solve(dt1$imat[,,5], sch1[5,]), solve(dt1$imat[,,6], sch1[6,]), solve(dt1$imat[,,7], sch1[7,]), solve(dt1$imat[,,8], sch1[8,]), solve(dt1$imat[,,9], sch1[9,])) mine <- diag(1/dt1$nrisk[1:9]) %*% mine aeq(mine, afit$coef[1:9, -1]) rm(tfit, afit, mine, dt1, cfit, sch1) # # Check out the dfbeta matrix from aareg # Note that it is kept internally in time order, not data set order # Those who want residuals should use the resid function! # # First, the simple test case where I know the anwers # afit <- aareg(Surv(time, status) ~ x, test1, dfbeta=T) temp <- c(rep(0,6), #intercepts at time 1 c(2,-1,-1,0,0,0)/9, #alpha at time 1 c(0,0,0,2, -1, -1)/9, #intercepts at time 2 c(0,0,0,-2,1,1)/9) #alpha at time 2 aeq(afit$dfbeta, temp) # #Now a multivariate data set # afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, lung, dfbeta=T) ord <- order(lung$time, -lung$status) cfit <- coxph(Surv(time, status) ~ age + sex + ph.ecog, lung[ord,], method='breslow', iter=0, x=T) cdt <- coxph.detail(cfit, riskmat=T) # an arbitrary list of times acoef <- rowsum(afit$coef, afit$times) #per death time coefs indx <- match(cdt$time, afit$times) for (i in c(2,5,27,54,101, 135)) { lwho <- (cdt$riskmat[,i]==1) lmx <- cfit$x[lwho,] lmy <- 1*( cfit$y[lwho,2]==1 & cfit$y[lwho,1] == cdt$time[i]) fit <- lm(lmy~ lmx) cat("i=", i, "coef=", aeq(fit$coef, acoef[i,])) rr <- diag(resid(fit)) zz <- cbind(1,lmx) zzinv <- solve(t(zz) %*% zz) cat(" twt=", aeq(1/(diag(zzinv)), afit$tweight[indx[i],])) df <- t(zzinv %*% t(zz) %*% rr) cat(" dfbeta=", aeq(df, afit$dfbeta[lwho,,i]), "\n") } rm(afit, cfit, cdt, lwho, lmx, lmy, fit, rr, zz, df) # Repeat it with case weights ww <- rep(1:5, length=nrow(lung))/ 3.0 afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, lung, dfbeta=T, weights=ww) cfit <- coxph(Surv(time, status) ~ age + sex + ph.ecog, lung[ord,], method='breslow', iter=0, x=T, weight=ww[ord]) cdt <- coxph.detail(cfit, riskmat=T) acoef <- rowsum(afit$coef, afit$times) #per death time coefs for (i in c(2,5,27,54,101, 135)) { who <- (cdt$riskmat[,i]==1) x <- cfit$x[who,] y <- 1*( cfit$y[who,2]==1 & cfit$y[who,1] == cdt$time[i]) w <- cfit$weight[who] fit <- lm(y~x, weights=w) cat("i=", i, "coef=", aeq(fit$coef, acoef[i,])) rr <- diag(resid(fit)) zz <- cbind(1,x) zzinv <- solve(t(zz)%*% (w*zz)) cat(" twt=", aeq(1/(diag(zzinv)), afit$tweight[indx[i],])) df <- t(zzinv %*% t(zz) %*% (w*rr)) cat(" dfbeta=", aeq(df, afit$dfbeta[who,,i]), "\n") } rm(afit, cfit, cdt, who, x, y, fit, rr, zz, df) rm(ord, acoef) # # Check that the test statistic computed within aareg and # the one recomputed within summary.aareg are the same. # Of course, they could both be wrong, but at least they'll agree! # If the maxtime argument is used in summary, it recomputes the test, # even if we know that it wouldn't have had to. # # Because the 1-variable and >1 variable case have different code, test # them both. # afit <- aareg(Surv(time, status) ~ age, lung, dfbeta=T) asum <- summary(afit, maxtime=max(afit$times)) aeq(afit$test.stat, asum$test.stat) aeq(afit$test.var, asum$test.var) aeq(afit$test.var2, asum$test.var2) print(afit) afit <- aareg(Surv(time, status) ~ age, lung, dfbeta=T, test='nrisk') asum <- summary(afit, maxtime=max(afit$times)) aeq(afit$test.stat, asum$test.stat) aeq(afit$test.var, asum$test.var) aeq(afit$test.var2, asum$test.var2) summary(afit) # # Mulitvariate # afit <- aareg(Surv(time, status) ~ age + sex + ph.karno + pat.karno, lung, dfbeta=T) asum <- summary(afit, maxtime=max(afit$times)) aeq(afit$test.stat, asum$test.stat) aeq(afit$test.var, asum$test.var) aeq(afit$test.var2, asum$test.var2) print(afit) afit <- aareg(Surv(time, status) ~ age + sex + ph.karno + pat.karno, lung, dfbeta=T, test='nrisk') asum <- summary(afit, maxtime=max(afit$times)) aeq(afit$test.stat, asum$test.stat) aeq(afit$test.var, asum$test.var) aeq(afit$test.var2, asum$test.var2) summary(afit) # Weights play no role in the final computation of the test statistic, given # the coefficient matrix, nrisk, and dfbeta as inputs. (Weights do # change the inputs). So there is no need to reprise the above with # case weights. survival/tests/jasa.R0000644000175100001440000000660612160143136014353 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) expect <- survexp(futime ~ ratetable(age=(accept.dt - birth.dt), sex=1, year=accept.dt, race='white'), jasa, cohort=F, ratetable=survexp.usr) survdiff(Surv(jasa$futime, jasa$fustat) ~ offset(expect)) # Now fit the 6 models found in Kalbfleisch and Prentice, p139 sfit.1 <- coxph(Surv(start, stop, event)~ (age + surgery)*transplant, jasa1, method='breslow') sfit.2 <- coxph(Surv(start, stop, event)~ year*transplant, jasa1, method='breslow') sfit.3 <- coxph(Surv(start, stop, event)~ (age + year)*transplant, jasa1, method='breslow') sfit.4 <- coxph(Surv(start, stop, event)~ (year +surgery) *transplant, jasa1, method='breslow') sfit.5 <- coxph(Surv(start, stop, event)~ (age + surgery)*transplant + year , jasa1, method='breslow') sfit.6 <- coxph(Surv(start, stop, event)~ age*transplant + surgery + year, jasa1, method='breslow') summary(sfit.1) sfit.2 summary(sfit.3) sfit.4 sfit.5 sfit.6 # Survival curve for an "average" subject, # done once as overall, once via individual method surv1 <- survfit(sfit.1, newdata=list(age=-2, surgery=0, transplant=0)) newdata <- data.frame(start=c(0,50,100), stop=c(50,100, max(jasa1$stop)), event=c(1,1,1), age=rep(-2,3), surgery=rep(0,3), transplant=rep(0,3)) surv2 <- survfit(sfit.1, newdata, individual=T) # Have to use unclass to avoid [.survfit trying to pick curves, # remove the final element "call" because it won't match all.equal(unclass(surv1)[-length(surv1)], unclass(surv2)[-length(surv2)]) # Survival curve for a subject of age 50, with prior surgery, tx at 6 months # Remember that 'age' in jasa 1 was centered at 48 data <- data.frame(start=c(0,183), stop=c(183,3*365), event=c(1,1), age=c(2,2), surgery=c(1,1), transplant=c(0,1)) summary(survfit(sfit.1, data, individual=T)) # These should all give the same answer # When there are offsets, the default curve is always for someone with # the mean offset. j.age <- jasa$age -48 fit1 <- coxph(Surv(futime, fustat) ~ j.age, data=jasa) fit2 <- coxph(Surv(futime, fustat) ~ j.age, jasa, init=fit1$coef, iter=0) fit3 <- coxph(Surv(start, stop, event) ~ age, jasa1) fit4 <- coxph(Surv(start, stop, event) ~ offset(age*fit1$coef), jasa1) s1 <- survfit(fit1, list(j.age=fit3$means), censor=FALSE) s2 <- survfit(fit2, list(j.age=fit3$means), censor=FALSE) s3 <- survfit(fit3, censor=FALSE) s4 <- survfit(fit4, censor=FALSE) all.equal(s1$surv, s2$surv) all.equal(s1$surv, s3$surv) all.equal(s1$surv, s4$surv) # Still the same answer, fit multiple strata at once # Strata 1 has independent coefs of strata 2, so putting in # the other data should not affect it ll <- nrow(jasa1) ss <- rep(0:1, c(ll,ll)) tdata <- with(jasa1, data.frame(start=rep(start,2), stop=rep(stop,2), event=rep(event,2), ss=ss, age=rep(age,2), age2 = (rep(age,2))^2 * ss)) fit <- coxph(Surv(start, stop, event) ~ age*strata(ss) + age2, tdata) # Above replaced these 2 lines, which kill Splus5 as of 8/98 # Something with data frames, I expect. #fit <- coxph(Surv(rep(start,2), rep(stop,2), rep(event,2)) ~ # rep(age,2)*strata(ss) + I(rep(age,2)^2*ss) ) all.equal(fit$coef[1], fit3$coef) s5 <- survfit(fit, data.frame(age=fit3$means, age2=0, ss=0), censor=FALSE) all.equal(s5$surv[1:(s5$strata[1])], s3$surv) survival/tests/model.matrix.R0000644000175100001440000000424312466142446016047 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Test out the revised model.matrix code # test1 <- data.frame(time= c(9, 3,1,1,6,6,8), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0), z= factor(c('a', 'a', 'b', 'b', 'c', 'c', 'a'))) fit1 <- coxph(Surv(time, status) ~ z, test1, iter=1) fit2 <- coxph(Surv(time, status) ~z, test1, x=T, iter=1) all.equal(model.matrix(fit1), fit2$x) # This has no level 'b', make sure dummies recode properly test2 <- data.frame(time= c(9, 3,1,1,6,6,8), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0), z= factor(c('a', 'a', 'a', 'a', 'c', 'c', 'a'))) ftest <- model.frame(fit1, data=test2) all.equal(levels(ftest$z), levels(test1$z)) # xtest will have one more row than the others, since it does not delete # the observation with a missing value for status xtest <- model.matrix(fit1, data=test2) dummy <- fit2$x dummy[,1] <- 0 all.equal(xtest[-2,], dummy, check.attributes=FALSE) # The case of a strata by factor interaction # Use iter=0 since there are too many covariates and it won't converge test1$x2 <- factor(rep(1:2, length=7)) fit3 <- coxph(Surv(time, status) ~ strata(x2)*z, test1, iter=0) xx <- model.matrix(fit3) all.equal(attr(xx, "assign"), c(2,2,3,3)) all.equal(colnames(xx), c("zb", "zc", "strata(x2)2:zb", "strata(x2)2:zc")) all.equal(attr(xx, "contrasts"), list("strata(x2)"= "contr.treatment", z="contr.treatment")) fit3b <- coxph(Surv(time, status) ~ strata(x2)*z, test1, iter=0, x=TRUE) all.equal(fit3b$x, xx) # A model with a tt term fit4 <- coxph(Surv(time, status) ~ tt(x) + x, test1, iter=0, tt = function(x, t, ...) x*t) ff <- model.frame(fit4) # There is 1 subject in the final risk set, 4 at risk at time 6, 6 at time 1 # The .strata. variable numbers from last time point to first all.equal(ff$.strata., rep(1:3, c(1, 4,6))) all.equal(ff[["tt(x)"]], ff$x* c(9,6,1)[ff$.strata.]) xx <- model.matrix(fit4) all.equal(xx[,1], ff[[2]], check.attributes=FALSE) survival/tests/fr_simple.R0000644000175100001440000000427712350363660015426 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Test the logic of the penalized code by fitting some no-frailty models # (theta=0). It should give exactly the same answers as 'ordinary' coxph. # test1 <- data.frame(time= c(4, 3,1,1,2,2,3), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0)) test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) zz <- rep(0, nrow(test1)) tfit1 <- coxph(Surv(time,status) ~x, test1, eps=1e-7) tfit2 <- coxph(Surv(time,status) ~x + frailty(zz, theta=0, sparse=T), test1) tfit3 <- coxph(Surv(zz,time,status) ~x + frailty(zz, theta=0, sparse=T), test1) temp <- c('coefficients', 'var', 'loglik', 'linear.predictors', 'means', 'n', 'concordance') all.equal(tfit1[temp], tfit2[temp]) all.equal(tfit2[temp], tfit3[temp]) zz <- rep(0, nrow(test2)) tfit1 <- coxph(Surv(start, stop, event) ~x, test2, eps=1e-7) tfit2 <- coxph(Surv(start, stop, event) ~ x + frailty(zz, theta=0, sparse=T), test2) all.equal(tfit1[temp], tfit2[temp]) # # Repeat the above tests, but with a strata added # Because the data set is simply doubled, the loglik will double, # beta is the same, variance is halved. # test3 <- rbind(test1, test1) test3$x2 <- rep(1:2, rep(nrow(test1),2)) zz <- rep(0, nrow(test3)) tfit1 <- coxph(Surv(time,status) ~x + strata(x2), test3, eps=1e-7) tfit2 <- coxph(Surv(time,status) ~x + frailty(zz, theta=0, sparse=T) + strata(x2), test3) tfit3 <- coxph(Surv(zz,time,status) ~x + frailty(zz, theta=0, sparse=T) + strata(x2), test3) all.equal(tfit1[temp], tfit2[temp]) all.equal(tfit2[temp], tfit3[temp]) test4 <- rbind(test2, test2) test4$x2 <- rep(1:2, rep(nrow(test2),2)) zz <- rep(0, nrow(test4)) tfit1 <- coxph(Surv(start, stop, event) ~x, test4, eps=1e-7) tfit2 <- coxph(Surv(start, stop, event) ~ x + frailty(zz, theta=0, sparse=T), test4) all.equal(tfit1[temp], tfit2[temp]) rm(test3, test4, tfit1, tfit2, tfit3, temp, zz) survival/tests/difftest.R0000644000175100001440000000314411732700061015237 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Test some more features of surv.diff # # First, what happens when one group is a dummy # # # The AML data, with a third group of early censorings "tacked on" # aml3 <- list(time= c( 9, 13, 13, 18, 23, 28, 31, 34, 45, 48, 161, 5, 5, 8, 8, 12, 16, 23, 27, 30, 33, 43, 45, 1, 2, 2, 3, 3, 3, 4), status= c( 1,1,0,1,1,0,1,1,0,1,0, 1,1,1,1,1,0,1,1,1,1,1,1, 0,0,0,0,0,0,0), x = as.factor(c(rep("Maintained", 11), rep("Nonmaintained", 12), rep("Dummy",7) ))) aml3 <- data.frame(aml3) # These should give the same result (chisq, df), but the second has an # extra group survdiff(Surv(time, status) ~x, aml) survdiff(Surv(time, status) ~x, aml3) # # Now a test of the stratified log-rank # There are no tied times within institution, so the coxph program # can be used to give a complete test # fit <- survdiff(Surv(time, status) ~ pat.karno + strata(inst), cancer) cfit <- coxph(Surv(time, status) ~ factor(pat.karno) + strata(inst), cancer, iter=0) tdata <- na.omit(cancer[,c('time', 'status', 'pat.karno', 'inst')]) temp1 <- tapply(tdata$status-1, list(tdata$pat.karno, tdata$inst), sum) temp1 <- ifelse(is.na(temp1), 0, temp1) temp2 <- tapply(cfit$resid, list(tdata$pat.karno, tdata$inst), sum) temp2 <- ifelse(is.na(temp2), 0, temp2) temp2 <- temp1 - temp2 #Now temp1=observed, temp2=expected all.equal(c(temp1), c(fit$obs)) all.equal(c(temp2), c(fit$exp)) all.equal(fit$var[-1,-1], solve(cfit$var)) rm(tdata, temp1, temp2) survival/tests/ovarian.R0000644000175100001440000000353111741355706015102 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Test the coxph program on the Ovarian data # attach(ovarian) summary(survfit(Surv(futime, fustat)~1), censor=TRUE) # Various models coxph(Surv(futime, fustat)~ age) coxph(Surv(futime, fustat)~ resid.ds) coxph(Surv(futime, fustat)~ rx) coxph(Surv(futime, fustat)~ ecog.ps) coxph(Surv(futime, fustat)~ resid.ds + rx + ecog.ps) coxph(Surv(futime, fustat)~ age + rx + ecog.ps) coxph(Surv(futime, fustat)~ age + resid.ds + ecog.ps) coxph(Surv(futime, fustat)~ age + resid.ds + rx) # Residuals fit <- coxph(Surv(futime, fustat)~ age + resid.ds + rx + ecog.ps ) resid(fit) resid(fit, 'dev') resid(fit, 'scor') resid(fit, 'scho') fit <- coxph(Surv(futime, fustat) ~ age + ecog.ps + strata(rx)) summary(fit) summary(survfit(fit)) sfit <- survfit(fit, list(age=c(30,70), ecog.ps=c(2,3))) #two columns sfit summary(sfit) detach() # Check of offset + surv, added 7/2000 fit1 <- coxph(Surv(futime, fustat) ~ age + rx, ovarian, control=coxph.control(eps=1e-8)) fit2 <- coxph(Surv(futime, fustat) ~ age + offset(rx*fit1$coef[2]), ovarian, control=coxph.control(eps=1e-8)) all.equal(fit1$coef[1], fit2$coef[1]) fit <- coxph(Surv(futime, fustat) ~ age + offset(rx), ovarian) survfit(fit, censor=FALSE)$surv^exp(-1.5) # Check it by hand -- there are no tied times # Remember that offsets from survfit are centered, which is 1.5 for # this data set. eta <- fit$coef*(ovarian$age - fit$mean) + (ovarian$rx - 1.5) ord <- order(ovarian$futime) risk <- exp(eta[ord]) rsum <- rev(cumsum(rev(risk))) # cumulative risk at each time point dead <- (ovarian$fustat[ord]==1) baseline <- cumsum(1/rsum[dead]) all.equal(survfit(fit, censor=FALSE)$surv, exp(-baseline)) rm(fit, fit1, fit2, ord, eta, risk, rsum, dead, baseline, sfit) survival/tests/quantile.Rout.save0000644000175100001440000000706712701744412016753 0ustar hornikusers R Under development (unstable) (2016-03-23 r70368) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # > # Formal test of the quantile routine for survfit > library(survival) > aeq <- function(x, y, ...) all.equal(as.vector(x), as.vector(y), ...) > > # There are 8 cases: strata Y/N, ncol(surv) >1, conf.int = T/F > # Subcase: the quantile exactly agrees with a horizontal segment of > # the curve or not. > # First do the 4 cases where fit$surv is a vector > # > test1 <- data.frame(time= c(9, 3,1,1,6,6,8, 10), + status=c(1,NA,1,0,1,1,0, 0), + x= c(0, 2,1,1,1,0,0, 0)) > > # True survival = (6/7) * (3/5) * (1/2) for overall > # The q's are chosen to include a point < first jump, mid, after last jump, > # and exact intersections with the "flats" of the curve. > # > qq <- c(13/14, 6/7, 2/3, .5, 9/35, .1) > > # Nothing on the right hand side, simple survival (no strata) > fit1 <- survfit(Surv(time, status) ~ 1, test1, conf.type='none') > aeq(quantile(fit1, 1-qq), c(1, 3.5, 6, 9, 9.5, NA)) #without conf.int [1] TRUE > > fit2 <- survfit(Surv(time, status) ~ 1, test1) #with conf.int > aeq(quantile(fit2, 1-qq), + list(quantile = c(1, 3.5, 6, 9, 9.5, NA), + lower = c(1,1,1,6,6,9), + upper = rep(as.numeric(NA), 6)), check.attributes=FALSE) [1] TRUE > aeq(quantile(fit2, 1-qq, FALSE), c(1, 3.5, 6, 9, 9.5, NA)) [1] TRUE > > > # Now a variable on the right (strata in the result) > # curve 0: (t=6, S=3/4), (t=9, S=3/8) > # curve 1: (t=1, S=2/3), (t=6, S= 0) > fit1 <- survfit(Surv(time, status) ~ x, test1, conf.type='none') > aeq(quantile(fit1, 1-qq), + matrix(c(6,6,9,9,NA,NA, 1,1,3.5, 6,6,6), nrow=2, byrow=T)) [1] TRUE > > fit2 <- survfit(Surv(time, status) ~ x, test1) > aeq(quantile(fit2, 1-qq, FALSE), + matrix(c(6,6,9,9,NA,NA, 1,1,3.5, 6,6,6), nrow=2, byrow=T)) [1] TRUE > > temp <- quantile(fit2, 1-qq) > aeq(temp$quantile, matrix(c(6,6,9,9,NA,NA, 1,1,3.5, 6,6,6), nrow=2, byrow=T)) [1] TRUE > aeq(temp$lower, matrix(c(6,6,6,6,9,9, 1,1,1,1, NA,NA), nrow=2, byrow=T)) [1] TRUE > aeq(temp$upper, rep(as.numeric(NA), 12)) [1] TRUE > > # Second major case set -- a survfit object where fit$surv is a matrix > # This arises from coxph models > # There is only 1 subject with ph.ecog=3 which is a nice edge case > cfit <- coxph(Surv(time, status) ~ age + strata(ph.ecog), lung) > sfit <- survfit(cfit, newdata=data.frame(age=c(50, 70))) > qtot <- quantile(sfit, qq) > for (i in 1:4) { + for (j in 1:2) { + temp <- quantile(sfit[i,j], qq) + print(c(aeq(qtot$quantile[i,j,], temp$quantile), + aeq(qtot$upper[i,j,], temp$upper), + aeq(qtot$lower[i,j,], temp$lower))) + } + } [1] TRUE TRUE TRUE [1] TRUE TRUE TRUE [1] TRUE TRUE TRUE [1] TRUE TRUE TRUE [1] TRUE TRUE TRUE [1] TRUE TRUE TRUE [1] TRUE TRUE TRUE [1] TRUE TRUE TRUE > temp <- quantile(sfit, qq, conf.int=FALSE) > all.equal(qtot$quantile, temp) [1] TRUE > > > > > > proc.time() user system elapsed 0.324 0.032 0.355 survival/tests/cancer.Rout.save0000644000175100001440000002310412714071436016355 0ustar hornikusers R Under development (unstable) (2016-03-23 r70368) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # Test out all of the routines on a more complex data set > # > temp <- survfit(Surv(time, status) ~ ph.ecog, lung) > summary(temp, times=c(30*1:11, 365*1:3)) Call: survfit(formula = Surv(time, status) ~ ph.ecog, data = lung) 1 observation deleted due to missingness ph.ecog=0 time n.risk n.event survival std.err lower 95% CI upper 95% CI 30 60 3 0.952 0.0268 0.9012 1.000 60 58 2 0.921 0.0341 0.8562 0.990 90 56 2 0.889 0.0396 0.8146 0.970 120 56 0 0.889 0.0396 0.8146 0.970 150 55 1 0.873 0.0419 0.7946 0.959 180 52 2 0.841 0.0461 0.7553 0.936 210 48 2 0.808 0.0498 0.7164 0.912 240 45 0 0.808 0.0498 0.7164 0.912 270 38 2 0.770 0.0543 0.6709 0.884 300 33 2 0.727 0.0591 0.6203 0.853 330 29 2 0.681 0.0637 0.5670 0.818 365 22 6 0.535 0.0728 0.4100 0.699 730 5 11 0.193 0.0707 0.0943 0.396 ph.ecog=1 time n.risk n.event survival std.err lower 95% CI upper 95% CI 30 111 2 0.982 0.0124 0.9583 1.000 60 110 3 0.956 0.0193 0.9186 0.994 90 104 4 0.920 0.0255 0.8718 0.972 120 99 5 0.876 0.0310 0.8174 0.939 150 93 6 0.823 0.0359 0.7556 0.896 180 82 8 0.751 0.0407 0.6756 0.836 210 68 9 0.666 0.0450 0.5831 0.760 240 57 6 0.604 0.0474 0.5176 0.704 270 53 4 0.561 0.0487 0.4729 0.665 300 46 3 0.527 0.0495 0.4384 0.633 330 40 4 0.480 0.0504 0.3903 0.589 365 34 4 0.431 0.0509 0.3417 0.543 730 7 21 0.114 0.0388 0.0582 0.222 ph.ecog=2 time n.risk n.event survival std.err lower 95% CI upper 95% CI 30 46 5 0.9000 0.0424 0.82057 0.987 60 43 2 0.8600 0.0491 0.76900 0.962 90 40 3 0.8000 0.0566 0.69647 0.919 120 34 4 0.7174 0.0641 0.60216 0.855 150 31 3 0.6541 0.0680 0.53342 0.802 180 26 6 0.5275 0.0719 0.40385 0.689 210 21 4 0.4431 0.0717 0.32266 0.608 240 17 3 0.3766 0.0705 0.26100 0.543 270 17 0 0.3766 0.0705 0.26100 0.543 300 13 3 0.3102 0.0677 0.20223 0.476 330 11 2 0.2624 0.0651 0.16135 0.427 365 9 2 0.2147 0.0614 0.12258 0.376 730 1 6 0.0371 0.0345 0.00601 0.229 ph.ecog=3 time n.risk n.event survival std.err lower 95% CI upper 95% CI 30 1 0 1 0 1 1 60 1 0 1 0 1 1 90 1 0 1 0 1 1 > print(temp[2:3]) Call: survfit(formula = Surv(time, status) ~ ph.ecog, data = lung) 1 observation deleted due to missingness n events median 0.95LCL 0.95UCL ph.ecog=1 113 82 306 268 429 ph.ecog=2 50 44 199 156 288 > > temp <- survfit(Surv(time, status)~1, lung, type='fleming', + conf.int=.9, conf.type='log-log', error='tsiatis') > summary(temp, times=30 *1:5) Call: survfit(formula = Surv(time, status) ~ 1, data = lung, type = "fleming", conf.int = 0.9, conf.type = "log-log", error = "tsiatis") time n.risk n.event survival std.err lower 90% CI upper 90% CI 30 219 10 0.956 0.0135 0.928 0.974 60 213 7 0.926 0.0173 0.891 0.950 90 201 10 0.882 0.0213 0.842 0.913 120 189 10 0.838 0.0244 0.793 0.874 150 179 10 0.794 0.0268 0.745 0.834 > > temp <- survdiff(Surv(time, status) ~ inst, lung, rho=.5) > print(temp, digits=6) Call: survdiff(formula = Surv(time, status) ~ inst, data = lung, rho = 0.5) n=227, 1 observation deleted due to missingness. N Observed Expected (O-E)^2/E (O-E)^2/V inst=1 36 21.190058 17.455181 0.799149708 1.171232977 inst=2 5 3.173330 1.964395 0.744007932 0.860140808 inst=3 19 10.663476 11.958755 0.140294489 0.200472362 inst=4 4 2.245347 3.559344 0.485085848 0.677874608 inst=5 9 5.010883 4.500982 0.057765161 0.077128402 inst=6 14 8.862602 7.078516 0.449665221 0.582743947 inst=7 8 4.445647 4.416133 0.000197254 0.000253632 inst=10 4 2.901923 2.223283 0.207150016 0.249077097 inst=11 18 7.807867 9.525163 0.309611863 0.422142221 inst=12 23 14.009656 12.216768 0.263117640 0.365712493 inst=13 20 9.140983 11.863298 0.624699853 0.874238212 inst=15 6 3.170744 3.558447 0.042241456 0.057938955 inst=16 16 8.870360 9.992612 0.126038005 0.175170113 inst=21 13 9.263733 4.460746 5.171484268 6.149354145 inst=22 17 8.278566 11.971473 1.139171459 1.645863937 inst=26 6 1.627074 3.542694 1.035821659 1.286365543 inst=32 7 1.792468 2.679904 0.293869782 0.343966668 inst=33 2 0.929177 0.416202 0.632249272 0.676682390 Chisq= 15.1 on 17 degrees of freedom, p= 0.590384 > > temp <- coxph(Surv(time, status) ~ ph.ecog + ph.karno + pat.karno + wt.loss + + sex + age + meal.cal + strata(inst), lung) > summary(temp) Call: coxph(formula = Surv(time, status) ~ ph.ecog + ph.karno + pat.karno + wt.loss + sex + age + meal.cal + strata(inst), data = lung) n= 167, number of events= 120 (61 observations deleted due to missingness) coef exp(coef) se(coef) z Pr(>|z|) ph.ecog 0.7299987 2.0750779 0.2689397 2.714 0.00664 ** ph.karno 0.0130512 1.0131368 0.0137362 0.950 0.34204 pat.karno -0.0140955 0.9860034 0.0093680 -1.505 0.13242 wt.loss -0.0148821 0.9852281 0.0084811 -1.755 0.07931 . sex -0.6612534 0.5162039 0.2339979 -2.826 0.00471 ** age 0.0050920 1.0051050 0.0137288 0.371 0.71071 meal.cal -0.0002398 0.9997602 0.0003019 -0.794 0.42701 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 exp(coef) exp(-coef) lower .95 upper .95 ph.ecog 2.0751 0.4819 1.2249 3.5153 ph.karno 1.0131 0.9870 0.9862 1.0408 pat.karno 0.9860 1.0142 0.9681 1.0043 wt.loss 0.9852 1.0150 0.9690 1.0017 sex 0.5162 1.9372 0.3263 0.8166 age 1.0051 0.9949 0.9784 1.0325 meal.cal 0.9998 1.0002 0.9992 1.0004 Concordance= 0.696 (se = 0.115 ) Rsquare= 0.167 (max possible= 0.912 ) Likelihood ratio test= 30.6 on 7 df, p=7.377e-05 Wald test = 28.15 on 7 df, p=0.0002066 Score (logrank) test = 30.72 on 7 df, p=7e-05 > cox.zph(temp) rho chisq p ph.ecog 0.0276 0.1078 0.7427 ph.karno 0.1331 2.0018 0.1571 pat.karno 0.0250 0.0841 0.7718 wt.loss -0.0386 0.2122 0.6451 sex 0.0399 0.1800 0.6713 age 0.0639 0.5600 0.4543 meal.cal 0.1611 3.6945 0.0546 GLOBAL NA 9.0115 0.2518 > cox.zph(temp, transform='identity') rho chisq p ph.ecog 0.0221 0.0688 0.793 ph.karno 0.1217 1.6743 0.196 pat.karno 0.0302 0.1227 0.726 wt.loss -0.0516 0.3790 0.538 sex 0.0449 0.2280 0.633 age 0.0719 0.7085 0.400 meal.cal 0.1808 4.6537 0.031 GLOBAL NA 10.0537 0.186 > > coxph(Surv(rep(0,length(time)), time, status) ~ ph.ecog + ph.karno + pat.karno + + wt.loss + sex + age + meal.cal + strata(inst), lung) Call: coxph(formula = Surv(rep(0, length(time)), time, status) ~ ph.ecog + ph.karno + pat.karno + wt.loss + sex + age + meal.cal + strata(inst), data = lung) coef exp(coef) se(coef) z p ph.ecog 0.729999 2.075078 0.268940 2.71 0.0066 ph.karno 0.013051 1.013137 0.013736 0.95 0.3420 pat.karno -0.014095 0.986003 0.009368 -1.50 0.1324 wt.loss -0.014882 0.985228 0.008481 -1.75 0.0793 sex -0.661253 0.516204 0.233998 -2.83 0.0047 age 0.005092 1.005105 0.013729 0.37 0.7107 meal.cal -0.000240 0.999760 0.000302 -0.79 0.4270 Likelihood ratio test=30.6 on 7 df, p=7.38e-05 n= 167, number of events= 120 (61 observations deleted due to missingness) > > # > # Tests of using "." > # > fit1 <- coxph(Surv(time, status) ~ . - meal.cal - wt.loss - inst, lung) > fit2 <- update(fit1, .~. - ph.karno) > fit3 <- coxph(Surv(time, status) ~ age + sex + ph.ecog + pat.karno, lung) > all.equal(fit2, fit3) [1] TRUE > > proc.time() user system elapsed 1.816 0.088 1.902 survival/tests/r_peterson.R0000644000175100001440000000270411732700061015610 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Data courtesy of Bercedis Peterson, Duke University. # v4 of survreg fails due to 2 groups that have only 1 subject; the coef # for them easily gets out of hand. In fact, this data set is my toughest # test of the minimizer. # # A shrinkage model for this coefficient is therefore interesting peterson <- data.frame( scan('data.peterson', what=list(grp=0, time=0, status=0))) fitp <- survreg(Surv(time, status) ~ factor(grp), peterson) summary(fitp) # Now a shrinkage model. Give the group coefficients # about 1/2 the scale parameter of the original model, i.e., .18. # ffit <- survreg(Surv(time, status) ~ frailty(grp, theta=.1), peterson) ffit # # Try 3 degrees of freedom, since there are 6 groups # compare them to the unconstrained ones. The frailty coefs are # on a "sum to constant" constraint rather than "first coef=0", so # some conversion is neccessary # ffit3 <- survreg(Surv(time, status) ~ frailty(grp, df=3), peterson) print(ffit3) temp <- mean(c(0, fitp$coef[-1])) - mean(ffit3$frail) temp2 <- c(fitp$coef[1] + temp, c(0,fitp$coef[-1]) - temp) xx <- rbind(c(nrow(peterson), table(peterson$grp)), temp2, c(ffit3$coef, ffit3$frail)) dimnames(xx) <- list(c("N", "factor", "frailty"), c("Intercept", paste("grp", 1:6))) signif(xx,3) rm(ffit, ffit3, temp, temp2, xx, fitp) survival/tests/rounding.Rout.save0000644000175100001440000000217211732700061016741 0ustar hornikusers R version 2.11.0 (2010-04-22) Copyright (C) 2010 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > # > # Survival curves could fail with data that was almost exact. > # The calculations use both unique() and table(), which don't > # necessarily give the same number of values. > # Check that the routine handles this properly > # > > tdata <- data.frame(time=c(1,2, sqrt(2)^2, 2, sqrt(2)^2), + status=rep(1,5), + group=c(1,1,1,2,2)) > fit <- survfit(Surv(time, status) ~ group, data=tdata) > > all.equal(sum(fit$strata), length(fit$time)) [1] TRUE > survival/tests/r_capacitor.Rout.save0000644000175100001440000000506011732700061017401 0ustar hornikusers R version 2.7.1 (2008-06-23) Copyright (C) 2008 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > capacitor <- read.table('data.capacitor', row.names=1, + col.names=c('', 'days', 'event', 'voltage')) > > fitig <- survreg(Surv(days, event)~voltage, + dist = "gaussian", data = capacitor) > summary(fitig) Call: survreg(formula = Surv(days, event) ~ voltage, data = capacitor, dist = "gaussian") Value Std. Error z p (Intercept) 1764.9 163.387 10.80 3.36e-27 voltage -53.9 5.545 -9.72 2.56e-22 Log(scale) 4.8 0.105 45.56 0.00e+00 Scale= 121 Gaussian distribution Loglik(model)= -361.9 Loglik(intercept only)= -420.1 Chisq= 116.33 on 1 degrees of freedom, p= 0 Number of Newton-Raphson Iterations: 6 n= 125 > > fitix <- survreg(Surv(days, event)~voltage, + dist = "extreme", data = capacitor) > summary(fitix) Call: survreg(formula = Surv(days, event) ~ voltage, data = capacitor, dist = "extreme") Value Std. Error z p (Intercept) 2055.59 180.349 11.4 4.28e-30 voltage -62.21 5.967 -10.4 1.88e-25 Log(scale) 4.53 0.108 41.9 0.00e+00 Scale= 92.9 Extreme value distribution Loglik(model)= -360 Loglik(intercept only)= -427.1 Chisq= 134.25 on 1 degrees of freedom, p= 0 Number of Newton-Raphson Iterations: 7 n= 125 > > fitil <- survreg(Surv(days, event)~voltage, + dist = "logistic", data = capacitor) > summary(fitil) Call: survreg(formula = Surv(days, event) ~ voltage, data = capacitor, dist = "logistic") Value Std. Error z p (Intercept) 1811.56 148.853 12.2 4.48e-34 voltage -55.48 4.986 -11.1 9.39e-29 Log(scale) 4.19 0.117 35.8 2.03e-280 Scale= 66.3 Logistic distribution Loglik(model)= -360.4 Loglik(intercept only)= -423.7 Chisq= 126.5 on 1 degrees of freedom, p= 0 Number of Newton-Raphson Iterations: 6 n= 125 > survival/tests/summary_survfit.R0000644000175100001440000001013013065012510016673 0ustar hornikusers## check that the scale option to summary.survfit works ## Marc Schwartz reported this as a bug in 2.35-3. library(survival) fit <- survfit(Surv(futime, fustat) ~rx, data=ovarian) temp1 <- summary(fit) temp2 <- summary(fit, scale=365.25) all.equal(temp1$time/365.25, temp2$time) all.equal(temp1$rmean.endtime/365.25, temp2$rmean.endtime) all.equal(temp1$table[,5:6]/365.25, temp2$table[,5:6]) temp <- names(fit) temp <- temp[!temp %in% c("time", "table", "rmean.endtime")] all.equal(temp1[temp], temp2[temp]) # Reprise, using the rmean option temp1 <- summary(fit, rmean=300) temp2 <- summary(fit, rmean=300, scale=365.25) all.equal(temp1$time/365.25, temp2$time) all.equal(temp1$rmean.endtime/365.25, temp2$rmean.endtime) all.equal(temp1$table[,5:6]/365.25, temp2$table[,5:6]) all.equal(temp1[temp], temp2[temp]) # Repeat using multi-state data. Time is in months for mgus2 etime <- with(mgus2, ifelse(pstat==0, futime, ptime)) event <- with(mgus2, ifelse(pstat==0, 2*death, 1)) event <- factor(event, 0:2, labels=c("censor", "pcm", "death")) mfit <- survfit(Surv(etime, event) ~ sex, mgus2) temp1 <- summary(mfit) temp2 <- summary(mfit, scale=12) all.equal(temp1$time/12, temp2$time) all.equal(temp1$rmean.endtime/12, temp2$rmean.endtime) all.equal(temp1$table[,3]/12, temp2$table[,3]) temp <- names(temp1) temp <- temp[!temp %in% c("time", "table", "rmean.endtime")] all.equal(temp1[temp], temp2[temp]) # Reprise, using the rmean option temp1 <- summary(mfit, rmean=240) temp2 <- summary(mfit, rmean=240, scale=12) all.equal(temp1$time/12, temp2$time) all.equal(temp1$rmean.endtime/12, temp2$rmean.endtime) all.equal(temp1$table[,3]/12, temp2$table[,3]) all.equal(temp1[temp], temp2[temp]) # The n.risk values from summary.survfit were off when there are multiple # curves (version 2.39-2) # Verify all components by subscripting m1 <- mfit[1,] m2 <- mfit[2,] s1 <- summary(m1, times=c(0,100, 200, 300)) s2 <- summary(m2, times=c(0,100, 200, 300)) s3 <- summary(mfit, times=c(0,100, 200, 300)) tfun <- function(what) { if (is.matrix(s3[[what]])) all.equal(rbind(s1[[what]], s2[[what]]), s3[[what]]) else all.equal(c(s1[[what]], s2[[what]]), s3[[what]]) } tfun('n') tfun("time") tfun("n.risk") tfun("n.event") tfun("n.censor") tfun("pstate") all.equal(rbind(s1$p0, s2$p0), s3$p0, check.attributes=FALSE) tfun("std.err") tfun("lower") tfun("upper") # Check the cumulative sums temp <- rbind(0, 0, colSums(m1$n.event[m1$time <= 100,]), colSums(m1$n.event[m1$time <= 200, ]), colSums(m1$n.event[m1$time <= 300, ])) all.equal(s1$n.event, apply(temp,2, diff)) temp <- rbind(0, 0, colSums(m2$n.event[m2$time <= 100,]), colSums(m2$n.event[m2$time <= 200, ]), colSums(m2$n.event[m2$time <= 300, ])) all.equal(s2$n.event, apply(temp,2, diff)) temp <- c(0, 0,sum(m1$n.censor[m1$time <= 100]), sum(m1$n.censor[m1$time <= 200]), sum(m1$n.censor[m1$time <= 300])) all.equal(s1$n.censor, diff(temp)) # check the same with survfit objects s1 <- summary(fit[1], times=c(0, 200, 400, 600)) s2 <- summary(fit[2], times=c(0, 200, 400, 600)) s3 <- summary(fit, times=c(0, 200, 400, 600)) tfun('n') tfun("time") tfun("n.risk") tfun("n.event") tfun("n.censor") tfun("surv") tfun("std.err") tfun("lower") tfun("upper") f2 <- fit[2] temp <- c(0, 0, sum(f2$n.event[f2$time <= 200]), sum(f2$n.event[f2$time <= 400]), sum(f2$n.event[f2$time <= 600])) all.equal(s2$n.event, diff(temp)) f1 <- fit[1] temp <- c(0, 0,sum(f1$n.censor[f1$time <= 200]), sum(f1$n.censor[f1$time <= 400]), sum(f1$n.censor[f1$time <= 600])) all.equal(s1$n.censor, diff(temp)) # # A check on the censor option # s1 <- summary(fit[1]) s2 <- summary(fit[2]) s3 <- summary(fit) tfun('n') tfun("time") tfun("n.risk") tfun("n.event") tfun("n.censor") tfun("surv") tfun("std.err") tfun("lower") tfun("upper") s1 <- summary(mfit[1]) s2 <- summary(mfit[2]) s3 <- summary(mfit) tfun('n') tfun("time") tfun("n.risk") tfun("n.event") tfun("n.censor") tfun("surv") tfun("std.err") tfun("lower") tfun("upper") survival/tests/survSplit.R0000644000175100001440000000104412756620557015461 0ustar hornikuserslibrary(survival) # Make sure that the old-style and new-style calls both work # new style vet2 <- survSplit(Surv(time, status) ~ ., data= veteran, cut=c(90, 180), episode= "tgroup", id="id") vet2[1:7, c("id", "tstart", "time", "status", "tgroup", "age", "karno")] # old style vet3 <- survSplit(veteran, end='time', event='status', cut=c(90,180), episode="tgroup", id="id") all.equal(vet2, vet3) all.equal(nrow(vet2), nrow(veteran) + sum(veteran$time >90) + sum(veteran$time > 180)) survival/tests/data.interval0000644000175100001440000000161711732700061015766 0ustar hornikusers This data set is to test interval censoring. It has 2 left censored, 14 right censored, 2 exact and 8 interval censored observations, grafted onto covariates from the ovarian data set. "ltime","rtime","age","resid.ds","rx","ecog.ps" "1",NA,150,72.3315,2,1,1 "2",NA,150,74.4932,2,1,1 "3",146,166,66.4658,2,1,2 "4",421,NA,53.3644,2,2,1 "5",421,421,50.3397,2,1,1 "6",448,NA,56.4301,1,1,2 "7",454,474,56.937,2,2,2 "8",465,485,59.8548,2,2,2 "9",477,NA,64.1753,2,1,1 "10",553,573,55.1781,1,2,2 "11",628,648,56.7562,1,1,2 "12",744,NA,50.1096,1,2,1 "13",769,NA,59.6301,2,2,2 "14",770,NA,57.0521,2,2,1 "15",803,NA,39.2712,1,1,1 "16",855,NA,43.1233,1,1,2 "17",1040,NA,38.8932,2,1,2 "18",1106,NA,44.6,1,1,1 "19",1129,NA,53.9068,1,2,1 "20",1206,NA,44.2055,2,2,1 "21",1227,NA,59.589,1,2,2 "22",258,278,74.5041,2,1,2 "23",319,339,43.137,2,1,1 "24",343,363,63.2192,1,2,2 "25",375,375,64.4247,2,2,1 "26",377,NA,58.3096,1,2,1 survival/tests/testnull.Rout.save0000644000175100001440000000242711732700061016771 0ustar hornikusers R version 2.7.1 (2008-06-23) Copyright (C) 2008 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # A test of NULL models > # > fit1 <- coxph(Surv(stop, event) ~ rx + strata(number), bladder, iter=0) > fit2 <- coxph(Surv(stop, event) ~ strata(number), bladder) > > all.equal(fit1$loglik[2], fit2$loglik) [1] TRUE > all.equal(fit1$resid, fit2$resid) [1] TRUE > > > fit1 <- coxph(Surv(start, stop, event) ~ rx + strata(number), bladder2, iter=0) > fit2 <- coxph(Surv(start, stop, event) ~ strata(number), bladder2) > > all.equal(fit1$loglik[2], fit2$loglik) [1] TRUE > all.equal(fit1$resid, fit2$resid) [1] TRUE > survival/tests/bladder.R0000644000175100001440000000244611732700061015030 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Fit the models found in Wei et. al. # wfit <- coxph(Surv(stop, event) ~ (rx + size + number)* strata(enum) + cluster(id), bladder, method='breslow') wfit # Check the rx coefs versus Wei, et al, JASA 1989 rx <- c(1,4,5,6) # the treatment coefs above cmat <- diag(4); cmat[1,] <- 1; #contrast matrix wfit$coef[rx] %*% cmat # the coefs in their paper (table 5) t(cmat) %*% wfit$var[rx,rx] %*% cmat # var matrix (eqn 3.2) # Anderson-Gill fit fita <- coxph(Surv(start, stop, event) ~ rx + size + number + cluster(id), bladder2, method='breslow') summary(fita) # Prentice fits. Their model 1 a and b are the same fit1p <- coxph(Surv(stop, event) ~ rx + size + number, bladder2, subset=(enum==1), method='breslow') fit2pa <- coxph(Surv(stop, event) ~ rx + size + number, bladder2, subset=(enum==2), method='breslow') fit2pb <- coxph(Surv(stop-start, event) ~ rx + size + number, bladder2, subset=(enum==2), method='breslow') fit3pa <- coxph(Surv(stop, event) ~ rx + size + number, bladder2, subset=(enum==3), method='breslow') #and etc. fit1p fit2pa fit2pb fit3pa rm(rx, cmat, wfit, fita, fit1p, fit2pa, fit2pb, fit3pa) survival/tests/stratatest.Rout.save0000644000175100001440000000453711732700061017321 0ustar hornikusers R version 2.7.1 (2008-06-23) Copyright (C) 2008 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # Trivial test of stratified residuals > # Make a second strata = replicate of the first, and I should get the > # exact same answers > test1 <- data.frame(time= c(9, 3,1,1,6,6,8), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0)) > test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), + stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), + event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), + x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) > > temp <- as.matrix(test1) > n <- nrow(temp) > ndead<- sum(test1$status[!is.na(test1$status)]) > temp <- data.frame(rbind(temp, temp)) #later releases of S have rbind.data.frame > tstrat <- rep(1:2, c(n,n)) > > fit1 <- coxph(Surv(time, status) ~x, test1) > fit2 <- coxph(Surv(time, status) ~x + strata(tstrat), temp) > > all.equal(resid(fit1) , (resid(fit2))[1:n]) [1] TRUE > all.equal(resid(fit1, type='score') , (resid(fit2, type='score'))[1:n]) [1] TRUE > all.equal(resid(fit1, type='schoe') , (resid(fit2, type='schoe'))[1:ndead]) [1] TRUE > > > #AG model > temp <- as.matrix(test2) > n <- nrow(temp) > ndead<- sum(test2$event[!is.na(test2$event)]) > temp <- data.frame(rbind(temp, temp)) > tstrat <- rep(1:2, c(n,n)) > > fit1 <- coxph(Surv(start, stop, event) ~x, test2) > fit2 <- coxph(Surv(start, stop, event) ~x + strata(tstrat), temp) > > all.equal(resid(fit1) , (resid(fit2))[1:n]) [1] TRUE > all.equal(resid(fit1, type='score') , (resid(fit2, type='score'))[1:n]) [1] TRUE > all.equal(resid(fit1, type='schoe') , (resid(fit2, type='schoe'))[1:ndead]) [1] TRUE > survival/tests/gray1.rda0000644000175100001440000000644012656727727015051 0ustar hornikusers‹íÙ{TÍiÛðÝ © IR¢R9WhB¨†J„‰ÎÉ‹v”=C%¥ÈH'‘t>+©TƒôT¨br¬¦bš„æýµçþ]×{ßk=k½k½ëùã]ëÙëÛþìµÛ‡ßﾯë^{ß{©µÞpëá@\ !Á]sIqîJL )Æ9d—›®@ ¡ z@|ÐÁGÉpB¹˜xÕÒ¼  ©¥ “bô§ ?@{ömÄVÚ¨$ÚiÆ´—f2zÐþ"ÏhE{y4m\:cc?íÚø&Ú„-Œ¹Œ%´‰òŒ“i¯ª3ºÓ¦ÔÑ^§½þc c>cmj(íY´iZŒ;ýÑÞ̦M—gÌ¡ÍÐaÜF›¹“6{mÎTÆùŒ´ù>BÚpeÁÚ"[FÚRo!íAåí0ÆoBʲbÚ; 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These numbers were derived in multiple # codes. # aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) grank <- function(x, time, grp, wt) unlist(tapply(x, grp, rank)) grank2 <- function(x, time, grp, wt) { #for case weights if (length(wt)==0) wt <- rep(1, length(x)) z <- double(length(x)) for (i in unique(grp)) { indx <- which(grp==i) temp <- tapply(wt[indx], x[indx], sum) temp <- temp/2 + c(0, cumsum(temp)[-length(temp)]) z[indx] <- temp[match(x[indx], names(temp))] } z } tdata <- aml[aml$x=='Maintained',] tdata$y <- c(1,6,2,7,3,7,3,8,4,4,5) tdata$wt <- c(1,2,3,2,1,2,3,4,3,2,1) fit <- survConcordance(Surv(time, status) ~y, tdata) aeq(fit$stats[1:4], c(14,24,2,0)) cfit <- coxph(Surv(time, status) ~ tt(y), tdata, tt=grank, method='breslow', iter=0, x=T) cdt <- coxph.detail(cfit) aeq(4*sum(cdt$imat),fit$stats[5]^2) aeq(2*sum(cdt$score), diff(fit$stats[2:1])) # Lots of ties tempx <- Surv(c(1,2,2,2,3,4,4,4,5,2), c(1,0,1,0,1,0,1,1,0,1)) tempy <- c(5,5,4,4,3,3,7,6,5,4) fit2 <- survConcordance(tempx ~ tempy) aeq(fit2$stats[1:4], c(13,13,5,2)) cfit2 <- coxph(tempx ~ tt(tempy), tt=grank, method='breslow', iter=0) aeq(4/cfit2$var, fit2$stats[5]^2) # Bigger data fit3 <- survConcordance(Surv(time, status) ~ age, lung) aeq(fit3$stats[1:4], c(10717, 8706, 591, 28)) cfit3 <- coxph(Surv(time, status) ~ tt(age), lung, iter=0, method='breslow', tt=grank, x=T) cdt <- coxph.detail(cfit3) aeq(4*sum(cdt$imat),fit3$stats[5]^2) aeq(2*sum(cdt$score), diff(fit3$stats[2:1])) # More ties fit4 <- survConcordance(Surv(time, status) ~ ph.ecog, lung) aeq(fit4$stats[1:4], c(8392, 4258, 7137, 28)) cfit4 <- coxph(Surv(time, status) ~ tt(ph.ecog), lung, iter=0, method='breslow', tt=grank) aeq(4/cfit4$var, fit4$stats[5]^2) # Case weights fit5 <- survConcordance(Surv(time, status) ~ y, tdata, weight=wt) fit6 <- survConcordance(Surv(time, status) ~y, tdata[rep(1:11,tdata$wt),]) aeq(fit5$stats[1:4], c(70, 91, 7, 0)) # checked by hand aeq(fit5$stats[1:3], fit6$stats[1:3]) #spurious "tied on time" value, ignore aeq(fit5$std, fit6$std) cfit5 <- coxph(Surv(time, status) ~ tt(y), tdata, weight=wt, iter=0, method='breslow', tt=grank2) cfit6 <- coxph(Surv(time, status) ~ tt(y), tdata[rep(1:11,tdata$wt),], iter=0, method='breslow', tt=grank) aeq(4/cfit6$var, fit6$stats[5]^2) aeq(cfit5$var, cfit6$var) # Start, stop simplest cases fit7 <- survConcordance(Surv(rep(0,11), time, status) ~ y, tdata) aeq(fit7$stats, fit$stats) aeq(fit7$std.err, fit$std.err) fit7 <- survConcordance(Surv(rep(0,11), time, status) ~ y, tdata, weight=wt) aeq(fit5$stats, fit7$stats) # Multiple intervals for some, but same risk sets as tdata tdata2 <- data.frame(time1=c(0,3, 5, 6,7, 0, 4,17, 7, 0,16, 2, 0, 0,9, 5), time2=c(3,9, 13, 7,13, 18, 17,23, 28, 16,31, 34, 45, 9,48, 60), status=c(0,1, 1, 0,0, 1, 0,1, 0, 0,1, 1, 0, 0,1, 0), y = c(1,1, 6, 2,2, 7, 3,3, 7, 3,3, 8, 4, 4,4, 5), wt= c(1,1, 2, 3,3, 2, 1,1, 2, 3,3, 4, 3, 2,2, 1)) fit8 <- survConcordance(Surv(time1, time2, status) ~y, tdata2, weight=wt) aeq(fit5$stats, fit8$stats) aeq(fit5$std.err, fit8$std.err) cfit8 <- coxph(Surv(time1, time2, status) ~ tt(y), tdata2, weight=wt, iter=0, method='breslow', tt=grank2) aeq(4/cfit8$var, fit8$stats[5]^2) aeq(fit8$stats[5]/(2*sum(fit8$stats[1:3])), fit8$std.err) # Stratified tdata3 <- data.frame(time1=c(tdata2$time1, rep(0, nrow(lung))), time2=c(tdata2$time2, lung$time), status = c(tdata2$status, lung$status -1), x = c(tdata2$y, lung$ph.ecog), wt= c(tdata2$wt, rep(1, nrow(lung))), grp=rep(1:2, c(nrow(tdata2), nrow(lung)))) fit9 <- survConcordance(Surv(time1, time2, status) ~x + strata(grp), data=tdata3, weight=wt) aeq(fit9$stats[1,], fit5$stats) aeq(fit9$stats[2,], fit4$stats) survival/tests/book4.R0000644000175100001440000001003312701744412014445 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Tests from the appendix of Therneau and Grambsch # d. Data set 2 and Efron estimate # test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) byhand <- function(beta, newx=0) { r <- exp(beta) loglik <- 4*beta - (log(r+1) + log(r+2) + 2*log(3*r+2) + 2*log(3*r+1) + log(2*r +2)) u <- 1/(r+1) + 1/(3*r+1) + 2*(1/(3*r+2) + 1/(2*r+2)) - ( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1)) imat <- r*(1/(r+1)^2 + 2/(r+2)^2 + 6/(3*r+2)^2 + 6/(3*r+1)^2 + 6/(3*r+2)^2 + 4/(2*r +2)^2) hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), 1/(3*r+2), 1/(2*r +2) ) # The matrix of weights, one row per obs, one col per time # deaths at 2,3,6,7,8,9 wtmat <- matrix(c(1,0,0,0,1, 0, 0,0,0,0, 0,1,0,1,1, 0, 0,0,0,0, 0,0,1,1,1, 0, 1,1,0,0, 0,0,0,1,1, 0, 1,1,0,0, 0,0,0,0,1, 1, 1,1,0,0, 0,0,0,0,0, 1, 1,1,1,1, 0,0,0,0,0,.5,.5,1,1,1), ncol=7) wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat x <- c(1,0,0,1,0,1,1,1,0,0) status <- c(1,1,1,1,1,1,1,0,0,0) xbar <- colSums(wtmat*x)/ colSums(wtmat) n <- length(x) # Table of sums for score and Schoenfeld resids hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time dM <- -hazmat #Expected part for (i in 1:5) dM[i,i] <- dM[i,i] +1 #observed dM[6:7,6:7] <- dM[6:7,6:7] +.5 # observed mart <- rowSums(dM) # Table of sums for score and Schoenfeld resids # Looks like the last table of appendix E.2.1 of the book resid <- dM * outer(x, xbar, '-') score <- rowSums(resid) scho <- colSums(resid) # We need to add the ties back up (they are symmetric) scho[6:7] <- rep(mean(scho[6:7]), 2) list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard, mart=mart, score=score, rmat=resid, scho=scho) } aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) fit0 <-coxph(Surv(start, stop, event) ~x, test2, iter=0) truth0 <- byhand(0,0) aeq(truth0$loglik, fit0$loglik[1]) aeq(1/truth0$imat, fit0$var) aeq(truth0$mart, fit0$resid) aeq(truth0$scho, resid(fit0, 'schoen')) aeq(truth0$score, resid(fit0, 'score')) fit <- coxph(Surv(start, stop, event) ~x, test2, eps=1e-8) truth <- byhand(fit$coef, 0) aeq(truth$loglik, fit$loglik[2]) aeq(1/truth$imat, fit$var) aeq(truth$mart, fit$resid) aeq(truth$scho, resid(fit, 'schoen')) aeq(truth$score, resid(fit, 'score')) # Reprise the test, with strata # offseting the times ensures that we will get the wrong risk sets # if strata were not kept separate test2b <- rbind(test2, test2, test2) test2b$group <- rep(1:3, each= nrow(test2)) test2b$start <- test2b$start + test2b$group test2b$stop <- test2b$stop + test2b$group fit0 <- coxph(Surv(start, stop, event) ~ x + strata(group), test2b, iter=0) aeq(3*truth0$loglik, fit0$loglik[1]) aeq(3*truth0$imat, 1/fit0$var) aeq(rep(truth0$mart,3), fit0$resid) aeq(rep(truth0$scho,3), resid(fit0, 'schoen')) aeq(rep(truth0$score,3), resid(fit0, 'score')) fit3 <- coxph(Surv(start, stop, event) ~x + strata(group), test2b, eps=1e-8) aeq(3*truth$loglik, fit3$loglik[2]) aeq(3*truth$imat, 1/fit3$var) aeq(rep(truth$mart,3), fit3$resid) aeq(rep(truth$scho,3), resid(fit3, 'schoen')) aeq(rep(truth$score,3), resid(fit3, 'score')) # # Done with the formal test, now print out lots of bits # resid(fit) resid(fit, 'scor') resid(fit, 'scho') predict(fit, type='lp') predict(fit, type='risk') predict(fit, type='expected') predict(fit, type='terms') predict(fit, type='lp', se.fit=T) predict(fit, type='risk', se.fit=T) predict(fit, type='expected', se.fit=T) predict(fit, type='terms', se.fit=T) summary(survfit(fit)) summary(survfit(fit, list(x=2))) survival/tests/turnbull.R0000644000175100001440000001367011732700061015303 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # The test data set from Turnbull, JASA 1974, 169-73. # # status 0=right censored # 1=exact # 2=left censored # aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) turnbull <- data.frame( time =c( 1,1,1, 2,2,2, 3,3,3, 4,4,4), status=c( 1,0,2, 1,0,2, 1,0,2, 1,0,2), n =c(12,3,2, 6,2,4, 2,0,2, 3,3,5)) # # Compute the K-M for the Turnbull data # via a slow EM calculation # emsurv <- function(time, status, wt, verbose=T) { left.cen <- (status==2) if (!any(left.cen)) stop("No left censored data!") if (!any(status==1))stop("Must have some exact death times") tempy <- Surv(time[!left.cen], status[!left.cen]) ww <- wt[!left.cen] tempx <- factor(rep(1, sum(!left.cen))) tfit <- survfit(tempy~tempx, weight=ww) if (verbose) cat("Iteration 0, survival=", format(round(tfit$surv[tfit$n.event>0],3)), "\n") stimes <- tfit$time[tfit$n.event>0] ltime <- time[left.cen] lwt <- wt[left.cen] tempx <- factor(rep(1, length(stimes) + sum(!left.cen))) tempy <- Surv(c(time[!left.cen], stimes), c(status[!left.cen], rep(1, length(stimes)))) for (iter in 1:4) { wt2 <- stimes*0 ssurv <- tfit$surv[tfit$n.event>0] sjump <- diff(c(1, ssurv)) for (j in 1:(length(ltime))) { k <- sum(ltime[j]>=stimes) #index of the death time if (k==0) stop("Left censored observation before the first death") wt2[1:k] <- wt2[1:k] + lwt[j]*sjump[1:k] /(ssurv[k]-1) } tfit <- survfit(tempy~tempx, weight=c(ww, wt2)) if (verbose) { cat("Iteration", iter, "survival=", format(round(tfit$surv[tfit$n.event>0],3)), "\n") cat(" weights=", format(round(wt2,3)), "\n") } } survfit(tempy ~ tempx, weights=c(ww, wt2)) } temp <-emsurv(turnbull$time, turnbull$status, turnbull$n) print(summary(temp)) # First check, use the data from Turnbull, JASA 1974, 169-173. tdata <- data.frame(time =c(1,1,1,2,2,2,3,3,3,4,4,4), status=rep(c(1,0,2),4), n =c(12,3,2,6,2,4,2,0,2,3,3,5)) tfit <- survfit(Surv(time, time, status, type='interval') ~1, tdata, weight=n) all.equal(round(tfit$surv,3), c(.538, .295, .210, .095)) # Second check, compare to a reversed survival curve # This is not as simple a test as one might think, because left and right # censored observations are not treated symmetrically by the routine: # time <= y for left and time> y for right (this is to make the routine # correct for the common situation of panel data). # To get equivalence, make the left censoreds happen just a little bit # earlier. The left-continuous/right-continuous shift is also a bother. # test1 <- data.frame(time= c(9, 3,1,1,6,6,8), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0)) fit1 <- survfit(Surv(time, status) ~1, test1) temp <- ifelse(test1$status==0, 4.99,5) - test1$time fit2 <- survfit(Surv(temp, status, type='left') ~1, test1) all.equal(round(fit1$surv[1:2],5), round(1-fit2$surv[3:2],5)) rm(tdata, tfit, fit1, temp, fit2) # # Create a data set similar to the one provided by Al Zinsmeister # It is a hard test case for survfit.turnbull # time1 <- c(rep(0,100), rep(1,200), 100, 200, 210, 220, rep(365,100), rep(366,5), 731:741) time2 <- c((1:100)*3, 10+1:100, rep(365:366, c(60,40)), NA, 500, NA, 450, rep(730,90), rep(NA,10), c(528,571,691,730,731), NA, 1095:1099, NA, 1400, 1200, 772, 1461) zfit <- survfit(Surv(time1, time2, type='interval2') ~1) # # There are 100 intervals of the form (0,x) where x is from 3 to 300, # and 200 more of the form (1,x) where x is from 11 to 366. These # lead to a mass point in the interval (1,3), which is placed at 2. # The starting estimate has far too little mass placed here, and it takes # the EM a long time to realize that most of the weight for the first 300 # subjects goes here. With acceleration, it takes 16 iterations, without # it takes >40. (On Al's orginal data, without accel still wasn't there after # 165 iters!) # # The next 4 obs give rise to potential jumps at 100.5, 200.5, 211.5, and # 221. However, the final estimate has no mass at all on any of these. # Assume mass of a,b, and c at 2, 100.5 and 365.5, and consider the # contributions: # 123 obs that overlap a only # 137 obs that overlap a and b # 40 obs that overlap a, b, c # 1 obs that overlap b, c # 108 obs that overlap c (200, 210,200, 365, and 366 starting points) # For some trial values of a,b,c, compare the loglik to that of (a+b),0,c # First one: a^123 (a+b)^137 (a+b+c)^40 (b+c) c^108 # Second: (a+b)^123 (a+b)^137 (a+b+c)^40 c c^108 # Likelhood improves if (1 + b/a)^123 > 1+ b/c, which is true for almost # all a and c. In particular, at the solution a and c are approx .7 and # .18, respectively. # # The program can't see this coming, of course, and so iterates towards a # KM with epsilon sized jumps at 100.5, 200.5, and 211.5. Whether these # intervals should be removed during iteration, as detected, is an open # question for me. # # # True solution: mass points at 2, 365.5, 408, and 756.5, of sizes a, b, c, d # Likelihood: a^260 (a+b)^40 (b+c)^92 (b+c+d)^12 c^5 d^11 # Solution: a=0.6958, b=0.1674, c=0.1079, d=0.0289 tfun <- function(x) { if (length(x) ==3) x <- c(x, .03) x <- x/sum(x) #make probabilities sum to 1 loglik <- 260*log(x[1]) + 40*log(x[1]+x[2]) + 92*log(x[2] + x[3]) + 12*log(x[2]+x[3]+x[4]) + 5*log(x[3]) + 11*log(x[4]) -loglik #find the max, not the min } nfit <- nlminb(start=c(.7,.15, .1), tfun, lower=0, upper=1) nparm <- c(nfit$par, .03) nparm <- nparm / sum(nparm) zparm <- -diff(c(1, zfit$surv[match(c(2, 365.5, 408, 756.5), zfit$time)])) aeq(round(tfun(nparm),4), round(tfun(zparm),4)) # .0001 is the tolerance in survfit.turnbull rm(tfun, nfit, nparm, zparm, time1, time2, zfit) survival/tests/mstate.R0000644000175100001440000002063113003735752014734 0ustar hornikusers# # A tiny multi-state example # library(survival) aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) mtest <- data.frame(id= c(1, 1, 1, 2, 3, 4, 4, 4, 5, 5), t1= c(0, 4, 9, 0, 2, 0, 2, 8, 1, 3), t2= c(4, 9, 10, 5, 9, 2, 8, 9, 3, 11), st= c(1, 2, 1, 2, 3, 1, 3, 0, 2, 0)) mtest$state <- factor(mtest$st, 0:3, c("censor", "a", "b", "c")) mtest <- mtest[c(1,3,2,4,5,7,6,10, 9, 8),] #not in time order mfit <- survfit(Surv(t1, t2, state) ~ 1, mtest, id=id) # True results # #time state probabilities # entry a b c entry a b c # #0 124 1 0 0 0 #1+ 1245 #2+ 1235 4 3/4 1/4 0 0 4 -> a, add 3 #3+ 123 4 5 9/16 1/4 3/16 0 5 -> b #4+ 23 14 5 6/16 7/16 3/16 0 1 -> a #5+ 3 14 5 3/16 7/16 6/16 0 2 -> b, exits #8+ 3 1 5 4 3/16 7/32 6/16 7/32 4 -> c #9+ 15 0 0 19/32 13/32 1->b, 3->c & exit # 10+ 1 5 19/64 19/64 13/32 1->a # In mfit, the "entry" state is last in the matrices all.equal(mfit$n.risk, matrix(c(0,1,1,2,2,1,0,0, 0,0,1,1,1,1,2,1, 0,0,0,0,0,1,0,0, 4,4,3,2,1,1,0,0), ncol=4)) all.equal(mfit$pstate, matrix(c(8, 8, 14, 14, 7, 0, 9.5, 9.5, 0, 6, 6, 12, 12,19,9.5, 9.5, 0, 0, 0, 0, 7, 13, 13, 13, 24, 18, 12, 6, 6, 0, 0, 0)/32, ncol=4)) all.equal(mfit$n.event, matrix(c(1,0,1,0,0,0,1,0, 0,1,0,1,0,1,0,0, 0,0,0,0,1,1,0,0, 0,0,0,0,0,0,0,0), ncol=4)) all.equal(mfit$time, c(2, 3, 4, 5, 8, 9, 10, 11)) # Somewhat more complex. # Scramble the input data # Not everyone starts at the same time or in the same state # Two "istates" that vary, only the first should be noticed. # Case weights # tdata <- data.frame(id= c(1, 1, 1, 2, 3, 4, 4, 4, 5, 5), t1= c(0, 4, 9, 1, 2, 0, 2, 8, 1, 3), t2= c(4, 9, 10, 5, 9, 2, 8, 9, 3, 11), st= c(1, 2, 1, 2, 3, 1, 3, 0, 3, 0), i0= c(4, 4, 4, 1, 4, 4, 4, 1, 2, 2)) tdata$st <- factor(tdata$st, c(0:4), labels=c("censor", "1", "2", "3", "entry")) tfun <- function(wt, data=tdata) { reorder <- c(10, 9, 1, 2, 5, 4, 3, 7, 8, 6) new <- data[reorder,] new$wt <- rep(wt,length=10)[reorder] new } # These weight vectors are in the order of tdata # w[9] is the weight for subject 5 at time 1.5, for instance p0 <- function(w) c(w[4], w[9], 0, w[1]+ w[6])/ (w[1]+ w[4] + w[6] + w[9]) # aj2 = Aalen-Johansen H matrix at time 2, etc. aj2 <- function(w) { rbind(c(1, 0, 0, 0), # state a (1) stays put c(0, 1, 0, 0), c(0, 0, 1, 0), c(w[6], 0, 0, w[1])/(w[1] + w[6])) #subject 4 moves to 'a' } aj3 <- function(w) rbind(c(1, 0, 0, 0), c(0, 0, 1, 0), # 5 moves from b to c c(0, 0, 1, 0), c(0, 0, 0, 1)) aj4 <- function(w) rbind(c(1, 0, 0, 0), c(0, 1, 0, 0), c(0, 0, 1, 0), c(w[1], 0, 0, w[5])/(w[1] + w[5])) #1 moves from 4 to a aj5 <- function(w) rbind(c(w[2]+w[7], w[4], 0, 0)/(w[2]+ w[4] + w[7]), #2 to b c(0, 1, 0, 0), c(0, 0, 1, 0), c(0, 0, 0, 1)) aj8 <- function(w) rbind(c(w[2], 0, w[7], 0)/(w[2]+ w[7]), # 4 to c c(0, 1, 0, 0), c(0, 0, 1, 0), c(0, 0, 0, 1)) aj9 <- function(w) rbind(c(0, 1, 0, 0), # 1 to b c(0, 1, 0, 0), c(0, 0, 1, 0), c(0, 0, 1 ,0)) # 3 to c aj10 <- function(w)rbind(c(1, 0, 0, 0), c(1, 0, 0, 0), #1 back to a c(0, 0, 1, 0), c(0, 0, 0, 1)) #time state # a b c entry # #1 2 5 14 initial distribution #2 24 5 1 4 -> a, add 3 #3 24 5 13 5 from b to c #4 124 5 3 1 -> a #5 14 5 3 2 -> b, exits #8 1 45 3 4 -> c #9 1 45 1->b, 3->c & exit #10 1 45 1->a # P is a product of matrices dopstate <- function(w) { p1 <- p0(w) p2 <- p1 %*% aj2(w) p3 <- p2 %*% aj3(w) p4 <- p3 %*% aj4(w) p5 <- p4 %*% aj5(w) p8 <- p5 %*% aj8(w) p9 <- p8 %*% aj9(w) p10<- p9 %*% aj10(w) rbind(p2, p3, p4, p5, p8, p9, p10, p10) } # Check the pstate estimate w1 <- rep(1, 10) mtest2 <- tfun(w1) mfit2 <- survfit(Surv(t1, t2, st) ~ 1, tdata, id=id, istate=i0) # ordered aeq(mfit2$pstate, dopstate(w1)) aeq(mfit2$p0, p0(w1)) mfit2b <- survfit(Surv(t1, t2, st) ~ 1, mtest2, id=id, istate=i0)#scrambled aeq(mfit2b$pstate, dopstate(w1)) aeq(mfit2b$p0, p0(w1)) mfit2b$call <- mfit2$call <- NULL all.equal(mfit2b, mfit2) # Now the harder one, where subjects change weights mtest3 <- tfun(1:10) mfit3 <- survfit(Surv(t1, t2, st) ~ 1, mtest3, id=id, istate=i0, weights=wt, influence=TRUE) aeq(mfit3$p0, p0(1:10)) aeq(mfit3$pstate, dopstate(1:10)) # The derivative of a matrix product AB is (dA)B + A(dB) where dA is the # elementwise derivative of A and etc for B. # dp0 creates the derivatives of p0 with respect to each subject, a 5 by 4 # matrix dp0 <- function(w) { p <- p0(w) w0 <- w[c(1,4,6,9)] # the 4 obs at the start, subjects 1, 2, 4, 5 rbind(c(0, 0, 0, 1) - p, # subject 1 affects p[4] c(1, 0, 0, 0) - p, # subject 2 affects p0[1] 0, # subject 3 affects none c(0, 0, 0, 1) - p, # subject 4 affect p[4] c(0, 1, 0, 0) - p) / sum(w0) } dp2 <- function(w) { h2 <- aj2(w) # H matrix at time 2 part1 <- dp0(w) %*% h2 # 1 and 4 in state 4, obs 1 and 6, 4 moves to a mult <- p0(w)[4]/(w[1] + w[6]) #p(t-) / weights in state part2 <- rbind((c(0,0,0,1)- h2[4,]) * mult, 0, 0, (c(1,0,0,0) - h2[4,]) * mult, 0) part1 + part2 } dp3 <- function(w) { dp2(w) %*% aj3(w) } dp4 <- function(w) { h4 <- aj4(w) # H matrix at time 4 part1 <- dp3(w) %*% h4 # subjects 1 and 3 in state 4, obs 1 and 5, 1 moves to a mult <- dopstate(w)[2,4]/ (w[1] + w[5]) # p_4(time 4-0) / wt part2 <- rbind((c(1,0,0,0)- h4[4,]) * mult, 0, (c(0,0,0,1)- h4[4,]) * mult, 0, 0) part1 + part2 } dp5 <- function(w) { h5 <- aj5(w) # H matrix at time 5 part1 <- dp4(w) %*% h5 # subjects 124 in state 1, obs 2,4,7, 2 goes to 2 mult <- dopstate(w)[3,1]/ (denom <- w[2] + w[4] + w[7]) part2 <- rbind((c(1,0,0,0)- h5[1,]) * mult, (c(0,1,0,0)- h5[1,]) * mult, 0, (c(1,0,0,0)- h5[1,]) * mult, 0) part1 + part2 } dp8 <- function(w) { h8 <- aj8(w) # H matrix at time 8 part1 <- dp5(w) %*% h8 # subjects 14 in state 1, obs 2 &7, 4 goes to c mult <- dopstate(w)[4, 1]/ (w[2] + w[7]) part2 <- rbind((c(1,0,0,0)- h8[1,]) * mult, 0, 0, (c(0,0,1,0)- h8[1,]) * mult, 0) part1 + part2 } dp9 <- function(w) dp8(w) %*% aj9(w) dp10<- function(w) dp9(w) %*% aj10(w) w1 <- 1:10 aeq(mfit3$influence[,1,], dp0(w1)) aeq(mfit3$influence[,2,], dp2(w1)) aeq(mfit3$influence[,3,], dp3(w1)) aeq(mfit3$influence[,4,], dp4(w1)) aeq(mfit3$influence[,5,], dp5(w1)) aeq(mfit3$influence[,6,], dp8(w1)) aeq(mfit3$influence[,7,], dp9(w1)) aeq(mfit3$influence[,8,], dp10(w1)) aeq(mfit3$influence[,9,], dp10(w1)) # no changes at time 11 aeq(mfit3$cumhaz[,,1], aj2(w1)- diag(4)) aeq(mfit3$cumhaz[,,2] - mfit3$cumhaz[,,1], aj3(w1)- diag(4)) aeq(mfit3$cumhaz[,,3] - mfit3$cumhaz[,,2], aj4(w1)- diag(4)) aeq(mfit3$cumhaz[,,4] - mfit3$cumhaz[,,3], aj5(w1)- diag(4)) aeq(mfit3$cumhaz[,,5] - mfit3$cumhaz[,,4], aj8(w1)- diag(4)) aeq(mfit3$cumhaz[,,6] - mfit3$cumhaz[,,5], aj9(w1)- diag(4)) survival/tests/coxsurv4.Rout.save0000644000175100001440000000511612160143136016712 0ustar hornikusers R version 3.0.1 (2013-05-16) -- "Good Sport" Copyright (C) 2013 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > > # Strata by covariate interactions, a case pointed out in early 2011 > # by Frank Harrell, which as it turns out had never been computed > # correctly by any version of the package. Which shows how often this > # case arises in practice. > # > aeq <- function(x, y, ...) all.equal(as.vector(x), as.vector(y)) > fit1 <- coxph(Surv(time, status) ~ wt.loss + age*strata(sex) + strata(ph.ecog), + data=lung) > tdata <- data.frame(wt.loss=c(10,5,0,10, 15,20,25), + age =c(50,60,50,60,70,40,21), + sex =c(1,1,2,2,1,1,1), + ph.ecog=c(0,0,1,1,2,2,2)) > surv1 <- survfit(fit1, newdata=tdata) > > fit2 <- coxph(Surv(time, status) ~ wt.loss + age + I(age*0), data=lung, + init=fit1$coef, iter=0, subset=(sex==1 & ph.ecog==0)) > fit2$var <- fit1$var > > surv2 <- survfit(fit2, newdata=list(wt.loss=c(10,5), age=c(50,60))) > s1 <- surv1[1:2] > aeq(s1$surv, surv2$surv) #first a vector, second a matrix [1] TRUE > aeq(s1$std.err, surv2$std.err) [1] TRUE > aeq(s1[1]$time, surv2$time) [1] TRUE > aeq(s1[1]$n.event, surv2$n.event) [1] TRUE > > fit3 <- coxph(Surv(time, status) ~ wt.loss + age + I(age*1), + data=lung, init=fit1$coef, iter=0, + subset=(sex==2 & ph.ecog==1)) > fit3$var <- fit1$var > surv3 <- survfit(fit3, newdata=list(wt.loss=c(0,10), age=c(50,60))) > aeq(surv1[3:4]$surv, surv3$surv) [1] TRUE > aeq(surv1[3:4]$std, surv3$std) [1] TRUE > > fit4 <- coxph(Surv(time, status) ~ wt.loss + age + I(age*0), + data=lung, init=fit1$coef, iter=0, + subset=(sex==1 & ph.ecog==2)) > fit4$var <- fit1$var > surv4 <- survfit(fit4, newdata=list(wt.loss=c(15,20,25), age=c(70,40,21))) > > aeq(surv1[5:7]$surv, surv4$surv) [1] TRUE > aeq(surv1[5:7]$std.err, surv4$std.err) [1] TRUE > aeq(surv1[5]$n.risk, surv4$n.risk) [1] TRUE > > > proc.time() user system elapsed 0.324 0.052 0.356 survival/tests/r_strata.Rout.save0000644000175100001440000001146011732700061016733 0ustar hornikusers R version 2.11.1 (2010-05-31) Copyright (C) 2010 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # Test out the strata capabilities > # > tol <- survreg.control()$rel.tolerance > aeq <- function(x,y,...) all.equal(as.vector(x), as.vector(y), ...) > > # intercept only models > fit1 <- survreg(Surv(time, status) ~ strata(sex), lung) > fit2 <- survreg(Surv(time, status) ~ strata(sex) + sex, lung) > fit3a<- survreg(Surv(time,status) ~1, lung, subset=(sex==1)) > fit3b<- survreg(Surv(time,status) ~1, lung, subset=(sex==2)) > > fit1 Call: survreg(formula = Surv(time, status) ~ strata(sex), data = lung) Coefficients: (Intercept) 6.062171 Scale: sex=1 sex=2 0.8167551 0.6533036 Loglik(model)= -1152.5 Loglik(intercept only)= -1152.5 n= 228 > fit2 Call: survreg(formula = Surv(time, status) ~ strata(sex) + sex, data = lung) Coefficients: (Intercept) sex 5.494409 0.380171 Scale: sex=1 sex=2 0.8084294 0.6355816 Loglik(model)= -1147.1 Loglik(intercept only)= -1152.5 Chisq= 10.9 on 1 degrees of freedom, p= 0.00096 n= 228 > aeq(fit2$scale, c(fit3a$scale, fit3b$scale), tolerance=tol) [1] TRUE > aeq(fit2$loglik[2], (fit3a$loglik + fit3b$loglik)[2], tolerance=tol) [1] TRUE > aeq(fit2$coef[1] + 1:2*fit2$coef[2], c(fit3a$coef, fit3b$coef), tolerance=tol) [1] TRUE > > #penalized models > fit1 <- survreg(Surv(time, status) ~ pspline(age, theta=.92)+ + strata(sex), lung) > fit2 <- survreg(Surv(time, status) ~ pspline(age, theta=.92)+ + strata(sex) + sex, lung) > fit1 Call: survreg(formula = Surv(time, status) ~ pspline(age, theta = 0.92) + strata(sex), data = lung) coef se(coef) se2 Chisq DF p (Intercept) 6.9036 0.8469 0.5688 66.45 1.00 3.3e-16 pspline(age, theta = 0.92 -0.0124 0.0067 0.0067 3.45 1.00 6.3e-02 pspline(age, theta = 0.92 2.53 2.65 4.0e-01 Scale: sex=1 sex=2 0.807 0.654 Iterations: 1 outer, 4 Newton-Raphson Theta= 0.92 Degrees of freedom for terms= 0.5 3.6 2.0 Likelihood ratio test=6.54 on 3.1 df, p=0.0937 n= 228 > fit2 Call: survreg(formula = Surv(time, status) ~ pspline(age, theta = 0.92) + strata(sex) + sex, data = lung) coef se(coef) se2 Chisq DF p (Intercept) 6.3729 0.84471 0.59118 56.92 1.00 4.5e-14 pspline(age, theta = 0.92 -0.0111 0.00666 0.00666 2.77 1.00 9.6e-02 pspline(age, theta = 0.92 2.46 2.68 4.2e-01 sex 0.3686 0.11711 0.11685 9.91 1.00 1.6e-03 Scale: sex=1 sex=2 0.800 0.636 Iterations: 1 outer, 5 Newton-Raphson Theta= 0.92 Degrees of freedom for terms= 0.5 3.7 1.0 2.0 Likelihood ratio test=16.8 on 4.2 df, p=0.00245 n= 228 > > age1 <- ifelse(lung$sex==1, lung$age, mean(lung$age)) > age2 <- ifelse(lung$sex==2, lung$age, mean(lung$age)) > fit3 <- survreg(Surv(time,status) ~ pspline(age1, theta=.92) + + pspline(age2, theta=.95) + sex + strata(sex), lung) > fit3a<- survreg(Surv(time,status) ~pspline(age, theta=.92), lung, + subset=(sex==1)) > fit3b<- survreg(Surv(time,status) ~pspline(age, theta=.95), lung, + subset=(sex==2)) > fit3b<- survreg(Surv(time,status) ~pspline(age, theta=.95), + lung[lung$sex==2,], x=T) > # > # The above line is tricky, and it took me a long time to realize > # it's necessity. The range of age1 = range(age) = 39-82. That for > # age2 = range of females = 41-77. The basis functions for pspline are > # based on age. If I used data=lung, subset=(sex==2) in fit3b (earlier > # form of the test, the pspline function is called before the subset > # occurs, and fit3b has a different basis for the second spline than > # fit3 does; leading to failure of the all.equal tests below. A theta > # of .95 on one basis is not exactly the same as a theta of .95 on the > # other. Coefficients were within 1%, but not the same. > > aeq(fit3$scale, c(fit3a$scale, fit3b$scale)) [1] TRUE > aeq(fit3$loglik[2], (fit3a$loglik + fit3b$loglik)[2]) [1] TRUE > pred <- predict(fit3) > aeq(pred[lung$sex==1] , predict(fit3a)) [1] TRUE > aeq(pred[lung$sex==2], predict(fit3b)) [1] TRUE > > > > > survival/tests/r_strata.R0000644000175100001440000000443711732700061015254 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Test out the strata capabilities # tol <- survreg.control()$rel.tolerance aeq <- function(x,y,...) all.equal(as.vector(x), as.vector(y), ...) # intercept only models fit1 <- survreg(Surv(time, status) ~ strata(sex), lung) fit2 <- survreg(Surv(time, status) ~ strata(sex) + sex, lung) fit3a<- survreg(Surv(time,status) ~1, lung, subset=(sex==1)) fit3b<- survreg(Surv(time,status) ~1, lung, subset=(sex==2)) fit1 fit2 aeq(fit2$scale, c(fit3a$scale, fit3b$scale), tolerance=tol) aeq(fit2$loglik[2], (fit3a$loglik + fit3b$loglik)[2], tolerance=tol) aeq(fit2$coef[1] + 1:2*fit2$coef[2], c(fit3a$coef, fit3b$coef), tolerance=tol) #penalized models fit1 <- survreg(Surv(time, status) ~ pspline(age, theta=.92)+ strata(sex), lung) fit2 <- survreg(Surv(time, status) ~ pspline(age, theta=.92)+ strata(sex) + sex, lung) fit1 fit2 age1 <- ifelse(lung$sex==1, lung$age, mean(lung$age)) age2 <- ifelse(lung$sex==2, lung$age, mean(lung$age)) fit3 <- survreg(Surv(time,status) ~ pspline(age1, theta=.92) + pspline(age2, theta=.95) + sex + strata(sex), lung) fit3a<- survreg(Surv(time,status) ~pspline(age, theta=.92), lung, subset=(sex==1)) fit3b<- survreg(Surv(time,status) ~pspline(age, theta=.95), lung, subset=(sex==2)) fit3b<- survreg(Surv(time,status) ~pspline(age, theta=.95), lung[lung$sex==2,], x=T) # # The above line is tricky, and it took me a long time to realize # it's necessity. The range of age1 = range(age) = 39-82. That for # age2 = range of females = 41-77. The basis functions for pspline are # based on age. If I used data=lung, subset=(sex==2) in fit3b (earlier # form of the test, the pspline function is called before the subset # occurs, and fit3b has a different basis for the second spline than # fit3 does; leading to failure of the all.equal tests below. A theta # of .95 on one basis is not exactly the same as a theta of .95 on the # other. Coefficients were within 1%, but not the same. aeq(fit3$scale, c(fit3a$scale, fit3b$scale)) aeq(fit3$loglik[2], (fit3a$loglik + fit3b$loglik)[2]) pred <- predict(fit3) aeq(pred[lung$sex==1] , predict(fit3a)) aeq(pred[lung$sex==2], predict(fit3b)) survival/tests/book4.Rout.save0000644000175100001440000002151412701744412016140 0ustar hornikusers R Under development (unstable) (2016-03-23 r70368) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # Tests from the appendix of Therneau and Grambsch > # d. Data set 2 and Efron estimate > # > test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), + stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), + event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), + x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) > > byhand <- function(beta, newx=0) { + r <- exp(beta) + loglik <- 4*beta - (log(r+1) + log(r+2) + 2*log(3*r+2) + 2*log(3*r+1) + + log(2*r +2)) + u <- 1/(r+1) + 1/(3*r+1) + 2*(1/(3*r+2) + 1/(2*r+2)) - + ( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1)) + imat <- r*(1/(r+1)^2 + 2/(r+2)^2 + 6/(3*r+2)^2 + + 6/(3*r+1)^2 + 6/(3*r+2)^2 + 4/(2*r +2)^2) + + hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), + 1/(3*r+2), 1/(2*r +2) ) + + + # The matrix of weights, one row per obs, one col per time + # deaths at 2,3,6,7,8,9 + wtmat <- matrix(c(1,0,0,0,1, 0, 0,0,0,0, + 0,1,0,1,1, 0, 0,0,0,0, + 0,0,1,1,1, 0, 1,1,0,0, + 0,0,0,1,1, 0, 1,1,0,0, + 0,0,0,0,1, 1, 1,1,0,0, + 0,0,0,0,0, 1, 1,1,1,1, + 0,0,0,0,0,.5,.5,1,1,1), ncol=7) + wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat + + x <- c(1,0,0,1,0,1,1,1,0,0) + status <- c(1,1,1,1,1,1,1,0,0,0) + xbar <- colSums(wtmat*x)/ colSums(wtmat) + n <- length(x) + + # Table of sums for score and Schoenfeld resids + hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time + dM <- -hazmat #Expected part + for (i in 1:5) dM[i,i] <- dM[i,i] +1 #observed + dM[6:7,6:7] <- dM[6:7,6:7] +.5 # observed + mart <- rowSums(dM) + + # Table of sums for score and Schoenfeld resids + # Looks like the last table of appendix E.2.1 of the book + resid <- dM * outer(x, xbar, '-') + score <- rowSums(resid) + scho <- colSums(resid) + + # We need to add the ties back up (they are symmetric) + scho[6:7] <- rep(mean(scho[6:7]), 2) + + list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard, + mart=mart, score=score, rmat=resid, + scho=scho) + } > > > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > fit0 <-coxph(Surv(start, stop, event) ~x, test2, iter=0) > truth0 <- byhand(0,0) > aeq(truth0$loglik, fit0$loglik[1]) [1] TRUE > aeq(1/truth0$imat, fit0$var) [1] TRUE > aeq(truth0$mart, fit0$resid) [1] TRUE > aeq(truth0$scho, resid(fit0, 'schoen')) [1] TRUE > aeq(truth0$score, resid(fit0, 'score')) [1] TRUE > > > fit <- coxph(Surv(start, stop, event) ~x, test2, eps=1e-8) > truth <- byhand(fit$coef, 0) > aeq(truth$loglik, fit$loglik[2]) [1] TRUE > aeq(1/truth$imat, fit$var) [1] TRUE > aeq(truth$mart, fit$resid) [1] TRUE > aeq(truth$scho, resid(fit, 'schoen')) [1] TRUE > aeq(truth$score, resid(fit, 'score')) [1] TRUE > > # Reprise the test, with strata > # offseting the times ensures that we will get the wrong risk sets > # if strata were not kept separate > test2b <- rbind(test2, test2, test2) > test2b$group <- rep(1:3, each= nrow(test2)) > test2b$start <- test2b$start + test2b$group > test2b$stop <- test2b$stop + test2b$group > fit0 <- coxph(Surv(start, stop, event) ~ x + strata(group), test2b, iter=0) > aeq(3*truth0$loglik, fit0$loglik[1]) [1] TRUE > aeq(3*truth0$imat, 1/fit0$var) [1] TRUE > aeq(rep(truth0$mart,3), fit0$resid) [1] TRUE > aeq(rep(truth0$scho,3), resid(fit0, 'schoen')) [1] TRUE > aeq(rep(truth0$score,3), resid(fit0, 'score')) [1] TRUE > > fit3 <- coxph(Surv(start, stop, event) ~x + strata(group), test2b, eps=1e-8) > aeq(3*truth$loglik, fit3$loglik[2]) [1] TRUE > aeq(3*truth$imat, 1/fit3$var) [1] TRUE > aeq(rep(truth$mart,3), fit3$resid) [1] TRUE > aeq(rep(truth$scho,3), resid(fit3, 'schoen')) [1] TRUE > aeq(rep(truth$score,3), resid(fit3, 'score')) [1] TRUE > > # > # Done with the formal test, now print out lots of bits > # > resid(fit) 1 2 3 4 5 6 0.50527611 0.66432995 0.79746211 0.22435805 -0.55144018 0.42933697 7 8 9 10 -0.01764508 -1.14132605 -0.45517594 -0.45517594 > resid(fit, 'scor') 1 2 3 4 5 6 7 0.2553039 -0.2183386 -0.4744295 -0.1101520 0.1137126 0.2491954 0.1057078 8 9 10 -0.4119611 0.2454808 0.2454808 > resid(fit, 'scho') 2 3 6 7 8 9 9 0.5052761 -0.3286599 -0.5949242 0.2539781 -0.7460219 0.4551759 0.4551759 > > predict(fit, type='lp') [1] -0.0105526 0.0105526 0.0105526 -0.0105526 0.0105526 -0.0105526 [7] -0.0105526 -0.0105526 0.0105526 0.0105526 > predict(fit, type='risk') [1] 0.9895029 1.0106085 1.0106085 0.9895029 1.0106085 0.9895029 0.9895029 [8] 0.9895029 1.0106085 1.0106085 > predict(fit, type='expected') 1 2 3 4 5 6 7 8 0.4947239 0.3356701 0.2025379 0.7756420 1.5514402 0.5706630 1.0176451 1.1413261 9 10 0.4551759 0.4551759 > predict(fit, type='terms') x 1 -0.0105526 2 0.0105526 3 0.0105526 4 -0.0105526 5 0.0105526 6 -0.0105526 7 -0.0105526 8 -0.0105526 9 0.0105526 10 0.0105526 attr(,"constant") [1] -0.0105526 > predict(fit, type='lp', se.fit=T) $fit 1 2 3 4 5 6 7 -0.0105526 0.0105526 0.0105526 -0.0105526 0.0105526 -0.0105526 -0.0105526 8 9 10 -0.0105526 0.0105526 0.0105526 $se.fit 1 2 3 4 5 6 7 8 0.3975884 0.3975884 0.3975884 0.3975884 0.3975884 0.3975884 0.3975884 0.3975884 9 10 0.3975884 0.3975884 > predict(fit, type='risk', se.fit=T) $fit 1 2 3 4 5 6 7 8 0.9895029 1.0106085 1.0106085 0.9895029 1.0106085 0.9895029 0.9895029 0.9895029 9 10 1.0106085 1.0106085 $se.fit 1 2 3 4 5 6 7 8 0.3954962 0.3996918 0.3996918 0.3954962 0.3996918 0.3954962 0.3954962 0.3954962 9 10 0.3996918 0.3996918 > predict(fit, type='expected', se.fit=T) $fit 1 2 3 4 5 6 7 8 0.4947239 0.3356701 0.2025379 0.7756420 1.5514402 0.5706630 1.0176451 1.1413261 9 10 0.4551759 0.4551759 $se.fit [1] 0.5331623 0.3940109 0.3241963 0.6388491 1.0026838 0.6453101 0.7848594 [8] 0.7848594 0.6401915 0.6401915 > predict(fit, type='terms', se.fit=T) $fit x 1 -0.0105526 2 0.0105526 3 0.0105526 4 -0.0105526 5 0.0105526 6 -0.0105526 7 -0.0105526 8 -0.0105526 9 0.0105526 10 0.0105526 attr(,"constant") [1] -0.0105526 $se.fit x 1 0.3975884 2 0.3975884 3 0.3975884 4 0.3975884 5 0.3975884 6 0.3975884 7 0.3975884 8 0.3975884 9 0.3975884 10 0.3975884 > > summary(survfit(fit)) Call: survfit(formula = fit) time n.risk n.event survival std.err lower 95% CI upper 95% CI 2 2 1 0.607 0.303 0.2277 1.000 3 3 1 0.435 0.262 0.1337 1.000 6 5 1 0.356 0.226 0.1029 1.000 7 4 1 0.277 0.189 0.0729 1.000 8 4 1 0.215 0.157 0.0516 0.899 9 5 2 0.137 0.109 0.0288 0.655 > summary(survfit(fit, list(x=2))) Call: survfit(formula = fit, newdata = list(x = 2)) time n.risk n.event survival std.err lower 95% CI upper 95% CI 2 2 1 0.616 0.465 0.14013 1 3 3 1 0.447 0.519 0.04568 1 6 5 1 0.368 0.504 0.02512 1 7 4 1 0.288 0.464 0.01232 1 8 4 1 0.226 0.418 0.00603 1 9 5 2 0.146 0.343 0.00147 1 > > proc.time() user system elapsed 0.244 0.020 0.259 survival/tests/r_tdist.Rout.save0000644000175100001440000001743011732700061016567 0ustar hornikusers R version 2.7.1 (2008-06-23) Copyright (C) 2008 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # Test out the t-distribution > # > > capacitor <- read.table('data.capacitor', row.names=1, + col.names=c('', 'days', 'event', 'voltage')) > # First, a t-dist with 500 df should be nearly identical to the Gaussian > > fitig <- survreg(Surv(days, event)~voltage, + dist = "gaussian", data = capacitor) > fit1 <- survreg(Surv(days, event) ~ voltage, + dist='t', parms=500, capacitor) > fitig Call: survreg(formula = Surv(days, event) ~ voltage, data = capacitor, dist = "gaussian") Coefficients: (Intercept) voltage 1764.93485 -53.87917 Scale= 121.4319 Loglik(model)= -361.9 Loglik(intercept only)= -420.1 Chisq= 116.33 on 1 degrees of freedom, p= 0 n= 125 > summary(fit1, corr=F) Call: survreg(formula = Surv(days, event) ~ voltage, data = capacitor, dist = "t", parms = 500) Value Std. Error z p (Intercept) 1765.8 163.137 10.82 2.64e-27 voltage -53.9 5.536 -9.74 2.06e-22 Log(scale) 4.8 0.106 45.44 0.00e+00 Scale= 121 Student-t distribution: parmameters= 500 Loglik(model)= -361.9 Loglik(intercept only)= -420.1 Chisq= 116.48 on 1 degrees of freedom, p= 0 Number of Newton-Raphson Iterations: 6 n= 125 > > # A more realistic fit > fit2 <- survreg(Surv(days, event) ~ voltage, + dist='t', parms=5, capacitor) > print(fit2) Call: survreg(formula = Surv(days, event) ~ voltage, data = capacitor, dist = "t", parms = 5) Coefficients: (Intercept) voltage 1819.28554 -55.74915 Scale= 96.84073 Loglik(model)= -360.4 Loglik(intercept only)= -424.7 Chisq= 128.55 on 1 degrees of freedom, p= 0 n= 125 > > xx <- seq(1,125, by=10) > resid(fit2, type='response')[xx] 1 11 21 31 41 51 61 -404.30257 -404.30257 -404.30257 -98.07767 -69.80767 -69.80767 -69.80767 71 81 91 101 111 121 -69.80767 -93.94023 97.43977 113.88722 -33.24278 -20.67278 > resid(fit2, type='deviance')[xx] 1 11 21 31 41 51 61 0.0933622 0.0933622 0.0933622 -2.2347398 0.7614136 0.7614136 0.7614136 71 81 91 101 111 121 0.7614136 -2.2156512 1.8511554 2.3107823 -2.0035571 -1.9821491 > resid(fit2, type='working') [xx] 1 11 21 31 41 51 61 86.38692 86.38692 86.38692 -148.70263 83.43717 83.43717 83.43717 71 81 91 101 111 121 83.43717 -137.49634 467.64123 200.98252 -34.84748 -21.05308 > resid(fit2, type='dfbeta')[xx,] (Intercept) voltage Log(scale) 1 0.2105054 -0.00703909 -1.743331e-04 11 0.2105054 -0.00703909 -1.743331e-04 21 0.2105054 -0.00703909 -1.743331e-04 31 -29.7982886 0.93975839 -1.076889e-02 41 9.6554540 -0.30502561 3.507039e-05 51 9.6554540 -0.30502561 3.507039e-05 61 9.6554540 -0.30502561 3.507039e-05 71 9.6554540 -0.30502561 3.507039e-05 81 -7.9425298 0.20791541 -6.194989e-03 91 16.3379622 -0.46035101 2.516742e-02 101 -13.8131372 0.53202477 4.665894e-03 111 0.7894992 -0.06147045 -1.308494e-02 121 -1.7672591 0.03187567 -1.433810e-02 > resid(fit2, type='dfbetas')[xx,] [,1] [,2] [,3] 1 0.001445482 -0.001447807 -0.0014173482 11 0.001445482 -0.001447807 -0.0014173482 21 0.001445482 -0.001447807 -0.0014173482 31 -0.204616568 0.193290466 -0.0875522695 41 0.066301320 -0.062737980 0.0002851263 51 0.066301320 -0.062737980 0.0002851263 61 0.066301320 -0.062737980 0.0002851263 71 0.066301320 -0.062737980 0.0002851263 81 -0.054539145 0.042764254 -0.0503659665 91 0.112188247 -0.094685467 0.2046140370 101 -0.094850975 0.109427398 0.0379342550 111 0.005421271 -0.012643305 -0.1063820631 121 -0.012135277 0.006556221 -0.1165704260 > resid(fit2, type='ldresp')[xx] 1 11 21 31 41 51 6.303033e-06 6.303033e-06 6.303033e-06 4.198946e-02 1.121526e-02 1.121526e-02 61 71 81 91 101 111 1.121526e-02 1.121526e-02 3.796054e-02 3.773652e-02 5.409081e-02 4.663892e-02 121 4.455789e-02 > resid(fit2, type='ldshape')[xx] 1 11 21 31 41 51 8.281125e-05 8.281125e-05 8.281125e-05 1.355729e-01 1.789400e-04 1.789400e-04 61 71 81 91 101 111 1.789400e-04 1.789400e-04 6.346182e-02 9.934752e-02 1.534546e-01 1.958545e-02 121 7.748320e-03 > resid(fit2, type='ldcase')[xx] 1 11 21 31 41 51 6.114509e-06 6.114509e-06 6.114509e-06 5.563427e-02 6.706055e-03 6.706055e-03 61 71 81 91 101 111 6.706055e-03 6.706055e-03 1.966021e-02 6.803951e-02 3.806159e-02 1.617087e-02 121 1.551988e-02 > resid(fit2, type='matrix')[xx,] g dg ddg ds dds 1 -0.00435825 4.361059e-05 -5.048286e-07 -0.01763187 -0.06488770 11 -0.00435825 4.361059e-05 -5.048286e-07 -0.01763187 -0.06488770 21 -0.00435825 4.361059e-05 -5.048286e-07 -0.01763187 -0.06488770 31 -6.10147902 -1.041351e-02 -7.002908e-05 0.02133278 -1.69495867 41 -0.28987533 3.893573e-03 -4.666473e-05 -0.27180126 0.04439884 51 -0.28987533 3.893573e-03 -4.666473e-05 -0.27180126 0.04439884 61 -0.28987533 3.893573e-03 -4.666473e-05 -0.27180126 0.04439884 71 -0.28987533 3.893573e-03 -4.666473e-05 -0.27180126 0.04439884 81 -6.05900320 -1.011644e-02 -7.357605e-05 -0.04965962 -1.59963182 91 -1.71338808 1.250705e-02 -2.674498e-05 1.21868456 -1.47261500 101 -6.27430559 1.141518e-02 -5.679687e-05 0.30004293 -2.03671532 111 -5.61156875 -4.155718e-03 -1.192545e-04 -0.86185235 -0.26993370 121 -5.56890563 -2.621343e-03 -1.245112e-04 -0.94580955 -0.10740203 dsg 1 0.0001604929 11 0.0001604929 21 0.0001604929 31 0.0172817991 41 -0.0006360167 51 -0.0006360167 61 -0.0006360167 71 -0.0006360167 81 0.0170281873 91 -0.0151130795 101 -0.0178836167 111 0.0081200691 121 0.0051953348 > > predict(fit2, type='response')[xx] [1] 704.30257 704.30257 704.30257 369.80767 369.80767 369.80767 369.80767 [8] 369.80767 202.56023 202.56023 35.31278 35.31278 35.31278 > predict(fit2, type='link')[xx] [1] 704.30257 704.30257 704.30257 369.80767 369.80767 369.80767 369.80767 [8] 369.80767 202.56023 202.56023 35.31278 35.31278 35.31278 > predict(fit2, type='terms')[xx,] 1 11 21 31 41 51 61 374.63428 374.63428 374.63428 40.13939 40.13939 40.13939 40.13939 71 81 91 101 111 121 40.13939 -127.10806 -127.10806 -294.35550 -294.35550 -294.35550 > predict(fit2, type='quantile')[xx] [1] 561.37687 561.37687 561.37687 226.88198 226.88198 226.88198 [7] 226.88198 226.88198 59.63453 59.63453 -107.61291 -107.61291 [13] -107.61291 > > rm(fitig, fit1, fit2, xx) > survival/tests/jasa.Rout.save0000644000175100001440000003142312656731455016054 0ustar hornikusers R Under development (unstable) (2016-01-29 r70039) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > expect <- survexp(futime ~ ratetable(age=(accept.dt - birth.dt), sex=1, + year=accept.dt, race='white'), jasa, cohort=F, + ratetable=survexp.usr) > > survdiff(Surv(jasa$futime, jasa$fustat) ~ offset(expect)) Call: survdiff(formula = Surv(jasa$futime, jasa$fustat) ~ offset(expect)) Observed Expected Z p 75.000 0.587 -97.119 0.000 > # Now fit the 6 models found in Kalbfleisch and Prentice, p139 > sfit.1 <- coxph(Surv(start, stop, event)~ (age + surgery)*transplant, + jasa1, method='breslow') > sfit.2 <- coxph(Surv(start, stop, event)~ year*transplant, + jasa1, method='breslow') > sfit.3 <- coxph(Surv(start, stop, event)~ (age + year)*transplant, + jasa1, method='breslow') > sfit.4 <- coxph(Surv(start, stop, event)~ (year +surgery) *transplant, + jasa1, method='breslow') > sfit.5 <- coxph(Surv(start, stop, event)~ (age + surgery)*transplant + year , + jasa1, method='breslow') > sfit.6 <- coxph(Surv(start, stop, event)~ age*transplant + surgery + year, + jasa1, method='breslow') > > summary(sfit.1) Call: coxph(formula = Surv(start, stop, event) ~ (age + surgery) * transplant, data = jasa1, method = "breslow") n= 170, number of events= 75 coef exp(coef) se(coef) z Pr(>|z|) age 0.01386 1.01395 0.01813 0.765 0.445 surgery -0.54652 0.57896 0.61091 -0.895 0.371 transplant 0.11572 1.12268 0.32729 0.354 0.724 age:transplant 0.03473 1.03534 0.02725 1.274 0.202 surgery:transplant -0.29037 0.74799 0.75819 -0.383 0.702 exp(coef) exp(-coef) lower .95 upper .95 age 1.014 0.9862 0.9786 1.051 surgery 0.579 1.7272 0.1748 1.917 transplant 1.123 0.8907 0.5911 2.132 age:transplant 1.035 0.9659 0.9815 1.092 surgery:transplant 0.748 1.3369 0.1692 3.306 Concordance= 0.595 (se = 0.037 ) Rsquare= 0.071 (max possible= 0.97 ) Likelihood ratio test= 12.45 on 5 df, p=0.02915 Wald test = 11.62 on 5 df, p=0.04031 Score (logrank) test = 12.02 on 5 df, p=0.03457 > sfit.2 Call: coxph(formula = Surv(start, stop, event) ~ year * transplant, data = jasa1, method = "breslow") coef exp(coef) se(coef) z p year -0.265 0.767 0.105 -2.52 0.012 transplant -0.287 0.750 0.514 -0.56 0.576 year:transplant 0.137 1.147 0.141 0.97 0.331 Likelihood ratio test=8.61 on 3 df, p=0.0349 n= 170, number of events= 75 > summary(sfit.3) Call: coxph(formula = Surv(start, stop, event) ~ (age + year) * transplant, data = jasa1, method = "breslow") n= 170, number of events= 75 coef exp(coef) se(coef) z Pr(>|z|) age 0.01558 1.01571 0.01734 0.899 0.36887 year -0.27413 0.76023 0.10588 -2.589 0.00962 ** transplant -0.59388 0.55218 0.54222 -1.095 0.27339 age:transplant 0.03380 1.03438 0.02795 1.209 0.22653 year:transplant 0.20228 1.22419 0.14247 1.420 0.15566 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 exp(coef) exp(-coef) lower .95 upper .95 age 1.0157 0.9845 0.9818 1.0508 year 0.7602 1.3154 0.6178 0.9356 transplant 0.5522 1.8110 0.1908 1.5981 age:transplant 1.0344 0.9668 0.9792 1.0926 year:transplant 1.2242 0.8169 0.9259 1.6185 Concordance= 0.63 (se = 0.037 ) Rsquare= 0.084 (max possible= 0.97 ) Likelihood ratio test= 14.85 on 5 df, p=0.01102 Wald test = 13.77 on 5 df, p=0.01716 Score (logrank) test = 14.06 on 5 df, p=0.01525 > sfit.4 Call: coxph(formula = Surv(start, stop, event) ~ (year + surgery) * transplant, data = jasa1, method = "breslow") coef exp(coef) se(coef) z p year -0.254 0.776 0.108 -2.36 0.018 surgery -0.237 0.789 0.628 -0.38 0.707 transplant -0.297 0.743 0.505 -0.59 0.557 year:transplant 0.165 1.180 0.142 1.17 0.243 surgery:transplant -0.550 0.577 0.776 -0.71 0.479 Likelihood ratio test=12.4 on 5 df, p=0.0302 n= 170, number of events= 75 > sfit.5 Call: coxph(formula = Surv(start, stop, event) ~ (age + surgery) * transplant + year, data = jasa1, method = "breslow") coef exp(coef) se(coef) z p age 0.0150 1.0152 0.0176 0.85 0.393 surgery -0.4202 0.6569 0.6156 -0.68 0.495 transplant 0.0741 1.0769 0.3311 0.22 0.823 year -0.1363 0.8726 0.0710 -1.92 0.055 age:transplant 0.0269 1.0273 0.0271 0.99 0.321 surgery:transplant -0.2966 0.7434 0.7580 -0.39 0.696 Likelihood ratio test=16.2 on 6 df, p=0.0127 n= 170, number of events= 75 > sfit.6 Call: coxph(formula = Surv(start, stop, event) ~ age * transplant + surgery + year, data = jasa1, method = "breslow") coef exp(coef) se(coef) z p age 0.0153 1.0154 0.0175 0.87 0.383 transplant 0.0446 1.0456 0.3217 0.14 0.890 surgery -0.6211 0.5373 0.3679 -1.69 0.091 year -0.1361 0.8728 0.0709 -1.92 0.055 age:transplant 0.0270 1.0274 0.0271 1.00 0.319 Likelihood ratio test=16.1 on 5 df, p=0.00669 n= 170, number of events= 75 > > # Survival curve for an "average" subject, > # done once as overall, once via individual method > surv1 <- survfit(sfit.1, newdata=list(age=-2, surgery=0, transplant=0)) > newdata <- data.frame(start=c(0,50,100), stop=c(50,100, max(jasa1$stop)), + event=c(1,1,1), age=rep(-2,3), surgery=rep(0,3), + transplant=rep(0,3)) > surv2 <- survfit(sfit.1, newdata, individual=T) > # Have to use unclass to avoid [.survfit trying to pick curves, > # remove the final element "call" because it won't match > all.equal(unclass(surv1)[-length(surv1)], + unclass(surv2)[-length(surv2)]) [1] TRUE > > > # Survival curve for a subject of age 50, with prior surgery, tx at 6 months > # Remember that 'age' in jasa 1 was centered at 48 > data <- data.frame(start=c(0,183), stop=c(183,3*365), event=c(1,1), + age=c(2,2), surgery=c(1,1), transplant=c(0,1)) > summary(survfit(sfit.1, data, individual=T)) Call: survfit(formula = sfit.1, newdata = data, individual = T) time n.risk n.event survival std.err lower 95% CI upper 95% CI 0.5 103 1 0.994 0.00722 0.980 1.000 1.0 102 3 0.975 0.01860 0.939 1.000 2.0 99 3 0.956 0.02914 0.900 1.000 4.0 96 2 0.943 0.03605 0.875 1.000 5.0 94 2 0.930 0.04286 0.849 1.000 7.0 92 1 0.923 0.04623 0.837 1.000 8.0 91 1 0.917 0.04959 0.824 1.000 11.0 89 1 0.910 0.05294 0.812 1.000 15.0 88 3 0.890 0.06278 0.775 1.000 16.0 85 1 0.883 0.06608 0.763 1.000 17.0 84 1 0.877 0.06928 0.751 1.000 20.0 83 2 0.864 0.07538 0.728 1.000 27.0 81 1 0.857 0.07849 0.716 1.000 29.0 80 1 0.850 0.08160 0.705 1.000 31.0 78 1 0.844 0.08473 0.693 1.000 34.0 77 1 0.837 0.08786 0.681 1.000 35.0 76 1 0.830 0.09098 0.669 1.000 36.0 75 1 0.823 0.09412 0.658 1.000 38.0 74 1 0.816 0.09727 0.646 1.000 39.0 72 2 0.802 0.10349 0.623 1.000 42.0 70 1 0.795 0.10664 0.611 1.000 44.0 69 1 0.788 0.10982 0.600 1.000 49.0 68 1 0.781 0.11300 0.588 1.000 50.0 67 1 0.774 0.11614 0.577 1.000 52.0 66 1 0.767 0.11925 0.565 1.000 57.0 65 1 0.760 0.12238 0.554 1.000 60.0 64 1 0.752 0.12552 0.542 1.000 65.0 63 1 0.745 0.12866 0.531 1.000 67.0 62 2 0.730 0.13494 0.508 1.000 68.0 60 1 0.722 0.13809 0.497 1.000 71.0 59 2 0.707 0.14420 0.474 1.000 76.0 57 1 0.699 0.14729 0.463 1.000 77.0 56 1 0.691 0.15043 0.451 1.000 79.0 55 1 0.683 0.15362 0.439 1.000 80.0 54 1 0.674 0.15680 0.428 1.000 84.0 53 1 0.666 0.16005 0.416 1.000 89.0 52 1 0.657 0.16326 0.404 1.000 95.0 51 1 0.648 0.16648 0.392 1.000 99.0 50 1 0.639 0.16972 0.380 1.000 101.0 49 1 0.630 0.17293 0.368 1.000 109.0 47 1 0.621 0.17611 0.356 1.000 148.0 45 1 0.611 0.17927 0.344 1.000 152.0 44 1 0.601 0.18236 0.332 1.000 164.0 43 1 0.592 0.18551 0.320 1.000 185.0 41 1 0.583 0.12737 0.380 0.894 187.0 40 1 0.574 0.12889 0.370 0.891 206.0 39 1 0.565 0.13036 0.359 0.888 218.0 38 1 0.556 0.13180 0.349 0.885 262.0 37 1 0.546 0.13320 0.339 0.881 284.0 35 2 0.527 0.13585 0.318 0.874 307.0 33 1 0.517 0.13707 0.308 0.869 333.0 32 1 0.507 0.13823 0.297 0.865 339.0 31 1 0.497 0.13930 0.287 0.861 342.0 29 1 0.486 0.14029 0.276 0.856 583.0 21 1 0.471 0.14187 0.261 0.850 674.0 17 1 0.452 0.14361 0.243 0.843 732.0 16 1 0.433 0.14506 0.225 0.835 851.0 14 1 0.410 0.14622 0.204 0.825 979.0 11 1 0.383 0.14698 0.180 0.813 995.0 10 1 0.356 0.14735 0.158 0.801 1031.0 9 1 0.330 0.14743 0.137 0.792 > > # These should all give the same answer > # When there are offsets, the default curve is always for someone with > # the mean offset. > j.age <- jasa$age -48 > fit1 <- coxph(Surv(futime, fustat) ~ j.age, data=jasa) > fit2 <- coxph(Surv(futime, fustat) ~ j.age, jasa, init=fit1$coef, iter=0) > fit3 <- coxph(Surv(start, stop, event) ~ age, jasa1) > fit4 <- coxph(Surv(start, stop, event) ~ offset(age*fit1$coef), jasa1) > > s1 <- survfit(fit1, list(j.age=fit3$means), censor=FALSE) > s2 <- survfit(fit2, list(j.age=fit3$means), censor=FALSE) > s3 <- survfit(fit3, censor=FALSE) > s4 <- survfit(fit4, censor=FALSE) > > all.equal(s1$surv, s2$surv) [1] TRUE > all.equal(s1$surv, s3$surv) [1] TRUE > all.equal(s1$surv, s4$surv) [1] TRUE > > # Still the same answer, fit multiple strata at once > # Strata 1 has independent coefs of strata 2, so putting in > # the other data should not affect it > ll <- nrow(jasa1) > ss <- rep(0:1, c(ll,ll)) > tdata <- with(jasa1, data.frame(start=rep(start,2), stop=rep(stop,2), + event=rep(event,2), ss=ss, age=rep(age,2), + age2 = (rep(age,2))^2 * ss)) > fit <- coxph(Surv(start, stop, event) ~ age*strata(ss) + age2, tdata) > # Above replaced these 2 lines, which kill Splus5 as of 8/98 > # Something with data frames, I expect. > #fit <- coxph(Surv(rep(start,2), rep(stop,2), rep(event,2)) ~ > # rep(age,2)*strata(ss) + I(rep(age,2)^2*ss) ) > all.equal(fit$coef[1], fit3$coef) [1] TRUE > s5 <- survfit(fit, data.frame(age=fit3$means, age2=0, ss=0), censor=FALSE) > all.equal(s5$surv[1:(s5$strata[1])], s3$surv) [1] TRUE > > > > proc.time() user system elapsed 0.344 0.040 0.379 survival/tests/book6.R0000644000175100001440000000741111732700061014450 0ustar hornikuserslibrary(survival) options(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type # Tests of the weighted Cox model # This is section 1.3 of my appendix -- no yet found in any of the # printings though, it awaits the next edition # # Efron approximation # aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) testw1 <- data.frame(time= c(1,1,2,2,2,2,3,4,5), status= c(1,0,1,1,1,0,0,1,0), x= c(2,0,1,1,0,1,0,1,0), wt = c(1,2,3,4,3,2,1,2,1)) xx <- testw1$wt # Efron estimate byhand <- function(beta, newx=0) { r <- exp(beta) a <- 7*r +3; b<- 4*r+2 loglik <- 11*beta - (log(r^2 + 11*r +7) + 10*log(11*r +5)/3 + 10*log(a*2/3 +b)/3 + 10*log(a/3 +b)/3 +2*log(2*r+1)) hazard <- c(1/(r^2 + 11*r +7), 10/(3*c(11*r +5, a*2/3 +b, a/3+b)), 2/(2*r+1)) temp <- c(hazard[1], hazard[1]+hazard[2] + hazard[3]*2/3 + hazard[4]/3, cumsum(hazard)[4:5]) risk <- c(r^2, 1,r,r,1,r,1,r,1) expected <- risk* temp[c(1,1,2,2,2,3,3,4,4)] # The matrix of weights, one row per obs, one col per death # deaths at 1,2,2,2, and 4 riskmat <- matrix(c(1,1,1,1,1,1,1,1,1, 0,0,1,1,1,1,1,1,1, 0,0,2/3,2/3,2/3,1,1,1,1, 0,0,1/3,1/3,1/3,1,1,1,1, 0,0,0,0,0,0,0,1,1), ncol=5) wtmat <- diag(c(r^2, 2, 3*r, 4*r, 3, 2*r, 1, 2*r, 1)) %*% riskmat x <- c(2,0,1,1,0,1,0,1,0) xbar <- colSums(x*wtmat)/ colSums(wtmat) imat <- (4*r^2 + 11*r)*hazard[1] - xbar[1]^2 + 10* mean(xbar[2:4] - xbar[2:4]^2) + 2*(xbar[5] - xbar[5]^2) status <- c(1,0,1,1,1,0,0,1,0) wt <- c(1,2,3,4,3,2,1,2,1) # Table of sums for score resids hazmat <- riskmat %*% diag(c(1,10/3,10/3, 10/3,2)/colSums(wtmat)) dM <- -risk*hazmat #Expected part dM[1,1] <- dM[1,1] +1 # deaths at time 1 for (i in 2:4) dM[3:5, i] <- dM[3:5,i] + 1/3 dM[8,5] <- dM[8,5] +1 mart <- rowSums(dM) resid <-dM * outer(x, xbar ,'-') # Increments to the variance of the hazard var.g <- cumsum(hazard^2* c(1,3/10, 3/10, 3/10, 1/2)) var.d <- cumsum((xbar-newx)*hazard) sxbar <- c(xbar[1], mean(xbar[2:4]), xbar[5]) #xbar for Schoen list(loglik=loglik, imat=imat, hazard=hazard, xbar=xbar, mart=status-expected, expected=expected, score=rowSums(resid), schoen=c(2,1,1,0,1) - sxbar[c(1,2,2,2,3)], varhaz=((var.g + var.d^2/imat)* exp(2*beta*newx))[c(1,4,5)]) } # Verify temp <- byhand(0,0) aeq(temp$xbar, c(13/19, 11/16, 26/38, 19/28, 2/3)) aeq(temp$hazard, c(1/19, 5/24, 5/19, 5/14, 2/3)) fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt, iter=0) fit <- coxph(Surv(time, status) ~x, testw1, weights=wt) truth0 <- byhand(0,pi) aeq(fit0$loglik[1], truth0$loglik) aeq(1/truth0$imat, fit0$var) aeq(truth0$mart, fit0$resid) aeq(truth0$scho, resid(fit0, 'schoen')) aeq(truth0$score, resid(fit0, 'score')) sfit <- survfit(fit0, list(x=pi), censor=FALSE) aeq(sfit$std.err^2, truth0$var) aeq(-log(sfit$surv), cumsum(truth0$hazard)[c(1,4,5)]) truth <- byhand(fit$coef, .3) aeq(truth$loglik, fit$loglik[2]) aeq(1/truth$imat, fit$var) aeq(truth$mart, fit$resid) aeq(truth$scho, resid(fit, 'schoen')) aeq(truth$score, resid(fit, 'score')) sfit <- survfit(fit, list(x=.3), censor=FALSE) aeq(sfit$std.err^2, truth$var) aeq(-log(sfit$surv), (cumsum(truth$hazard)* exp(fit$coef*.3))[c(1,4,5)]) fit0 summary(fit) resid(fit0, type='score') resid(fit0, type='scho') resid(fit, type='score') resid(fit, type='scho') rr1 <- resid(fit, type='mart') rr2 <- resid(fit, type='mart', weighted=T) aeq(rr2/rr1, testw1$wt) rr1 <- resid(fit, type='score') rr2 <- resid(fit, type='score', weighted=T) aeq(rr2/rr1, testw1$wt) survival/tests/finegray.R0000644000175100001440000001637213055115147015247 0ustar hornikuserslibrary(survival) # Test data set 1 for Fine-Gray regression fdata <- data.frame(time =c(1,2,3,4,4,4,5,5,6,8,8, 9,10,12), status=factor(c(1,2,0,1,0,0,2,1,0,0,2, 0,1 ,0), 0:2, c("cen", "type1", "type2")), x =c(5,4,3,1,2,1,1,2,2,4,6,1,2, 0), id = 1:14) test1 <- finegray(Surv(time, status) ~., fdata, count="fgcount") test2 <- finegray(Surv(time, status) ~x, fdata, etype="type2") # When creating the censoring time distribution remember that # censors happen after deaths, so the distribution does not drop until # time 3+, 4+, 6+, 8+ and 9+ csurv <- list(time=c(0, 3, 4, 6, 8, 9), p = cumprod(c(1, 11/12, 8/10, 5/6, 3/4, 2/3))) # # For estimation of event type 1, the first subject of event type # 2 will have weights of curve$p over (0,3], (3,4], (4,6], (6,8], (8,9] # and (9,12]. All that really matters is the weight at times 1, 4, 5, # and 10, however, which are the points at which events of type 1 happen # # The next subject of event type 2 occurs at time 5, and will have a # weight of (9,12] /(4,5] = (5*4*2)/(7*5*3) = 8/21 at time 10. The last # censor at time 6 has a weight of 2/3 at time 10. all.equal(test1$id, c(1, 2,2,2,2, 3:6, 7, 7, 8:11, 11, 12:14)) twt <- c(1, csurv$p[c(1,2,3,6)], 1,1,1, 1, 1, 5/12, 1,1,1, 1, 1/2, 1,1,1) all.equal(test1$fgwt, twt) #extra obs will end at times found in csurv$time, or max(time)=12 all.equal(test1$fgstop[test1$fgcount>0], c(4,6,12, 12,12)) # # Verify the data reproduces a multi-state curve # censoring times may be different in the two setups so only # compare at the event times sfit <- survfit(Surv(time, status) ~1, fdata) sfit1<- survfit(Surv(fgstart, fgstop, fgstatus) ~1, test1, weight=fgwt) i1 <- sfit$n.event[,1] > 0 i2 <- sfit1$n.event > 0 all.equal(sfit$pstate[i1, 1], 1- sfit1$surv[i2]) sfit2 <- survfit(Surv(fgstart, fgstop, fgstatus) ~1, test2, weight=fgwt) i1 <- sfit$n.event[,2] > 0 i2 <- sfit2$n.event > 0 all.equal(sfit$pstate[i1, 2], 1- sfit2$surv[i2]) # Test strata. Make a single data set that has fdata for the first 19 # rows, then fdata with outcomes switched for the second 19. It should # reprise test1 and test2 in a single call. fdata2 <- rbind(fdata, fdata) fdata2$group <- rep(1:2, each=nrow(fdata)) temp <- c(1,3,2)[as.numeric(fdata$status)] fdata2$status[fdata2$group==2] <- factor(temp, 1:3, levels(fdata$status)) test3 <- finegray(Surv(time, status) ~ .+ strata(group), fdata2) vtemp <- c("fgstart", "fgstop", "fgstatus", "fgwt") all.equal(test3[1:19, vtemp], test1[,vtemp]) all.equal(test3[20:38, vtemp], test2[,vtemp], check.attributes=FALSE) # # Test data set 2: use the larger MGUS data set # Time is in months which leads to lots of ties etime <- with(mgus2, ifelse(pstat==0, futime, ptime)) event <- with(mgus2, ifelse(pstat==0, 2*death, 1)) e2 <- factor(event, 0:2, c('censor', 'pcm', 'death')) edata <- finegray(Surv(etime, e2) ~ sex + id, mgus2, etype="pcm") # Build G(t) = the KM of the censoring distribution # An event at time x is not "at risk" for censoring at time x (Geskus 2011) tt <- sort(unique(etime)) # all the times ntime <- length(tt) nrisk <- nevent <- double(ntime) for (i in 1:ntime) { nrisk[i] <- sum((etime > tt[i] & event >0) | (etime >= tt[i] & event==0)) nevent[i] <- sum(etime == tt[i] & event==0) } G <- cumprod(1- nevent/nrisk) # The weight is defined as w(t)= G(t-)/G(s-) where s is the event time # for a subject who experiences an endpoint other then the one of interest type2 <- event[edata$id]==2 # the rows to be expanded # These rows are copied over as is: endpoint 1 and censors all(edata$fgstop[!type2] == etime[edata$id[!type2]]) all(edata$fgstart[!type2] ==0) all(edata$fgwt[!type2] ==1) tdata <- edata[type2,] #expanded rows first <- match(tdata$id, tdata$id) #points to the first row for each subject Gwt <- c(1, G)[match(tdata$fgstop, tt)] # G(t-) all.equal(tdata$fgwt, Gwt/Gwt[first]) # Test data 3, left truncation. # Ties are assumed to be ordered as event, censor, entry # H(t) = truncation distribution, and is calculated on a reverse time scale # Since there is only one row per subject every obs is a "start" event. # Per equation 5 and 6 of Geskus both G and H are right continuous functions # (the value at t- epsilon is different than the value at t). fdata <- data.frame(time1 = c(0,0,0,3,2,0,0,1,0,7,5, 0, 0, 0), time2 = c(1,2,3,4,4,4,5,5,6,8,8, 9,10,12), status= c(1,2,0,1,0,0,2,1,0,0,2, 0, 1 ,0), x = c(5,4,3,1,2,1,1,2,2,4,6, 1, 2, 0), id = 1:14) tt <- sort(unique(c(fdata$time1, fdata$time2))) ntime <- length(tt) Grisk <- Gevent <- double(ntime) Hrisk <- Hevent <- double(ntime) for (i in 1:ntime) { Grisk[i] <- with(fdata, sum((time2 > tt[i] & status >0 & time1 < tt[i]) | (time2 >= tt[i] & status ==0 & time1 < tt[i]))) Gevent[i]<- with(fdata, sum(time2 == tt[i] & status==0)) Hrisk[i] <- with(fdata, sum(time2 > tt[i] & time1 <= tt[i])) Hevent[i]<- with(fdata, sum(time1 == tt[i])) } G <- cumprod(1- Gevent/pmax(1,Grisk)) G2 <- survfit(Surv(time1, time2 - .1*(status !=0), status==0) ~1, fdata) all.equal(G2$surv[G2$n.event>0], G[Gevent>0]) H <- double(ntime) # The loop below uses the definition of equation 6 in Geskus for (i in 1:ntime) H[i] <- prod((1- Hevent/pmax(1, Hrisk))[-(i:1)]) H2 <- rev(cumprod(rev(1 - Hevent/pmax(1, Hrisk)))) #alternate form H3 <- survfit(Surv(-time2, -time1, rep(1,14)) ~1, fdata) # alternate 3 all.equal(tt, -rev(H3$time)) # c(0,H) = H(t-), H2 = H(t-) already due to the time reversal all.equal(c(0, H), c(H2, 1)) all.equal(H2, rev(H3$surv)) fg <- finegray(Surv(time1, time2, factor(status, 0:2)) ~ x, id=id, fdata) stat2 <- !is.na(match(fg$id, fdata$id[fdata$status==2])) #expanded ids all(fg$fgwt[!stat2] ==1) #ordinary rows are left alone all(fg$fgstart[!stat2] == fdata$time1[fdata$status !=2]) all(fg$fgstop[!stat2] == fdata$time2[fdata$status !=2]) tdata <- fg[stat2,] index <- match(tdata$id, tdata$id) # points to the first row for each Gwt <- c(1, G)[match(tdata$fgstop, tt)] # G(t-) Hwt <- c(0, H)[match(tdata$fgstop, tt)] # H(t-) all.equal(tdata$fgwt, Gwt*Hwt/(Gwt*Hwt)[index]) # # Test data 4: mgus2 data on age scale # The answer is incorrect due to roundoff, but consistent # start <- mgus2$age # age in years end <- start + etime/12 #etime in months tt <- sort(unique(c(start, end))) # all the times ntime <- length(tt) Grisk <- Gevent <- double(ntime) Hrisk <- Hevent <- double(ntime) for (i in 1:ntime) { Grisk[i] <- sum(((end > tt[i] & event >0) | (end >= tt[i] & event==0)) & (tt[i] > start)) Gevent[i] <- sum(end == tt[i] & event==0) Hrisk[i] <- sum(start <= tt[i] & end > tt[i]) Hevent[i] <- sum(start == tt[i]) } G <- cumprod(1 - Gevent/pmax(1, Grisk)) # pmax to avoid 0/0 H <- rev(cumprod(rev(1-Hevent/pmax(1,Hrisk)))) H <- c(H[-1], 1) #make it right continuous wdata <- finegray(Surv(start, end, e2) ~ ., id=id, mgus2, timefix=FALSE) type2 <- event[wdata$id]==2 # the rows to be expanded tdata <- wdata[type2,] first <- match(tdata$id, tdata$id) Gwt <- c(1, G)[match(tdata$fgstop, tt)] # G(t-) Hwt <- c(0, H)[match(tdata$fgstop, tt)] # H(t-) all.equal(tdata$fgwt, (Gwt/Gwt[first]) * (Hwt / Hwt[first])) survival/tests/data.motor0000644000175100001440000000067011732700061015300 0ustar hornikusers150 8064 0 150 8064 0 150 8064 0 150 8064 0 150 8064 0 150 8064 0 150 8064 0 150 8064 0 150 8064 0 150 8064 0 170 1764 1 170 2772 1 170 3444 1 170 3542 1 170 3780 1 170 4860 1 170 5196 1 170 5448 0 170 5448 0 170 5448 0 190 408 1 190 408 1 190 1344 1 190 1344 1 190 1440 1 190 1680 0 190 1680 0 190 1680 0 190 1680 0 190 1680 0 220 408 1 220 408 1 220 504 1 220 504 1 220 504 1 220 528 0 220 528 0 220 528 0 220 528 0 220 528 0 survival/tests/fr_resid.R0000644000175100001440000000603612466153737015250 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # The residual methods treat a sparse frailty as a fixed offset with # no variance # aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) kfit1 <- coxph(Surv(time, status) ~ age + sex + frailty(id, dist='gauss'), kidney) tempf <- predict(kfit1, type='terms')[,3] temp <- kfit1$frail[match(kidney$id, sort(unique(kidney$id)))] #all.equal(unclass(tempf), unclass(temp)) all.equal(as.vector(tempf), as.vector(temp)) # Now fit a model with explicit offset kfitx <- coxph(Surv(time, status) ~ age + sex + offset(tempf),kidney, eps=1e-7) # These are not always precisely the same, due to different iteration paths aeq(kfitx$coef, kfit1$coef) # This will make them identical kfitx <- coxph(Surv(time, status) ~ age + sex + offset(temp),kidney, iter=0, init=kfit1$coef) aeq(resid(kfit1), resid(kfitx)) aeq(resid(kfit1, type='score'), resid(kfitx, type='score')) aeq(resid(kfit1, type='schoe'), resid(kfitx, type='schoe')) # These are not the same, due to a different variance matrix # The frailty model's variance is about 2x the naive "assume an offset" var # Expect a value of about 0.5 aeq(resid(kfit1, type='dfbeta'), resid(kfitx, type='dfbeta')) # Force equality zed <- kfitx zed$var <- kfit1$var aeq(resid(kfit1, type='dfbeta'), resid(zed, type='dfbeta')) # The score residuals are equal, however. temp1 <- resid(kfit1, type='score') temp2 <- resid(kfitx, type='score') aeq(temp1, temp2) # # Now for some tests of predicted values # aeq(predict(kfit1, type='expected'), predict(kfitx, type='expected')) aeq(predict(kfit1, type='lp'), predict(kfitx, type='lp')) temp1 <- predict(kfit1, type='terms', se.fit=T) temp2 <- predict(kfitx, type='terms', se.fit=T) aeq(temp1$fit[,1:2], temp2$fit) # the next is not equal, all.equal returns a character string in that case is.character(aeq(temp1$se.fit[,1:2], temp2$se.fit)) mean(temp1$se.fit[,1:2]/ temp2$se.fit) aeq(as.vector(temp1$se.fit[,3])^2, as.vector(kfit1$fvar[match(kidney$id, sort(unique(kidney$id)))])) print(temp1) kfit1 kfitx rm(temp1, temp2, kfitx, zed, tempf) # # The special case of a single sparse frailty # kfit1 <- coxph(Surv(time, status) ~ frailty(id, dist='gauss'), kidney) tempf <- predict(kfit1, type='terms') temp <- kfit1$frail[match(kidney$id, sort(unique(kidney$id)))] all.equal(as.vector(tempf), as.vector(temp)) # Now fit a model with explicit offset kfitx <- coxph(Surv(time, status) ~ offset(tempf),kidney, eps=1e-7) aeq(resid(kfit1), resid(kfitx)) aeq(resid(kfit1, type='deviance'), resid(kfitx, type='deviance')) # # Some tests of predicted values # aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) aeq(predict(kfit1, type='expected'), predict(kfitx, type='expected')) aeq(predict(kfit1, type='lp'), predict(kfitx, type='lp')) temp1 <- predict(kfit1, type='terms', se.fit=T) aeq(temp1$fit, kfitx$linear) aeq(temp1$se.fit^2, kfit1$fvar[match(kidney$id, sort(unique(kidney$id)))]) temp1 kfit1 survival/tests/mstate.Rout.save0000644000175100001440000002345013004232520016405 0ustar hornikusers R version 3.2.3 (2015-12-10) -- "Wooden Christmas-Tree" Copyright (C) 2015 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. 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Type 'q()' to quit R. > # > # A tiny multi-state example > # > library(survival) > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > mtest <- data.frame(id= c(1, 1, 1, 2, 3, 4, 4, 4, 5, 5), + t1= c(0, 4, 9, 0, 2, 0, 2, 8, 1, 3), + t2= c(4, 9, 10, 5, 9, 2, 8, 9, 3, 11), + st= c(1, 2, 1, 2, 3, 1, 3, 0, 2, 0)) > > mtest$state <- factor(mtest$st, 0:3, c("censor", "a", "b", "c")) > mtest <- mtest[c(1,3,2,4,5,7,6,10, 9, 8),] #not in time order > > mfit <- survfit(Surv(t1, t2, state) ~ 1, mtest, id=id) > > # True results > # > #time state probabilities > # entry a b c entry a b c > # > #0 124 1 0 0 0 > #1+ 1245 > #2+ 1235 4 3/4 1/4 0 0 4 -> a, add 3 > #3+ 123 4 5 9/16 1/4 3/16 0 5 -> b > #4+ 23 14 5 6/16 7/16 3/16 0 1 -> a > #5+ 3 14 5 3/16 7/16 6/16 0 2 -> b, exits > #8+ 3 1 5 4 3/16 7/32 6/16 7/32 4 -> c > #9+ 15 0 0 19/32 13/32 1->b, 3->c & exit > # 10+ 1 5 19/64 19/64 13/32 1->a > > # In mfit, the "entry" state is last in the matrices > all.equal(mfit$n.risk, matrix(c(0,1,1,2,2,1,0,0, + 0,0,1,1,1,1,2,1, + 0,0,0,0,0,1,0,0, + 4,4,3,2,1,1,0,0), ncol=4)) [1] TRUE > all.equal(mfit$pstate, matrix(c(8, 8, 14, 14, 7, 0, 9.5, 9.5, + 0, 6, 6, 12, 12,19,9.5, 9.5, + 0, 0, 0, 0, 7, 13, 13, 13, + 24, 18, 12, 6, 6, 0, 0, 0)/32, ncol=4)) [1] TRUE > all.equal(mfit$n.event, matrix(c(1,0,1,0,0,0,1,0, + 0,1,0,1,0,1,0,0, + 0,0,0,0,1,1,0,0, + 0,0,0,0,0,0,0,0), ncol=4)) [1] TRUE > all.equal(mfit$time, c(2, 3, 4, 5, 8, 9, 10, 11)) [1] TRUE > > > # Somewhat more complex. > # Scramble the input data > # Not everyone starts at the same time or in the same state > # Two "istates" that vary, only the first should be noticed. > # Case weights > # > tdata <- data.frame(id= c(1, 1, 1, 2, 3, 4, 4, 4, 5, 5), + t1= c(0, 4, 9, 1, 2, 0, 2, 8, 1, 3), + t2= c(4, 9, 10, 5, 9, 2, 8, 9, 3, 11), + st= c(1, 2, 1, 2, 3, 1, 3, 0, 3, 0), + i0= c(4, 4, 4, 1, 4, 4, 4, 1, 2, 2)) > > tdata$st <- factor(tdata$st, c(0:4), + labels=c("censor", "1", "2", "3", "entry")) > > tfun <- function(wt, data=tdata) { + reorder <- c(10, 9, 1, 2, 5, 4, 3, 7, 8, 6) + new <- data[reorder,] + new$wt <- rep(wt,length=10)[reorder] + new + } > > # These weight vectors are in the order of tdata > # w[9] is the weight for subject 5 at time 1.5, for instance > p0 <- function(w) c(w[4], w[9], 0, w[1]+ w[6])/ (w[1]+ w[4] + w[6] + w[9]) > > # aj2 = Aalen-Johansen H matrix at time 2, etc. > aj2 <- function(w) { + rbind(c(1, 0, 0, 0), # state a (1) stays put + c(0, 1, 0, 0), + c(0, 0, 1, 0), + c(w[6], 0, 0, w[1])/(w[1] + w[6])) #subject 4 moves to 'a' + } > aj3 <- function(w) rbind(c(1, 0, 0, 0), + c(0, 0, 1, 0), # 5 moves from b to c + c(0, 0, 1, 0), + c(0, 0, 0, 1)) > aj4 <- function(w) rbind(c(1, 0, 0, 0), + c(0, 1, 0, 0), + c(0, 0, 1, 0), + c(w[1], 0, 0, w[5])/(w[1] + w[5])) #1 moves from 4 to a > aj5 <- function(w) rbind(c(w[2]+w[7], w[4], 0, 0)/(w[2]+ w[4] + w[7]), #2 to b + c(0, 1, 0, 0), + c(0, 0, 1, 0), + c(0, 0, 0, 1)) > aj8 <- function(w) rbind(c(w[2], 0, w[7], 0)/(w[2]+ w[7]), # 4 to c + c(0, 1, 0, 0), + c(0, 0, 1, 0), + c(0, 0, 0, 1)) > aj9 <- function(w) rbind(c(0, 1, 0, 0), # 1 to b + c(0, 1, 0, 0), + c(0, 0, 1, 0), + c(0, 0, 1 ,0)) # 3 to c > aj10 <- function(w)rbind(c(1, 0, 0, 0), + c(1, 0, 0, 0), #1 back to a + c(0, 0, 1, 0), + c(0, 0, 0, 1)) > > #time state > # a b c entry > # > #1 2 5 14 initial distribution > #2 24 5 1 4 -> a, add 3 > #3 24 5 13 5 from b to c > #4 124 5 3 1 -> a > #5 14 5 3 2 -> b, exits > #8 1 45 3 4 -> c > #9 1 45 1->b, 3->c & exit > #10 1 45 1->a > > # P is a product of matrices > dopstate <- function(w) { + p1 <- p0(w) + p2 <- p1 %*% aj2(w) + p3 <- p2 %*% aj3(w) + p4 <- p3 %*% aj4(w) + p5 <- p4 %*% aj5(w) + p8 <- p5 %*% aj8(w) + p9 <- p8 %*% aj9(w) + p10<- p9 %*% aj10(w) + rbind(p2, p3, p4, p5, p8, p9, p10, p10) + } > > # Check the pstate estimate > w1 <- rep(1, 10) > mtest2 <- tfun(w1) > mfit2 <- survfit(Surv(t1, t2, st) ~ 1, tdata, id=id, istate=i0) # ordered > aeq(mfit2$pstate, dopstate(w1)) [1] TRUE > aeq(mfit2$p0, p0(w1)) [1] TRUE > > mfit2b <- survfit(Surv(t1, t2, st) ~ 1, mtest2, id=id, istate=i0)#scrambled > aeq(mfit2b$pstate, dopstate(w1)) [1] TRUE > aeq(mfit2b$p0, p0(w1)) [1] TRUE > > mfit2b$call <- mfit2$call <- NULL > all.equal(mfit2b, mfit2) [1] TRUE > > # Now the harder one, where subjects change weights > mtest3 <- tfun(1:10) > mfit3 <- survfit(Surv(t1, t2, st) ~ 1, mtest3, id=id, istate=i0, + weights=wt, influence=TRUE) > aeq(mfit3$p0, p0(1:10)) [1] TRUE > aeq(mfit3$pstate, dopstate(1:10)) [1] TRUE > > > # The derivative of a matrix product AB is (dA)B + A(dB) where dA is the > # elementwise derivative of A and etc for B. > # dp0 creates the derivatives of p0 with respect to each subject, a 5 by 4 > # matrix > dp0 <- function(w) { + p <- p0(w) + w0 <- w[c(1,4,6,9)] # the 4 obs at the start, subjects 1, 2, 4, 5 + rbind(c(0, 0, 0, 1) - p, # subject 1 affects p[4] + c(1, 0, 0, 0) - p, # subject 2 affects p0[1] + 0, # subject 3 affects none + c(0, 0, 0, 1) - p, # subject 4 affect p[4] + c(0, 1, 0, 0) - p) / sum(w0) + } > > > dp2 <- function(w) { + h2 <- aj2(w) # H matrix at time 2 + part1 <- dp0(w) %*% h2 + + # 1 and 4 in state 4, obs 1 and 6, 4 moves to a + mult <- p0(w)[4]/(w[1] + w[6]) #p(t-) / weights in state + part2 <- rbind((c(0,0,0,1)- h2[4,]) * mult, + 0, + 0, + (c(1,0,0,0) - h2[4,]) * mult, + 0) + part1 + part2 + } > > dp3 <- function(w) { + dp2(w) %*% aj3(w) + } > > dp4 <- function(w) { + h4 <- aj4(w) # H matrix at time 4 + part1 <- dp3(w) %*% h4 + + # subjects 1 and 3 in state 4, obs 1 and 5, 1 moves to a + mult <- dopstate(w)[2,4]/ (w[1] + w[5]) # p_4(time 4-0) / wt + part2 <- rbind((c(1,0,0,0)- h4[4,]) * mult, + 0, + (c(0,0,0,1)- h4[4,]) * mult, + 0, + 0) + part1 + part2 + } > dp5 <- function(w) { + h5 <- aj5(w) # H matrix at time 5 + part1 <- dp4(w) %*% h5 + + # subjects 124 in state 1, obs 2,4,7, 2 goes to 2 + mult <- dopstate(w)[3,1]/ (denom <- w[2] + w[4] + w[7]) + part2 <- rbind((c(1,0,0,0)- h5[1,]) * mult, + (c(0,1,0,0)- h5[1,]) * mult, + 0, + (c(1,0,0,0)- h5[1,]) * mult, + 0) + part1 + part2 + } > dp8 <- function(w) { + h8 <- aj8(w) # H matrix at time 8 + part1 <- dp5(w) %*% h8 + + # subjects 14 in state 1, obs 2 &7, 4 goes to c + mult <- dopstate(w)[4, 1]/ (w[2] + w[7]) + part2 <- rbind((c(1,0,0,0)- h8[1,]) * mult, + 0, + 0, + (c(0,0,1,0)- h8[1,]) * mult, + 0) + part1 + part2 + } > dp9 <- function(w) dp8(w) %*% aj9(w) > dp10<- function(w) dp9(w) %*% aj10(w) > > w1 <- 1:10 > aeq(mfit3$influence[,1,], dp0(w1)) [1] TRUE > aeq(mfit3$influence[,2,], dp2(w1)) [1] TRUE > aeq(mfit3$influence[,3,], dp3(w1)) [1] TRUE > aeq(mfit3$influence[,4,], dp4(w1)) [1] TRUE > aeq(mfit3$influence[,5,], dp5(w1)) [1] TRUE > aeq(mfit3$influence[,6,], dp8(w1)) [1] TRUE > aeq(mfit3$influence[,7,], dp9(w1)) [1] TRUE > aeq(mfit3$influence[,8,], dp10(w1)) [1] TRUE > aeq(mfit3$influence[,9,], dp10(w1)) # no changes at time 11 [1] TRUE > > aeq(mfit3$cumhaz[,,1], aj2(w1)- diag(4)) [1] TRUE > aeq(mfit3$cumhaz[,,2] - mfit3$cumhaz[,,1], aj3(w1)- diag(4)) [1] TRUE > aeq(mfit3$cumhaz[,,3] - mfit3$cumhaz[,,2], aj4(w1)- diag(4)) [1] TRUE > aeq(mfit3$cumhaz[,,4] - mfit3$cumhaz[,,3], aj5(w1)- diag(4)) [1] TRUE > aeq(mfit3$cumhaz[,,5] - mfit3$cumhaz[,,4], aj8(w1)- diag(4)) [1] TRUE > aeq(mfit3$cumhaz[,,6] - mfit3$cumhaz[,,5], aj9(w1)- diag(4)) [1] TRUE > > proc.time() user system elapsed 1.269 0.067 1.343 survival/tests/testci.R0000644000175100001440000001072613003736104014726 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) aeq <- function(x,y,...) all.equal(as.vector(x), as.vector(y),...) # # Test out the survfit.ci function, which does competing risk # estimates # # First trivial test tdata <- data.frame(time=c(1,2,2,3,3,3,5,6), status = c(0,1,0,1,0,1,0,1), event = c(1,1,2,2,1,2,3,2), grp = c(1,2,1,2,1,2,1,2)) fit <- survfit(Surv(time, status*event, type='mstate') ~1, tdata) byhand <- function() { #everyone starts in state 0 p1 <- c(1,0,0) p2 <- c(6/7, 1/7, 0) # 0-1 transition at time 2 u2 <- matrix(rep(c(1/49, -1/49, 0), each=8), ncol=3) #leverage matrix at time 2 u2[1,] <- 0 #subject 1 is not present u2[2,1:2] <- u2[2, 1:2] + c(-1/7, 1/7) p3 <- c((6/7)*(3/5), 1/7, 12/35) # 0-2 transition at time 3, 5 at risk h3 <- matrix(c(3/5, 0, 2/5, 0,1,0, 0,1,0), byrow=T, ncol=3) #hazard mat u3 <- u2 %*% h3 u3[4:8,1] <- u3[4:8,1] + p2[1]*2/25 u3[4:8,3] <- u3[4:8,3] -p2[1]*2/25 u3[4,] <- u3[4,] + c(-p2[1]/5, 0, p2[1]/5) u3[6,] <- u3[4,] p6 <- c(0, 1/7, 6/7) # 0-2 at time 6, 1 at risk h6 <- matrix(c(-1,0,1,0,1,0,0,1,0), byrow=T, ncol=3) u6 <- cbind(0, u3[,2], -u3[,2]) V <- rbind(0, colSums(u2^2), colSums(u3^2), colSums(u3^2), colSums(u6^2)) list(P=rbind(p1, p2, p3, p3, p6), u2=u2, u3=u3, u6=u6, V=V) } bfit <- byhand() aeq(fit$pstate, bfit$P[,c(2,3,1)]) aeq(fit$n.risk[,3], c(8,7,5,2,1)) aeq(fit$n.event[,1:2], c(0,1,0,0,0, 0,0 ,2,0,1)) aeq(fit$std^2, bfit$V[,c(2,3,1)]) # Times purposely has values that are before the start, exact, intermediate # and after the end of the observed times sfit <- summary(fit, times=c(0, 1, 3.5, 6, 7), extend=TRUE) aeq(sfit$pstate, rbind(c(0,0,1), bfit$P[c(1,3,5,5), c(2,3,1)])) aeq(sfit$n.risk[,3], c(8,8, 2, 1, 0)) aeq(sfit$n.event, matrix(c(0,0,1,0,0, 0,0,2,1,0, 0,0,0,0,0), ncol=3)) # # For this we need the competing risks MGUS data set, first # event # tdata <- mgus1[mgus1$enum==1,] # Ensure the old-style call using "etype" works (backwards compatability) fit1 <- survfit(Surv(stop, status) ~ 1, etype=event, tdata) fit1b <-survfit(Surv(stop, event) ~1, tdata) indx <- match("call", names(fit1)) all.equal(unclass(fit1)[-indx], unclass(fit1b)[-indx]) # Now get the overall survival, and the hazard for progression fit2 <- survfit(Surv(stop, status) ~1, tdata) #overall to "first bad thing" fit3 <- survfit(Surv(stop, status*(event=='pcm')) ~1, tdata, type='fleming') fit4 <- survfit(Surv(stop, status*(event=='death')) ~1, tdata, type='fleming') aeq(fit1$n.risk[,3], fit2$n.risk) aeq(rowSums(fit1$n.event), fit2$n.event) # Classic CI formula # integral [hazard(t) S(t-0) dt], where S= "survival to first event" haz1 <- diff(c(0, -log(fit3$surv))) #Aalen hazard estimate for progression haz2 <- diff(c(0, -log(fit4$surv))) #Aalen estimate for death tsurv <- c(1, fit2$surv[-length(fit2$surv)]) #lagged survival ci1 <- cumsum(haz1 *tsurv) ci2 <- cumsum(haz2 *tsurv) aeq(cbind(ci1, ci2), fit1$pstate[,1:2]) # # Now, make sure that it works for subgroups # fit1 <- survfit(Surv(stop, event) ~ sex, tdata) fit2 <- survfit(Surv(stop, event) ~ 1, tdata, subset=(sex=='female')) fit3 <- survfit(Surv(stop, event) ~ 1, tdata, subset=(sex=='male')) aeq(fit2$pstate, fit1$pstate[1:fit1$strata[1],]) aeq(fit2$std, fit1$std[1:fit1$strata[1],]) aeq(fit3$pstate, fit1$pstate[-(1:fit1$strata[1]),]) # A second test of cumulative incidence # compare results to Bob Gray's functions # The file gray1 is the result of # library(cmprsk) # tstat <- ifelse(tdata$status==0, 0, 1+ (tdata$event=='death')) # gray1 <- cuminc(tdata$stop, tstat) load("gray1.rda") fit2 <- survfit(Surv(stop, event) ~ 1, tdata) if (FALSE) { # lines of the two graphs should overlay plot(gray1[[1]]$time, gray1[[1]]$est, type='l', ylim=range(c(gray1[[1]]$est, gray1[[2]]$est)), xlab="Time") lines(gray1[[2]]$time, gray1[[2]]$est, lty=2) matlines(fit2$time, fit2$pstate, col=2, lty=1:2, type='s') } # To formally match these is a bit of a nuisance. # The cuminc function returns a full step function, and survfit only # the bottoms of the steps. temp1 <- tapply(gray1[[1]]$est, gray1[[1]]$time, max)[-1] #toss time 0 indx1 <- match(names(temp1), fit2$time) aeq(temp1, fit2$pstate[indx1,1]) survival/tests/coxsurv.Rout.save0000644000175100001440000000604013054045730016627 0ustar hornikusers R version 3.3.2 (2016-10-31) -- "Sincere Pumpkin Patch" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: x86_64-apple-darwin13.4.0 (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # Test out subscripting in the case of a coxph survival curve > # > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > fit <- coxph(Surv(time, status) ~ age + sex + meal.cal + strata(ph.ecog), + data=cancer) > surv1 <- survfit(fit) > temp <- surv1[2:3] > > which <- cumsum(surv1$strata) > zed <- (which[1]+1):(which[3]) > aeq(surv1$surv[zed], temp$surv) [1] TRUE > aeq(surv1$time[zed], temp$time) [1] TRUE > > # This call should not create a model frame in the code -- so same > # answer but a different path through the underlying code > fit <- coxph(Surv(time, status) ~ age + sex + meal.cal + strata(ph.ecog), + x=T, data=cancer) > surv2 <- survfit(fit) > all.equal(surv1, surv2) [1] TRUE > > # > # Now a result with a matrix of survival curves > # > dummy <- data.frame(age=c(30,40,60), sex=c(1,2,2), meal.cal=c(500, 1000, 1500)) > surv2 <- survfit(fit, newdata=dummy) > > zed <- 1:which[1] > aeq(surv2$surv[zed,1], surv2[1,1]$surv) [1] TRUE > aeq(surv2$surv[zed,2], surv2[1,2]$surv) [1] TRUE > aeq(surv2$surv[zed,3], surv2[1,3]$surv) [1] TRUE > aeq(surv2$surv[zed, ], surv2[1,1:3]$surv) [1] TRUE > aeq(surv2$surv[zed], (surv2[1]$surv)[,1]) [1] TRUE > aeq(surv2$surv[zed, ], surv2[1, ]$surv) [1] TRUE > > # And the depreciated form - call with a named vector as 'newdata' > # the resulting $call component won't match so delete it before comparing > surv3 <- survfit(fit, c(age=40, sex=2, meal.cal=1000)) > all.equal(unclass(surv2[,2])[-length(surv3)], unclass(surv3)[-length(surv3)]) [1] TRUE > > > > # Test out offsets, which have recently become popular due to a Langholz paper > fit1 <- coxph(Surv(time, status) ~ age + ph.ecog, lung) > fit2 <- coxph(Surv(time, status) ~ age + offset(ph.ecog * fit1$coef[2]), lung) > > surv1 <- survfit(fit1, newdata=data.frame(age=50, ph.ecog=1)) > surv2 <- survfit(fit2, newdata=data.frame(age=50, ph.ecog=1)) > all.equal(surv1$surv, surv2$surv) [1] TRUE > > # > # Check out the start.time option > # > surv3 <- survfit(fit1, newdata=data.frame(age=50, ph.ecog=1), + start.time=100) > index <- match(surv3$time, surv1$time) > rescale <- summary(surv1, time=100)$surv > all.equal(surv3$surv, surv1$surv[index]/rescale) [1] TRUE > > > proc.time() user system elapsed 0.769 0.054 0.843 survival/tests/r_user.Rout.save0000644000175100001440000000305611732700061016415 0ustar hornikusers R version 2.9.0 (2009-04-17) Copyright (C) 2009 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) #preserve length of missings > library(survival) Loading required package: splines > > # > # Check out using a "user specified" distribution > # > mydist <- c(survreg.distributions$extreme, survreg.distributions$weibull[-1]) > mydist$name <- "Weibull2" > mydist$dist <- NULL > > fit1 <- survreg(Surv(time, status) ~ age + ph.ecog, lung) > fit2 <- survreg(Surv(time, status) ~ age + ph.ecog, lung, dist=mydist) > > all.equal(fit1$coef, fit2$coef) [1] TRUE > all.equal(fit1$var, fit2$var) [1] TRUE > > # > # And with an data set containing interval censoring > # > idat <- read.table('data.interval', skip=3, header=T, sep=',') > > fit1 <- survreg(Surv(ltime, rtime, type='interval2') ~ age + ecog.ps, idat) > fit2 <- survreg(Surv(ltime, rtime, type='interval2') ~ age + ecog.ps, + data=idat, dist=mydist) > > all.equal(fit1$coef, fit2$coef) [1] TRUE > all.equal(fit1$var, fit2$var) [1] TRUE > all.equal(fit1$log, fit2$log) [1] TRUE > > survival/tests/tiedtime.R0000644000175100001440000000200013053306433015224 0ustar hornikuserslibrary(survival) # # The survival code was failing for certain data sets when called as # survfit(Surv(time2-time1, status) ~ ...... # The issue was how tied floating point numbers are handled, and the # fact that unique(x), factor(x) and tapply(x) are not guarranteed to # all be the same. # This test fails in survival 2.36-5, fixed in 2.36-6. Data sets that # can cause it are few and far between. # load('ties.rda') x <- time2 -time1 # Here is the heart of the old problem # length(unique(x))== length(table(x)) # And the prior fix which worked ALMOST always # x <- round(x, 15) # length(unique(round(x,15)))== length(table(round(x,15))) fit1 <- survfit(Surv(x) ~1) length(fit1$time) == length(fit1$surv) # a second test, once "rounding.R" tdata <- data.frame(time=c(1,2, sqrt(2)^2, 2, sqrt(2)^2), status=rep(1,5), group=c(1,1,1,2,2)) fit <- survfit(Surv(time, status) ~ group, data=tdata) all.equal(sum(fit$strata), length(fit$time)) survival/tests/r_sas.Rout.save0000644000175100001440000004214413055331410016224 0ustar hornikusers R Under development (unstable) (2017-02-21 r72241) -- "Unsuffered Consequences" Copyright (C) 2017 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # Reproduce example 1 in the SAS lifereg documentation > # > > # this fit doesn't give the same log-lik that they claim > motor <- read.table('data.motor', col.names=c('temp', 'time', 'status')) > fit1 <- survreg(Surv(time, status) ~ I(1000/(273.2+temp)), motor, + subset=(temp>150), dist='lognormal') > summary(fit1) Call: survreg(formula = Surv(time, status) ~ I(1000/(273.2 + temp)), data = motor, subset = (temp > 150), dist = "lognormal") Value Std. Error z p (Intercept) -10.471 2.772 -3.78 1.58e-04 I(1000/(273.2 + temp)) 8.322 1.284 6.48 9.13e-11 Log(scale) -0.504 0.183 -2.75 5.96e-03 Scale= 0.604 Log Normal distribution Loglik(model)= -145.9 Loglik(intercept only)= -155 Chisq= 18.3 on 1 degrees of freedom, p= 1.9e-05 Number of Newton-Raphson Iterations: 6 n= 30 > > # This one, with the loglik on the transformed scale (the inappropriate > # scale, Ripley & Venables would argue) does agree. > # All coefs are of course identical. > fit2 <- survreg(Surv(log(time), status) ~ I(1000/(273.2+temp)), motor, + subset=(temp>150), dist='gaussian') > > > # Give the quantile estimates, which is the lower half of "output 48.1.5" > # in the SAS 9.2 manual > > pp1 <- predict(fit1, newdata=list(temp=c(130,150)), p=c(.1, .5, .9), + type='quantile', se=T) > pp2 <- predict(fit1, newdata=list(temp=c(130,150)), p=c(.1, .5, .9), + type='uquantile', se=T) > pp1 $fit [,1] [,2] [,3] [1,] 12033.185 26095.677 56592.20 [2,] 4536.877 9838.864 21336.98 $se.fit [,1] [,2] [,3] [1,] 5482.338 11359.450 26036.917 [2,] 1443.072 2901.155 7172.343 > > temp130 <- matrix(0, nrow=3, ncol=6) > temp130[,1] <- pp1$fit[1,] > temp130[,2] <- pp1$se.fit[1,] > temp130[,3] <- pp2$fit[1,] > temp130[,4] <- pp2$se.fit[1,] > temp130[,5] <- exp(pp2$fit[1,] - 1.64*pp2$se.fit[1,]) > temp130[,6] <- exp(pp2$fit[1,] + 1.64*pp2$se.fit[1,]) > dimnames(temp130) <- list(c("p=.1", "p=.2", "p=.3"), + c("Time", "se(time)", "log(time)", "se[log(time)]", + "lower 90", "upper 90")) > print(temp130) Time se(time) log(time) se[log(time)] lower 90 upper 90 p=.1 12033.18 5482.338 9.395424 0.4556015 5700.089 25402.68 p=.2 26095.68 11359.450 10.169525 0.4353001 12779.950 53285.37 p=.3 56592.20 26036.917 10.943626 0.4600796 26611.422 120349.71 > > # A set of examples, copied from the manual pages of SAS procedure > # "reliability", which is part of their QC product. > # > > color <- c("black", "red", "green", "blue", "magenta", "red4", + "orange", "DarkGreen", "cyan2", "DarkViolet") > palette(color) > pdf(file='reliability.pdf') > > # > # Insulating fluids example > # > fluid <- read.table('data.fluid', col.names=c('time', 'voltage')) > > # Adding a -1 to the fit just causes the each group to have it's own > # intercept, rather than a global intercept + constrasts. The strata > # statement allows each to have a separate scale > ffit <- survreg(Surv(time) ~ voltage + strata(voltage) -1, fluid) > > # Get predicted quantiles at each of the voltages > # By default predict() would give a line of results for each observation, > # I only want the unique set of x's, i.e., only 4 cases > uvolt <- sort(unique(fluid$voltage)) #the unique levels > plist <- c(1, 2, 5, 1:9 *10, 95, 99)/100 > pred <- predict(ffit, type='quantile', p=plist, + newdata=data.frame(voltage=factor(uvolt))) > tfun <- function(x) log(-log(1-x)) > > matplot(t(pred), tfun(plist), type='l', log='x', lty=1, + col=1:4, yaxt='n') > axis(2, tfun(plist), format(100*plist), adj=1) > > kfit <- survfit(Surv(time) ~ voltage, fluid, type='fleming') #KM fit > for (i in 1:4) { + temp <- kfit[i] + points(temp$time, tfun(1-temp$surv), col=i, pch=i) + } > > # Now a table > temp <- array(0, dim=c(4,4,4)) #4 groups by 4 parameters by 4 stats > temp[,1,1] <- ffit$coef # "EV Location" in SAS manual > temp[,2,1] <- ffit$scale # "EV scale" > temp[,3,1] <- exp(ffit$coef) # "Weibull Scale" > temp[,4,1] <- 1/ffit$scale # "Weibull Shape" > > temp[,1,2] <- sqrt(diag(ffit$var))[1:4] #standard error > temp[,2,2] <- sqrt(diag(ffit$var))[5:8] * ffit$scale > temp[,3,2] <- temp[,1,2] * temp[,3,1] > temp[,4,2] <- temp[,2,2] / (temp[,2,1])^2 > > temp[,1,3] <- temp[,1,1] - 1.96*temp[,1,2] #lower conf limits > temp[,1,4] <- temp[,1,1] + 1.96*temp[,1,2] # upper > # log(scale) is the natural parameter, in which the routine did its fitting > # and on which the std errors were computed > temp[,2, 3] <- exp(log(ffit$scale) - 1.96*sqrt(diag(ffit$var))[5:8]) > temp[,2, 4] <- exp(log(ffit$scale) + 1.96*sqrt(diag(ffit$var))[5:8]) > > temp[,3, 3:4] <- exp(temp[,1,3:4]) > temp[,4, 3:4] <- 1/temp[,2,4:3] > > dimnames(temp) <- list(uvolt, c("EV Location", "EV Scale", "Weibull scale", + "Weibull shape"), + c("Estimate", "SE", "lower 95% CI", "uppper 95% CI")) > print(aperm(temp, c(2,3,1)), digits=5) , , 26kV Estimate SE lower 95% CI uppper 95% CI EV Location 6.86249 1.10404 4.69857 9.0264 EV Scale 1.83423 0.96114 0.65677 5.1227 Weibull scale 955.74665 1055.18620 109.78973 8320.0103 Weibull shape 0.54519 0.28568 0.19521 1.5226 , , 30kV Estimate SE lower 95% CI uppper 95% CI EV Location 4.35133 0.30151 3.76037 4.9423 EV Scale 0.94446 0.22544 0.59156 1.5079 Weibull scale 77.58159 23.39176 42.96420 140.0911 Weibull shape 1.05881 0.25274 0.66318 1.6904 , , 34kV Estimate SE lower 95% CI uppper 95% CI EV Location 2.50326 0.31476 1.88632 3.1202 EV Scale 1.29732 0.22895 0.91796 1.8334 Weibull scale 12.22222 3.84707 6.59509 22.6506 Weibull shape 0.77082 0.13603 0.54542 1.0894 , , 38kV Estimate SE lower 95% CI uppper 95% CI EV Location 0.00092629 0.27318 -0.53450 0.53635 EV Scale 0.73367610 0.20380 0.42565 1.26460 Weibull scale 1.00092672 0.27343 0.58596 1.70976 Weibull shape 1.36299929 0.37861 0.79077 2.34933 > > rm(temp, uvolt, plist, pred, ffit, kfit) > > ##################################################################### > # Turbine cracks data > cracks <- read.table('data.cracks', col.names=c('time1', 'time2', 'n')) > cfit <- survreg(Surv(time1, time2, type='interval2') ~1, + dist='weibull', data=cracks, weight=n) > > summary(cfit) Call: survreg(formula = Surv(time1, time2, type = "interval2") ~ 1, data = cracks, weights = n, dist = "weibull") Value Std. Error z p (Intercept) 4.272 0.0744 57.43 0.00e+00 Log(scale) -0.396 0.0987 -4.01 6.06e-05 Scale= 0.673 Weibull distribution Loglik(model)= -309.7 Loglik(intercept only)= -309.7 Number of Newton-Raphson Iterations: 5 n= 9 > #Their output also has Wiebull scale = exp(cfit$coef), shape = 1/(cfit$scale) > > # Draw the SAS plot > # The "type=fleming" argument reflects that they estimate hazards rather than > # survival, and forces a Nelson-Aalen hazard estimate > # > plist <- c(1, 2, 5, 1:8 *10)/100 > plot(qsurvreg(plist, cfit$coef, cfit$scale), tfun(plist), log='x', + yaxt='n', type='l', + xlab="Weibull Plot for Time", ylab="Percent") > axis(2, tfun(plist), format(100*plist), adj=1) > > kfit <- survfit(Surv(time1, time2, type='interval2') ~1, data=cracks, + weight=n, type='fleming') > # Only plot point where n.event > 0 > # Why? I'm trying to match them. Personally, all should be plotted. > who <- (kfit$n.event > 0) > points(kfit$time[who], tfun(1-kfit$surv[who]), pch='+') > points(kfit$time[who], tfun(1-kfit$upper[who]), pch='-') > points(kfit$time[who], tfun(1-kfit$lower[who]), pch='-') > > text(rep(3,6), seq(.5, -1.0, length=6), + c("Scale", "Shape", "Right Censored", "Left Censored", + "Interval Censored", "Fit"), adj=0) > text(rep(9,6), seq(.5, -1.0, length=6), + c(format(round(exp(cfit$coef), 2)), + format(round(1/cfit$scale, 2)), + format(tapply(cracks$n, cfit$y[,3], sum)), "ML"), adj=1) > > # Now a portion of his percentiles table > # I don't get the same SE as SAS, I haven't checked out why. The > # estimates and se for the underlying Weibull model are the same. > temp <- predict(cfit, type='quantile', p=plist, se=T) > tempse <- sqrt(temp$se[1,]) > mat <- cbind(temp$fit[1,], tempse, + temp$fit[1,] -1.96*tempse, temp$fit[1,] + 1.96*tempse) > dimnames(mat) <- list(plist*100, c("Estimate", "SE", "Lower .95", "Upper .95")) > print(mat) Estimate SE Lower .95 Upper .95 1 3.239372 0.965006 1.347960 5.130784 2 5.183283 1.121677 2.984796 7.381770 5 9.705766 1.337420 7.084422 12.327109 10 15.757758 1.491460 12.834497 18.681020 20 26.115947 1.622573 22.935705 29.296190 30 35.812585 1.704575 32.471618 39.153553 40 45.610018 1.809448 42.063500 49.156536 50 56.014351 1.973350 52.146585 59.882116 60 67.592818 2.214072 63.253237 71.932400 70 81.233457 2.543490 76.248217 86.218697 80 98.764571 2.991889 92.900469 104.628673 > > # > # The cracks data has a particularly easy estimate, so use > # it to double check code > time <- c(cracks$time2[1], (cracks$time1 + cracks$time2)[2:8]/2, + cracks$time1[9]) > cdf <- cumsum(cracks$n)/sum(cracks$n) > all.equal(kfit$time, time) [1] TRUE > all.equal(kfit$surv, 1-cdf[c(1:8,8)]) [1] TRUE > rm(time, cdf, kfit) > > > ####################################################### > # > # Valve data > # The input data has id, time, and an indicator of whether there was an > # event at that time: -1=no, 1=yes. No one has an event at their last time. > # Convert the data to (start, stop] form > # The input data has two engines with dual failures: 328 loses 2 valves at > # time 653, and number 402 loses 2 at time 139. For each, fudge the first > # time to be .1 days earlier. > # > temp <- matrix(scan('data.valve'), byrow=T, ncol=3) Read 267 items > > n <- nrow(temp) > valve <- data.frame(id=temp[,1], + time1 = c(0, ifelse(diff(temp[,1])==0, temp[-n,2],0)), + time2 = temp[,2], + status= as.numeric(temp[,3]==1)) > > indx <- (1:nrow(valve))[valve$time1==valve$time2] > valve$time1[indx] <- valve$time1[indx] - .1 > valve$time2[indx-1] <- valve$time2[indx-1] - .1 > > kfit <- survfit(Surv(time1, time2, status) ~1, valve, type='fh2') > > plot(kfit, fun='cumhaz', ylab="Sample Mean Cumulative Failures", xlab='Time', + ylim=range(-log(kfit$lower))) > title("Valve replacement data") > > # The summary.survfit function doesn't have an option for printing out > # cumulative hazards instead of survival --- need to add that > # so I just reprise the central code of print.summary.survfit > xx <- summary(kfit) > temp <- cbind(xx$time, xx$n.risk, xx$n.event, -log(xx$surv), + xx$std.err/xx$surv, -log(xx$upper), -log(xx$lower)) > dimnames(temp) <- list(rep("", nrow(temp)), + c("time", "n.risk", "n.event", "Cum haz", "std.err", + "lower 95%", "upper 95%")) > print(temp, digits=2) time n.risk n.event Cum haz std.err lower 95% upper 95% 61 41 1 0.024 0.025 0.00000 0.073 76 41 1 0.049 0.035 0.00000 0.117 84 41 1 0.073 0.043 0.00000 0.157 87 41 1 0.098 0.049 0.00077 0.194 92 41 1 0.122 0.055 0.01373 0.230 98 41 1 0.146 0.060 0.02779 0.265 120 41 1 0.171 0.065 0.04268 0.299 139 41 1 0.195 0.070 0.05823 0.332 139 41 1 0.220 0.074 0.07432 0.365 165 41 1 0.244 0.078 0.09085 0.397 166 41 1 0.268 0.082 0.10778 0.429 202 41 1 0.293 0.086 0.12503 0.460 206 41 1 0.317 0.089 0.14257 0.492 249 41 1 0.341 0.092 0.16038 0.523 254 41 1 0.366 0.096 0.17841 0.553 258 41 1 0.390 0.099 0.19665 0.584 265 41 1 0.415 0.102 0.21508 0.614 276 41 1 0.439 0.105 0.23369 0.644 298 41 1 0.463 0.108 0.25245 0.674 323 41 1 0.488 0.110 0.27136 0.704 326 41 1 0.512 0.113 0.29041 0.734 328 41 1 0.537 0.116 0.30958 0.764 344 41 1 0.561 0.118 0.32887 0.793 348 41 1 0.585 0.121 0.34827 0.822 349 41 1 0.610 0.123 0.36777 0.852 367 41 1 0.634 0.126 0.38736 0.881 377 41 1 0.659 0.128 0.40705 0.910 404 40 1 0.684 0.131 0.42720 0.940 408 40 1 0.709 0.133 0.44745 0.970 410 40 1 0.734 0.136 0.46777 0.999 449 40 1 0.759 0.138 0.48818 1.029 479 40 1 0.784 0.140 0.50866 1.058 497 40 1 0.809 0.143 0.52922 1.088 538 40 1 0.834 0.145 0.54985 1.117 539 40 1 0.859 0.147 0.57054 1.147 561 40 1 0.884 0.149 0.59129 1.176 563 40 1 0.909 0.151 0.61211 1.205 570 40 1 0.934 0.153 0.63299 1.234 573 40 1 0.959 0.155 0.65392 1.263 581 38 1 0.985 0.158 0.67578 1.294 586 34 1 1.014 0.160 0.69970 1.329 604 22 1 1.060 0.167 0.73221 1.387 621 17 1 1.119 0.178 0.77014 1.467 635 16 1 1.181 0.189 0.81038 1.552 640 16 1 1.244 0.200 0.85188 1.635 646 13 1 1.320 0.215 0.89854 1.742 653 9 1 1.432 0.245 0.95056 1.913 653 9 1 1.543 0.272 1.00909 2.076 > > # Note that I have the same estimates but different SE's. We are using a > # different estimator. It's a statistical argument as to which is > # better (one could defend both sides): do you favor JASA or Technometrics? > rm(temp, kfit, indx, xx) > > ###################################################### > # Turbine data, lognormal fit > turbine <- read.table('data.turbine', + col.names=c("time1", "time2", "n")) > > tfit <- survreg(Surv(time1, time2, type='interval2') ~1, turbine, + dist='lognormal', weights=n, subset=(n>0)) > > summary(tfit) Call: survreg(formula = Surv(time1, time2, type = "interval2") ~ 1, data = turbine, weights = n, subset = (n > 0), dist = "lognormal") Value Std. Error z p (Intercept) 3.700 0.0708 52.23 0.00000 Log(scale) -0.329 0.1232 -2.67 0.00763 Scale= 0.72 Log Normal distribution Loglik(model)= -190.7 Loglik(intercept only)= -190.7 Number of Newton-Raphson Iterations: 6 n= 21 > > # Now, do his plot, but put bootstrap confidence bands on it! > # First, make a simple data set without weights > tdata <- turbine[rep(1:nrow(turbine), turbine$n),] > > qstat <- function(data) { + temp <- survreg(Surv(time1, time2, type='interval2') ~1, data=data, + dist='lognormal') + qsurvreg(plist, temp$coef, temp$scale, dist='lognormal') + } > > {if (exists('bootstrap')) { + set.seed(1953) # a good year :-) + bfit <- bootstrap(tdata, qstat, B=1000) + bci <- limits.bca(bfit, probs=c(.025, .975)) + } + else { + values <- matrix(0, nrow=1000, ncol=length(plist)) + n <- nrow(tdata) + for (i in 1:1000) { + subset <- sample(1:n, n, replace=T) + values[i,] <- qstat(tdata[subset,]) + } + bci <- t(apply(values,2, quantile, c(.05, .95))) + } + } > xmat <- cbind(qsurvreg(plist, tfit$coef, tfit$scale, dist='lognormal'), + bci) > > > matplot(xmat, qnorm(plist), + type='l', lty=c(1,2,2), col=c(1,1,1), + log='x', yaxt='n', ylab='Percent', + xlab='Time of Cracking (Hours x 100)') > axis(2, qnorm(plist), format(100*plist), adj=1) > title("Turbine Data") > kfit <- survfit(Surv(time1, time2, type='interval2') ~1, data=tdata) > points(kfit$time, qnorm(1-kfit$surv), pch='+') > > dev.off() #close the plot file pdf 2 > > > proc.time() user system elapsed 5.568 0.076 5.644 survival/tests/finegray.Rout.save0000644000175100001440000002072713055116151016727 0ustar hornikusers R Under development (unstable) (2017-02-21 r72241) -- "Unsuffered Consequences" Copyright (C) 2017 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > # Test data set 1 for Fine-Gray regression > fdata <- data.frame(time =c(1,2,3,4,4,4,5,5,6,8,8, 9,10,12), + status=factor(c(1,2,0,1,0,0,2,1,0,0,2, 0,1 ,0), 0:2, + c("cen", "type1", "type2")), + x =c(5,4,3,1,2,1,1,2,2,4,6,1,2, 0), + id = 1:14) > test1 <- finegray(Surv(time, status) ~., fdata, count="fgcount") > test2 <- finegray(Surv(time, status) ~x, fdata, etype="type2") > > # When creating the censoring time distribution remember that > # censors happen after deaths, so the distribution does not drop until > # time 3+, 4+, 6+, 8+ and 9+ > csurv <- list(time=c(0, 3, 4, 6, 8, 9), + p = cumprod(c(1, 11/12, 8/10, 5/6, 3/4, 2/3))) > # > # For estimation of event type 1, the first subject of event type > # 2 will have weights of curve$p over (0,3], (3,4], (4,6], (6,8], (8,9] > # and (9,12]. All that really matters is the weight at times 1, 4, 5, > # and 10, however, which are the points at which events of type 1 happen > # > # The next subject of event type 2 occurs at time 5, and will have a > # weight of (9,12] /(4,5] = (5*4*2)/(7*5*3) = 8/21 at time 10. The last > # censor at time 6 has a weight of 2/3 at time 10. > > all.equal(test1$id, c(1, 2,2,2,2, 3:6, 7, 7, 8:11, 11, 12:14)) [1] TRUE > twt <- c(1, csurv$p[c(1,2,3,6)], 1,1,1, 1, 1, 5/12, 1,1,1, + 1, 1/2, 1,1,1) > all.equal(test1$fgwt, twt) [1] TRUE > #extra obs will end at times found in csurv$time, or max(time)=12 > all.equal(test1$fgstop[test1$fgcount>0], c(4,6,12, 12,12)) [1] TRUE > > # > # Verify the data reproduces a multi-state curve > # censoring times may be different in the two setups so only > # compare at the event times > sfit <- survfit(Surv(time, status) ~1, fdata) > sfit1<- survfit(Surv(fgstart, fgstop, fgstatus) ~1, test1, weight=fgwt) > i1 <- sfit$n.event[,1] > 0 > i2 <- sfit1$n.event > 0 > all.equal(sfit$pstate[i1, 1], 1- sfit1$surv[i2]) [1] TRUE > > sfit2 <- survfit(Surv(fgstart, fgstop, fgstatus) ~1, test2, weight=fgwt) > i1 <- sfit$n.event[,2] > 0 > i2 <- sfit2$n.event > 0 > all.equal(sfit$pstate[i1, 2], 1- sfit2$surv[i2]) [1] TRUE > > # Test strata. Make a single data set that has fdata for the first 19 > # rows, then fdata with outcomes switched for the second 19. It should > # reprise test1 and test2 in a single call. > fdata2 <- rbind(fdata, fdata) > fdata2$group <- rep(1:2, each=nrow(fdata)) > temp <- c(1,3,2)[as.numeric(fdata$status)] > fdata2$status[fdata2$group==2] <- factor(temp, 1:3, levels(fdata$status)) > test3 <- finegray(Surv(time, status) ~ .+ strata(group), fdata2) > vtemp <- c("fgstart", "fgstop", "fgstatus", "fgwt") > all.equal(test3[1:19, vtemp], test1[,vtemp]) [1] TRUE > all.equal(test3[20:38, vtemp], test2[,vtemp], check.attributes=FALSE) [1] TRUE > > # > # Test data set 2: use the larger MGUS data set > # Time is in months which leads to lots of ties > etime <- with(mgus2, ifelse(pstat==0, futime, ptime)) > event <- with(mgus2, ifelse(pstat==0, 2*death, 1)) > e2 <- factor(event, 0:2, c('censor', 'pcm', 'death')) > edata <- finegray(Surv(etime, e2) ~ sex + id, mgus2, etype="pcm") > > # Build G(t) = the KM of the censoring distribution > # An event at time x is not "at risk" for censoring at time x (Geskus 2011) > tt <- sort(unique(etime)) # all the times > ntime <- length(tt) > nrisk <- nevent <- double(ntime) > for (i in 1:ntime) { + nrisk[i] <- sum((etime > tt[i] & event >0) | (etime >= tt[i] & event==0)) + nevent[i] <- sum(etime == tt[i] & event==0) + } > G <- cumprod(1- nevent/nrisk) > > # The weight is defined as w(t)= G(t-)/G(s-) where s is the event time > # for a subject who experiences an endpoint other then the one of interest > type2 <- event[edata$id]==2 # the rows to be expanded > # These rows are copied over as is: endpoint 1 and censors > all(edata$fgstop[!type2] == etime[edata$id[!type2]]) [1] TRUE > all(edata$fgstart[!type2] ==0) [1] TRUE > all(edata$fgwt[!type2] ==1) [1] TRUE > > tdata <- edata[type2,] #expanded rows > first <- match(tdata$id, tdata$id) #points to the first row for each subject > Gwt <- c(1, G)[match(tdata$fgstop, tt)] # G(t-) > all.equal(tdata$fgwt, Gwt/Gwt[first]) [1] TRUE > > # Test data 3, left truncation. > # Ties are assumed to be ordered as event, censor, entry > # H(t) = truncation distribution, and is calculated on a reverse time scale > # Since there is only one row per subject every obs is a "start" event. > # Per equation 5 and 6 of Geskus both G and H are right continuous functions > # (the value at t- epsilon is different than the value at t). > fdata <- data.frame(time1 = c(0,0,0,3,2,0,0,1,0,7,5, 0, 0, 0), + time2 = c(1,2,3,4,4,4,5,5,6,8,8, 9,10,12), + status= c(1,2,0,1,0,0,2,1,0,0,2, 0, 1 ,0), + x = c(5,4,3,1,2,1,1,2,2,4,6, 1, 2, 0), + id = 1:14) > tt <- sort(unique(c(fdata$time1, fdata$time2))) > ntime <- length(tt) > Grisk <- Gevent <- double(ntime) > Hrisk <- Hevent <- double(ntime) > for (i in 1:ntime) { + Grisk[i] <- with(fdata, sum((time2 > tt[i] & status >0 & time1 < tt[i]) | + (time2 >= tt[i] & status ==0 & time1 < tt[i]))) + Gevent[i]<- with(fdata, sum(time2 == tt[i] & status==0)) + Hrisk[i] <- with(fdata, sum(time2 > tt[i] & time1 <= tt[i])) + Hevent[i]<- with(fdata, sum(time1 == tt[i])) + } > G <- cumprod(1- Gevent/pmax(1,Grisk)) > G2 <- survfit(Surv(time1, time2 - .1*(status !=0), status==0) ~1, fdata) > all.equal(G2$surv[G2$n.event>0], G[Gevent>0]) [1] TRUE > > H <- double(ntime) > # The loop below uses the definition of equation 6 in Geskus > for (i in 1:ntime) + H[i] <- prod((1- Hevent/pmax(1, Hrisk))[-(i:1)]) > H2 <- rev(cumprod(rev(1 - Hevent/pmax(1, Hrisk)))) #alternate form > H3 <- survfit(Surv(-time2, -time1, rep(1,14)) ~1, fdata) # alternate 3 > all.equal(tt, -rev(H3$time)) [1] TRUE > # c(0,H) = H(t-), H2 = H(t-) already due to the time reversal > all.equal(c(0, H), c(H2, 1)) [1] TRUE > all.equal(H2, rev(H3$surv)) [1] TRUE > > fg <- finegray(Surv(time1, time2, factor(status, 0:2)) ~ x, id=id, fdata) > stat2 <- !is.na(match(fg$id, fdata$id[fdata$status==2])) #expanded ids > all(fg$fgwt[!stat2] ==1) #ordinary rows are left alone [1] TRUE > all(fg$fgstart[!stat2] == fdata$time1[fdata$status !=2]) [1] TRUE > all(fg$fgstop[!stat2] == fdata$time2[fdata$status !=2]) [1] TRUE > > tdata <- fg[stat2,] > index <- match(tdata$id, tdata$id) # points to the first row for each > Gwt <- c(1, G)[match(tdata$fgstop, tt)] # G(t-) > Hwt <- c(0, H)[match(tdata$fgstop, tt)] # H(t-) > all.equal(tdata$fgwt, Gwt*Hwt/(Gwt*Hwt)[index]) [1] TRUE > > # > # Test data 4: mgus2 data on age scale > # The answer is incorrect due to roundoff, but consistent > # > start <- mgus2$age # age in years > end <- start + etime/12 #etime in months > tt <- sort(unique(c(start, end))) # all the times > ntime <- length(tt) > Grisk <- Gevent <- double(ntime) > Hrisk <- Hevent <- double(ntime) > for (i in 1:ntime) { + Grisk[i] <- sum(((end > tt[i] & event >0) | (end >= tt[i] & event==0)) & + (tt[i] > start)) + Gevent[i] <- sum(end == tt[i] & event==0) + Hrisk[i] <- sum(start <= tt[i] & end > tt[i]) + Hevent[i] <- sum(start == tt[i]) + } > G <- cumprod(1 - Gevent/pmax(1, Grisk)) # pmax to avoid 0/0 > H <- rev(cumprod(rev(1-Hevent/pmax(1,Hrisk)))) > H <- c(H[-1], 1) #make it right continuous > > wdata <- finegray(Surv(start, end, e2) ~ ., id=id, mgus2, timefix=FALSE) > type2 <- event[wdata$id]==2 # the rows to be expanded > tdata <- wdata[type2,] > first <- match(tdata$id, tdata$id) > > Gwt <- c(1, G)[match(tdata$fgstop, tt)] # G(t-) > Hwt <- c(0, H)[match(tdata$fgstop, tt)] # H(t-) > all.equal(tdata$fgwt, (Gwt/Gwt[first]) * (Hwt / Hwt[first])) [1] TRUE > > > proc.time() user system elapsed 2.176 0.052 2.226 survival/tests/r_resid.R0000644000175100001440000000767711732700061015075 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) fit1 <- survreg(Surv(futime, fustat) ~ age + ecog.ps, ovarian) fit4 <- survreg(Surv(log(futime), fustat) ~age + ecog.ps, ovarian, dist='extreme') print(fit1) summary(fit4) # Hypothesis (and I'm fairly sure): censorReg shares the fault of many # iterative codes -- it returns the loglik and variance for iteration k # but the coef vector of iteration k+1. Hence the "all.equal" tests # below don't come out perfect. # if (exists('censorReg')) { #true for Splus, not R fit2 <- censorReg(censor(futime, fustat) ~ age + ecog.ps, ovarian) fit3 <- survreg(Surv(futime, fustat) ~ age + ecog.ps, ovarian, iter=0, init=c(fit2$coef, log(fit2$scale))) aeq(resid(fit2, type='working')[,1], resid(fit3, type='working')) aeq(resid(fit2, type='response')[,1], resid(fit3, type='response')) temp <- sign(resid(fit3, type='working')) aeq(resid(fit2, type='deviance')[,1], temp*abs(resid(fit3, type='deviance'))) aeq(resid(fit2, type='deviance')[,1], resid(fit3, type='deviance')) } # # Now check fit1 and fit4, which should follow identical iteration paths # These tests should all be true # aeq(fit1$coef, fit4$coef) resid(fit1, type='working') resid(fit1, type='response') resid(fit1, type='deviance') resid(fit1, type='dfbeta') resid(fit1, type='dfbetas') resid(fit1, type='ldcase') resid(fit1, type='ldresp') resid(fit1, type='ldshape') resid(fit1, type='matrix') aeq(resid(fit1, type='working'),resid(fit4, type='working')) #aeq(resid(fit1, type='response'), resid(fit4, type='response'))#should differ aeq(resid(fit1, type='deviance'), resid(fit4, type='deviance')) aeq(resid(fit1, type='dfbeta'), resid(fit4, type='dfbeta')) aeq(resid(fit1, type='dfbetas'), resid(fit4, type='dfbetas')) aeq(resid(fit1, type='ldcase'), resid(fit4, type='ldcase')) aeq(resid(fit1, type='ldresp'), resid(fit4, type='ldresp')) aeq(resid(fit1, type='ldshape'), resid(fit4, type='ldshape')) aeq(resid(fit1, type='matrix'), resid(fit4, type='matrix')) # # Some tests of the quantile residuals # motor <- read.table('data.motor', col.names=c('temp', 'time', 'status')) # These should agree exactly with Ripley and Venables' book fit1 <- survreg(Surv(time, status) ~ temp, data=motor) summary(fit1) # # The first prediction has the SE that I think is correct # The third is the se found in an early draft of Ripley; fit1 ignoring # the variation in scale estimate, except via it's impact on the # upper left corner of the inverse information matrix. # Numbers 1 and 3 differ little for this dataset # predict(fit1, data.frame(temp=130), type='uquantile', p=c(.5, .1), se=T) fit2 <- survreg(Surv(time, status) ~ temp, data=motor, scale=fit1$scale) predict(fit2, data.frame(temp=130), type='uquantile', p=c(.5, .1), se=T) fit3 <- fit2 fit3$var <- fit1$var[1:2,1:2] predict(fit3, data.frame(temp=130), type='uquantile', p=c(.5, .1), se=T) pp <- seq(.05, .7, length=40) xx <- predict(fit1, data.frame(temp=130), type='uquantile', se=T, p=pp) #matplot(pp, cbind(xx$fit, xx$fit+2*xx$se, xx$fit - 2*xx$se), type='l') # # Now try out the various combinations of strata, #predicted, and # number of quantiles desired # fit1 <- survreg(Surv(time, status) ~ inst + strata(inst) + age + sex, lung) qq1 <- predict(fit1, type='quantile', p=.3, se=T) qq2 <- predict(fit1, type='quantile', p=c(.2, .3, .4), se=T) aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) aeq(qq1$fit, qq2$fit[,2]) aeq(qq1$se.fit, qq2$se.fit[,2]) qq3 <- predict(fit1, type='quantile', p=c(.2, .3, .4), se=T, newdata= lung[1:5,]) aeq(qq3$fit, qq2$fit[1:5,]) qq4 <- predict(fit1, type='quantile', p=c(.2, .3, .4), se=T, newdata=lung[7,]) aeq(qq4$fit, qq2$fit[7,]) qq5 <- predict(fit1, type='quantile', p=c(.2, .3, .4), se=T, newdata=lung) aeq(qq2$fit, qq5$fit) aeq(qq2$se.fit, qq5$se.fit) survival/tests/fr_lung.R0000644000175100001440000000131011732700061015054 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # A test with the lung data # This caused problems in one release # # First, get rid of some missings # lung2 <- na.omit(lung[c('time', 'status', 'wt.loss')]) # # Test the logliklihoods # fit <- coxph(Surv(time, status) ~ pspline(wt.loss,3), lung2, x=T) fit0<- coxph(Surv(time, status) ~ 1, lung2) fit1<- coxph(Surv(time, status) ~ fit$x, lung2, iter=0, init=fit$coef) all.equal(fit$loglik[1], fit0$loglik) all.equal(fit$loglik[2], fit1$loglik[2]) # # Check variances # imat <- solve(fit1$var) var2 <- fit$var %*% imat %*% fit$var all.equal(fit$var2, var2) survival/tests/pspline.R0000644000175100001440000000373512714101267015113 0ustar hornikuserslibrary(survival) # # Tests with the pspline function, to verify the prediction aspects # options(na.action=na.exclude) aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) spfit <- coxph(Surv(time, status) ~ pspline(age) + ph.ecog, lung) spfit2 <- coxph(Surv(time, status) ~ pspline(age) + ph.ecog, lung, x=TRUE) x2 <- model.matrix(spfit) all.equal(spfit2$x, x2) keep <- (lung$age < 60) x3 <- model.matrix(spfit, data=lung[keep,]) attr(x3, 'assign') <- NULL #subscripting loses the assign attr below all.equal(napredict(spfit$na.action,x2)[keep,], x3) p2 <- predict(spfit, newdata=lung[keep,]) aeq(p2, predict(spfit)[keep]) p3 <- survfit(spfit) p4 <- survfit(spfit, newdata=lung[1:2,]) temp <- scale(x2[1:2,], center=spfit$means, scale=FALSE)%*% coef(spfit) aeq(p3$time, p4$time) aeq(outer(-log(p3$surv), exp(temp), '*'), -log(p4$surv)) # Check out model.frame spfit3 <- coxph(Surv(time, status) ~ pspline(age) + sex, lung, model=TRUE) #avoid the missing value m2 <- model.frame(spfit3, data=lung[keep,]) all.equal(m2, spfit3$model[keep,], check.attributes=FALSE) # # Test of residuals, in response to a reported bug. The routines for # m-resids of penalized models were separate from other m-resid calcs; # refactored to change that. # These are three progam paths that should all lead to the same C routine fit <- coxph(Surv(tstart, tstop, status) ~ sex + treat + pspline(age), cgd) fit2 <- coxph(Surv(tstart, tstop, status) ~ fit$linear, cgd, iter=0, init=1) fit3 <- coxph(Surv(tstart, tstop, status) ~ offset(fit$linear), cgd) all.equal(fit$resid, fit2$resid) all.equal(fit$resid, fit3$resid) # # Check using coxph.detail. The matrix multiply below only is # valid for the breslow approximation. fit4 <- coxph(Surv(tstart, tstop, status) ~ sex + treat + pspline(age), cgd, ties='breslow') dt <- coxph.detail(fit4, riskmat=TRUE) rscore <- exp(fit4$linear) exp4 <- (rscore *dt$riskmat) %*% dt$hazard r4 <- cgd$status - exp4 aeq(r4, fit4$resid) survival/tests/book6.Rout.save0000644000175100001440000001431412656732353016154 0ustar hornikusers R Under development (unstable) (2016-01-29 r70039) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > > # Tests of the weighted Cox model > # This is section 1.3 of my appendix -- no yet found in any of the > # printings though, it awaits the next edition > # > # Efron approximation > # > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > testw1 <- data.frame(time= c(1,1,2,2,2,2,3,4,5), + status= c(1,0,1,1,1,0,0,1,0), + x= c(2,0,1,1,0,1,0,1,0), + wt = c(1,2,3,4,3,2,1,2,1)) > xx <- testw1$wt > > # Efron estimate > byhand <- function(beta, newx=0) { + r <- exp(beta) + a <- 7*r +3; b<- 4*r+2 + loglik <- 11*beta - (log(r^2 + 11*r +7) + 10*log(11*r +5)/3 + + 10*log(a*2/3 +b)/3 + 10*log(a/3 +b)/3 +2*log(2*r+1)) + + hazard <- c(1/(r^2 + 11*r +7), + 10/(3*c(11*r +5, a*2/3 +b, a/3+b)), 2/(2*r+1)) + temp <- c(hazard[1], hazard[1]+hazard[2] + hazard[3]*2/3 + hazard[4]/3, + cumsum(hazard)[4:5]) + risk <- c(r^2, 1,r,r,1,r,1,r,1) + expected <- risk* temp[c(1,1,2,2,2,3,3,4,4)] + + # The matrix of weights, one row per obs, one col per death + # deaths at 1,2,2,2, and 4 + riskmat <- matrix(c(1,1,1,1,1,1,1,1,1, + 0,0,1,1,1,1,1,1,1, + 0,0,2/3,2/3,2/3,1,1,1,1, + 0,0,1/3,1/3,1/3,1,1,1,1, + 0,0,0,0,0,0,0,1,1), ncol=5) + wtmat <- diag(c(r^2, 2, 3*r, 4*r, 3, 2*r, 1, 2*r, 1)) %*% riskmat + + x <- c(2,0,1,1,0,1,0,1,0) + xbar <- colSums(x*wtmat)/ colSums(wtmat) + imat <- (4*r^2 + 11*r)*hazard[1] - xbar[1]^2 + + 10* mean(xbar[2:4] - xbar[2:4]^2) + 2*(xbar[5] - xbar[5]^2) + + status <- c(1,0,1,1,1,0,0,1,0) + wt <- c(1,2,3,4,3,2,1,2,1) + # Table of sums for score resids + hazmat <- riskmat %*% diag(c(1,10/3,10/3, 10/3,2)/colSums(wtmat)) + dM <- -risk*hazmat #Expected part + dM[1,1] <- dM[1,1] +1 # deaths at time 1 + for (i in 2:4) dM[3:5, i] <- dM[3:5,i] + 1/3 + dM[8,5] <- dM[8,5] +1 + mart <- rowSums(dM) + resid <-dM * outer(x, xbar ,'-') + + # Increments to the variance of the hazard + var.g <- cumsum(hazard^2* c(1,3/10, 3/10, 3/10, 1/2)) + var.d <- cumsum((xbar-newx)*hazard) + + sxbar <- c(xbar[1], mean(xbar[2:4]), xbar[5]) #xbar for Schoen + list(loglik=loglik, imat=imat, hazard=hazard, xbar=xbar, + mart=status-expected, expected=expected, + score=rowSums(resid), schoen=c(2,1,1,0,1) - sxbar[c(1,2,2,2,3)], + varhaz=((var.g + var.d^2/imat)* exp(2*beta*newx))[c(1,4,5)]) + } > > # Verify > temp <- byhand(0,0) > aeq(temp$xbar, c(13/19, 11/16, 26/38, 19/28, 2/3)) [1] TRUE > aeq(temp$hazard, c(1/19, 5/24, 5/19, 5/14, 2/3)) [1] TRUE > > fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt, iter=0) > fit <- coxph(Surv(time, status) ~x, testw1, weights=wt) > > truth0 <- byhand(0,pi) > aeq(fit0$loglik[1], truth0$loglik) [1] TRUE > aeq(1/truth0$imat, fit0$var) [1] TRUE > aeq(truth0$mart, fit0$resid) [1] TRUE > aeq(truth0$scho, resid(fit0, 'schoen')) [1] TRUE > aeq(truth0$score, resid(fit0, 'score')) [1] TRUE > sfit <- survfit(fit0, list(x=pi), censor=FALSE) > aeq(sfit$std.err^2, truth0$var) [1] TRUE > aeq(-log(sfit$surv), cumsum(truth0$hazard)[c(1,4,5)]) [1] TRUE > > truth <- byhand(fit$coef, .3) > aeq(truth$loglik, fit$loglik[2]) [1] TRUE > aeq(1/truth$imat, fit$var) [1] TRUE > aeq(truth$mart, fit$resid) [1] TRUE > aeq(truth$scho, resid(fit, 'schoen')) [1] TRUE > aeq(truth$score, resid(fit, 'score')) [1] TRUE > > sfit <- survfit(fit, list(x=.3), censor=FALSE) > aeq(sfit$std.err^2, truth$var) [1] TRUE > aeq(-log(sfit$surv), (cumsum(truth$hazard)* exp(fit$coef*.3))[c(1,4,5)]) [1] TRUE > > > fit0 Call: coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt, iter = 0) coef exp(coef) se(coef) z p x 0.000 1.000 0.584 0 1 Likelihood ratio test=0 on 1 df, p=1 n= 9, number of events= 5 > summary(fit) Call: coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt) n= 9, number of events= 5 coef exp(coef) se(coef) z Pr(>|z|) x 0.8726 2.3931 0.7126 1.225 0.221 exp(coef) exp(-coef) lower .95 upper .95 x 2.393 0.4179 0.5921 9.672 Concordance= 0.638 (se = 0.159 ) Rsquare= 0.177 (max possible= 0.999 ) Likelihood ratio test= 1.75 on 1 df, p=0.1858 Wald test = 1.5 on 1 df, p=0.2207 Score (logrank) test = 1.58 on 1 df, p=0.2094 > resid(fit0, type='score') 1 2 3 4 5 6 1.24653740 0.03601108 0.14118105 0.14118105 -0.30336782 -0.27962308 7 8 9 0.60164259 -0.16851197 1.04608703 > resid(fit0, type='scho') 1 2 2 2 4 1.3157895 0.3165727 0.3165727 -0.6834273 0.3333333 > > resid(fit, type='score') 1 2 3 4 5 6 0.88116056 0.02477248 0.06057806 0.06057806 -0.59724033 -0.16737066 7 8 9 0.38040295 -0.13750290 0.66631324 > resid(fit, type='scho') 1 2 2 2 4 1.0325955 0.1621759 0.1621759 -0.8378241 0.1728229 > > rr1 <- resid(fit, type='mart') > rr2 <- resid(fit, type='mart', weighted=T) > aeq(rr2/rr1, testw1$wt) [1] TRUE > > rr1 <- resid(fit, type='score') > rr2 <- resid(fit, type='score', weighted=T) > aeq(rr2/rr1, testw1$wt) [1] TRUE > > > proc.time() user system elapsed 0.220 0.020 0.233 survival/tests/anova.Rout.save0000644000175100001440000000357212164375073016240 0ustar hornikusers R version 3.0.0 (2013-04-03) -- "Masked Marvel" Copyright (C) 2013 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # > # Test out anova, with strata terms > # > options(na.action=na.omit) > library(survival) Loading required package: splines > > fit1 <- coxph(Surv(time, status) ~ ph.ecog + wt.loss + strata(sex) + + poly(age,3), lung) > ztemp <- anova(fit1) > > tdata <- na.omit(lung[, c('time', 'status', 'ph.ecog', 'wt.loss', 'sex', 'age')]) > fit2 <- coxph(Surv(time, status)~ ph.ecog + wt.loss + poly(age,3) + strata(sex), + data=tdata) > ztemp2 <- anova(fit2) > all.equal(ztemp, ztemp2) [1] TRUE > > > fit2 <- coxph(Surv(time, status) ~ ph.ecog + wt.loss + strata(sex), tdata) > fit3 <- coxph(Surv(time, status) ~ ph.ecog + strata(sex), tdata) > > all.equal(ztemp$loglik, c(fit1$loglik[1], fit3$loglik[2], fit2$loglik[2], + fit1$loglik[2])) [1] TRUE > all.equal(ztemp$Chisq[-1], 2* diff(ztemp$loglik)) [1] TRUE > all.equal(ztemp$Df[-1], c(1,1,3)) [1] TRUE > > ztemp2 <- anova(fit3, fit2, fit1) > all.equal(ztemp2$loglik, ztemp$loglik[-1]) [1] TRUE > all.equal(ztemp2$Chisq[2:3], ztemp$Chisq[3:4]) [1] TRUE > # Change from ztemp2$P; it's a data frame and in R 3.0.2 abbreviated names > # give a warning > all.equal(ztemp2[[4]][2:3], ztemp[[4]][3:4]) [1] TRUE > > > > proc.time() user system elapsed 0.284 0.020 0.301 survival/tests/testci2.Rout.save0000644000175100001440000001465713004232520016476 0ustar hornikusers R version 3.2.3 (2015-12-10) -- "Wooden Christmas-Tree" Copyright (C) 2015 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > > # > # Test the multi-state version of the CI curve > # > tdata <- data.frame(id=c(1,1,1,1, 2,2,2, 3,3, 4,4,4,4, 5, 6, 6), + time1=c(0, 10,20,30, 0, 5, 15, 0, 20, 0, 6,18,34, 0, 0,15), + time2=c(10,20,30,40, 5, 15,25, 20, 22, 6,18,34,50,10,15,20), + status=c(1,1,1,1, 1,1,1, 1,0, 1,1,1,0,0,1,0), + event= letters[c(1,2,3,4, 2,4,3, 2,2, 3,1,2,2,1, 1,1)], + wt = c(2,2,2,2, 1,1,1, 3,3, 1,1,1,1, 2, 1,1), + stringsAsFactors=TRUE) > tdata$stat2 <- factor(tdata$status * as.numeric(tdata$event), + labels=c("censor", levels(tdata$event))) > > fit <- survfit(Surv(time1, time2, stat2) ~1, id=id, weight=wt, tdata, + influence=TRUE) > > # The exact figures for testci2. > # The subject data of id, weight, (transition time, transition) > > #1: 2 (10, 0->a) (20, a->b) (30, b->c) (40, c->d) no data after 40=censored > #2: 1 ( 5, 0->b) (15, b->d) (25, d->c) no data after 25 implies censored then > #3: 3 (20, 0->b) (22, censor) > #4: 1 ( 6, 0->c) (18, c->a) (34, a->b) (50, censor) > #5: 2 (10, censor) > #6: 1 (15, 0->a) (20, censor) > > # Each line below follows a subject through time as a (state, rdist weight) pair > # using the redistribute to the right algorithm. > # RDR algorithm: at each censoring (or last fu) a subject's weight is put into > # a "pool" for that state and their weight goes to zero. The pool is > # dynamically shared between all members of the state proportional to their > # original case weight, when someone leaves they take their portion of the > # pool to the new state. > > # Table of case weights and state, blank is weight of zero > # time 5 6 10 15 18 20 25 30 34 40 50 > # ----------------------------------------------------------------------- > # id, wt > # 1, 2 - - a a a b b c c d > # 2, 1 b b b d d d c > # 3, 3 - - - - - b > # 4, 1 - c c c a a a a b b b > # 5, 2 - - - > # 6, 1 - - - a a a > > # Pool weights > # 10 10+ 15 18 20 20+ 22+ 25 25+ 30 34 40 40+ > # - 0 2 3/2 3/2 0 > # a 0 0 1/2 1/2 1/4 5/4 5/4 5/4 5/4 5/4 > # b 0 0 0 0 7/4 7/4 19/4 19/4 19/4 5/4 5/4 5/4 > # c 0 0 0 0 0 1 23/4 23/4 > # d 0 0 0 0 0 23/4 31/4 > > # fit$pstate for time i and state j = total weight at that time/state in the > # above table (original weight + redistrib), divided by 10. > > # time 5 6 10 15 18 20 25 30 34 40 50 > truth <- matrix(c(0, 0, 2, 3, 4, 2, 1, 1, 0, 0, 0, + 1, 1, 1, 0, 0, 5, 2, 0, 1, 1, 1, + 0, 1, 1, 1, 0, 0, 1, 2, 2, 0, 0, + 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0) + + c(0, 0, 0, .5, .5, 1/4, 5/4, 5/4, 0, 0, 0, + 0, 0, 0, 0, 0, 7/4, 19/4, 0, 5/4, 5/4, 5/4, + 0, 0, 0, 0, 0, 0, 0, 23/4, 23/4, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 23/4, 31/4), + ncol=4) > truth <- truth[c(1:6, 6:11),]/10 #the explicit censor at 22 > > #dimnames(truth) <- list(c(5, 6, 10, 15, 18, 20, 25, 30, 34, 40, 50), > # c('a', 'b', 'c', 'd') > all.equal(truth, fit$pstate[,1:4]) [1] TRUE > > # Test the dfbetas > # It was a big surprise, but the epsilon where a finite difference approx to > # the derivative is most accurate is around 1e-7 = approx sqrt(precision). > # Smaller eps makes the all.equal test worse. > # There is a now a formal test in mstate.R, not approximate. > dfbeta <- 0*fit$influence[,-1,] # lose the first row > eps <- sqrt(.Machine$double.eps) > for (i in 1:6) { + twt <- tdata$wt + twt[tdata$id ==i] <- twt[tdata$id==i] + eps + tfit <- survfit(Surv(time1, time2, stat2) ~ cluster(id), tdata, + weight=twt) + dfbeta[i,,] <- (tfit$pstate - fit$pstate)/eps #finite difference approx + } > all.equal(dfbeta, fit$influence[,-1,], tolerance= eps*10) [1] TRUE > twt <- tdata$wt[match(1:6, tdata$id)] # six unique weights > temp <- dfbeta > for (i in 1:6) temp[i,,] <- temp[i,,]* twt[i] > std2 <- sqrt(apply(temp^2, 2:3, sum)) > > all.equal(fit$std, std2, tolerance=eps, check.attributes=FALSE) [1] TRUE > > if (FALSE) { + # a plot of the data that helped during creation of the example + plot(c(0,50), c(1,6), type='n', xlab='time', ylab='subject') + with(tdata, segments(time1, id, time2, id)) + with(tdata, text(time2, id, as.numeric(stat2)-1, cex=1.5, col=2)) + } > > if (FALSE) { + # The following lines test out 4 error messages in the routine + # + # Gap in follow-up time, id 2 + survfit(Surv(c(0,5,9,0,5,0), c(5,9,12, 4, 6, 3), factor(c(0,0,1,1,0,2))) ~1, + id=c(1,1,1,2,2,3)) + # mismatched weights + survfit(Surv(c(0,5,9,0,5,0), c(5,9,12, 5, 6, 3), factor(c(0,0,1,1,0,2))) ~1, + id=c(1,1,1,2,2,3), weights=c(1,1,2,1,1,4)) + # in two groups at once + survfit(Surv(c(0,5,9,0,5,0), c(5,9,12, 5, 6, 3), factor(c(0,0,1,1,0,2))) ~ + c(1,1,2,1,1,2), id=c(1,1,1,2,2,3)) + # state change that isn't a state change (went from 1 to 1) + survfit(Surv(c(0,5,9,0,5,0), c(5,9,12, 5, 6, 3), factor(c(0,1,1,1,0,2))) ~1, + id=c(1,1,1,2,2,3)) + } > > > proc.time() user system elapsed 1.271 0.066 1.344 survival/tests/prednew.R0000644000175100001440000000503712113157116015077 0ustar hornikusers# # Make sure that the newdata argument works for various # predictions # We purposely use a subset of the lung data that has only some # of the levels of the ph.ecog library(survival) options(na.action=na.exclude, contrasts=c('contr.treatment', 'contr.poly')) aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) myfit <- coxph(Surv(time, status) ~ age + factor(ph.ecog) + strata(sex), lung) keep <- which(lung$inst<13 & (lung$ph.ecog==1 | lung$ph.ecog==2)) p1 <- predict(myfit, type='lp') p2 <- predict(myfit, type="lp", newdata=lung[keep,]) p3 <- predict(myfit, type='lp', se.fit=TRUE) p4 <- predict(myfit, type="lp", newdata=lung[keep,], se.fit=TRUE) aeq(p1[keep], p2) aeq(p1, p3$fit) aeq(p1[keep], p4$fit) aeq(p3$se.fit[keep], p4$se.fit) p1 <- predict(myfit, type='risk') p2 <- predict(myfit, type="risk", newdata=lung[keep,]) p3 <- predict(myfit, type='risk', se.fit=TRUE) p4 <- predict(myfit, type="risk", newdata=lung[keep,], se.fit=TRUE) aeq(p1[keep], p2) aeq(p1, p3$fit) aeq(p1[keep], p4$fit) aeq(p3$se.fit[keep], p4$se.fit) # The all.equal fails for type=expected, Efron approx, and tied death # times due to use of an approximation. See comments in the source code. myfit <- coxph(Surv(time, status) ~ age + factor(ph.ecog) + strata(sex), data=lung, method='breslow') p1 <- predict(myfit, type='expected') p2 <- predict(myfit, type="expected", newdata=lung[keep,]) p3 <- predict(myfit, type='expected', se.fit=TRUE) p4 <- predict(myfit, type="expected", newdata=lung[keep,], se.fit=TRUE) aeq(p1[keep], p2) aeq(p1, p3$fit) aeq(p1[keep], p4$fit) aeq(p3$se.fit[keep], p4$se.fit) p1 <- predict(myfit, type='terms') p2 <- predict(myfit, type="terms",newdata=lung[keep,]) p3 <- predict(myfit, type='terms', se.fit=T) p4 <- predict(myfit, type="terms",newdata=lung[keep,], se.fit=T) aeq(p1[keep,], p2) aeq(p1, p3$fit) aeq(p1[keep,], p4$fit) aeq(p3$se.fit[keep,], p4$se.fit) # # Check out the logic whereby predict does not need to # recover the model frame. The first call should not # need to do so, the second should in each case. # myfit <- coxph(Surv(time, status) ~ age + factor(sex), lung, x=T) p1 <- predict(myfit, type='risk', se=T) myfit2 <- coxph(Surv(time, status) ~ age + factor(sex), lung) p2 <- predict(myfit2, type='risk', se=T) aeq(p1$fit, p2$fit) aeq(p1$se, p2$se) p1 <- predict(myfit, type='expected', se=T) p2 <- predict(myfit2, type='expected', se=T) aeq(p1$fit, p2$fit) aeq(p1$se.fit, p2$se.fit) p1 <- predict(myfit, type='terms', se=T) p2 <- predict(myfit2, type='terms', se=T) aeq(p1$fit, p2$fit) aeq(p1$se.fit, p2$se.fit) survival/tests/survreg2.Rout.save0000644000175100001440000000642112334225345016702 0ustar hornikusers R Under development (unstable) (2014-05-11 r65563) -- "Unsuffered Consequences" Copyright (C) 2014 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > options(na.action=na.exclude, contrasts=c('contr.treatment', 'contr.poly')) > > # Verify stratified fits in a simple way, but combining two data > # sets and doing a single fit > # > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > tdata <- data.frame(time=c(lung$time, ovarian$futime), + status=c(lung$status-1, ovarian$fustat), + group =rep(0:1, c(nrow(lung), nrow(ovarian)))) > fit1 <- survreg(Surv(time, status) ~ 1, lung) > fit2 <- survreg(Surv(futime, fustat) ~ 1, ovarian) > fit3 <- survreg(Surv(time, status) ~ group + strata(group), tdata) > > aeq(c(fit1$coef, fit2$coef-fit1$coef), fit3$coef) [1] TRUE > aeq(c(fit1$scale, fit2$scale), fit3$scale) [1] TRUE > aeq(fit1$loglik[2] + fit2$loglik[2], fit3$loglik[2]) [1] TRUE > > # > # Test out the cluster term in survreg, which means first a test > # of the dfbeta residuals > # I also am checking that missing values propogate > test1 <- data.frame(time= c(9, 3,1,1,6,6,8), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0)) > fit1 <- survreg(Surv(time, status) ~ x + cluster(1:7), test1) > > db1 <- resid(fit1, 'dfbeta') > ijack <-db1 > eps <- 1e-7 > for (i in 1:7) { + temp <- rep(1.0,7) + temp[i] <- 1-eps + tfit <- survreg(Surv(time, status) ~ x, test1, weight=temp) + ijack[i,] <- c(tfit$coef, log(tfit$scale)) + } > ijack[2,] <- NA # stick the NA back in > ijack <- (rep(c(fit1$coef, log(fit1$scale)), each=nrow(db1)) - ijack)/eps > all.equal(db1, ijack, tolerance=eps) [1] TRUE > all.equal(t(db1[-2,])%*% db1[-2,], fit1$var) [1] TRUE > > # This is a harder test since there are multiple strata and multiple > # obs/subject. Use of enum + strata(enum) in essenence fits a different > # baseline Weibull to each strata, with common coefficients for rx, size, and > # number. > fit1 <- survreg(Surv(stop-start, event) ~ rx + size + number + + factor(enum) + strata(enum), data=bladder2) > > db1 <- resid(fit1, type='dfbeta', collapse=bladder2$id) > ijack <- db1 # a matrix of the same size > for (i in 1:nrow(db1)) { + twt <- rep(1., nrow(bladder2)) + twt[bladder2$id==i] <- 1-eps + tfit <- survreg(Surv(stop-start, event) ~ rx + size + number + + factor(enum) + strata(enum), data=bladder2, + weight=twt) + ijack[i,] <- c(coef(tfit), log(tfit$scale)) + } > ijack <- (rep(c(fit1$coef, log(fit1$scale)), each=nrow(db1)) - ijack)/eps > all.equal(db1, ijack, tolerance=eps*2) [1] TRUE > > > proc.time() user system elapsed 0.732 0.028 0.759 survival/tests/survfit2.Rout.save0000644000175100001440000000213011732700061016672 0ustar hornikusers R version 2.11.0 (2010-04-22) Copyright (C) 2010 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > # > # Check out the Dory&Korn confidence interval option > # > tdata <- data.frame(time= 1:10, + status=c(1,0,1,0,1,0,0,0,1,0)) > > fit1 <- survfit(Surv(time, status) ~1, tdata, conf.lower='modified') > fit2 <- survfit(Surv(time, status) ~1, tdata) > > stdlow <- fit2$std * sqrt(c(1, 10/9, 1, 8/7, 1, 6/5, 6/4, 6/3, 1, 2/1)) > lower <- exp(log(fit2$surv) - qnorm(.975)*stdlow) > all.equal(fit1$lower, lower, check.attributes=FALSE) [1] TRUE > survival/tests/fr_rat1.Rout.save0000644000175100001440000000734212536401430016457 0ustar hornikusers R Under development (unstable) (2015-06-04 r68474) -- "Unsuffered Consequences" Copyright (C) 2015 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # Tests using the rats data > # > # (Female rats, from Mantel et al, Cancer Research 37, > # 3863-3868, November 77) > > rfit <- coxph(Surv(time,status) ~ rx + frailty(litter), rats, + method='breslow', subset= (sex=='f')) > names(rfit) [1] "coefficients" "var" "var2" [4] "loglik" "iter" "linear.predictors" [7] "residuals" "means" "concordance" [10] "method" "frail" "fvar" [13] "df" "df2" "penalty" [16] "pterms" "assign2" "history" [19] "coxlist1" "printfun" "n" [22] "nevent" "terms" "assign" [25] "wald.test" "y" "formula" [28] "call" > rfit Call: coxph(formula = Surv(time, status) ~ rx + frailty(litter), data = rats, subset = (sex == "f"), method = "breslow") coef se(coef) se2 Chisq DF p rx 0.906 0.323 0.319 7.882 1.0 0.005 frailty(litter) 16.888 13.8 0.253 Iterations: 6 outer, 25 Newton-Raphson Variance of random effect= 0.474 I-likelihood = -181.1 Degrees of freedom for terms= 1.0 13.9 Likelihood ratio test=36.3 on 14.8 df, p=0.00144 n= 150 > > rfit$iter [1] 6 25 > rfit$df [1] 0.975943 13.854864 > rfit$history[[1]] $theta [1] 0.4742849 $done c.loglik TRUE $history theta loglik c.loglik [1,] 0.0000000 -181.8451 -181.8451 [2,] 1.0000000 -168.3683 -181.5458 [3,] 0.5000000 -173.3117 -181.0788 [4,] 0.3090061 -175.9446 -181.1490 [5,] 0.4645720 -173.7590 -181.0775 [6,] 0.4736210 -173.6431 -181.0773 $c.loglik [1] -181.0773 > > rfit1 <- coxph(Surv(time,status) ~ rx + frailty(litter, theta=1), rats, + method='breslow', subset=(sex=="f")) > rfit1 Call: coxph(formula = Surv(time, status) ~ rx + frailty(litter, theta = 1), data = rats, subset = (sex == "f"), method = "breslow") coef se(coef) se2 Chisq DF p rx 0.918 0.327 0.321 7.851 1.0 0.0051 frailty(litter, theta = 1 27.245 22.7 0.2324 Iterations: 1 outer, 6 Newton-Raphson Variance of random effect= 1 I-likelihood = -181.5 Degrees of freedom for terms= 1.0 22.7 Likelihood ratio test=50.7 on 23.7 df, p=0.001 n= 150 > > rfit2 <- coxph(Surv(time,status) ~ frailty(litter), rats, subset=(sex=='f')) > rfit2 Call: coxph(formula = Surv(time, status) ~ frailty(litter), data = rats, subset = (sex == "f")) coef se(coef) se2 Chisq DF p frailty(litter) 18 14.6 0.24 Iterations: 6 outer, 22 Newton-Raphson Variance of random effect= 0.504 I-likelihood = -184.8 Degrees of freedom for terms= 14.6 Likelihood ratio test=30 on 14.6 df, p=0.0101 n= 150 > > proc.time() user system elapsed 0.216 0.028 0.237 survival/tests/survreg2.R0000644000175100001440000000455012271462471015221 0ustar hornikuserslibrary(survival) options(na.action=na.exclude, contrasts=c('contr.treatment', 'contr.poly')) # Verify stratified fits in a simple way, but combining two data # sets and doing a single fit # aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) tdata <- data.frame(time=c(lung$time, ovarian$futime), status=c(lung$status-1, ovarian$fustat), group =rep(0:1, c(nrow(lung), nrow(ovarian)))) fit1 <- survreg(Surv(time, status) ~ 1, lung) fit2 <- survreg(Surv(futime, fustat) ~ 1, ovarian) fit3 <- survreg(Surv(time, status) ~ group + strata(group), tdata) aeq(c(fit1$coef, fit2$coef-fit1$coef), fit3$coef) aeq(c(fit1$scale, fit2$scale), fit3$scale) aeq(fit1$loglik[2] + fit2$loglik[2], fit3$loglik[2]) # # Test out the cluster term in survreg, which means first a test # of the dfbeta residuals # I also am checking that missing values propogate test1 <- data.frame(time= c(9, 3,1,1,6,6,8), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0)) fit1 <- survreg(Surv(time, status) ~ x + cluster(1:7), test1) db1 <- resid(fit1, 'dfbeta') ijack <-db1 eps <- 1e-7 for (i in 1:7) { temp <- rep(1.0,7) temp[i] <- 1-eps tfit <- survreg(Surv(time, status) ~ x, test1, weight=temp) ijack[i,] <- c(tfit$coef, log(tfit$scale)) } ijack[2,] <- NA # stick the NA back in ijack <- (rep(c(fit1$coef, log(fit1$scale)), each=nrow(db1)) - ijack)/eps all.equal(db1, ijack, tolerance=eps) all.equal(t(db1[-2,])%*% db1[-2,], fit1$var) # This is a harder test since there are multiple strata and multiple # obs/subject. Use of enum + strata(enum) in essenence fits a different # baseline Weibull to each strata, with common coefficients for rx, size, and # number. fit1 <- survreg(Surv(stop-start, event) ~ rx + size + number + factor(enum) + strata(enum), data=bladder2) db1 <- resid(fit1, type='dfbeta', collapse=bladder2$id) ijack <- db1 # a matrix of the same size for (i in 1:nrow(db1)) { twt <- rep(1., nrow(bladder2)) twt[bladder2$id==i] <- 1-eps tfit <- survreg(Surv(stop-start, event) ~ rx + size + number + factor(enum) + strata(enum), data=bladder2, weight=twt) ijack[i,] <- c(coef(tfit), log(tfit$scale)) } ijack <- (rep(c(fit1$coef, log(fit1$scale)), each=nrow(db1)) - ijack)/eps all.equal(db1, ijack, tolerance=eps*2) survival/tests/book3.R0000644000175100001440000001200412701744412014444 0ustar hornikuserslibrary(survival) options(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type # # Tests from the appendix of Therneau and Grambsch # c. Data set 2 and Breslow estimate # test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) fit0 <-coxph(Surv(start, stop, event) ~x, test2, iter=0, method='breslow') byhand <- function(beta, newx=0) { r <- exp(beta) loglik <- 4*beta - log(r+1) - log(r+2) - 3*log(3*r+2) - 2*log(3*r+1) u <- 1/(r+1) + 1/(3*r+1) + 4/(3*r+2) - ( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1)) imat <- r/(r+1)^2 + 2*r/(r+2)^2 + 6*r/(3*r+2)^2 + 3*r/(3*r+1)^2 + 3*r/(3*r+1)^2 + 12*r/(3*r+2)^2 hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), 2/(3*r+2) ) xbar <- c(r/(r+1), r/(r+2), 3*r/(3*r+2), 3*r/(3*r+1), 3*r/(3*r+1), 3*r/(3*r+2)) # The matrix of weights, one row per obs, one col per time # deaths at 2,3,6,7,8,9 wtmat <- matrix(c(1,0,0,0,1,0,0,0,0,0, 0,1,0,1,1,0,0,0,0,0, 0,0,1,1,1,0,1,1,0,0, 0,0,0,1,1,0,1,1,0,0, 0,0,0,0,1,1,1,1,0,0, 0,0,0,0,0,1,1,1,1,1), ncol=6) wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat x <- c(1,0,0,1,0,1,1,1,0,0) status <- c(1,1,1,1,1,1,1,0,0,0) xbar <- colSums(wtmat*x)/ colSums(wtmat) n <- length(x) # Table of sums for score and Schoenfeld resids hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time dM <- -hazmat #Expected part for (i in 1:6) dM[i,i] <- dM[i,i] +1 #observed dM[7,6] <- dM[7,6] +1 # observed mart <- rowSums(dM) # Table of sums for score and Schoenfeld resids # Looks like the last table of appendix E.2.1 of the book resid <- dM * outer(x, xbar, '-') score <- rowSums(resid) scho <- colSums(resid) # We need to split the two tied times up, to match coxph scho <- c(scho[1:5], scho[6]/2, scho[6]/2) var.g <- cumsum(hazard*hazard /c(1,1,1,1,1,2)) var.d <- cumsum( (xbar-newx)*hazard) surv <- exp(-cumsum(hazard) * exp(beta*newx)) varhaz <- (var.g + var.d^2/imat)* exp(2*beta*newx) list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard, mart=mart, score=score, rmat=resid, scho=scho, surv=surv, var=varhaz) } aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) fit0 <-coxph(Surv(start, stop, event) ~x, test2, iter=0, method='breslow') truth0 <- byhand(0,0) aeq(truth0$loglik, fit0$loglik[1]) aeq(1/truth0$imat, fit0$var) aeq(truth0$mart, fit0$resid) aeq(truth0$scho, resid(fit0, 'schoen')) aeq(truth0$score, resid(fit0, 'score')) sfit <- survfit(fit0, list(x=0), censor=FALSE) aeq(sfit$std.err^2, truth0$var) aeq(sfit$surv, truth0$surv) beta1 <- truth0$u/truth0$imat fit1 <- coxph(Surv(start, stop, event) ~x, test2, iter=1, ties="breslow") aeq(beta1, coef(fit1)) truth <- byhand(-0.084526081, 0) fit <- coxph(Surv(start, stop, event) ~x, test2, eps=1e-8, method='breslow') aeq(truth$loglik, fit$loglik[2]) aeq(1/truth$imat, fit$var) aeq(truth$mart, fit$resid) aeq(truth$scho, resid(fit, 'schoen')) aeq(truth$score, resid(fit, 'score')) expect <- predict(fit, type='expected', newdata=test2) #force recalc aeq(test2$event -fit$resid, expect) #tests the predict function sfit <- survfit(fit, list(x=0), censor=FALSE) aeq(sfit$std.err^2, truth$var) aeq(-log(sfit$surv), (cumsum(truth$haz))) # Reprise the test, with strata # offseting the times ensures that we will get the wrong risk sets # if strata were not kept separate test2b <- rbind(test2, test2, test2) test2b$group <- rep(1:3, each= nrow(test2)) test2b$start <- test2b$start + test2b$group test2b$stop <- test2b$stop + test2b$group fit0 <- coxph(Surv(start, stop, event) ~ x + strata(group), test2b, iter=0, method="breslow") aeq(3*truth0$loglik, fit0$loglik[1]) aeq(3*truth0$imat, 1/fit0$var) aeq(rep(truth0$mart,3), fit0$resid) aeq(rep(truth0$scho,3), resid(fit0, 'schoen')) aeq(rep(truth0$score,3), resid(fit0, 'score')) fit1 <- coxph(Surv(start, stop, event) ~ x + strata(group), test2b, iter=1, method="breslow") aeq(fit1$coef, beta1) fit3 <- coxph(Surv(start, stop, event) ~x + strata(group), test2b, eps=1e-8, method='breslow') aeq(3*truth$loglik, fit3$loglik[2]) aeq(3*truth$imat, 1/fit3$var) aeq(rep(truth$mart,3), fit3$resid) aeq(rep(truth$scho,3), resid(fit3, 'schoen')) aeq(rep(truth$score,3), resid(fit3, 'score')) # # Done with the formal test, now print out lots of bits # resid(fit) resid(fit, 'scor') resid(fit, 'scho') predict(fit, type='lp') predict(fit, type='risk') predict(fit, type='expected') predict(fit, type='terms') predict(fit, type='lp', se.fit=T) predict(fit, type='risk', se.fit=T) predict(fit, type='expected', se.fit=T) predict(fit, type='terms', se.fit=T) summary(survfit(fit)) summary(survfit(fit, list(x=2))) survival/tests/book1.Rout.save0000644000175100001440000001621512350326212016131 0ustar hornikusers R Under development (unstable) (2014-05-11 r65563) -- "Unsuffered Consequences" Copyright (C) 2014 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > > # > # Tests from the appendix of Therneau and Grambsch > # a. Data set 1 and Breslow estimate > # The data below is not in time order, to also test sorting, and has 1 NA > # > test1 <- data.frame(time= c(9, 3,1,1,6,6,8), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0)) > > # Breslow estimate > byhand1 <- function(beta, newx=0) { + r <- exp(beta) + loglik <- 2*beta - (log(3*r+3) + 2*log(r+3)) + u <- (6 + 3*r - r^2) / ((r+1)*(r+3)) + imat <- r/(r+1)^2 + 6*r/(r+3)^2 + + x <- c(1,1,1,0,0,0) + status <- c(1,0,1,1,0,1) + xbar <- c(r/(r+1), r/(r+3), 0, 0) # at times 1, 6, 8 and 9 + haz <- c(1/(3*r+3), 2/(r+3), 0, 1 ) + ties <- c(1,1,2,2,3,4) + wt <- c(r,r,r,1,1,1) + mart <- c(1,0,1,1,0,1) - wt* (cumsum(haz))[ties] #martingale residual + + a <- 3*(r+1)^2; b<- (r+3)^2 + score <- c((2*r+3)/a, -r/a, -r/a + 3*(3-r)/b, r/a - r*(r+1)/b, + r/a + 2*r/b, r/a + 2*r/b) + + # Schoenfeld residual + scho <- c(1/(r+1), 1- (r/(3+r)), 0-(r/(3+r)) , 0) + + surv <- exp(-cumsum(haz)* exp(beta*newx)) + varhaz.g <- cumsum(c(1/(3*r+3)^2, 2/(r+3)^2, 0, 1 )) + + varhaz.d <- cumsum((newx-xbar) * haz) + + varhaz <- (varhaz.g + varhaz.d^2/ imat) * exp(2*beta*newx) + + names(xbar) <- names(haz) <- 1:4 + names(surv) <- names(varhaz) <- 1:4 + list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=haz, + mart=mart, score=score, + scho=scho, surv=surv, var=varhaz, + varhaz.g=varhaz.g, varhaz.d=varhaz.d) + } > > > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > fit0 <-coxph(Surv(time, status) ~x, test1, iter=0, method='breslow') > truth0 <- byhand1(0,0) > aeq(truth0$loglik, fit0$loglik[1]) [1] TRUE > aeq(1/truth0$imat, fit0$var) [1] TRUE > aeq(truth0$mart, fit0$resid[c(2:6,1)]) [1] TRUE > aeq(truth0$scho, resid(fit0, 'schoen')) [1] TRUE > aeq(truth0$score, resid(fit0, 'score')[c(3:7,1)]) [1] TRUE > sfit <- survfit(fit0, list(x=0)) > aeq(sfit$std.err^2, c(7/180, 2/9, 2/9, 11/9)) [1] TRUE > aeq(resid(fit0, 'score'), c(5/24, NA, 5/12, -1/12, 7/24, -1/24, 5/24)) [1] TRUE > > fit1 <- coxph(Surv(time, status) ~x, test1, iter=1, method='breslow') > aeq(fit1$coef, 8/5) [1] TRUE > > # This next gives an ignorable warning message > fit2 <- coxph(Surv(time, status) ~x, test1, method='breslow', iter=2) Warning message: In fitter(X, Y, strats, offset, init, control, weights = weights, : Ran out of iterations and did not converge > aeq(round(fit2$coef, 6), 1.472724) [1] TRUE > > fit <- coxph(Surv(time, status) ~x, test1, method='breslow', eps=1e-8) > aeq(round(fit$coef,7), 1.4752849) [1] TRUE > truth <- byhand1(fit$coef, 0) > aeq(truth$loglik, fit$loglik[2]) [1] TRUE > aeq(1/truth$imat, fit$var) [1] TRUE > aeq(truth$mart, fit$resid[c(2:6,1)]) [1] TRUE > aeq(truth$scho, resid(fit, 'schoen')) [1] TRUE > aeq(truth$score, resid(fit, 'score')[c(3:7,1)]) [1] TRUE > expect <- predict(fit, type='expected', newdata=test1) #force recalc > aeq(test1$status[-2] -fit$resid, expect[-2]) #tests the predict function [1] TRUE > > sfit <- survfit(fit, list(x=0), censor=FALSE) > aeq(sfit$std.err^2, truth$var[c(1,2,4)]) # sfit skips time 8 (no events there) [1] TRUE > aeq(-log(sfit$surv), (cumsum(truth$haz))[c(1,2,4)]) [1] TRUE > sfit <- survfit(fit, list(x=0), censor=TRUE) > aeq(sfit$std.err^2, truth$var) [1] TRUE > aeq(-log(sfit$surv), (cumsum(truth$haz))) [1] TRUE > > > # > # Done with the formal test, now print out lots of bits > # > resid(fit) 1 2 3 4 5 6 7 -0.3333333 NA 0.7287136 -0.2712864 -0.4574271 0.6666667 -0.3333333 > resid(fit, 'scor') 1 2 3 4 5 6 0.21138938 NA 0.13564322 -0.05049744 -0.12624360 -0.38168095 7 0.21138938 > resid(fit, 'scho') 1 6 6 9 0.1861407 0.4069297 -0.5930703 0.0000000 > > predict(fit, type='lp') [1] -0.7376425 NA 0.7376425 0.7376425 0.7376425 -0.7376425 -0.7376425 > predict(fit, type='risk') [1] 0.4782401 NA 2.0910001 2.0910001 2.0910001 0.4782401 0.4782401 > predict(fit, type='expected') 1 2 3 4 5 6 7 1.3333333 NA 0.2712864 0.2712864 1.4574271 0.3333333 0.3333333 > predict(fit, type='terms') x 1 -0.7376425 2 NA 3 0.7376425 4 0.7376425 5 0.7376425 6 -0.7376425 7 -0.7376425 > predict(fit, type='lp', se.fit=T) $fit 1 2 3 4 5 6 7 -0.7376425 NA 0.7376425 0.7376425 0.7376425 -0.7376425 -0.7376425 $se.fit 1 2 3 4 5 6 7 0.6278672 NA 0.6278672 0.6278672 0.6278672 0.6278672 0.6278672 > predict(fit, type='risk', se.fit=T) $fit 1 2 3 4 5 6 7 0.4782401 NA 2.0910001 2.0910001 2.0910001 0.4782401 0.4782401 $se.fit 1 2 3 4 5 6 7 0.4342009 NA 0.9079142 0.9079142 0.9079142 0.4342009 0.4342009 > predict(fit, type='expected', se.fit=T) $fit 1 2 3 4 5 6 7 1.3333333 NA 0.2712864 0.2712864 1.4574271 0.3333333 0.3333333 $se.fit [1] 1.0540926 NA 0.2785989 0.2785989 1.1069433 0.3333333 0.3333333 > predict(fit, type='terms', se.fit=T) $fit x 1 -0.7376425 2 NA 3 0.7376425 4 0.7376425 5 0.7376425 6 -0.7376425 7 -0.7376425 $se.fit x 1 0.6278672 2 NA 3 0.6278672 4 0.6278672 5 0.6278672 6 0.6278672 7 0.6278672 > > summary(survfit(fit)) Call: survfit(formula = fit) time n.risk n.event survival std.err lower 95% CI upper 95% CI 1 6 1 0.8783 0.122 0.66827 1 6 4 2 0.4981 0.218 0.21125 1 9 1 1 0.0615 0.150 0.00051 1 > summary(survfit(fit, list(x=2))) Call: survfit(formula = fit, newdata = list(x = 2)) time n.risk n.event survival std.err lower 95% CI upper 95% CI 1 6 1 3.05e-01 6.50e-01 4.72e-03 1 6 4 2 1.71e-03 1.98e-02 2.33e-13 1 9 1 1 8.52e-12 5.29e-10 1.22e-64 1 > > proc.time() user system elapsed 0.240 0.028 0.265 survival/tests/nested.R0000644000175100001440000000065012052731313014710 0ustar hornikuserslibrary(survival) # # A test of nesting. It makes sure the model.frame is built correctly # tfun <- function(fit, mydata) { survfit(fit, newdata=mydata) } myfit <- coxph(Surv(time, status) ~ age + factor(sex), lung) temp1 <- tfun(myfit, lung[1:5,]) temp2 <- survfit(myfit, lung[1:5,]) indx <- match('call', names(temp1)) #the call components won't match all.equal(unclass(temp1)[-indx], unclass(temp2)[-indx]) survival/tests/book1.R0000644000175100001440000000673312350317501014451 0ustar hornikuserslibrary(survival) options(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type # # Tests from the appendix of Therneau and Grambsch # a. Data set 1 and Breslow estimate # The data below is not in time order, to also test sorting, and has 1 NA # test1 <- data.frame(time= c(9, 3,1,1,6,6,8), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0)) # Breslow estimate byhand1 <- function(beta, newx=0) { r <- exp(beta) loglik <- 2*beta - (log(3*r+3) + 2*log(r+3)) u <- (6 + 3*r - r^2) / ((r+1)*(r+3)) imat <- r/(r+1)^2 + 6*r/(r+3)^2 x <- c(1,1,1,0,0,0) status <- c(1,0,1,1,0,1) xbar <- c(r/(r+1), r/(r+3), 0, 0) # at times 1, 6, 8 and 9 haz <- c(1/(3*r+3), 2/(r+3), 0, 1 ) ties <- c(1,1,2,2,3,4) wt <- c(r,r,r,1,1,1) mart <- c(1,0,1,1,0,1) - wt* (cumsum(haz))[ties] #martingale residual a <- 3*(r+1)^2; b<- (r+3)^2 score <- c((2*r+3)/a, -r/a, -r/a + 3*(3-r)/b, r/a - r*(r+1)/b, r/a + 2*r/b, r/a + 2*r/b) # Schoenfeld residual scho <- c(1/(r+1), 1- (r/(3+r)), 0-(r/(3+r)) , 0) surv <- exp(-cumsum(haz)* exp(beta*newx)) varhaz.g <- cumsum(c(1/(3*r+3)^2, 2/(r+3)^2, 0, 1 )) varhaz.d <- cumsum((newx-xbar) * haz) varhaz <- (varhaz.g + varhaz.d^2/ imat) * exp(2*beta*newx) names(xbar) <- names(haz) <- 1:4 names(surv) <- names(varhaz) <- 1:4 list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=haz, mart=mart, score=score, scho=scho, surv=surv, var=varhaz, varhaz.g=varhaz.g, varhaz.d=varhaz.d) } aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) fit0 <-coxph(Surv(time, status) ~x, test1, iter=0, method='breslow') truth0 <- byhand1(0,0) aeq(truth0$loglik, fit0$loglik[1]) aeq(1/truth0$imat, fit0$var) aeq(truth0$mart, fit0$resid[c(2:6,1)]) aeq(truth0$scho, resid(fit0, 'schoen')) aeq(truth0$score, resid(fit0, 'score')[c(3:7,1)]) sfit <- survfit(fit0, list(x=0)) aeq(sfit$std.err^2, c(7/180, 2/9, 2/9, 11/9)) aeq(resid(fit0, 'score'), c(5/24, NA, 5/12, -1/12, 7/24, -1/24, 5/24)) fit1 <- coxph(Surv(time, status) ~x, test1, iter=1, method='breslow') aeq(fit1$coef, 8/5) # This next gives an ignorable warning message fit2 <- coxph(Surv(time, status) ~x, test1, method='breslow', iter=2) aeq(round(fit2$coef, 6), 1.472724) fit <- coxph(Surv(time, status) ~x, test1, method='breslow', eps=1e-8) aeq(round(fit$coef,7), 1.4752849) truth <- byhand1(fit$coef, 0) aeq(truth$loglik, fit$loglik[2]) aeq(1/truth$imat, fit$var) aeq(truth$mart, fit$resid[c(2:6,1)]) aeq(truth$scho, resid(fit, 'schoen')) aeq(truth$score, resid(fit, 'score')[c(3:7,1)]) expect <- predict(fit, type='expected', newdata=test1) #force recalc aeq(test1$status[-2] -fit$resid, expect[-2]) #tests the predict function sfit <- survfit(fit, list(x=0), censor=FALSE) aeq(sfit$std.err^2, truth$var[c(1,2,4)]) # sfit skips time 8 (no events there) aeq(-log(sfit$surv), (cumsum(truth$haz))[c(1,2,4)]) sfit <- survfit(fit, list(x=0), censor=TRUE) aeq(sfit$std.err^2, truth$var) aeq(-log(sfit$surv), (cumsum(truth$haz))) # # Done with the formal test, now print out lots of bits # resid(fit) resid(fit, 'scor') resid(fit, 'scho') predict(fit, type='lp') predict(fit, type='risk') predict(fit, type='expected') predict(fit, type='terms') predict(fit, type='lp', se.fit=T) predict(fit, type='risk', se.fit=T) predict(fit, type='expected', se.fit=T) predict(fit, type='terms', se.fit=T) summary(survfit(fit)) summary(survfit(fit, list(x=2))) survival/tests/fr_kidney.R0000644000175100001440000000454011732700061015402 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # From: McGilchrist and Aisbett, Biometrics 47, 461-66, 1991 # Data on the recurrence times to infection, at the point of insertion of # the catheter, for kidney patients using portable dialysis equipment. # Catheters may be removed for reasons other than infection, in which case # the observation is censored. Each patient has exactly 2 observations. # Variables: patient, time, status, age, # sex (1=male, 2=female), # disease type (0=GN, 1=AN, 2=PKD, 3=Other) # author's estimate of the frailty aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) # I don't match their answers, and I think that I'm right kfit <- coxph(Surv(time, status)~ age + sex + disease + frailty(id), kidney) kfit1<- coxph(Surv(time, status) ~age + sex + disease + frailty(id, theta=1), kidney, iter=20) kfit0 <- coxph(Surv(time, status)~ age + sex + disease, kidney) temp <- coxph(Surv(time, status) ~age + sex + disease + frailty(id, theta=1, sparse=F), kidney) # Check out the EM based score equations # temp1 and kfit1 should have essentially the same coefficients # temp2 should equal kfit1$frail # equality won't be exact because of the different iteration paths temp1 <- coxph(Surv(time, status) ~ age + sex + disease + offset(kfit1$frail[id]), kidney) rr <- tapply(resid(temp1), kidney$id, sum) temp2 <- log(rr/1 +1) aeq(temp1$coef, kfit1$coef, tolerance=.005) aeq(temp2, kfit1$frail, tolerance=.005) kfit kfit1 kfit0 temp # # Now fit the data using REML # kfitm1 <- coxph(Surv(time,status) ~ age + sex + disease + frailty(id, dist='gauss'), kidney) kfitm2 <- coxph(Surv(time,status) ~ age + sex + disease + frailty(id, dist='gauss', sparse=F), kidney) kfitm1 summary(kfitm2) # # Fit the kidney data using AIC # # gamma, corrected aic coxph(Surv(time, status) ~ age + sex + frailty(id, method='aic', caic=T), kidney) coxph(Surv(time, status) ~ age + sex + frailty(id, dist='t'), kidney) coxph(Surv(time, status) ~ age + sex + frailty(id, dist='gauss', method='aic', caic=T), kidney) # uncorrected aic coxph(Surv(time, status) ~ age + sex + frailty(id, method='aic', caic=F), kidney) coxph(Surv(time, status) ~ age + sex + frailty(id, dist='t', caic=F), kidney) survival/tests/r_sas.R0000644000175100001440000002313513055116445014547 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Reproduce example 1 in the SAS lifereg documentation # # this fit doesn't give the same log-lik that they claim motor <- read.table('data.motor', col.names=c('temp', 'time', 'status')) fit1 <- survreg(Surv(time, status) ~ I(1000/(273.2+temp)), motor, subset=(temp>150), dist='lognormal') summary(fit1) # This one, with the loglik on the transformed scale (the inappropriate # scale, Ripley & Venables would argue) does agree. # All coefs are of course identical. fit2 <- survreg(Surv(log(time), status) ~ I(1000/(273.2+temp)), motor, subset=(temp>150), dist='gaussian') # Give the quantile estimates, which is the lower half of "output 48.1.5" # in the SAS 9.2 manual pp1 <- predict(fit1, newdata=list(temp=c(130,150)), p=c(.1, .5, .9), type='quantile', se=T) pp2 <- predict(fit1, newdata=list(temp=c(130,150)), p=c(.1, .5, .9), type='uquantile', se=T) pp1 temp130 <- matrix(0, nrow=3, ncol=6) temp130[,1] <- pp1$fit[1,] temp130[,2] <- pp1$se.fit[1,] temp130[,3] <- pp2$fit[1,] temp130[,4] <- pp2$se.fit[1,] temp130[,5] <- exp(pp2$fit[1,] - 1.64*pp2$se.fit[1,]) temp130[,6] <- exp(pp2$fit[1,] + 1.64*pp2$se.fit[1,]) dimnames(temp130) <- list(c("p=.1", "p=.2", "p=.3"), c("Time", "se(time)", "log(time)", "se[log(time)]", "lower 90", "upper 90")) print(temp130) # A set of examples, copied from the manual pages of SAS procedure # "reliability", which is part of their QC product. # color <- c("black", "red", "green", "blue", "magenta", "red4", "orange", "DarkGreen", "cyan2", "DarkViolet") palette(color) pdf(file='reliability.pdf') # # Insulating fluids example # fluid <- read.table('data.fluid', col.names=c('time', 'voltage')) # Adding a -1 to the fit just causes the each group to have it's own # intercept, rather than a global intercept + constrasts. The strata # statement allows each to have a separate scale ffit <- survreg(Surv(time) ~ voltage + strata(voltage) -1, fluid) # Get predicted quantiles at each of the voltages # By default predict() would give a line of results for each observation, # I only want the unique set of x's, i.e., only 4 cases uvolt <- sort(unique(fluid$voltage)) #the unique levels plist <- c(1, 2, 5, 1:9 *10, 95, 99)/100 pred <- predict(ffit, type='quantile', p=plist, newdata=data.frame(voltage=factor(uvolt))) tfun <- function(x) log(-log(1-x)) matplot(t(pred), tfun(plist), type='l', log='x', lty=1, col=1:4, yaxt='n') axis(2, tfun(plist), format(100*plist), adj=1) kfit <- survfit(Surv(time) ~ voltage, fluid, type='fleming') #KM fit for (i in 1:4) { temp <- kfit[i] points(temp$time, tfun(1-temp$surv), col=i, pch=i) } # Now a table temp <- array(0, dim=c(4,4,4)) #4 groups by 4 parameters by 4 stats temp[,1,1] <- ffit$coef # "EV Location" in SAS manual temp[,2,1] <- ffit$scale # "EV scale" temp[,3,1] <- exp(ffit$coef) # "Weibull Scale" temp[,4,1] <- 1/ffit$scale # "Weibull Shape" temp[,1,2] <- sqrt(diag(ffit$var))[1:4] #standard error temp[,2,2] <- sqrt(diag(ffit$var))[5:8] * ffit$scale temp[,3,2] <- temp[,1,2] * temp[,3,1] temp[,4,2] <- temp[,2,2] / (temp[,2,1])^2 temp[,1,3] <- temp[,1,1] - 1.96*temp[,1,2] #lower conf limits temp[,1,4] <- temp[,1,1] + 1.96*temp[,1,2] # upper # log(scale) is the natural parameter, in which the routine did its fitting # and on which the std errors were computed temp[,2, 3] <- exp(log(ffit$scale) - 1.96*sqrt(diag(ffit$var))[5:8]) temp[,2, 4] <- exp(log(ffit$scale) + 1.96*sqrt(diag(ffit$var))[5:8]) temp[,3, 3:4] <- exp(temp[,1,3:4]) temp[,4, 3:4] <- 1/temp[,2,4:3] dimnames(temp) <- list(uvolt, c("EV Location", "EV Scale", "Weibull scale", "Weibull shape"), c("Estimate", "SE", "lower 95% CI", "uppper 95% CI")) print(aperm(temp, c(2,3,1)), digits=5) rm(temp, uvolt, plist, pred, ffit, kfit) ##################################################################### # Turbine cracks data cracks <- read.table('data.cracks', col.names=c('time1', 'time2', 'n')) cfit <- survreg(Surv(time1, time2, type='interval2') ~1, dist='weibull', data=cracks, weight=n) summary(cfit) #Their output also has Wiebull scale = exp(cfit$coef), shape = 1/(cfit$scale) # Draw the SAS plot # The "type=fleming" argument reflects that they estimate hazards rather than # survival, and forces a Nelson-Aalen hazard estimate # plist <- c(1, 2, 5, 1:8 *10)/100 plot(qsurvreg(plist, cfit$coef, cfit$scale), tfun(plist), log='x', yaxt='n', type='l', xlab="Weibull Plot for Time", ylab="Percent") axis(2, tfun(plist), format(100*plist), adj=1) kfit <- survfit(Surv(time1, time2, type='interval2') ~1, data=cracks, weight=n, type='fleming') # Only plot point where n.event > 0 # Why? I'm trying to match them. Personally, all should be plotted. who <- (kfit$n.event > 0) points(kfit$time[who], tfun(1-kfit$surv[who]), pch='+') points(kfit$time[who], tfun(1-kfit$upper[who]), pch='-') points(kfit$time[who], tfun(1-kfit$lower[who]), pch='-') text(rep(3,6), seq(.5, -1.0, length=6), c("Scale", "Shape", "Right Censored", "Left Censored", "Interval Censored", "Fit"), adj=0) text(rep(9,6), seq(.5, -1.0, length=6), c(format(round(exp(cfit$coef), 2)), format(round(1/cfit$scale, 2)), format(tapply(cracks$n, cfit$y[,3], sum)), "ML"), adj=1) # Now a portion of his percentiles table # I don't get the same SE as SAS, I haven't checked out why. The # estimates and se for the underlying Weibull model are the same. temp <- predict(cfit, type='quantile', p=plist, se=T) tempse <- sqrt(temp$se[1,]) mat <- cbind(temp$fit[1,], tempse, temp$fit[1,] -1.96*tempse, temp$fit[1,] + 1.96*tempse) dimnames(mat) <- list(plist*100, c("Estimate", "SE", "Lower .95", "Upper .95")) print(mat) # # The cracks data has a particularly easy estimate, so use # it to double check code time <- c(cracks$time2[1], (cracks$time1 + cracks$time2)[2:8]/2, cracks$time1[9]) cdf <- cumsum(cracks$n)/sum(cracks$n) all.equal(kfit$time, time) all.equal(kfit$surv, 1-cdf[c(1:8,8)]) rm(time, cdf, kfit) ####################################################### # # Valve data # The input data has id, time, and an indicator of whether there was an # event at that time: -1=no, 1=yes. No one has an event at their last time. # Convert the data to (start, stop] form # The input data has two engines with dual failures: 328 loses 2 valves at # time 653, and number 402 loses 2 at time 139. For each, fudge the first # time to be .1 days earlier. # temp <- matrix(scan('data.valve'), byrow=T, ncol=3) n <- nrow(temp) valve <- data.frame(id=temp[,1], time1 = c(0, ifelse(diff(temp[,1])==0, temp[-n,2],0)), time2 = temp[,2], status= as.numeric(temp[,3]==1)) indx <- (1:nrow(valve))[valve$time1==valve$time2] valve$time1[indx] <- valve$time1[indx] - .1 valve$time2[indx-1] <- valve$time2[indx-1] - .1 kfit <- survfit(Surv(time1, time2, status) ~1, valve, type='fh2') plot(kfit, fun='cumhaz', ylab="Sample Mean Cumulative Failures", xlab='Time', ylim=range(-log(kfit$lower))) title("Valve replacement data") # The summary.survfit function doesn't have an option for printing out # cumulative hazards instead of survival --- need to add that # so I just reprise the central code of print.summary.survfit xx <- summary(kfit) temp <- cbind(xx$time, xx$n.risk, xx$n.event, -log(xx$surv), xx$std.err/xx$surv, -log(xx$upper), -log(xx$lower)) dimnames(temp) <- list(rep("", nrow(temp)), c("time", "n.risk", "n.event", "Cum haz", "std.err", "lower 95%", "upper 95%")) print(temp, digits=2) # Note that I have the same estimates but different SE's. We are using a # different estimator. It's a statistical argument as to which is # better (one could defend both sides): do you favor JASA or Technometrics? rm(temp, kfit, indx, xx) ###################################################### # Turbine data, lognormal fit turbine <- read.table('data.turbine', col.names=c("time1", "time2", "n")) tfit <- survreg(Surv(time1, time2, type='interval2') ~1, turbine, dist='lognormal', weights=n, subset=(n>0)) summary(tfit) # Now, do his plot, but put bootstrap confidence bands on it! # First, make a simple data set without weights tdata <- turbine[rep(1:nrow(turbine), turbine$n),] qstat <- function(data) { temp <- survreg(Surv(time1, time2, type='interval2') ~1, data=data, dist='lognormal') qsurvreg(plist, temp$coef, temp$scale, dist='lognormal') } {if (exists('bootstrap')) { set.seed(1953) # a good year :-) bfit <- bootstrap(tdata, qstat, B=1000) bci <- limits.bca(bfit, probs=c(.025, .975)) } else { values <- matrix(0, nrow=1000, ncol=length(plist)) n <- nrow(tdata) for (i in 1:1000) { subset <- sample(1:n, n, replace=T) values[i,] <- qstat(tdata[subset,]) } bci <- t(apply(values,2, quantile, c(.05, .95))) } } xmat <- cbind(qsurvreg(plist, tfit$coef, tfit$scale, dist='lognormal'), bci) matplot(xmat, qnorm(plist), type='l', lty=c(1,2,2), col=c(1,1,1), log='x', yaxt='n', ylab='Percent', xlab='Time of Cracking (Hours x 100)') axis(2, qnorm(plist), format(100*plist), adj=1) title("Turbine Data") kfit <- survfit(Surv(time1, time2, type='interval2') ~1, data=tdata) points(kfit$time, qnorm(1-kfit$surv), pch='+') dev.off() #close the plot file survival/tests/fr_ovarian.R0000644000175100001440000000065711732700061015563 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Test on the ovarian data fit1 <- coxph(Surv(futime, fustat) ~ rx + age, ovarian) fit2 <- coxph(Surv(futime, fustat) ~ rx + pspline(age, df=2), data=ovarian) fit2$iter fit2$df fit2$history fit4 <- coxph(Surv(futime, fustat) ~ rx + pspline(age, df=4), data=ovarian) fit4 survival/tests/survtest.R0000644000175100001440000000435311732700061015331 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Simple test of (start, stop] Kaplan-Meier curves, using the test2 data # set # test1 <- data.frame(time= c(9, 3,1,1,6,6,8), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0)) test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) fit1 <- survfit(Surv(start, stop, event) ~1, test2, type='fh2', error='tsiatis') fit2 <- survfit(Surv(start, stop, event) ~x, test2, start.time=3, type='fh2') cfit1<- survfit(coxph(Surv(start, stop, event)~1, test2)) cfit2<- survfit(coxph(Surv(start, stop, event) ~ strata(x), test2, subset=-1)) deaths <- (fit1$n.event + fit1$n.censor)>0 aeq(fit1$time[deaths], cfit1$time) aeq(fit1$n.risk[deaths], cfit1$n.risk) aeq(fit1$n.event[deaths], cfit1$n.event) aeq(fit1$surv[deaths], cfit1$surv) aeq(fit1$std.err[deaths], cfit1$std.err) deaths <- (fit2$n.event + fit2$n.censor)>0 aeq(fit2$time[deaths], cfit2$time) aeq(fit2$n.risk[deaths], cfit2$n.risk) aeq(fit2$n.event[deaths], cfit2$n.event) aeq(fit2$surv[deaths], cfit2$surv) fit3 <- survfit(Surv(start, stop, event) ~1, test2) #Kaplan-Meier aeq(fit3$n, 10) aeq(fit3$time, c(1:9,14,17)) aeq(fit3$n.risk, c(0,2,3,3,4,5,4,4,5,2,1)) aeq(fit3$n.event,c(0,1,1,0,0,1,1,1,2,0,0)) aeq(fit3$surv[fit3$n.event>0], c(.5, 1/3, 4/15, 1/5, 3/20, 9/100)) # # Verify that both surv AND n.risk are right between time points. # fit <- survfit(Surv(time, status) ~1, test1) temp <- summary(fit, time=c(.5,1, 1.5, 6, 7.5, 8, 8.9, 9, 10), extend=TRUE) aeq(temp$n.risk, c(6,6,4,4,2,2,1,1,0)) aeq(temp$surv, c(1, fit$surv[c(1,1,2,2,3,3,4,4)])) aeq(temp$n.event, c(0,1,0,2,0,0,0,1,0)) aeq(temp$std.err, c(0, (fit$surv*fit$std.err)[c(1,1,2,2,3,3,4,4)])) fit <- survfit(Surv(start, stop, event) ~1, test2) temp <- summary(fit, times=c(.5, 1.5, 2.5, 3, 6.5, 14.5, 16.5)) aeq(temp$surv, c(1, fit$surv[c(1,2,3,6, 10,10)])) aeq(temp$n.risk, c(0, 2, 3, 3, 4, 1,1)) survival/tests/mrtest.R0000644000175100001440000000164411732700061014750 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) {if (is.R()) mdy.date <- function(m, d, y) { y <- ifelse(y<100, y+1900, y) as.Date(paste(m,d,y, sep='/'), "%m/%d/%Y") } else mdy.date <- function(m,d,y) { y <- ifelse(y<100, y+1900, y) timeDate(paste(y, m, d, sep='/'), in.format="%Y/%m/%d") } } # # A test of the match.ratetable function, specifically the # change to allow partial matching of strings # Note that 10,000 days old is 27.4 years # aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) temp1 <- data.frame(year=mdy.date(2,2,1960:1964), age = 10000 + 1:5, sex = c('M', 'fema', 'f', 'ma', 'F')) temp2 <- ratetable(year=temp1$year, age=temp1$age, sex=temp1$sex) temp3 <- match.ratetable(temp2, survexp.us) aeq(temp3$R[,2], c(1,2,2,1,2)) survival/tests/r_stanford.Rout.save0000644000175100001440000000741211732700061017257 0ustar hornikusers R version 2.9.0 (2009-04-17) Copyright (C) 2009 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # The Stanford data from 1980 is used in Escobar and Meeker, Biometrics 1992. > # t5 = T5 mismatch score > # Their case numbers correspond to a data set sorted by age > # > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > stanford2$t5 <- ifelse(stanford2$t5 <0, NA, stanford2$t5) > stanford2 <- stanford2[order(stanford2$age, stanford2$time),] > stanford2$time <- ifelse(stanford2$time==0, .5, stanford2$time) > > cage <- stanford2$age - mean(stanford2$age) > fit1 <- survreg(Surv(time, status) ~ cage + I(cage^2), stanford2, + dist='lognormal') > fit1 Call: survreg(formula = Surv(time, status) ~ cage + I(cage^2), data = stanford2, dist = "lognormal") Coefficients: (Intercept) cage I(cage^2) 6.717591081 -0.061908619 -0.003504315 Scale= 2.362872 Loglik(model)= -863.6 Loglik(intercept only)= -868.8 Chisq= 10.5 on 2 degrees of freedom, p= 0.0053 n= 184 > ldcase <- resid(fit1, type='ldcase') > ldresp <- resid(fit1, type='ldresp') > # The ldcase and ldresp should be compared to table 1 in Escobar and > # Meeker, Biometrics 1992, p519; the colums they label as (1/2) A_{ii} > # They give data for selected cases, entered below as mdata > mdata <- cbind(c(1,2,4,5,12,16,23,61,66,72,172,182,183,184), + c(.035, .244, .141, .159, .194, .402, 0,0, .143, .403, + .178, .033, .005, .015), + c(.138, .145, .073, .076, .104, .159, 0,0, .109, .184, + .116, .063, .103, .144)) > dimnames(mdata) <- list(NULL, c("case#", "ldcase", "ldresp")) > aeq(round(ldcase[mdata[,1]],3), mdata[,2]) [1] TRUE > aeq(round(ldresp[mdata[,1]],3), mdata[,3]) [1] TRUE > > plot1 <- function() { + # make their figure 1, 2, and 6 + temp <- predict(fit1, type='quantile', p=c(.1, .5, .9)) + plot(stanford2$age, stanford2$time, log='y', xlab="Age", ylab="Days", + ylim=range(stanford2$time, temp)) + matlines(stanford2$age, temp, lty=c(1,2,2), col=1) + + n <- length(ldcase) + plot(1:n, ldcase, xlab="Case Number", ylab="(1/2) A", type='l') + title (main="Case weight pertubations") + plot(1:n, ldresp, xlab="Case Number", ylab="(1/2) A", + ylim=c(0, .2), type='l') + title(main="Response pertubations") + indx <- which(ldresp > .07) + text(indx, ldresp[indx]+ .005, indx%%10, cex=.6) + } > > postscript('meekerplot.ps') > plot1() > dev.off() null device 1 > # > # Stanford predictions in other ways > # > fit2 <- survreg(Surv(time, status) ~ poly(age,2), stanford2, + dist='lognormal') > > p1 <- predict(fit1, type='response') > p2 <- predict(fit2, type='response') > aeq(p1, p2) [1] TRUE > > p3 <- predict(fit2, type='terms', se=T) > p4 <- predict(fit2, type='lp', se=T) > p5 <- predict(fit1, type='lp', se=T) > # aeq(p3$fit + attr(p3$fit, 'constant'), p4$fit) #R is missing the attribute > aeq(p4$fit, p5$fit) [1] TRUE > aeq(p3$se.fit, p4$se.fit) #this one should be false [1] "Mean relative difference: 0.758395" > aeq(p4$se.fit, p5$se.fit) #this one true [1] TRUE > > survival/tests/clogit.R0000644000175100001440000000164211732700061014711 0ustar hornikuserslibrary(survival) # # Test of the clogit function, and indirectly of the exact option # # Data set logan has the occupation of fathers, we create a # multinomial response # nresp <- length(levels(logan$occupation)) n <- nrow(logan) indx <- rep(1:n, nresp) logan2 <- data.frame(logan[indx,], id = indx, occ2 = factor(rep(levels(logan$occupation), each=n))) logan2$y <- (logan2$occupation == logan2$occ2) #We expect two NA coefficients, so ignore the warning fit1 <- clogit(y ~ occ2 + occ2:education + occ2:race + strata(id), logan2) #since there is only one death per group, all methods are equal dummy <- rep(1, nrow(logan2)) fit2 <- coxph(Surv(dummy, y) ~ occ2 + occ2:education + occ2:race + strata(id), logan2, method='breslow') all.equal(fit1$coef, fit2$coef) all.equal(fit1$loglik, fit2$loglik) all.equal(fit1$var, fit2$var) all.equal(fit1$resid, fit2$resid) survival/tests/factor.R0000644000175100001440000000203311732700061014701 0ustar hornikusers# # Ensure that factors work in prediction # library(survival) options(na.action="na.exclude") # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) tfit <- coxph(Surv(time, status) ~ age + factor(ph.ecog), lung) p1 <- predict(tfit, type='risk') # Testing NA handling is important too keep <- (is.na(lung$ph.ecog) | lung$ph.ecog !=1) lung2 <- lung[keep,] p2 <- predict(tfit, type='risk', newdata=lung[keep,]) aeq(p1[keep], p2) # Same, for survreg tfit <- survreg(Surv(time, status) ~ age + factor(ph.ecog), lung) p1 <- predict(tfit, type='response') p2 <- predict(tfit, type='response', newdata=lung2) aeq(p1[keep], p2) # Now repeat it tossing the missings options(na.action=na.omit) keep2 <- (lung$ph.ecog[!is.na(lung$ph.ecog)] !=1) tfit2 <- survreg(Surv(time, status) ~ age + factor(ph.ecog), lung) p3 <- predict(tfit2, type='response') p4 <- predict(tfit2, type='response', newdata=lung2, na.action=na.omit) aeq(p3[keep2] , p4) survival/tests/book7.Rout.save0000644000175100001440000000550412533657433016155 0ustar hornikusers R Under development (unstable) (2015-05-14 r68368) -- "Unsuffered Consequences" Copyright (C) 2015 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > options(na.action=na.exclude) > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > > # > # Tests from the appendix of Therneau and Grambsch > # Data set 1 + exact method > > test1 <- data.frame(time= c(9, 3,1,1,6,6,8), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0)) > > byhand7 <- function(beta) { + r <- exp(beta) + loglik <- 2*(beta - log(3*r + 3)) + u <- 2/(r+1) + imat <- 2*r/(r+1)^2 + haz <- c(1/(3*r+3), 2/(r+3), 0, 1 ) + + ties <- c(1,1,2,2,3,4) + wt <- c(r,r,r,1,1,1) + mart <- c(1,0,1,1,0,1) - wt* (cumsum(haz))[ties] #martingale residual + + list(loglik=loglik, u=u, imat=imat, mart=mart) + } > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > fit0 <-coxph(Surv(time, status) ~x, test1, iter=0, method='exact') > truth0 <- byhand7(0) > aeq(truth0$loglik, fit0$loglik[1]) [1] TRUE > aeq(1/truth0$imat, fit0$var) [1] TRUE > aeq(truth0$mart, fit0$resid[c(2:6,1)]) [1] TRUE > > fit1 <- coxph(Surv(time, status) ~x, test1, iter=1, method='exact') > aeq(fit1$coef, truth0$u*fit0$var) [1] TRUE > truth1 <- byhand7(fit1$coef) > aeq(fit1$loglik[2], truth1$loglik) [1] TRUE > aeq(1/truth1$imat, fit1$var) [1] TRUE > aeq(truth1$mart, resid(fit1)[c(3:7,1)]) [1] TRUE > > # Beta is infinite for this model, so we will get a warning message > fit2 <- coxph(Surv(time, status) ~x, test1, method='exact') Warning message: In fitter(X, Y, strats, offset, init, control, weights = weights, : Loglik converged before variable 1 ; beta may be infinite. > aeq(resid(fit2)[-2], c(0, 2/3, -1/3, -4/3, 1, 0)) #values from the book [1] TRUE > > > # > # Now a multivariate case: start/stop data uses a different C routine > # > zz <- rep(0, nrow(lung)) > fit1 <- coxph(Surv(time, status) ~ age + ph.ecog + sex, lung, method="exact") > fit2 <- coxph(Surv(zz, time, status) ~ age + ph.ecog + sex, lung, + method="exact") > aeq(fit1$loglik, fit2$loglik) [1] TRUE > aeq(fit1$var, fit2$var) [1] TRUE > aeq(fit1$score, fit2$score) [1] TRUE > aeq(fit1$resid, fit2$resid) [1] TRUE > > proc.time() user system elapsed 0.712 0.028 0.737 survival/tests/r_donnell.R0000644000175100001440000000336213060317610015405 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Good initial values are key to this data set # It killed v4 of survreg; # data courtesy of Deborah Donnell, Fred Hutchinson Cancer Center # donnell <- scan("data.donnell", what=list(time1=0, time2=0, status=0)) donnell <- data.frame(donnell) dfit <- survreg(Surv(time1, time2, status, type='interval') ~1, donnell) summary(dfit) # # Fit the Donnell data using Statsci's code - should get the same coefs # if (exists('censorReg')) { dfitc <- censorReg(censor(time1, time2, status, type='interval') ~1, donnell) summary(dfitc) } # # Do a contour plot of the donnell data # npt <- 20 beta0 <- seq(.4, 3.6, length=npt) logsig <- seq(-1.4, 0.41, length=npt) donlog <- matrix(0,npt, npt) for (i in 1:npt) { for (j in 1:npt) { fit <- survreg(Surv(time1, time2, status, type='interval') ~1, donnell, init=c(beta0[i],logsig[j]), maxiter=0) donlog[i,j] <- fit$log[1] } } clev <- -c(51, 51.5, 52:60, 65, 75, 85, 100, 150) #clev <- seq(-51, -50, length=10) contour(beta0, logsig, pmax(donlog, -200), levels=clev, xlab="Intercept", ylab="Log(sigma)") points(2.39, log(.7885), pch=1, col=2) title("Donnell data") # # Compute the path of the iteration # # All the intermediate stops produce an ignorable "did not converge" # warning options(warn=-1) #turn them off niter <- 14 donpath <- matrix(0,niter+1,2) for (i in 0:niter){ fit <- survreg(Surv(time1, time2, status, type='interval') ~1, donnell, maxiter=i) donpath[i+1,] <- c(fit$coef, log(fit$scale)) } points(donpath[,1], donpath[,2]) lines(donpath[,1], donpath[,2], col=4) options(warn=0) #reset survival/tests/book2.Rout.save0000644000175100001440000001662212652733556016156 0ustar hornikusers R Under development (unstable) (2016-01-29 r70039) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > > # > # Tests from the appendix of Therneau and Grambsch > # b. Data set 1 and Efron estimate > # > test1 <- data.frame(time= c(9, 3,1,1,6,6,8), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0)) > > byhand <- function(beta, newx=0) { + r <- exp(beta) + loglik <- 2*beta - (log(3*r +3) + log((r+5)/2) + log(r+3)) + u <- (30 + 23*r - r^3)/ ((r+1)*(r+3)*(r+5)) + tfun <- function(x) x - x^2 + imat <- tfun(r/(r+1)) + tfun(r/(r+5)) + tfun(r/(r+3)) + + # The matrix of weights, one row per obs, one col per time + # Time of 1, 6, 6+0 (second death), and 9 + wtmat <- matrix(c(1,1,1,1,1,1, + 0,0,1,1,1,1, + 0,0,.5, .5, 1,1, + 0,0,0,0,0,1), ncol=4) + wtmat <- diag(c(r,r,r,1,1,1)) %*% wtmat + + x <- c(1,1,1,0,0,0) + status <- c(1,0,1,1,0,1) + xbar <- colSums(wtmat*x)/ colSums(wtmat) + haz <- 1/ colSums(wtmat) # one death at each of the times + + hazmat <- wtmat %*% diag(haz) #each subject's hazard over time + mart <- status - rowSums(hazmat) + + a <- r+1; b<- r+3; d<- r+5 # 'c' in the book, 'd' here + score <- c((2*r + 3)/ (3*a^2), + -r/ (3*a^2), + (675+ r*(1305 +r*(756 + r*(-4 +r*(-79 -13*r)))))/(3*(a*b*d)^2), + r*(1/(3*a^2) - a/(2*b^2) - b/(2*d^2)), + 2*r*(177 + r*(282 +r*(182 + r*(50 + 5*r)))) /(3*(a*b*d)^2), + 2*r*(177 + r*(282 +r*(182 + r*(50 + 5*r)))) /(3*(a*b*d)^2)) + + # Schoenfeld residual + d <- mean(xbar[2:3]) + scho <- c(1/(r+1), 1- d, 0- d , 0) + + surv <- exp(-cumsum(haz)* exp(beta*newx))[c(1,3,4)] + varhaz.g <- cumsum(haz^2) # since all numerators are 1 + + varhaz.d <- cumsum((newx-xbar) * haz) + + varhaz <- (varhaz.g + varhaz.d^2/ imat) * exp(2*beta*newx) + + list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=haz, + mart=mart, score=score, var.g=varhaz.g, var.d=varhaz.d, + scho=scho, surv=surv, var=varhaz[c(1,3,4)]) + } > > > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > fit0 <-coxph(Surv(time, status) ~x, test1, iter=0) > truth0 <- byhand(0,0) > aeq(truth0$loglik, fit0$loglik[1]) [1] TRUE > aeq(1/truth0$imat, fit0$var) [1] TRUE > aeq(truth0$mart, fit0$resid[c(2:6,1)]) [1] TRUE > aeq(resid(fit0), c(-3/4, NA, 5/6, -1/6, 5/12, 5/12, -3/4)) [1] TRUE > aeq(truth0$scho, resid(fit0, 'schoen')) [1] TRUE > aeq(truth0$score, resid(fit0, 'score')[c(3:7,1)]) [1] TRUE > sfit <- survfit(fit0, list(x=0), censor=FALSE) > aeq(sfit$std.err^2, truth0$var) [1] TRUE > aeq(sfit$surv, truth0$surv) [1] TRUE > > fit <- coxph(Surv(time, status) ~x, test1, eps=1e-8) > aeq(round(fit$coef,6), 1.676857) [1] TRUE > truebeta <- log(cos(acos((45/23)*sqrt(3/23))/3) * 2* sqrt(23/3)) > truth <- byhand(truebeta, 0) > aeq(truth$loglik, fit$loglik[2]) [1] TRUE > aeq(1/truth$imat, fit$var) [1] TRUE > aeq(truth$mart, fit$resid[c(2:6,1)]) [1] TRUE > aeq(truth$scho, resid(fit, 'schoen')) [1] TRUE > aeq(truth$score, resid(fit, 'score')[c(3:7,1)]) [1] TRUE > > # Per comments in the source code, the below is expected to fail for Efron > # at the tied death times. (When predicting for new data, predict > # treats a time in the new data set that exactly matches one in the original > # as being just after the original, i.e., experiences the full hazard > # jump there, in the same way that censors do.) > expect <- predict(fit, type='expected', newdata=test1) #force recalc > use <- !(test1$time==6 | is.na(test1$status)) > aeq(test1$status[use] - resid(fit)[use], expect[use]) [1] TRUE > > sfit <- survfit(fit, list(x=0), censor=FALSE) > aeq(sfit$surv, truth$surv) [1] TRUE > aeq(sfit$std.err^2, truth$var) [1] TRUE > > # > # Done with the formal test, now print out lots of bits > # > resid(fit) 1 2 3 4 5 6 7 -0.3655434 NA 0.7191707 -0.2808293 -0.4383414 0.7310869 -0.3655434 > resid(fit, 'scor') 1 2 3 4 5 6 7 0.2208584 NA 0.1132780 -0.0442340 -0.1029199 -0.4078409 0.2208584 > resid(fit, 'scho') 1 6 6 9 0.157512 0.421244 -0.578756 0.000000 > > predict(fit, type='lp') [1] -0.8384287 NA 0.8384287 0.8384287 0.8384287 -0.8384287 -0.8384287 > predict(fit, type='risk') [1] 0.4323894 NA 2.3127302 2.3127302 2.3127302 0.4323894 0.4323894 > predict(fit, type='expected') 1 2 3 4 5 6 7 1.3655434 NA 0.2808293 0.2808293 1.4383414 0.2689131 0.3655434 > predict(fit, type='terms') x 1 -0.8384287 2 NA 3 0.8384287 4 0.8384287 5 0.8384287 6 -0.8384287 7 -0.8384287 > predict(fit, type='lp', se.fit=T) $fit 1 2 3 4 5 6 7 -0.8384287 NA 0.8384287 0.8384287 0.8384287 -0.8384287 -0.8384287 $se.fit 1 2 3 4 5 6 7 0.6388078 NA 0.6388078 0.6388078 0.6388078 0.6388078 0.6388078 > predict(fit, type='risk', se.fit=T) $fit 1 2 3 4 5 6 7 0.4323894 NA 2.3127302 2.3127302 2.3127302 0.4323894 0.4323894 $se.fit 1 2 3 4 5 6 7 0.4200565 NA 0.9714774 0.9714774 0.9714774 0.4200565 0.4200565 > predict(fit, type='expected', se.fit=T) $fit 1 2 3 4 5 6 7 1.3655434 NA 0.2808293 0.2808293 1.4383414 0.2689131 0.3655434 $se.fit [1] 1.0649293 NA 0.2864593 0.2864593 1.5922983 0.3661617 0.3661617 > predict(fit, type='terms', se.fit=T) $fit x 1 -0.8384287 2 NA 3 0.8384287 4 0.8384287 5 0.8384287 6 -0.8384287 7 -0.8384287 $se.fit x 1 0.6388078 2 NA 3 0.6388078 4 0.6388078 5 0.6388078 6 0.6388078 7 0.6388078 > > summary(survfit(fit)) Call: survfit(formula = fit) time n.risk n.event survival std.err lower 95% CI upper 95% CI 1 6 1 0.8857 0.117 0.683036 1 6 4 2 0.4294 0.237 0.145743 1 9 1 1 0.0425 0.116 0.000198 1 > summary(survfit(fit, list(x=2))) Call: survfit(formula = fit, newdata = list(x = 2)) time n.risk n.event survival std.err lower 95% CI upper 95% CI 1 6 1 2.23e-01 5.97e-01 1.16e-03 1 6 4 2 2.87e-05 5.69e-04 3.96e-22 1 9 1 1 1.08e-17 1.04e-15 1.07e-99 1 > > proc.time() user system elapsed 0.232 0.012 0.238 survival/tests/testreg.Rout.save0000644000175100001440000002107011732700061016567 0ustar hornikusers R version 2.14.0 Under development (unstable) (2011-04-10 r55401) Copyright (C) 2011 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: x86_64-unknown-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) #preserve length of missings > library(survival) Loading required package: splines > > # > # Run a test that can be verified using other packages (we used SAS) > # > test1 <- data.frame(time= c(9, 3,1,1,6,6,8), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0)) > fit1w <- survreg(Surv(time, status) ~x, test1, dist='weibull') > fit1w Call: survreg(formula = Surv(time, status) ~ x, data = test1, dist = "weibull") Coefficients: (Intercept) x 2.2373335 -0.7442249 Scale= 0.4563163 Loglik(model)= -10.3 Loglik(intercept only)= -11.4 Chisq= 2.22 on 1 degrees of freedom, p= 0.14 n=6 (1 observation deleted due to missingness) > summary(fit1w) Call: survreg(formula = Surv(time, status) ~ x, data = test1, dist = "weibull") Value Std. Error z p (Intercept) 2.237 0.330 6.78 1.18e-11 x -0.744 0.486 -1.53 1.26e-01 Log(scale) -0.785 0.433 -1.81 6.99e-02 Scale= 0.456 Weibull distribution Loglik(model)= -10.3 Loglik(intercept only)= -11.4 Chisq= 2.22 on 1 degrees of freedom, p= 0.14 Number of Newton-Raphson Iterations: 8 n=6 (1 observation deleted due to missingness) > > fit1e <- survreg(Surv(time, status) ~x, test1, dist='exponential') > fit1e Call: survreg(formula = Surv(time, status) ~ x, data = test1, dist = "exponential") Coefficients: (Intercept) x 2.442347 -1.056053 Scale fixed at 1 Loglik(model)= -11.7 Loglik(intercept only)= -12.2 Chisq= 1.07 on 1 degrees of freedom, p= 0.3 n=6 (1 observation deleted due to missingness) > summary(fit1e) Call: survreg(formula = Surv(time, status) ~ x, data = test1, dist = "exponential") Value Std. Error z p (Intercept) 2.44 0.707 3.45 0.000552 x -1.06 1.000 -1.06 0.290944 Scale fixed at 1 Exponential distribution Loglik(model)= -11.7 Loglik(intercept only)= -12.2 Chisq= 1.07 on 1 degrees of freedom, p= 0.3 Number of Newton-Raphson Iterations: 4 n=6 (1 observation deleted due to missingness) > > fit1l <- survreg(Surv(time, status) ~x, test1, dist='loglogistic') > fit1l Call: survreg(formula = Surv(time, status) ~ x, data = test1, dist = "loglogistic") Coefficients: (Intercept) x 2.177208 -1.195672 Scale= 0.3847582 Loglik(model)= -10.7 Loglik(intercept only)= -12 Chisq= 2.7 on 1 degrees of freedom, p= 0.1 n=6 (1 observation deleted due to missingness) > summary(fit1l) Call: survreg(formula = Surv(time, status) ~ x, data = test1, dist = "loglogistic") Value Std. Error z p (Intercept) 2.177 0.365 5.96 2.48e-09 x -1.196 0.711 -1.68 9.25e-02 Log(scale) -0.955 0.396 -2.41 1.58e-02 Scale= 0.385 Log logistic distribution Loglik(model)= -10.7 Loglik(intercept only)= -12 Chisq= 2.7 on 1 degrees of freedom, p= 0.1 Number of Newton-Raphson Iterations: 4 n=6 (1 observation deleted due to missingness) > > fit1g <- survreg(Surv(time, status) ~x, test1, dist='lognormal') > summary(fit1g) Call: survreg(formula = Surv(time, status) ~ x, data = test1, dist = "lognormal") Value Std. Error z p (Intercept) 2.210 0.404 5.48 4.35e-08 x -1.268 0.585 -2.17 3.03e-02 Log(scale) -0.446 0.342 -1.30 1.93e-01 Scale= 0.64 Log Normal distribution Loglik(model)= -10.5 Loglik(intercept only)= -12.1 Chisq= 3.26 on 1 degrees of freedom, p= 0.071 Number of Newton-Raphson Iterations: 5 n=6 (1 observation deleted due to missingness) > # > # Do a test with the ovarian data > # > fitfw <- survreg(Surv(futime, fustat) ~ age + ecog.ps, ovarian, + dist='weibull') > fitfw Call: survreg(formula = Surv(futime, fustat) ~ age + ecog.ps, data = ovarian, dist = "weibull") Coefficients: (Intercept) age ecog.ps 12.28496723 -0.09702669 0.09977342 Scale= 0.6032744 Loglik(model)= -90 Loglik(intercept only)= -98 Chisq= 15.98 on 2 degrees of freedom, p= 0.00034 n= 26 > > fitfl <- survreg(Surv(futime, fustat) ~ age + ecog.ps, ovarian, + dist='loglogistic') > fitfl Call: survreg(formula = Surv(futime, fustat) ~ age + ecog.ps, data = ovarian, dist = "loglogistic") Coefficients: (Intercept) age ecog.ps 11.50853384 -0.08876814 0.09033348 Scale= 0.4464064 Loglik(model)= -89.5 Loglik(intercept only)= -97.4 Chisq= 15.67 on 2 degrees of freedom, p= 4e-04 n= 26 > > #test out interval censoring, using some dummy time values > > idat <- read.table('data.interval', skip=3, header=T, sep=',') > flsurv<- Surv(idat$ltime, idat$rtime, type='interval2') > > fitfw2 <- survreg(flsurv ~ age + ecog.ps, idat, dist='weibull') > summary(fitfw2) Call: survreg(formula = flsurv ~ age + ecog.ps, data = idat, dist = "weibull") Value Std. Error z p (Intercept) 12.3886 1.6027 7.730 1.08e-14 age -0.0986 0.0254 -3.885 1.02e-04 ecog.ps 0.0971 0.3776 0.257 7.97e-01 Log(scale) -0.4773 0.2583 -1.848 6.47e-02 Scale= 0.62 Weibull distribution Loglik(model)= -56.2 Loglik(intercept only)= -64 Chisq= 15.57 on 2 degrees of freedom, p= 0.00042 Number of Newton-Raphson Iterations: 6 n= 26 > > fitfl2 <- survreg(flsurv ~ age + ecog.ps, idat, dist='loglogistic') > summary(fitfl2) Call: survreg(formula = flsurv ~ age + ecog.ps, data = idat, dist = "loglogistic") Value Std. Error z p (Intercept) 11.5268 1.528 7.542 4.62e-14 age -0.0888 0.024 -3.703 2.13e-04 ecog.ps 0.0818 0.364 0.225 8.22e-01 Log(scale) -0.8023 0.271 -2.965 3.03e-03 Scale= 0.448 Log logistic distribution Loglik(model)= -55.9 Loglik(intercept only)= -63.5 Chisq= 15.35 on 2 degrees of freedom, p= 0.00046 Number of Newton-Raphson Iterations: 5 n= 26 > > fitfg2 <- survreg(flsurv ~ age + ecog.ps, idat, dist='lognormal') > summary(fitfg2) Call: survreg(formula = flsurv ~ age + ecog.ps, data = idat, dist = "lognormal") Value Std. Error z p (Intercept) 11.1548 1.4347 7.775 7.56e-15 age -0.0855 0.0238 -3.598 3.20e-04 ecog.ps 0.2066 0.3828 0.540 5.89e-01 Log(scale) -0.2297 0.2508 -0.916 3.60e-01 Scale= 0.795 Log Normal distribution Loglik(model)= -56 Loglik(intercept only)= -63.5 Chisq= 14.94 on 2 degrees of freedom, p= 0.00057 Number of Newton-Raphson Iterations: 5 n= 26 > > logt <- c(survreg.distributions$t, + survreg.distributions$weibull[c('trans', 'itrans', 'dtrans')]) > logt$name <- 'log(t)' > > fitft2 <- survreg(Surv(ltime, rtime, type='interval2') ~ age + ecog.ps, + idat, dist=logt, parm=100) > summary(fitft2) #should be quite close to fitfg2 Call: survreg(formula = Surv(ltime, rtime, type = "interval2") ~ age + ecog.ps, data = idat, dist = logt, parms = 100) Value Std. Error z p (Intercept) 11.1856 1.4419 7.758 8.66e-15 age -0.0858 0.0238 -3.609 3.07e-04 ecog.ps 0.1978 0.3814 0.519 6.04e-01 Log(scale) -0.2394 0.2522 -0.949 3.43e-01 Scale= 0.787 log(t) distribution: parmameters= 100 Loglik(model)= -56 Loglik(intercept only)= -63.5 Chisq= 14.97 on 2 degrees of freedom, p= 0.00056 Number of Newton-Raphson Iterations: 5 n= 26 > > # > # Check out the survreg density and probability functions > # > > # Gaussian > x <- -10:10 > p <- seq(.1, .95, length=25) > all.equal(dsurvreg(x, 1, 5, 'gaussian'), dnorm(x, 1, 5)) [1] TRUE > all.equal(psurvreg(x, 1, 5, 'gaussian'), pnorm(x, 1, 5)) [1] TRUE > all.equal(qsurvreg(p, 1, 5, 'gaussian'), qnorm(p, 1, 5)) [1] TRUE > > # Lognormal > x <- 1:10 > all.equal(dsurvreg(x, 1, 5, 'lognormal'), dlnorm(x, 1, 5)) [1] TRUE > all.equal(psurvreg(x, 1, 5, 'lognormal'), plnorm(x, 1, 5)) [1] TRUE > all.equal(qsurvreg(p, 1, 5, 'lognormal'), qlnorm(p, 1, 5)) [1] TRUE > > # Weibull > lambda <- exp(-2) > rho <- 1/3 > temp <- (lambda*x)^rho > all.equal(psurvreg(x, 2, 3), 1- exp(-temp)) [1] TRUE > all.equal(dsurvreg(x, 2, 3), lambda*rho*(lambda*x)^(rho-1)*exp(-temp)) [1] TRUE > survival/tests/doaml.R0000644000175100001440000000404511732700061014524 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) # # These results can be found in Miller # fit <- coxph(Surv(aml$time, aml$status) ~ aml$x, method='breslow') fit resid(fit, type='mart') resid(fit, type='score') resid(fit, type='scho') # Test the drop of an itercept: should have no effect fit2 <- coxph(Surv(time, status) ~ x -1, method='breslow', data=aml) aeq(fit$loglik, fit2$loglik) aeq(coef(fit), coef(fit2)) aeq(fit$var, fit2$var) fit <- survfit(Surv(aml$time, aml$status) ~ aml$x) fit summary(fit) survdiff(Surv(aml$time, aml$status)~ aml$x) # # Test out the weighted K-M # # First, equal case weights- shouldn't change the survival, but will # halve the variance temp2 <-survfit(Surv(aml$time, aml$status)~1, type='kaplan', weight=rep(2,23)) temp <-survfit(Surv(time, status)~1, aml) aeq(temp$surv, temp2$surv) aeq(temp$std.err^2, 2*temp2$std.err^2) # Risk weights-- use a null Cox model tfit <- coxph(Surv(aml$time, aml$status) ~ offset(log(1:23))) sfit <- survfit(tfit, type='aalen', censor=FALSE) # Now compute it by hand. The survfit program will produce a curve # corresponding to the mean offset. This is a change on 7/2010, # which caused S(new) = S(old)^exp(mean(log(1:23))). # Ties are a nuisance rscore <- exp(log(1:23) - mean(log(1:23)))[order(aml$time)] atime <- sort(aml$time) denom <- rev(cumsum(rev(rscore))) denom <- denom[match(unique(atime), atime)] deaths <- tapply(aml$status, aml$time, sum) chaz <- cumsum(deaths/denom) all.equal(sfit$surv, as.vector(exp(-chaz[deaths>0]))) cvar <- cumsum(deaths/denom^2) all.equal(sfit$std^2, as.vector(cvar[deaths>0])) # And the Efron result summary(survfit(tfit)) # Lots of ties, so its a good test case x1 <- coxph(Surv(time, status)~x, aml, method='efron') x1 x2 <- coxph(Surv(rep(0,23),time, status) ~x, aml, method='efron') aeq(x1$coef, x2$coef) rm(x1, x2, atime, denom, deaths, chaz,cvar, tfit, sfit, temp, temp2, fit) survival/tests/coxsurv2.R0000644000175100001440000000414711732700061015226 0ustar hornikuserslibrary(survival) # # Check that the survival curves from a Cox model with beta=0 # match ordinary survival # # Aalen surv1 <- survfit(Surv(time,status) ~ sex, data=lung, type='fleming', error='tsiatis') fit1 <- coxph(Surv(time, status) ~ age + strata(sex), data=lung, iter=0, method='breslow') fit1$var <- 0*fit1$var #sneaky, causes the extra term in the Cox variance # calculation to be zero surv2 <- survfit(fit1, type='aalen', vartype='tsiatis') surv3 <- survfit(fit1) arglist <- c('n', 'time', 'n.risk','n.event', 'n.censor', 'surv', 'strata', 'std.err', 'upper', 'lower') all.equal(unclass(surv1)[arglist], unclass(surv2)[arglist]) all.equal(unclass(surv1)[arglist], unclass(surv3)[arglist]) # Efron method surv1 <- survfit(Surv(time,status) ~ sex, data=lung, type='fh2', error='tsiatis') surv2 <- survfit(fit1, type='efron', vartype='efron') all.equal(unclass(surv1)[arglist], unclass(surv2)[arglist]) # Kaplan-Meier surv1 <- survfit(Surv(time,status) ~ sex, data=lung) surv2 <- survfit(fit1, type='kalb', vartype='green') all.equal(unclass(surv1)[arglist], unclass(surv2)[arglist]) # Now add some random weights rwt <- runif(nrow(lung), .5, 3) surv1 <- survfit(Surv(time,status) ~ sex, data=lung, type='fleming', error='tsiatis', weight=rwt) fit1 <- coxph(Surv(time, status) ~ age + strata(sex), data=lung, iter=0, method='breslow', weight=rwt) fit1$var <- 0*fit1$var #sneaky surv2 <- survfit(fit1, type='aalen', vartype='tsiatis') surv3 <- survfit(fit1) all.equal(unclass(surv1)[arglist], unclass(surv2)[arglist]) all.equal(unclass(surv1)[arglist], unclass(surv3)[arglist]) # Efron method surv1 <- survfit(Surv(time,status) ~ sex, data=lung, type='fh2', error='tsiatis', weight=rwt) surv2 <- survfit(fit1, type='efron', vartype='efron') all.equal(unclass(surv1)[arglist], unclass(surv2)[arglist]) # Kaplan-Meier surv1 <- survfit(Surv(time,status) ~ sex, data=lung, weight=rwt) surv2 <- survfit(fit1, type='kalb', vartype='green') all.equal(unclass(surv1)[arglist], unclass(surv2)[arglist]) survival/tests/r_donnell.Rout.save0000644000175100001440000000571013065015064017074 0ustar hornikusers R Under development (unstable) (2017-03-17 r72360) -- "Unsuffered Consequences" Copyright (C) 2017 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # Good initial values are key to this data set > # It killed v4 of survreg; > # data courtesy of Deborah Donnell, Fred Hutchinson Cancer Center > # > > donnell <- scan("data.donnell", what=list(time1=0, time2=0, status=0)) Read 210 records > donnell <- data.frame(donnell) > > dfit <- survreg(Surv(time1, time2, status, type='interval') ~1, donnell) > summary(dfit) Call: survreg(formula = Surv(time1, time2, status, type = "interval") ~ 1, data = donnell) Value Std. Error z p (Intercept) 2.390 0.804 2.972 0.00295 Log(scale) -0.237 0.346 -0.687 0.49232 Scale= 0.789 Weibull distribution Loglik(model)= -51 Loglik(intercept only)= -51 Number of Newton-Raphson Iterations: 11 n= 210 > > # > # Fit the Donnell data using Statsci's code - should get the same coefs > # > if (exists('censorReg')) { + dfitc <- censorReg(censor(time1, time2, status, type='interval') ~1, + donnell) + summary(dfitc) + } > # > # Do a contour plot of the donnell data > # > npt <- 20 > beta0 <- seq(.4, 3.6, length=npt) > logsig <- seq(-1.4, 0.41, length=npt) > donlog <- matrix(0,npt, npt) > > for (i in 1:npt) { + for (j in 1:npt) { + fit <- survreg(Surv(time1, time2, status, type='interval') ~1, + donnell, init=c(beta0[i],logsig[j]), + maxiter=0) + donlog[i,j] <- fit$log[1] + } + } > > clev <- -c(51, 51.5, 52:60, 65, 75, 85, 100, 150) > #clev <- seq(-51, -50, length=10) > > contour(beta0, logsig, pmax(donlog, -200), levels=clev, xlab="Intercept", + ylab="Log(sigma)") > points(2.39, log(.7885), pch=1, col=2) > title("Donnell data") > # > # Compute the path of the iteration > # > # All the intermediate stops produce an ignorable "did not converge" > # warning > options(warn=-1) #turn them off > niter <- 14 > donpath <- matrix(0,niter+1,2) > for (i in 0:niter){ + fit <- survreg(Surv(time1, time2, status, type='interval') ~1, + donnell, maxiter=i) + donpath[i+1,] <- c(fit$coef, log(fit$scale)) + } > points(donpath[,1], donpath[,2]) > lines(donpath[,1], donpath[,2], col=4) > options(warn=0) #reset > > proc.time() user system elapsed 2.160 0.072 2.231 survival/tests/prednew.Rout.save0000644000175100001440000000720112113162124016552 0ustar hornikusers R Under development (unstable) (2013-02-24 r62054) -- "Unsuffered Consequences" Copyright (C) 2013 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # > # Make sure that the newdata argument works for various > # predictions > # We purposely use a subset of the lung data that has only some > # of the levels of the ph.ecog > library(survival) Loading required package: splines > options(na.action=na.exclude, contrasts=c('contr.treatment', 'contr.poly')) > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > myfit <- coxph(Surv(time, status) ~ age + factor(ph.ecog) + strata(sex), lung) > > keep <- which(lung$inst<13 & (lung$ph.ecog==1 | lung$ph.ecog==2)) > p1 <- predict(myfit, type='lp') > p2 <- predict(myfit, type="lp", newdata=lung[keep,]) > p3 <- predict(myfit, type='lp', se.fit=TRUE) > p4 <- predict(myfit, type="lp", newdata=lung[keep,], se.fit=TRUE) > aeq(p1[keep], p2) [1] TRUE > aeq(p1, p3$fit) [1] TRUE > aeq(p1[keep], p4$fit) [1] TRUE > aeq(p3$se.fit[keep], p4$se.fit) [1] TRUE > > p1 <- predict(myfit, type='risk') > p2 <- predict(myfit, type="risk", newdata=lung[keep,]) > p3 <- predict(myfit, type='risk', se.fit=TRUE) > p4 <- predict(myfit, type="risk", newdata=lung[keep,], se.fit=TRUE) > aeq(p1[keep], p2) [1] TRUE > aeq(p1, p3$fit) [1] TRUE > aeq(p1[keep], p4$fit) [1] TRUE > aeq(p3$se.fit[keep], p4$se.fit) [1] TRUE > > # The all.equal fails for type=expected, Efron approx, and tied death > # times due to use of an approximation. See comments in the source code. > myfit <- coxph(Surv(time, status) ~ age + factor(ph.ecog) + strata(sex), + data=lung, method='breslow') > p1 <- predict(myfit, type='expected') > p2 <- predict(myfit, type="expected", newdata=lung[keep,]) > p3 <- predict(myfit, type='expected', se.fit=TRUE) > p4 <- predict(myfit, type="expected", newdata=lung[keep,], se.fit=TRUE) > aeq(p1[keep], p2) [1] TRUE > aeq(p1, p3$fit) [1] TRUE > aeq(p1[keep], p4$fit) [1] TRUE > aeq(p3$se.fit[keep], p4$se.fit) [1] TRUE > > p1 <- predict(myfit, type='terms') > p2 <- predict(myfit, type="terms",newdata=lung[keep,]) > p3 <- predict(myfit, type='terms', se.fit=T) > p4 <- predict(myfit, type="terms",newdata=lung[keep,], se.fit=T) > aeq(p1[keep,], p2) [1] TRUE > aeq(p1, p3$fit) [1] TRUE > aeq(p1[keep,], p4$fit) [1] TRUE > aeq(p3$se.fit[keep,], p4$se.fit) [1] TRUE > > # > # Check out the logic whereby predict does not need to > # recover the model frame. The first call should not > # need to do so, the second should in each case. > # > myfit <- coxph(Surv(time, status) ~ age + factor(sex), lung, x=T) > p1 <- predict(myfit, type='risk', se=T) > myfit2 <- coxph(Surv(time, status) ~ age + factor(sex), lung) > p2 <- predict(myfit2, type='risk', se=T) > aeq(p1$fit, p2$fit) [1] TRUE > aeq(p1$se, p2$se) [1] TRUE > > p1 <- predict(myfit, type='expected', se=T) > p2 <- predict(myfit2, type='expected', se=T) > aeq(p1$fit, p2$fit) [1] TRUE > aeq(p1$se.fit, p2$se.fit) [1] TRUE > > p1 <- predict(myfit, type='terms', se=T) > p2 <- predict(myfit2, type='terms', se=T) > aeq(p1$fit, p2$fit) [1] TRUE > aeq(p1$se.fit, p2$se.fit) [1] TRUE > > proc.time() user system elapsed 0.380 0.016 0.394 survival/tests/r_user.R0000644000175100001440000000152511732700061014727 0ustar hornikusersoptions(na.action=na.exclude) #preserve length of missings library(survival) # # Check out using a "user specified" distribution # mydist <- c(survreg.distributions$extreme, survreg.distributions$weibull[-1]) mydist$name <- "Weibull2" mydist$dist <- NULL fit1 <- survreg(Surv(time, status) ~ age + ph.ecog, lung) fit2 <- survreg(Surv(time, status) ~ age + ph.ecog, lung, dist=mydist) all.equal(fit1$coef, fit2$coef) all.equal(fit1$var, fit2$var) # # And with an data set containing interval censoring # idat <- read.table('data.interval', skip=3, header=T, sep=',') fit1 <- survreg(Surv(ltime, rtime, type='interval2') ~ age + ecog.ps, idat) fit2 <- survreg(Surv(ltime, rtime, type='interval2') ~ age + ecog.ps, data=idat, dist=mydist) all.equal(fit1$coef, fit2$coef) all.equal(fit1$var, fit2$var) all.equal(fit1$log, fit2$log) survival/tests/ratetable.Rout.save0000644000175100001440000001256711732700061017070 0ustar hornikusers R version 2.11.1 (2010-05-31) Copyright (C) 2010 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # Generate each of the messages from is.ratetable > # > {if (is.R()) mdy.date <- function(m, d, y) { + y <- ifelse(y<100, y+1900, y) + as.Date(paste(m,d,y, sep='/'), "%m/%d/%Y") + } + else mdy.date <- function(m,d,y) { + y <- ifelse(y<100, y+1900, y) + timeDate(paste(y, m, d, sep='/'), in.format="%Y/%m/%d") + } + } > > temp <- runif(21*2*4) > > # Good > attributes(temp) <- list(dim=c(21,2,4), + dimnames=list(c(as.character(75:95)), c("male","female"), + c(as.character(2000:2003))), + dimid=c("age","sex","year"), + type=c(2,1,4), + cutpoints=list(c(75:95), NULL, mdy.date(1,1,2000) +c(0:3)*366.25), + class='ratetable') > is.ratetable(temp) [1] TRUE > > # Factor problem + cutpoints length > attributes(temp) <- list(dim=c(21,2,4), + dimnames=list(c(as.character(75:95)), c("male","female"), + c(as.character(2000:2003))), + dimid=c("age","sex","year"), + type=c(1,1,2), + cutpoints=list(c(75:95), NULL, mdy.date(1,1,2000) +c(0:4)*366.25), + class='ratetable') > is.ratetable(temp, verbose=T) [1] "type[ 1 ] is 1; cutpoint should be null" [2] "wrong length for cutpoints 3" > > > # missing dimid attribute + unsorted cutpoint > attributes(temp) <- list(dim=c(21,2,4), + dimnames=list(c(as.character(75:95)), c("male","female"), + c(as.character(2000:2003))), + type=c(2,1,3), + cutpoints=list(c(75:95), NULL, mdy.date(1,1,2000) +c(4:1)*366.25), + class='ratetable') > is.ratetable(temp, verbose=T) [1] "missing attribute: dimid" "wrong length for dimid" [3] "unsorted cutpoints for dimension 3" > > # wrong length for dimid and type, illegal type > attributes(temp) <- list(dim=c(21,2,4), + dimnames=list(c(as.character(75:95)), c("male","female"), + c(as.character(2000:2003))), + dimid=c("age","sex","year", "zed"), + type=c(2,1,3,6), + cutpoints=list(c(75:95), NULL, mdy.date(1,1,2000) +c(0:3)*366.25), + class='ratetable') > is.ratetable(temp, verbose=T) [1] "wrong length for dimid" [2] "type attribute must be 1, 2, 3, or 4" [3] "wrong length for type attribute" > > > # Print and summary > print(survexp.us[1:30,,c('1953', '1985')] ) Rate table with dimension(s): age sex year , , 1953 male female 0-1d 1.157372e-02 8.844000e-03 1-7d 1.446302e-03 1.027012e-03 7-28d 1.379175e-04 1.106070e-04 28-365d 2.814865e-05 2.346732e-05 1 6.169963e-06 5.423669e-06 2 3.860391e-06 3.161334e-06 3 2.909162e-06 2.424089e-06 4 2.448747e-06 1.950051e-06 5 2.210350e-06 1.692520e-06 6 1.988411e-06 1.481583e-06 7 1.813065e-06 1.298053e-06 8 1.684303e-06 1.169315e-06 9 1.593900e-06 1.087146e-06 10 1.569249e-06 1.051541e-06 11 1.626780e-06 1.043325e-06 12 1.771975e-06 1.089887e-06 13 2.062389e-06 1.199447e-06 14 2.462443e-06 1.347361e-06 15 2.944779e-06 1.550072e-06 16 3.410754e-06 1.752797e-06 17 3.819231e-06 1.928140e-06 18 4.164702e-06 2.056914e-06 19 4.504735e-06 2.169256e-06 20 4.822866e-06 2.289823e-06 21 5.086174e-06 2.410395e-06 22 5.278187e-06 2.511789e-06 23 5.335795e-06 2.613186e-06 24 5.286423e-06 2.714587e-06 25 5.198648e-06 2.815992e-06 26 5.130079e-06 2.917400e-06 , , 1985 male female 0-1d 4.429985e-03 3.701977e-03 1-7d 3.595869e-04 2.735770e-04 7-28d 6.385309e-05 5.193376e-05 28-365d 1.277308e-05 9.947467e-06 1 2.451492e-06 2.108968e-06 2 1.739100e-06 1.341882e-06 3 1.369277e-06 1.013196e-06 4 1.122754e-06 7.940941e-07 5 9.995021e-07 7.530142e-07 6 9.173378e-07 6.571643e-07 7 8.488687e-07 5.887021e-07 8 7.530153e-07 5.339338e-07 9 6.297793e-07 4.791661e-07 10 5.202416e-07 4.517830e-07 11 5.202416e-07 4.517830e-07 12 7.530134e-07 5.202412e-07 13 1.232311e-06 6.571636e-07 14 1.862374e-06 8.351727e-07 15 2.533686e-06 1.026887e-06 16 3.150341e-06 1.204921e-06 17 3.657474e-06 1.341877e-06 18 4.041315e-06 1.424054e-06 19 4.315527e-06 1.465144e-06 20 4.603481e-06 1.506233e-06 21 4.864041e-06 1.561021e-06 22 5.069759e-06 1.615810e-06 23 5.138331e-06 1.643205e-06 24 5.152035e-06 1.670600e-06 25 5.110881e-06 1.697995e-06 26 5.097158e-06 1.725391e-06 > summary(survexp.usr) Rate table with 4 dimensions: age ranges from 0 to 39812.25; with 113 categories sex has levels of: male female race has levels of: white black year ranges from 1940-01-01 to 2004-01-01; with 65 categories > survival/tests/book2.R0000644000175100001440000000765212650522315014457 0ustar hornikuserslibrary(survival) options(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type # # Tests from the appendix of Therneau and Grambsch # b. Data set 1 and Efron estimate # test1 <- data.frame(time= c(9, 3,1,1,6,6,8), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0)) byhand <- function(beta, newx=0) { r <- exp(beta) loglik <- 2*beta - (log(3*r +3) + log((r+5)/2) + log(r+3)) u <- (30 + 23*r - r^3)/ ((r+1)*(r+3)*(r+5)) tfun <- function(x) x - x^2 imat <- tfun(r/(r+1)) + tfun(r/(r+5)) + tfun(r/(r+3)) # The matrix of weights, one row per obs, one col per time # Time of 1, 6, 6+0 (second death), and 9 wtmat <- matrix(c(1,1,1,1,1,1, 0,0,1,1,1,1, 0,0,.5, .5, 1,1, 0,0,0,0,0,1), ncol=4) wtmat <- diag(c(r,r,r,1,1,1)) %*% wtmat x <- c(1,1,1,0,0,0) status <- c(1,0,1,1,0,1) xbar <- colSums(wtmat*x)/ colSums(wtmat) haz <- 1/ colSums(wtmat) # one death at each of the times hazmat <- wtmat %*% diag(haz) #each subject's hazard over time mart <- status - rowSums(hazmat) a <- r+1; b<- r+3; d<- r+5 # 'c' in the book, 'd' here score <- c((2*r + 3)/ (3*a^2), -r/ (3*a^2), (675+ r*(1305 +r*(756 + r*(-4 +r*(-79 -13*r)))))/(3*(a*b*d)^2), r*(1/(3*a^2) - a/(2*b^2) - b/(2*d^2)), 2*r*(177 + r*(282 +r*(182 + r*(50 + 5*r)))) /(3*(a*b*d)^2), 2*r*(177 + r*(282 +r*(182 + r*(50 + 5*r)))) /(3*(a*b*d)^2)) # Schoenfeld residual d <- mean(xbar[2:3]) scho <- c(1/(r+1), 1- d, 0- d , 0) surv <- exp(-cumsum(haz)* exp(beta*newx))[c(1,3,4)] varhaz.g <- cumsum(haz^2) # since all numerators are 1 varhaz.d <- cumsum((newx-xbar) * haz) varhaz <- (varhaz.g + varhaz.d^2/ imat) * exp(2*beta*newx) list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=haz, mart=mart, score=score, var.g=varhaz.g, var.d=varhaz.d, scho=scho, surv=surv, var=varhaz[c(1,3,4)]) } aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) fit0 <-coxph(Surv(time, status) ~x, test1, iter=0) truth0 <- byhand(0,0) aeq(truth0$loglik, fit0$loglik[1]) aeq(1/truth0$imat, fit0$var) aeq(truth0$mart, fit0$resid[c(2:6,1)]) aeq(resid(fit0), c(-3/4, NA, 5/6, -1/6, 5/12, 5/12, -3/4)) aeq(truth0$scho, resid(fit0, 'schoen')) aeq(truth0$score, resid(fit0, 'score')[c(3:7,1)]) sfit <- survfit(fit0, list(x=0), censor=FALSE) aeq(sfit$std.err^2, truth0$var) aeq(sfit$surv, truth0$surv) fit <- coxph(Surv(time, status) ~x, test1, eps=1e-8) aeq(round(fit$coef,6), 1.676857) truebeta <- log(cos(acos((45/23)*sqrt(3/23))/3) * 2* sqrt(23/3)) truth <- byhand(truebeta, 0) aeq(truth$loglik, fit$loglik[2]) aeq(1/truth$imat, fit$var) aeq(truth$mart, fit$resid[c(2:6,1)]) aeq(truth$scho, resid(fit, 'schoen')) aeq(truth$score, resid(fit, 'score')[c(3:7,1)]) # Per comments in the source code, the below is expected to fail for Efron # at the tied death times. (When predicting for new data, predict # treats a time in the new data set that exactly matches one in the original # as being just after the original, i.e., experiences the full hazard # jump there, in the same way that censors do.) expect <- predict(fit, type='expected', newdata=test1) #force recalc use <- !(test1$time==6 | is.na(test1$status)) aeq(test1$status[use] - resid(fit)[use], expect[use]) sfit <- survfit(fit, list(x=0), censor=FALSE) aeq(sfit$surv, truth$surv) aeq(sfit$std.err^2, truth$var) # # Done with the formal test, now print out lots of bits # resid(fit) resid(fit, 'scor') resid(fit, 'scho') predict(fit, type='lp') predict(fit, type='risk') predict(fit, type='expected') predict(fit, type='terms') predict(fit, type='lp', se.fit=T) predict(fit, type='risk', se.fit=T) predict(fit, type='expected', se.fit=T) predict(fit, type='terms', se.fit=T) summary(survfit(fit)) summary(survfit(fit, list(x=2))) survival/tests/r_scale.R0000644000175100001440000000325512141742354015050 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Verify that scale can be fixed at a value # coefs will differ slightly due to different iteration paths tol <- .001 # Intercept only models fit1 <- survreg(Surv(time,status) ~ 1, lung) fit2 <- survreg(Surv(time,status) ~ 1, lung, scale=fit1$scale) all.equal(fit1$coef, fit2$coef, tolerance= tol) all.equal(fit1$loglik, fit2$loglik, tolerance= tol) # The two robust variance matrices are not the same, since removing # an obs has a different effect on the two models. This just # checks for failure, not for correctness fit3 <- survreg(Surv(time,status) ~ 1, lung, robust=TRUE) fit4 <- survreg(Surv(time,status) ~ 1, lung, scale=fit1$scale, robust=TRUE) # multiple covariates fit1 <- survreg(Surv(time,status) ~ age + ph.karno, lung) fit2 <- survreg(Surv(time,status) ~ age + ph.karno, lung, scale=fit1$scale) all.equal(fit1$coef, fit2$coef, tolerance=tol) all.equal(fit1$loglik[2], fit2$loglik[2], tolerance=tol) fit3 <- survreg(Surv(time,status) ~ age + ph.karno, lung, robust=TRUE) fit4 <- survreg(Surv(time,status) ~ age + ph.karno, lung, scale=fit1$scale, robust=TRUE) # penalized models fit1 <- survreg(Surv(time, status) ~ pspline(age), lung) fit2 <- survreg(Surv(time, status) ~ pspline(age), lung, scale=fit1$scale) all.equal(fit1$coef, fit2$coef, tolerance=tol) all.equal(fit1$loglik[2], fit2$loglik[2], tolerance=tol) fit3 <- survreg(Surv(time,status) ~ pspline(age) + ph.karno, lung, robust=TRUE) fit4 <- survreg(Surv(time,status) ~ pspline(age) + ph.karno, lung, scale=fit1$scale, robust=TRUE) survival/tests/tt.Rout.save0000644000175100001440000000465312710416542015556 0ustar hornikusers R Under development (unstable) (2016-04-12 r70470) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > > # A contrived example for the tt function > # > mkdata <- function(n, beta) { + age <- runif(n, 20, 60) + x <- rbinom(n, 1, .5) + + futime <- rep(40, n) # everyone has 40 years of follow-up + status <- rep(0, n) + dtime <- runif(n/2, 1, 40) # 1/2 of them die + dtime <- sort(dtime) + + # The risk is set to beta[1]*x + beta[2]* f(current_age) + # where f= 0 up to age 40, rises linear to age 70, flat after that + for (i in 1:length(dtime)) { + atrisk <- (futime >= dtime[i]) + c.age <- age + dtime + age2 <- pmin(30, pmax(0, c.age-40)) + xbeta <- beta[1]*x + beta[2]*age2 + + # Select a death according to risk + risk <- ifelse(atrisk, exp(xbeta), 0) + dead <- sample(1:n, 1, prob=risk/sum(risk)) + + futime[dead] <- dtime[i] + status[dead] <- 1 + } + data.frame(futime=futime, status=status, age=age, x=x, risk=risk) + } > tdata <- mkdata(500, c(log(1.5), 2/30)) > > fit1 <- coxph(Surv(futime, status) ~ x + pspline(age), tdata) > fit2 <- coxph(Surv(futime, status) ~ x + tt(age), tdata, + tt= function(x, t, ...) pspline(x+t)) > > dfit <- coxph(Surv(futime, status) ~ x + tt(age), tdata, + tt= function(x, t, ...) x+t, iter=0, x=T) > > # > # Check that cluster, weight, and offset were correctly expanded > # > tdata <- data.frame(tdata, grp=sample(1:100, 500, replace=TRUE), + casewt = sample(1:5, 500, replace=TRUE), + zz = rnorm(500)) > dfit2 <- coxph(Surv(futime, status) ~ x + tt(age) + offset(zz) + cluster(grp), + weight=casewt, data=tdata, + tt= function(x, t, ...) x+t) > > proc.time() user system elapsed 7.400 0.376 7.779 survival/tests/ovarian.Rout.save0000644000175100001440000003110712656731426016572 0ustar hornikusers R Under development (unstable) (2016-01-29 r70039) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # Test the coxph program on the Ovarian data > # > > attach(ovarian) > > summary(survfit(Surv(futime, fustat)~1), censor=TRUE) Call: survfit(formula = Surv(futime, fustat) ~ 1) time n.risk n.event survival std.err lower 95% CI upper 95% CI 59 26 1 0.962 0.0377 0.890 1.000 115 25 1 0.923 0.0523 0.826 1.000 156 24 1 0.885 0.0627 0.770 1.000 268 23 1 0.846 0.0708 0.718 0.997 329 22 1 0.808 0.0773 0.670 0.974 353 21 1 0.769 0.0826 0.623 0.949 365 20 1 0.731 0.0870 0.579 0.923 377 19 0 0.731 0.0870 0.579 0.923 421 18 0 0.731 0.0870 0.579 0.923 431 17 1 0.688 0.0919 0.529 0.894 448 16 0 0.688 0.0919 0.529 0.894 464 15 1 0.642 0.0965 0.478 0.862 475 14 1 0.596 0.0999 0.429 0.828 477 13 0 0.596 0.0999 0.429 0.828 563 12 1 0.546 0.1032 0.377 0.791 638 11 1 0.497 0.1051 0.328 0.752 744 10 0 0.497 0.1051 0.328 0.752 769 9 0 0.497 0.1051 0.328 0.752 770 8 0 0.497 0.1051 0.328 0.752 803 7 0 0.497 0.1051 0.328 0.752 855 6 0 0.497 0.1051 0.328 0.752 1040 5 0 0.497 0.1051 0.328 0.752 1106 4 0 0.497 0.1051 0.328 0.752 1129 3 0 0.497 0.1051 0.328 0.752 1206 2 0 0.497 0.1051 0.328 0.752 1227 1 0 0.497 0.1051 0.328 0.752 > > # Various models > coxph(Surv(futime, fustat)~ age) Call: coxph(formula = Surv(futime, fustat) ~ age) coef exp(coef) se(coef) z p age 0.1616 1.1754 0.0497 3.25 0.0012 Likelihood ratio test=14.3 on 1 df, p=0.000156 n= 26, number of events= 12 > coxph(Surv(futime, fustat)~ resid.ds) Call: coxph(formula = Surv(futime, fustat) ~ resid.ds) coef exp(coef) se(coef) z p resid.ds 1.209 3.351 0.672 1.8 0.072 Likelihood ratio test=3.76 on 1 df, p=0.0525 n= 26, number of events= 12 > coxph(Surv(futime, fustat)~ rx) Call: coxph(formula = Surv(futime, fustat) ~ rx) coef exp(coef) se(coef) z p rx -0.596 0.551 0.587 -1.02 0.31 Likelihood ratio test=1.05 on 1 df, p=0.305 n= 26, number of events= 12 > coxph(Surv(futime, fustat)~ ecog.ps) Call: coxph(formula = Surv(futime, fustat) ~ ecog.ps) coef exp(coef) se(coef) z p ecog.ps 0.398 1.489 0.586 0.68 0.5 Likelihood ratio test=0.47 on 1 df, p=0.494 n= 26, number of events= 12 > > coxph(Surv(futime, fustat)~ resid.ds + rx + ecog.ps) Call: coxph(formula = Surv(futime, fustat) ~ resid.ds + rx + ecog.ps) coef exp(coef) se(coef) z p resid.ds 1.347 3.844 0.680 1.98 0.048 rx -0.749 0.473 0.595 -1.26 0.208 ecog.ps 0.453 1.573 0.590 0.77 0.443 Likelihood ratio test=6.03 on 3 df, p=0.11 n= 26, number of events= 12 > coxph(Surv(futime, fustat)~ age + rx + ecog.ps) Call: coxph(formula = Surv(futime, fustat) ~ age + rx + ecog.ps) coef exp(coef) se(coef) z p age 0.1470 1.1583 0.0463 3.17 0.0015 rx -0.8146 0.4428 0.6342 -1.28 0.1990 ecog.ps 0.1032 1.1087 0.6064 0.17 0.8649 Likelihood ratio test=15.9 on 3 df, p=0.00118 n= 26, number of events= 12 > coxph(Surv(futime, fustat)~ age + resid.ds + ecog.ps) Call: coxph(formula = Surv(futime, fustat) ~ age + resid.ds + ecog.ps) coef exp(coef) se(coef) z p age 0.142 1.153 0.052 2.74 0.0061 resid.ds 0.663 1.940 0.750 0.88 0.3773 ecog.ps 0.166 1.181 0.615 0.27 0.7867 Likelihood ratio test=15.1 on 3 df, p=0.00173 n= 26, number of events= 12 > coxph(Surv(futime, fustat)~ age + resid.ds + rx) Call: coxph(formula = Surv(futime, fustat) ~ age + resid.ds + rx) coef exp(coef) se(coef) z p age 0.1285 1.1372 0.0473 2.72 0.0066 resid.ds 0.6964 2.0065 0.7585 0.92 0.3586 rx -0.8489 0.4279 0.6392 -1.33 0.1842 Likelihood ratio test=16.8 on 3 df, p=0.000789 n= 26, number of events= 12 > > # Residuals > fit <- coxph(Surv(futime, fustat)~ age + resid.ds + rx + ecog.ps ) > resid(fit) 1 2 3 4 5 6 0.84103277 0.54424388 0.59670824 -0.11281376 0.75111588 -0.32609026 7 8 9 10 11 12 0.59998927 0.29570718 -2.15325805 0.76243469 0.06474272 -0.11680752 13 14 15 16 17 18 -1.22562781 -0.63474839 -0.07535824 -0.17058905 -0.22986038 -0.14654862 19 20 21 22 23 24 -0.18762920 -0.12771548 -0.53373114 -0.65480022 0.95866131 0.82111675 25 26 0.55136554 -0.09154014 > resid(fit, 'dev') 1 2 3 4 5 6 1.41281595 0.69505907 0.78916003 -0.47500266 1.13106322 -0.80757694 7 8 9 10 11 12 0.79532966 0.33122166 -2.07521471 1.16179002 0.06619519 -0.48333740 13 14 15 16 17 18 -1.56564862 -1.12671948 -0.38822221 -0.58410453 -0.67802711 -0.54138455 19 20 21 22 23 24 -0.61258338 -0.50540178 -1.03318066 -0.54976346 2.11059000 1.34157009 25 26 0.70736314 -0.42787881 > resid(fit, 'scor') age resid.ds rx ecog.ps 1 2.26503249 0.05686357 -0.10565379 -0.42661688 2 3.02525428 0.04641312 -0.08623662 -0.34821275 3 -0.06851355 0.07131430 -0.13250357 0.06167527 4 0.94597623 -0.02541510 -0.06423496 0.05971729 5 -5.41507168 0.21605962 -0.32258092 -0.39333909 6 1.48999552 0.24899474 0.14035143 -0.15380664 7 -0.68612431 0.13740891 0.28392482 0.29196506 8 0.93116906 0.08428957 0.16040160 0.18430641 9 -8.20092595 -0.51356176 0.95647608 1.11337112 10 0.95287510 -0.31078224 0.21463992 0.17363388 11 2.85526159 0.09417730 -0.14186603 -0.07586086 12 0.92721107 0.07495002 -0.05400751 0.07061578 13 -1.93962967 -0.43919871 -0.56668535 -0.48467672 14 0.63185387 -0.22745949 -0.29348437 0.38373600 15 1.41495195 0.04835392 0.04051535 0.04555769 16 2.54591188 0.10945916 0.09171493 -0.06745975 17 4.40282381 -0.08236953 0.12358137 -0.09089870 18 1.97071836 0.09403352 0.07878991 0.08859570 19 0.77692371 0.12039304 -0.08675286 0.11343089 20 1.76784279 -0.04576632 -0.05905095 0.07721016 21 -0.82272526 0.34247077 -0.24677770 -0.21106494 22 -3.48057998 -0.03965965 0.07368852 -0.26669335 23 -14.86623758 0.28137017 -0.52279208 -0.43881151 24 3.96084273 -0.56566921 0.34648950 0.44907410 25 4.30025715 0.15241262 0.22417527 -0.20390438 26 0.31490641 0.07091764 -0.05212198 0.04845623 > resid(fit, 'scho') age resid.ds rx ecog.ps 59 2.69315603 0.06761160 -0.1256239 -0.5072536 115 5.36390105 0.08039116 -0.1493686 -0.6031318 156 -0.89877512 0.10683985 -0.1985108 0.1984379 268 6.95664326 0.12857949 -0.2389036 0.2388157 329 -15.73656605 0.28889883 -0.5367805 -0.4634169 353 4.06104389 -0.70587654 0.4535120 0.5282024 365 5.50035833 0.25348264 0.4796230 -0.4413864 431 -8.06809505 0.27490176 -0.4297023 -0.5248323 464 -2.15471559 0.23158421 0.5066040 0.4814387 475 0.57065051 0.25226659 0.5518479 0.5244351 563 0.06487219 -0.47274522 0.3319974 0.2747028 638 1.64752655 -0.50593437 -0.6446947 0.2939883 > > fit <- coxph(Surv(futime, fustat) ~ age + ecog.ps + strata(rx)) > summary(fit) Call: coxph(formula = Surv(futime, fustat) ~ age + ecog.ps + strata(rx)) n= 26, number of events= 12 coef exp(coef) se(coef) z Pr(>|z|) age 0.13853 1.14858 0.04801 2.885 0.00391 ** ecog.ps -0.09670 0.90783 0.62994 -0.154 0.87800 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 exp(coef) exp(-coef) lower .95 upper .95 age 1.1486 0.8706 1.0454 1.262 ecog.ps 0.9078 1.1015 0.2641 3.120 Concordance= 0.819 (se = 0.134 ) Rsquare= 0.387 (max possible= 0.874 ) Likelihood ratio test= 12.71 on 2 df, p=0.001736 Wald test = 8.43 on 2 df, p=0.01476 Score (logrank) test = 12.24 on 2 df, p=0.002195 > summary(survfit(fit)) Call: survfit(formula = fit) rx=1 time n.risk n.event survival std.err lower 95% CI upper 95% CI 59 13 1 0.978 0.0266 0.9275 1 115 12 1 0.951 0.0478 0.8620 1 156 11 1 0.910 0.0760 0.7722 1 268 10 1 0.862 0.1055 0.6776 1 329 9 1 0.737 0.1525 0.4909 1 431 8 1 0.627 0.1704 0.3680 1 638 5 1 0.333 0.2296 0.0865 1 rx=2 time n.risk n.event survival std.err lower 95% CI upper 95% CI 353 13 1 0.943 0.0560 0.839 1.000 365 12 1 0.880 0.0812 0.735 1.000 464 9 1 0.789 0.1143 0.594 1.000 475 8 1 0.697 0.1349 0.477 1.000 563 7 1 0.597 0.1494 0.366 0.975 > sfit <- survfit(fit, list(age=c(30,70), ecog.ps=c(2,3))) #two columns > sfit Call: survfit(formula = fit, newdata = list(age = c(30, 70), ecog.ps = c(2, 3))) n events median 0.95LCL 0.95UCL rx=1, 1 13 7 NA NA NA rx=2, 1 13 5 NA NA NA rx=1, 2 13 7 268 115 NA rx=2, 2 13 5 365 353 NA > summary(sfit) Call: survfit(formula = fit, newdata = list(age = c(30, 70), ecog.ps = c(2, 3))) rx=1 time n.risk n.event survival1 survival2 59 13 1 0.999 0.87905 115 12 1 0.999 0.74575 156 11 1 0.998 0.57398 268 10 1 0.996 0.41764 329 9 1 0.992 0.16673 431 8 1 0.988 0.06489 638 5 1 0.973 0.00161 rx=2 time n.risk n.event survival1 survival2 353 13 1 0.999 0.7092 365 12 1 0.997 0.4738 464 9 1 0.994 0.2494 475 8 1 0.991 0.1207 563 7 1 0.987 0.0489 > detach() > > > # Check of offset + surv, added 7/2000 > fit1 <- coxph(Surv(futime, fustat) ~ age + rx, ovarian, + control=coxph.control(eps=1e-8)) > fit2 <- coxph(Surv(futime, fustat) ~ age + offset(rx*fit1$coef[2]), ovarian, + control=coxph.control(eps=1e-8)) > all.equal(fit1$coef[1], fit2$coef[1]) [1] TRUE > > fit <- coxph(Surv(futime, fustat) ~ age + offset(rx), ovarian) > survfit(fit, censor=FALSE)$surv^exp(-1.5) [1] 0.9977751 0.9951975 0.9917927 0.9881504 0.9825769 0.9770280 0.9704304 [8] 0.9603196 0.9499085 0.9385539 0.9217097 0.9031334 > > # Check it by hand -- there are no tied times > # Remember that offsets from survfit are centered, which is 1.5 for > # this data set. > eta <- fit$coef*(ovarian$age - fit$mean) + (ovarian$rx - 1.5) > ord <- order(ovarian$futime) > risk <- exp(eta[ord]) > rsum <- rev(cumsum(rev(risk))) # cumulative risk at each time point > dead <- (ovarian$fustat[ord]==1) > baseline <- cumsum(1/rsum[dead]) > all.equal(survfit(fit, censor=FALSE)$surv, exp(-baseline)) [1] TRUE > > rm(fit, fit1, fit2, ord, eta, risk, rsum, dead, baseline, sfit) > > proc.time() user system elapsed 0.280 0.012 0.284 survival/tests/fr_kidney.Rout.save0000644000175100001440000003205612656731522017106 0ustar hornikusers R Under development (unstable) (2016-01-29 r70039) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # From: McGilchrist and Aisbett, Biometrics 47, 461-66, 1991 > # Data on the recurrence times to infection, at the point of insertion of > # the catheter, for kidney patients using portable dialysis equipment. > # Catheters may be removed for reasons other than infection, in which case > # the observation is censored. Each patient has exactly 2 observations. > > # Variables: patient, time, status, age, > # sex (1=male, 2=female), > # disease type (0=GN, 1=AN, 2=PKD, 3=Other) > # author's estimate of the frailty > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > # I don't match their answers, and I think that I'm right > kfit <- coxph(Surv(time, status)~ age + sex + disease + frailty(id), kidney) > kfit1<- coxph(Surv(time, status) ~age + sex + disease + + frailty(id, theta=1), kidney, iter=20) > kfit0 <- coxph(Surv(time, status)~ age + sex + disease, kidney) > temp <- coxph(Surv(time, status) ~age + sex + disease + + frailty(id, theta=1, sparse=F), kidney) > > > # Check out the EM based score equations > # temp1 and kfit1 should have essentially the same coefficients > # temp2 should equal kfit1$frail > # equality won't be exact because of the different iteration paths > temp1 <- coxph(Surv(time, status) ~ age + sex + disease + + offset(kfit1$frail[id]), kidney) > rr <- tapply(resid(temp1), kidney$id, sum) > temp2 <- log(rr/1 +1) > aeq(temp1$coef, kfit1$coef, tolerance=.005) [1] TRUE > aeq(temp2, kfit1$frail, tolerance=.005) [1] TRUE > > > > kfit Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id), data = kidney) coef se(coef) se2 Chisq DF p age 3.18e-03 1.11e-02 1.11e-02 8.14e-02 1 0.775 sex -1.48e+00 3.58e-01 3.58e-01 1.71e+01 1 3.5e-05 diseaseGN 8.80e-02 4.06e-01 4.06e-01 4.68e-02 1 0.829 diseaseAN 3.51e-01 4.00e-01 4.00e-01 7.70e-01 1 0.380 diseasePKD -1.43e+00 6.31e-01 6.31e-01 5.14e+00 1 0.023 frailty(id) 2.71e-05 0 0.933 Iterations: 6 outer, 35 Newton-Raphson Variance of random effect= 5e-07 I-likelihood = -179.1 Degrees of freedom for terms= 1 1 3 0 Likelihood ratio test=17.6 on 5 df, p=0.00342 n= 76 > kfit1 Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id, theta = 1), data = kidney, iter = 20) coef se(coef) se2 Chisq DF p age 0.00389 0.01959 0.00943 0.03933 1.0 0.84280 sex -2.00764 0.59104 0.41061 11.53834 1.0 0.00068 diseaseGN 0.35335 0.71653 0.38015 0.24319 1.0 0.62191 diseaseAN 0.52341 0.72298 0.40463 0.52413 1.0 0.46909 diseasePKD -0.45938 1.08977 0.66088 0.17770 1.0 0.67336 frailty(id, theta = 1) 28.50571 18.8 0.06909 Iterations: 1 outer, 14 Newton-Raphson Variance of random effect= 1 I-likelihood = -182.5 Degrees of freedom for terms= 0.2 0.5 1.1 18.8 Likelihood ratio test=63.8 on 20.6 df, p=2.53e-06 n= 76 > kfit0 Call: coxph(formula = Surv(time, status) ~ age + sex + disease, data = kidney) coef exp(coef) se(coef) z p age 0.00318 1.00319 0.01115 0.29 0.775 sex -1.48314 0.22692 0.35823 -4.14 3.5e-05 diseaseGN 0.08796 1.09194 0.40637 0.22 0.829 diseaseAN 0.35079 1.42020 0.39972 0.88 0.380 diseasePKD -1.43111 0.23904 0.63111 -2.27 0.023 Likelihood ratio test=17.6 on 5 df, p=0.00342 n= 76, number of events= 58 > temp Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id, theta = 1, sparse = F), data = kidney) coef se(coef) se2 Chisq DF p age 0.00389 0.01865 0.01120 0.04342 1.0 0.83494 sex -2.00763 0.57624 0.40799 12.13849 1.0 0.00049 diseaseGN 0.35335 0.67865 0.43154 0.27109 1.0 0.60260 diseaseAN 0.52340 0.68910 0.44038 0.57690 1.0 0.44753 diseasePKD -0.45934 1.01394 0.71297 0.20523 1.0 0.65053 frailty(id, theta = 1, sp 26.23016 18.7 0.11573 Iterations: 1 outer, 5 Newton-Raphson Variance of random effect= 1 I-likelihood = -182.5 Degrees of freedom for terms= 0.4 0.5 1.4 18.7 Likelihood ratio test=63.8 on 21 df, p=3.27e-06 n= 76 > > # > # Now fit the data using REML > # > kfitm1 <- coxph(Surv(time,status) ~ age + sex + disease + + frailty(id, dist='gauss'), kidney) > kfitm2 <- coxph(Surv(time,status) ~ age + sex + disease + + frailty(id, dist='gauss', sparse=F), kidney) > kfitm1 Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id, dist = "gauss"), data = kidney) coef se(coef) se2 Chisq DF p age 0.00489 0.01497 0.01059 0.10678 1.0 0.74384 sex -1.69728 0.46101 0.36170 13.55454 1.0 0.00023 diseaseGN 0.17986 0.54485 0.39273 0.10897 1.0 0.74131 diseaseAN 0.39294 0.54482 0.39816 0.52016 1.0 0.47077 diseasePKD -1.13631 0.82519 0.61728 1.89621 1.0 0.16850 frailty(id, dist = "gauss 17.89195 12.1 0.12376 Iterations: 7 outer, 42 Newton-Raphson Variance of random effect= 0.493 Degrees of freedom for terms= 0.5 0.6 1.7 12.1 Likelihood ratio test=47.5 on 14.9 df, p=2.82e-05 n= 76 > summary(kfitm2) Call: coxph(formula = Surv(time, status) ~ age + sex + disease + frailty(id, dist = "gauss", sparse = F), data = kidney) n= 76, number of events= 58 coef se(coef) se2 Chisq DF p age 0.004924 0.0149 0.01084 0.11 1.00 0.74000 sex -1.702037 0.4631 0.36134 13.51 1.00 0.00024 diseaseGN 0.181733 0.5413 0.40169 0.11 1.00 0.74000 diseaseAN 0.394416 0.5428 0.40520 0.53 1.00 0.47000 diseasePKD -1.131602 0.8175 0.62981 1.92 1.00 0.17000 frailty(id, dist = "gauss 18.13 12.27 0.12000 exp(coef) exp(-coef) lower .95 upper .95 age 1.0049 0.9951 0.97601 1.0347 sex 0.1823 5.4851 0.07355 0.4519 diseaseGN 1.1993 0.8338 0.41515 3.4646 diseaseAN 1.4835 0.6741 0.51196 4.2988 diseasePKD 0.3225 3.1006 0.06497 1.6010 gauss:1 1.7011 0.5879 0.51805 5.5856 gauss:2 1.4241 0.7022 0.38513 5.2662 gauss:3 1.1593 0.8626 0.38282 3.5108 gauss:4 0.6226 1.6063 0.23397 1.6566 gauss:5 1.2543 0.7972 0.39806 3.9526 gauss:6 1.1350 0.8811 0.38339 3.3599 gauss:7 1.9726 0.5069 0.56938 6.8342 gauss:8 0.6196 1.6140 0.21662 1.7721 gauss:9 0.8231 1.2149 0.28884 2.3456 gauss:10 0.5030 1.9882 0.17468 1.4482 gauss:11 0.7565 1.3218 0.27081 2.1134 gauss:12 1.1048 0.9052 0.33430 3.6510 gauss:13 1.3022 0.7679 0.42746 3.9673 gauss:14 0.5912 1.6915 0.18537 1.8855 gauss:15 0.5449 1.8352 0.18580 1.5980 gauss:16 1.0443 0.9576 0.31424 3.4702 gauss:17 0.9136 1.0945 0.30004 2.7820 gauss:18 0.9184 1.0889 0.32476 2.5970 gauss:19 0.6426 1.5562 0.19509 2.1166 gauss:20 1.1698 0.8549 0.34528 3.9631 gauss:21 0.3336 2.9974 0.10202 1.0910 gauss:22 0.6871 1.4554 0.23531 2.0064 gauss:23 1.4778 0.6767 0.47560 4.5918 gauss:24 1.0170 0.9832 0.31555 3.2779 gauss:25 0.8096 1.2352 0.27491 2.3843 gauss:26 0.6145 1.6274 0.21491 1.7570 gauss:27 1.0885 0.9187 0.32819 3.6101 gauss:28 1.5419 0.6485 0.49231 4.8292 gauss:29 1.3785 0.7254 0.43766 4.3421 gauss:30 1.3748 0.7274 0.44444 4.2530 gauss:31 1.4447 0.6922 0.47031 4.4380 gauss:32 1.1993 0.8339 0.35207 4.0850 gauss:33 1.9449 0.5142 0.55229 6.8491 gauss:34 0.8617 1.1605 0.27685 2.6820 gauss:35 1.7031 0.5872 0.52657 5.5084 gauss:36 0.8275 1.2085 0.22811 3.0015 gauss:37 1.4707 0.6800 0.38936 5.5549 gauss:38 1.0479 0.9543 0.30685 3.5789 Iterations: 6 outer, 21 Newton-Raphson Variance of random effect= 0.5090956 Degrees of freedom for terms= 0.5 0.6 1.7 12.3 Concordance= 0.796 (se = 0.046 ) Likelihood ratio test= 117.9 on 15.14 df, p=0 > # > # Fit the kidney data using AIC > # > > # gamma, corrected aic > coxph(Surv(time, status) ~ age + sex + frailty(id, method='aic', caic=T), + kidney) Call: coxph(formula = Surv(time, status) ~ age + sex + frailty(id, method = "aic", caic = T), data = kidney) coef se(coef) se2 Chisq DF p age 0.00364 0.01048 0.00891 0.12053 1.00 0.72846 sex -1.31953 0.39556 0.32497 11.12781 1.00 0.00085 frailty(id, method = "aic 13.55258 7.81 0.08692 Iterations: 9 outer, 63 Newton-Raphson Variance of random effect= 0.203 I-likelihood = -182.1 Degrees of freedom for terms= 0.7 0.7 7.8 Likelihood ratio test=33.3 on 9.21 df, p=0.000137 n= 76 > > coxph(Surv(time, status) ~ age + sex + frailty(id, dist='t'), kidney) Call: coxph(formula = Surv(time, status) ~ age + sex + frailty(id, dist = "t"), data = kidney) coef se(coef) se2 Chisq DF p age 0.00561 0.01203 0.00872 0.21774 1.0 0.64077 sex -1.65487 0.48294 0.38527 11.74180 1.0 0.00061 frailty(id, dist = "t") 20.33462 13.9 0.11752 Iterations: 8 outer, 58 Newton-Raphson Variance of random effect= 0.825 Degrees of freedom for terms= 0.5 0.6 13.9 Likelihood ratio test=48.6 on 15.1 df, p=2.18e-05 n= 76 > coxph(Surv(time, status) ~ age + sex + frailty(id, dist='gauss', method='aic', + caic=T), kidney) Call: coxph(formula = Surv(time, status) ~ age + sex + frailty(id, dist = "gauss", method = "aic", caic = T), data = kidney) coef se(coef) se2 Chisq DF p age 0.00303 0.01031 0.00895 0.08646 1.00 0.7687 sex -1.15152 0.36368 0.30556 10.02558 1.00 0.0015 frailty(id, dist = "gauss 12.35238 6.76 0.0800 Iterations: 7 outer, 41 Newton-Raphson Variance of random effect= 0.185 Degrees of freedom for terms= 0.8 0.7 6.8 Likelihood ratio test=28.4 on 8.22 df, p=0.000476 n= 76 > > > # uncorrected aic > coxph(Surv(time, status) ~ age + sex + frailty(id, method='aic', caic=F), + kidney) Call: coxph(formula = Surv(time, status) ~ age + sex + frailty(id, method = "aic", caic = F), data = kidney) coef se(coef) se2 Chisq DF p age 0.00785 0.01503 0.00823 0.27284 1.0 0.60143 sex -1.88990 0.56114 0.39941 11.34311 1.0 0.00076 frailty(id, method = "aic 37.45897 19.7 0.00918 Iterations: 8 outer, 87 Newton-Raphson Variance of random effect= 0.886 I-likelihood = -182.8 Degrees of freedom for terms= 0.3 0.5 19.7 Likelihood ratio test=61.2 on 20.5 df, p=6.25e-06 n= 76 Warning message: In coxpenal.fit(X, Y, strats, offset, init = init, control, weights = weights, : Inner loop failed to coverge for iterations 4 > > coxph(Surv(time, status) ~ age + sex + frailty(id, dist='t', caic=F), kidney) Call: coxph(formula = Surv(time, status) ~ age + sex + frailty(id, dist = "t", caic = F), data = kidney) coef se(coef) se2 Chisq DF p age 0.00561 0.01203 0.00872 0.21774 1.0 0.64077 sex -1.65487 0.48294 0.38527 11.74180 1.0 0.00061 frailty(id, dist = "t", c 20.33462 13.9 0.11752 Iterations: 8 outer, 58 Newton-Raphson Variance of random effect= 0.825 Degrees of freedom for terms= 0.5 0.6 13.9 Likelihood ratio test=48.6 on 15.1 df, p=2.18e-05 n= 76 > > proc.time() user system elapsed 0.376 0.028 0.399 survival/tests/singtest.R0000644000175100001440000000143512030335206015265 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # A simple test of an overdetermined system # Should give a set of NA coefficients # test1 <- data.frame(time= c(4, 3,1,1,2,2,3), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0)) temp <- rep(0:3, rep(7,4)) stest <- data.frame(start = 10*temp, stop = 10*temp + test1$time, status = rep(test1$status,4), x = c(test1$x+ 1:7, rep(test1$x,3)), epoch = rep(1:4, rep(7,4))) # Will create a warning about a singular X matrix fit1 <- coxph(Surv(start, stop, status) ~ x * factor(epoch), stest) fit1$coef # elements 2:4 should be NA all.equal(is.na(fit1$coef), c(F,T,T,T,F,F,F), check.attributes=FALSE) survival/tests/data.cracks0000644000175100001440000000017711732700061015410 0ustar hornikusersNA 6.12 5 6.12 19.92 16 19.92 29.64 12 29.64 35.40 18 35.40 39.72 18 39.72 45.24 2 45.24 52.32 6 52.32 63.48 17 63.48 NA 73 survival/tests/testci2.R0000644000175100001440000001274513003736134015016 0ustar hornikuserslibrary(survival) # # Test the multi-state version of the CI curve # tdata <- data.frame(id=c(1,1,1,1, 2,2,2, 3,3, 4,4,4,4, 5, 6, 6), time1=c(0, 10,20,30, 0, 5, 15, 0, 20, 0, 6,18,34, 0, 0,15), time2=c(10,20,30,40, 5, 15,25, 20, 22, 6,18,34,50,10,15,20), status=c(1,1,1,1, 1,1,1, 1,0, 1,1,1,0,0,1,0), event= letters[c(1,2,3,4, 2,4,3, 2,2, 3,1,2,2,1, 1,1)], wt = c(2,2,2,2, 1,1,1, 3,3, 1,1,1,1, 2, 1,1), stringsAsFactors=TRUE) tdata$stat2 <- factor(tdata$status * as.numeric(tdata$event), labels=c("censor", levels(tdata$event))) fit <- survfit(Surv(time1, time2, stat2) ~1, id=id, weight=wt, tdata, influence=TRUE) # The exact figures for testci2. # The subject data of id, weight, (transition time, transition) #1: 2 (10, 0->a) (20, a->b) (30, b->c) (40, c->d) no data after 40=censored #2: 1 ( 5, 0->b) (15, b->d) (25, d->c) no data after 25 implies censored then #3: 3 (20, 0->b) (22, censor) #4: 1 ( 6, 0->c) (18, c->a) (34, a->b) (50, censor) #5: 2 (10, censor) #6: 1 (15, 0->a) (20, censor) # Each line below follows a subject through time as a (state, rdist weight) pair # using the redistribute to the right algorithm. # RDR algorithm: at each censoring (or last fu) a subject's weight is put into # a "pool" for that state and their weight goes to zero. The pool is # dynamically shared between all members of the state proportional to their # original case weight, when someone leaves they take their portion of the # pool to the new state. # Table of case weights and state, blank is weight of zero # time 5 6 10 15 18 20 25 30 34 40 50 # ----------------------------------------------------------------------- # id, wt # 1, 2 - - a a a b b c c d # 2, 1 b b b d d d c # 3, 3 - - - - - b # 4, 1 - c c c a a a a b b b # 5, 2 - - - # 6, 1 - - - a a a # Pool weights # 10 10+ 15 18 20 20+ 22+ 25 25+ 30 34 40 40+ # - 0 2 3/2 3/2 0 # a 0 0 1/2 1/2 1/4 5/4 5/4 5/4 5/4 5/4 # b 0 0 0 0 7/4 7/4 19/4 19/4 19/4 5/4 5/4 5/4 # c 0 0 0 0 0 1 23/4 23/4 # d 0 0 0 0 0 23/4 31/4 # fit$pstate for time i and state j = total weight at that time/state in the # above table (original weight + redistrib), divided by 10. # time 5 6 10 15 18 20 25 30 34 40 50 truth <- matrix(c(0, 0, 2, 3, 4, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 5, 2, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 0) + c(0, 0, 0, .5, .5, 1/4, 5/4, 5/4, 0, 0, 0, 0, 0, 0, 0, 0, 7/4, 19/4, 0, 5/4, 5/4, 5/4, 0, 0, 0, 0, 0, 0, 0, 23/4, 23/4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23/4, 31/4), ncol=4) truth <- truth[c(1:6, 6:11),]/10 #the explicit censor at 22 #dimnames(truth) <- list(c(5, 6, 10, 15, 18, 20, 25, 30, 34, 40, 50), # c('a', 'b', 'c', 'd') all.equal(truth, fit$pstate[,1:4]) # Test the dfbetas # It was a big surprise, but the epsilon where a finite difference approx to # the derivative is most accurate is around 1e-7 = approx sqrt(precision). # Smaller eps makes the all.equal test worse. # There is a now a formal test in mstate.R, not approximate. dfbeta <- 0*fit$influence[,-1,] # lose the first row eps <- sqrt(.Machine$double.eps) for (i in 1:6) { twt <- tdata$wt twt[tdata$id ==i] <- twt[tdata$id==i] + eps tfit <- survfit(Surv(time1, time2, stat2) ~ cluster(id), tdata, weight=twt) dfbeta[i,,] <- (tfit$pstate - fit$pstate)/eps #finite difference approx } all.equal(dfbeta, fit$influence[,-1,], tolerance= eps*10) twt <- tdata$wt[match(1:6, tdata$id)] # six unique weights temp <- dfbeta for (i in 1:6) temp[i,,] <- temp[i,,]* twt[i] std2 <- sqrt(apply(temp^2, 2:3, sum)) all.equal(fit$std, std2, tolerance=eps, check.attributes=FALSE) if (FALSE) { # a plot of the data that helped during creation of the example plot(c(0,50), c(1,6), type='n', xlab='time', ylab='subject') with(tdata, segments(time1, id, time2, id)) with(tdata, text(time2, id, as.numeric(stat2)-1, cex=1.5, col=2)) } if (FALSE) { # The following lines test out 4 error messages in the routine # # Gap in follow-up time, id 2 survfit(Surv(c(0,5,9,0,5,0), c(5,9,12, 4, 6, 3), factor(c(0,0,1,1,0,2))) ~1, id=c(1,1,1,2,2,3)) # mismatched weights survfit(Surv(c(0,5,9,0,5,0), c(5,9,12, 5, 6, 3), factor(c(0,0,1,1,0,2))) ~1, id=c(1,1,1,2,2,3), weights=c(1,1,2,1,1,4)) # in two groups at once survfit(Surv(c(0,5,9,0,5,0), c(5,9,12, 5, 6, 3), factor(c(0,0,1,1,0,2))) ~ c(1,1,2,1,1,2), id=c(1,1,1,2,2,3)) # state change that isn't a state change (went from 1 to 1) survfit(Surv(c(0,5,9,0,5,0), c(5,9,12, 5, 6, 3), factor(c(0,1,1,1,0,2))) ~1, id=c(1,1,1,2,2,3)) } survival/tests/fr_rat2.Rout.save0000644000175100001440000001306412656732253016473 0ustar hornikusers R Under development (unstable) (2016-01-29 r70039) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # From Gail, Sautner and Brown, Biometrics 36, 255-66, 1980 > > # 48 rats were injected with a carcinogen, and then randomized to either > # drug or placebo. The number of tumors ranges from 0 to 13; all rats were > # censored at 6 months after randomization. > > # Variables: rat, treatment (1=drug, 0=control), o > # observation # within rat, > # (start, stop] status > # The raw data has some intervals of zero length, i.e., start==stop. > # We add .1 to these times as an approximate solution > # > rat2 <- read.table('data.rat2', col.names=c('id', 'rx', 'enum', 'start', + 'stop', 'status')) > temp1 <- rat2$start > temp2 <- rat2$stop > for (i in 1:nrow(rat2)) { + if (temp1[i] == temp2[i]) { + temp2[i] <- temp2[i] + .1 + if (i < nrow(rat2) && rat2$id[i] == rat2$id[i+1]) { + temp1[i+1] <- temp1[i+1] + .1 + if (temp2[i+1] <= temp1[i+1]) temp2[i+1] <- temp1[i+1] + } + } + } > rat2$start <- temp1 > rat2$stop <- temp2 > > r2fit0 <- coxph(Surv(start, stop, status) ~ rx + cluster(id), rat2) > > r2fitg <- coxph(Surv(start, stop, status) ~ rx + frailty(id), rat2) > r2fitm <- coxph(Surv(start, stop, status) ~ rx + frailty.gaussian(id), rat2) > > r2fit0 Call: coxph(formula = Surv(start, stop, status) ~ rx + cluster(id), data = rat2) coef exp(coef) se(coef) robust se z p rx -0.827 0.438 0.151 0.204 -4.05 5.2e-05 Likelihood ratio test=32.9 on 1 df, p=9.89e-09 n= 253, number of events= 212 > r2fitg Call: coxph(formula = Surv(start, stop, status) ~ rx + frailty(id), data = rat2) coef se(coef) se2 Chisq DF p rx -0.838 0.219 0.152 14.572 1.0 0.00013 frailty(id) 57.285 26.4 0.00045 Iterations: 7 outer, 26 Newton-Raphson Variance of random effect= 0.317 I-likelihood = -779.1 Degrees of freedom for terms= 0.5 26.3 Likelihood ratio test=120 on 26.8 df, p=8.43e-14 n= 253 > r2fitm Call: coxph(formula = Surv(start, stop, status) ~ rx + frailty.gaussian(id), data = rat2) coef se(coef) se2 Chisq DF p rx -0.790 0.220 0.154 12.924 1.0 0.00032 frailty.gaussian(id) 60.939 24.9 7.3e-05 Iterations: 6 outer, 23 Newton-Raphson Variance of random effect= 0.303 Degrees of freedom for terms= 0.5 24.9 Likelihood ratio test=118 on 25.4 df, p=6.99e-14 n= 253 > > #This example is unusual: the frailties variances end up about the same, > # but the effect on rx differs. Double check it > # Because of different iteration paths, the coef won't be exactly the > # same, but darn close. > > temp <- coxph(Surv(start, stop, status) ~ rx + offset(r2fitm$frail[id]), rat2) > all.equal(temp$coef, r2fitm$coef[1], tolerance=1e-7) [1] TRUE > > temp <- coxph(Surv(start, stop, status) ~ rx + offset(r2fitg$frail[id]), rat2) > all.equal(temp$coef, r2fitg$coef[1], tolerance=1e-7) [1] TRUE > > # > # What do I get with AIC > # > r2fita1 <- coxph(Surv(start, stop, status) ~ rx + frailty(id, method='aic'), + rat2) > r2fita2 <- coxph(Surv(start, stop, status) ~ rx + frailty(id, method='aic', + dist='gauss'), rat2) > r2fita3 <- coxph(Surv(start, stop, status) ~ rx + frailty(id, dist='t'), + rat2) > > r2fita1 Call: coxph(formula = Surv(start, stop, status) ~ rx + frailty(id, method = "aic"), data = rat2) coef se(coef) se2 Chisq DF p rx -0.838 0.230 0.151 13.315 1.0 0.00026 frailty(id, method = "aic 60.406 28.2 0.00039 Iterations: 10 outer, 34 Newton-Raphson Variance of random effect= 0.375 I-likelihood = -779.2 Degrees of freedom for terms= 0.4 28.2 Likelihood ratio test=124 on 28.6 df, p=7.92e-14 n= 253 > r2fita2 Call: coxph(formula = Surv(start, stop, status) ~ rx + frailty(id, method = "aic", dist = "gauss"), data = rat2) coef se(coef) se2 Chisq DF p rx -0.785 0.245 0.154 10.300 1.0 0.0013 frailty(id, method = "aic 70.383 28.5 2.1e-05 Iterations: 9 outer, 33 Newton-Raphson Variance of random effect= 0.436 Degrees of freedom for terms= 0.4 28.5 Likelihood ratio test=125 on 28.9 df, p=5.93e-14 n= 253 > r2fita3 Call: coxph(formula = Surv(start, stop, status) ~ rx + frailty(id, dist = "t"), data = rat2) coef se(coef) se2 Chisq DF p rx -0.790 0.254 0.157 9.667 1 0.00188 frailty(id, dist = "t") 64.721 30 0.00024 Iterations: 7 outer, 29 Newton-Raphson Variance of random effect= 0.78 Degrees of freedom for terms= 0.4 30.0 Likelihood ratio test=126 on 30.4 df, p=1.39e-13 n= 253 > > proc.time() user system elapsed 0.288 0.024 0.306 survival/tests/testnull.R0000644000175100001440000000113311732700061015275 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # A test of NULL models # fit1 <- coxph(Surv(stop, event) ~ rx + strata(number), bladder, iter=0) fit2 <- coxph(Surv(stop, event) ~ strata(number), bladder) all.equal(fit1$loglik[2], fit2$loglik) all.equal(fit1$resid, fit2$resid) fit1 <- coxph(Surv(start, stop, event) ~ rx + strata(number), bladder2, iter=0) fit2 <- coxph(Surv(start, stop, event) ~ strata(number), bladder2) all.equal(fit1$loglik[2], fit2$loglik) all.equal(fit1$resid, fit2$resid) survival/tests/fr_cancer.R0000644000175100001440000000126111732700061015347 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Here is a test case with multiple smoothing terms # fit0 <- coxph(Surv(time, status) ~ ph.ecog + age, lung) fit1 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,3), lung) fit2 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,4), lung) fit3 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,8), lung) fit4 <- coxph(Surv(time, status) ~ ph.ecog + pspline(wt.loss,3), lung) fit5 <-coxph(Surv(time, status) ~ ph.ecog + pspline(age,3) + pspline(wt.loss,3), lung) fit1 fit2 fit3 fit4 fit5 rm(fit1, fit2, fit3, fit4, fit5) survival/tests/coxsurv4.R0000644000175100001440000000331712160143136015226 0ustar hornikuserslibrary(survival) # Strata by covariate interactions, a case pointed out in early 2011 # by Frank Harrell, which as it turns out had never been computed # correctly by any version of the package. Which shows how often this # case arises in practice. # aeq <- function(x, y, ...) all.equal(as.vector(x), as.vector(y)) fit1 <- coxph(Surv(time, status) ~ wt.loss + age*strata(sex) + strata(ph.ecog), data=lung) tdata <- data.frame(wt.loss=c(10,5,0,10, 15,20,25), age =c(50,60,50,60,70,40,21), sex =c(1,1,2,2,1,1,1), ph.ecog=c(0,0,1,1,2,2,2)) surv1 <- survfit(fit1, newdata=tdata) fit2 <- coxph(Surv(time, status) ~ wt.loss + age + I(age*0), data=lung, init=fit1$coef, iter=0, subset=(sex==1 & ph.ecog==0)) fit2$var <- fit1$var surv2 <- survfit(fit2, newdata=list(wt.loss=c(10,5), age=c(50,60))) s1 <- surv1[1:2] aeq(s1$surv, surv2$surv) #first a vector, second a matrix aeq(s1$std.err, surv2$std.err) aeq(s1[1]$time, surv2$time) aeq(s1[1]$n.event, surv2$n.event) fit3 <- coxph(Surv(time, status) ~ wt.loss + age + I(age*1), data=lung, init=fit1$coef, iter=0, subset=(sex==2 & ph.ecog==1)) fit3$var <- fit1$var surv3 <- survfit(fit3, newdata=list(wt.loss=c(0,10), age=c(50,60))) aeq(surv1[3:4]$surv, surv3$surv) aeq(surv1[3:4]$std, surv3$std) fit4 <- coxph(Surv(time, status) ~ wt.loss + age + I(age*0), data=lung, init=fit1$coef, iter=0, subset=(sex==1 & ph.ecog==2)) fit4$var <- fit1$var surv4 <- survfit(fit4, newdata=list(wt.loss=c(15,20,25), age=c(70,40,21))) aeq(surv1[5:7]$surv, surv4$surv) aeq(surv1[5:7]$std.err, surv4$std.err) aeq(surv1[5]$n.risk, surv4$n.risk) survival/tests/coxsurv3.Rout.save0000644000175100001440000001124511732700061016711 0ustar hornikusers R version 2.11.0 (2010-04-22) Copyright (C) 2010 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > # One more test on coxph survival curves, to test out the individual > # option. First fit a model with a time dependent covariate > # > test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), + stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), + event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), + x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) > > # True hazard function, from the validation document > lambda <- function(beta, x=0, method='efron') { + r <- exp(beta) + lambda <- c(1/(r+1), 1/(r+2), 1/(3*r +2), 1/(3*r+1), + 1/(3*r+1), 1/(3*r+2) + 1/(2*r +2)) + if (method == 'breslow') lambda[9] <- 2/(3*r +2) + list(time=c(2,3,6,7,8,9), lambda=lambda) + } > > fit <- coxph(Surv(start, stop, event) ~x, test2) > # A curve for someone who never changes > surv1 <-survfit(fit, newdata=list(x=0), censor=FALSE) > > true <- lambda(fit$coef, 0) > > aeq(true$time, surv1$time) [1] TRUE > aeq(-log(surv1$surv), cumsum(true$lambda)) [1] TRUE > > # Reprise it with a time dependent subject who doesn't change > data2 <- data.frame(start=c(0, 4, 9, 11), stop=c(4, 9, 11, 17), + event=c(0,0,0,0), x=c(0,0,0,0)) > surv2 <- survfit(fit, newdata=data2, individual=TRUE, censor=FALSE) > aeq(surv2$surv, surv1$surv) [1] TRUE > > > # > # Now a more complex data set with multiple strata > # > test3 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), + stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17, + 1:11), + event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0, + 0, 1, 1, 0, 0, 1, 1, 0, 1, 0,1), + x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0, + 1, 2, 3, 2, 1, 1, 1, 0, 2, 1,0), + grp = c(rep('a', 10), rep('b', 11))) > > fit2 <- coxph(Surv(start, stop, event) ~ x + strata(grp), test3) > > # The above tests show the program works for a simple case, use it to > # get a true baseline for strata 2 > fit2b <- coxph(Surv(start, stop, event) ~x, test3, + subset=(grp=='b'), init=fit2$coef, iter=0) > temp <- survfit(fit2b, newdata=list(x=0), censor=F) > true2 <- list(time=temp$time, lambda=diff(c(0, -log(temp$surv)))) > true1 <- lambda(fit2$coef, x=0) > > # Separate strata, one value > surv3 <- survfit(fit2, list(x=0), censor=FALSE) > aeq(true1$time, (surv3[1])$time) [1] TRUE > aeq(-log(surv3[1]$surv), cumsum(true1$lambda)) [1] TRUE > > data4 <- data.frame(start=c(0, 4, 9, 11), stop=c(4, 9, 11, 17), + event=c(0,0,0,0), x=c(0,0,0,0), grp=rep('a', 4)) > surv4a <- survfit(fit2, newdata=data4, individual=T, censor=FALSE) > aeq(-log(surv4a$surv), cumsum(true1$lambda)) [1] TRUE > > data4$grp <- rep('b',4) > surv4b <- survfit(fit2, newdata=data4, individual=T, censor=FALSE) > aeq(-log(surv4b$surv), cumsum(true2$lambda)) [1] TRUE > > > # Now for something more complex > # Subject 1 skips day 4. Since there were no events that day the survival > # will be the same, but the times will be different. > # Subject 2 spends some time in strata 1, some in strata 2, with > # moving covariates > # > data5 <- data.frame(start=c(0,5,9,11, + 0, 4, 3), + stop =c(4,9,11,17, 4,8,7), + event=rep(0,7), + x=c(1,1,1,1, 0,1,2), + grp=c('a', 'a', 'a', 'a', 'a', 'a', 'b'), + subject=c(1,1,1,1, 2,2,2)) > surv5 <- survfit(fit2, newdata=data5, censor=FALSE, id=subject) > > aeq(surv5[1]$time, c(2,3,5,6,7,8)) #surv1 has 2, 3, 6, 7, 8, 9 [1] TRUE > aeq(surv5[1]$surv, surv3[1]$surv ^ exp(fit2$coef)) [1] TRUE > > tlam <- c(true1$lambda[1:2]* exp(fit2$coef * data5$x[5]), + true1$lambda[3:5]* exp(fit2$coef * data5$x[6]), + true2$lambda[3:4]* exp(fit2$coef * data5$x[7])) > aeq(-log(surv5[2]$surv), cumsum(tlam)) [1] TRUE > > > > survival/tests/data.valve0000644000175100001440000000233611732700061015256 0ustar hornikusers251 761 -1 252 759 -1 327 98 1 327 667 -1 328 326 1 328 653 1 328 653 1 328 667 -1 329 665 -1 330 84 1 330 667 -1 331 87 1 331 663 -1 389 646 1 389 653 -1 390 92 1 390 653 -1 391 651 -1 392 258 1 392 328 1 392 377 1 392 621 1 392 650 -1 393 61 1 393 539 1 393 648 -1 394 254 1 394 276 1 394 298 1 394 640 1 394 644 -1 395 76 1 395 538 1 395 642 -1 396 635 1 396 641 -1 397 349 1 397 404 1 397 561 1 397 649 -1 398 631 -1 399 596 -1 400 120 1 400 479 1 400 614 -1 401 323 1 401 449 1 401 582 -1 402 139 1 402 139 1 402 589 -1 403 593 -1 404 573 1 404 589 -1 405 165 1 405 408 1 405 604 1 405 606 -1 406 249 1 406 594 -1 407 344 1 407 497 1 407 613 -1 408 265 1 408 586 1 408 595 -1 409 166 1 409 206 1 409 348 1 409 389 -1 410 601 -1 411 410 1 411 581 1 411 601 -1 412 611 -1 413 608 -1 414 587 -1 415 367 1 415 603 -1 416 202 1 416 563 1 416 570 1 416 585 -1 417 587 -1 418 578 -1 419 578 -1 420 586 -1 421 585 -1 422 582 -1 survival/tests/survSplit.Rout.save0000644000175100001440000000316512762305705017144 0ustar hornikusers R Under development (unstable) (2016-05-06 r70588) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > # Make sure that the old-style and new-style calls both work > > # new style > vet2 <- survSplit(Surv(time, status) ~ ., data= veteran, cut=c(90, 180), + episode= "tgroup", id="id") > vet2[1:7, c("id", "tstart", "time", "status", "tgroup", "age", "karno")] id tstart time status tgroup age karno 1 1 0 72 1 1 69 60 2 2 0 90 0 1 64 70 3 2 90 180 0 2 64 70 4 2 180 411 1 3 64 70 5 3 0 90 0 1 38 60 6 3 90 180 0 2 38 60 7 3 180 228 1 3 38 60 > > # old style > vet3 <- survSplit(veteran, end='time', event='status', cut=c(90,180), + episode="tgroup", id="id") > all.equal(vet2, vet3) [1] TRUE > > all.equal(nrow(vet2), nrow(veteran) + sum(veteran$time >90) + + sum(veteran$time > 180)) [1] TRUE > > > > proc.time() user system elapsed 1.128 0.088 1.212 survival/tests/survtest.Rout.save0000644000175100001440000000621211732700061017012 0ustar hornikusers R version 2.11.1 (2010-05-31) Copyright (C) 2010 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # Simple test of (start, stop] Kaplan-Meier curves, using the test2 data > # set > # > test1 <- data.frame(time= c(9, 3,1,1,6,6,8), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0)) > test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), + stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), + event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), + x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > fit1 <- survfit(Surv(start, stop, event) ~1, test2, type='fh2', + error='tsiatis') > fit2 <- survfit(Surv(start, stop, event) ~x, test2, start.time=3, + type='fh2') > > cfit1<- survfit(coxph(Surv(start, stop, event)~1, test2)) > cfit2<- survfit(coxph(Surv(start, stop, event) ~ strata(x), test2, subset=-1)) > > deaths <- (fit1$n.event + fit1$n.censor)>0 > aeq(fit1$time[deaths], cfit1$time) [1] TRUE > aeq(fit1$n.risk[deaths], cfit1$n.risk) [1] TRUE > aeq(fit1$n.event[deaths], cfit1$n.event) [1] TRUE > aeq(fit1$surv[deaths], cfit1$surv) [1] TRUE > aeq(fit1$std.err[deaths], cfit1$std.err) [1] TRUE > > deaths <- (fit2$n.event + fit2$n.censor)>0 > aeq(fit2$time[deaths], cfit2$time) [1] TRUE > aeq(fit2$n.risk[deaths], cfit2$n.risk) [1] TRUE > aeq(fit2$n.event[deaths], cfit2$n.event) [1] TRUE > aeq(fit2$surv[deaths], cfit2$surv) [1] TRUE > > fit3 <- survfit(Surv(start, stop, event) ~1, test2) #Kaplan-Meier > aeq(fit3$n, 10) [1] TRUE > aeq(fit3$time, c(1:9,14,17)) [1] TRUE > aeq(fit3$n.risk, c(0,2,3,3,4,5,4,4,5,2,1)) [1] TRUE > aeq(fit3$n.event,c(0,1,1,0,0,1,1,1,2,0,0)) [1] TRUE > aeq(fit3$surv[fit3$n.event>0], c(.5, 1/3, 4/15, 1/5, 3/20, 9/100)) [1] TRUE > # > # Verify that both surv AND n.risk are right between time points. > # > fit <- survfit(Surv(time, status) ~1, test1) > temp <- summary(fit, time=c(.5,1, 1.5, 6, 7.5, 8, 8.9, 9, 10), extend=TRUE) > > aeq(temp$n.risk, c(6,6,4,4,2,2,1,1,0)) [1] TRUE > aeq(temp$surv, c(1, fit$surv[c(1,1,2,2,3,3,4,4)])) [1] TRUE > aeq(temp$n.event, c(0,1,0,2,0,0,0,1,0)) [1] TRUE > aeq(temp$std.err, c(0, (fit$surv*fit$std.err)[c(1,1,2,2,3,3,4,4)])) [1] TRUE > > > fit <- survfit(Surv(start, stop, event) ~1, test2) > temp <- summary(fit, times=c(.5, 1.5, 2.5, 3, 6.5, 14.5, 16.5)) > aeq(temp$surv, c(1, fit$surv[c(1,2,3,6, 10,10)])) [1] TRUE > aeq(temp$n.risk, c(0, 2, 3, 3, 4, 1,1)) [1] TRUE > survival/tests/factor2.R0000644000175100001440000000163711732700061014774 0ustar hornikuserslibrary(survival) aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) options(na.action=na.exclude) # # More tests of factors in prediction, using a new data set # fit <- coxph(Surv(time, status) ~ factor(ph.ecog), lung) tdata <- data.frame(ph.ecog = factor(0:3)) p1 <- predict(fit, newdata=tdata, type='lp') p2 <- predict(fit, type='lp') aeq(p1, p2[match(0:3, lung$ph.ecog)]) fit2 <- coxph(Surv(time, status) ~ factor(ph.ecog) + factor(sex), lung) tdata <- expand.grid(ph.ecog = factor(0:3), sex=factor(1:2)) p1 <- predict(fit2, newdata=tdata, type='risk') xdata <- expand.grid(ph.ecog=factor(1:3), sex=factor(1:2)) p2 <- predict(fit2, newdata=xdata, type='risk') all.equal(p2, p1[c(2:4, 6:8)], check.attributes=FALSE) fit3 <- survreg(Surv(time, status) ~ factor(ph.ecog) + age, lung) tdata <- data.frame(ph.ecog=factor(0:3), age=50) predict(fit, type='lp', newdata=tdata) predict(fit3, type='lp', newdata=tdata) survival/tests/ratetable.R0000644000175100001440000000373011732700061015373 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Generate each of the messages from is.ratetable # {if (is.R()) mdy.date <- function(m, d, y) { y <- ifelse(y<100, y+1900, y) as.Date(paste(m,d,y, sep='/'), "%m/%d/%Y") } else mdy.date <- function(m,d,y) { y <- ifelse(y<100, y+1900, y) timeDate(paste(y, m, d, sep='/'), in.format="%Y/%m/%d") } } temp <- runif(21*2*4) # Good attributes(temp) <- list(dim=c(21,2,4), dimnames=list(c(as.character(75:95)), c("male","female"), c(as.character(2000:2003))), dimid=c("age","sex","year"), type=c(2,1,4), cutpoints=list(c(75:95), NULL, mdy.date(1,1,2000) +c(0:3)*366.25), class='ratetable') is.ratetable(temp) # Factor problem + cutpoints length attributes(temp) <- list(dim=c(21,2,4), dimnames=list(c(as.character(75:95)), c("male","female"), c(as.character(2000:2003))), dimid=c("age","sex","year"), type=c(1,1,2), cutpoints=list(c(75:95), NULL, mdy.date(1,1,2000) +c(0:4)*366.25), class='ratetable') is.ratetable(temp, verbose=T) # missing dimid attribute + unsorted cutpoint attributes(temp) <- list(dim=c(21,2,4), dimnames=list(c(as.character(75:95)), c("male","female"), c(as.character(2000:2003))), type=c(2,1,3), cutpoints=list(c(75:95), NULL, mdy.date(1,1,2000) +c(4:1)*366.25), class='ratetable') is.ratetable(temp, verbose=T) # wrong length for dimid and type, illegal type attributes(temp) <- list(dim=c(21,2,4), dimnames=list(c(as.character(75:95)), c("male","female"), c(as.character(2000:2003))), dimid=c("age","sex","year", "zed"), type=c(2,1,3,6), cutpoints=list(c(75:95), NULL, mdy.date(1,1,2000) +c(0:3)*366.25), class='ratetable') is.ratetable(temp, verbose=T) # Print and summary print(survexp.us[1:30,,c('1953', '1985')] ) summary(survexp.usr) survival/tests/data.donnell0000644000175100001440000001677411732700061015607 0ustar hornikusers0.558521561 1.000000000 0.000000000 1.059548255 1.000000000 0.000000000 1.659137577 1.000000000 0.000000000 0.561259411 1.000000000 0.000000000 1.108829569 1.000000000 0.000000000 1.530458590 1.000000000 0.000000000 0.550308008 1.000000000 0.000000000 1.065023956 1.000000000 0.000000000 1.546885695 1.000000000 0.000000000 0.668035592 1.000000000 0.000000000 1.048596851 1.000000000 0.000000000 1.549623546 1.000000000 0.000000000 0.594113621 1.000000000 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0.000000000 1.555099247 1.000000000 0.000000000 0.536618754 1.000000000 0.000000000 1.002053388 1.000000000 0.000000000 1.494866530 1.000000000 0.000000000 0.555783710 1.000000000 0.000000000 1.059548255 1.000000000 0.000000000 1.593429158 1.000000000 0.000000000 0.522929500 1.000000000 0.000000000 1.062286105 1.000000000 0.000000000 1.571526352 1.000000000 0.000000000 0.580424367 1.000000000 0.000000000 1.037645448 1.000000000 0.000000000 1.670088980 1.000000000 0.000000000 0.536618754 1.000000000 0.000000000 1.073237509 1.000000000 0.000000000 1.494866530 1.000000000 0.000000000 0.539356605 1.000000000 0.000000000 1.054072553 1.000000000 0.000000000 1.533196441 1.000000000 0.000000000 0.670773443 1.000000000 0.000000000 1.004791239 1.000000000 0.000000000 0.580424367 1.059548255 3.000000000 0.985626283 1.503080082 3.000000000 0.002737851 0.539356605 3.000000000 1.062286105 1.541409993 3.000000000 0.002737851 0.501026694 3.000000000 0.002737851 0.574948665 3.000000000 0.002737851 0.583162218 3.000000000 1.037645448 1.516769336 3.000000000 0.574948665 1.114305270 3.000000000 0.002737851 0.528405202 3.000000000 survival/tests/nested.Rout.save0000644000175100001440000000227512055203536016406 0ustar hornikusers R version 2.15.2 (2012-10-26) -- "Trick or Treat" Copyright (C) 2012 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > # > # A test of nesting. It makes sure the model.frame is built correctly > # > tfun <- function(fit, mydata) { + survfit(fit, newdata=mydata) + } > > myfit <- coxph(Surv(time, status) ~ age + factor(sex), lung) > > temp1 <- tfun(myfit, lung[1:5,]) > temp2 <- survfit(myfit, lung[1:5,]) > indx <- match('call', names(temp1)) #the call components won't match > > all.equal(unclass(temp1)[-indx], unclass(temp2)[-indx]) [1] TRUE > > > proc.time() user system elapsed 0.196 0.032 0.225 survival/tests/fr_simple.Rout.save0000644000175100001440000000661512701744412017107 0ustar hornikusers R Under development (unstable) (2016-03-23 r70368) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # Test the logic of the penalized code by fitting some no-frailty models > # (theta=0). It should give exactly the same answers as 'ordinary' coxph. > # > test1 <- data.frame(time= c(4, 3,1,1,2,2,3), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0)) > > test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), + stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), + event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), + x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) > > zz <- rep(0, nrow(test1)) > tfit1 <- coxph(Surv(time,status) ~x, test1, eps=1e-7) > tfit2 <- coxph(Surv(time,status) ~x + frailty(zz, theta=0, sparse=T), test1) > tfit3 <- coxph(Surv(zz,time,status) ~x + frailty(zz, theta=0, sparse=T), test1) Warning message: In coxph(Surv(zz, time, status) ~ x + frailty(zz, theta = 0, sparse = T), : a variable appears on both the left and right sides of the formula > > temp <- c('coefficients', 'var', 'loglik', 'linear.predictors', + 'means', 'n', 'concordance') > > all.equal(tfit1[temp], tfit2[temp]) [1] TRUE > all.equal(tfit2[temp], tfit3[temp]) [1] TRUE > > zz <- rep(0, nrow(test2)) > tfit1 <- coxph(Surv(start, stop, event) ~x, test2, eps=1e-7) > tfit2 <- coxph(Surv(start, stop, event) ~ x + frailty(zz, theta=0, sparse=T), + test2) > all.equal(tfit1[temp], tfit2[temp]) [1] TRUE > > > # > # Repeat the above tests, but with a strata added > # Because the data set is simply doubled, the loglik will double, > # beta is the same, variance is halved. > # > test3 <- rbind(test1, test1) > test3$x2 <- rep(1:2, rep(nrow(test1),2)) > zz <- rep(0, nrow(test3)) > tfit1 <- coxph(Surv(time,status) ~x + strata(x2), test3, eps=1e-7) > tfit2 <- coxph(Surv(time,status) ~x + frailty(zz, theta=0, sparse=T) + + strata(x2), test3) > tfit3 <- coxph(Surv(zz,time,status) ~x + frailty(zz, theta=0, sparse=T) + + strata(x2), test3) Warning message: In coxph(Surv(zz, time, status) ~ x + frailty(zz, theta = 0, sparse = T) + : a variable appears on both the left and right sides of the formula > > all.equal(tfit1[temp], tfit2[temp]) [1] TRUE > all.equal(tfit2[temp], tfit3[temp]) [1] TRUE > > > test4 <- rbind(test2, test2) > test4$x2 <- rep(1:2, rep(nrow(test2),2)) > zz <- rep(0, nrow(test4)) > tfit1 <- coxph(Surv(start, stop, event) ~x, test4, eps=1e-7) > tfit2 <- coxph(Surv(start, stop, event) ~ x + frailty(zz, theta=0, sparse=T), + test4) > all.equal(tfit1[temp], tfit2[temp]) [1] TRUE > > rm(test3, test4, tfit1, tfit2, tfit3, temp, zz) > > proc.time() user system elapsed 0.308 0.024 0.325 survival/tests/r_scale.Rout.save0000644000175100001440000000502212164374514016533 0ustar hornikusers R version 3.0.0 (2013-04-03) -- "Masked Marvel" Copyright (C) 2013 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # Verify that scale can be fixed at a value > # coefs will differ slightly due to different iteration paths > tol <- .001 > > # Intercept only models > fit1 <- survreg(Surv(time,status) ~ 1, lung) > fit2 <- survreg(Surv(time,status) ~ 1, lung, scale=fit1$scale) > all.equal(fit1$coef, fit2$coef, tolerance= tol) [1] TRUE > all.equal(fit1$loglik, fit2$loglik, tolerance= tol) [1] TRUE > > # The two robust variance matrices are not the same, since removing > # an obs has a different effect on the two models. This just > # checks for failure, not for correctness > fit3 <- survreg(Surv(time,status) ~ 1, lung, robust=TRUE) > fit4 <- survreg(Surv(time,status) ~ 1, lung, scale=fit1$scale, robust=TRUE) > > > # multiple covariates > fit1 <- survreg(Surv(time,status) ~ age + ph.karno, lung) > fit2 <- survreg(Surv(time,status) ~ age + ph.karno, lung, + scale=fit1$scale) > all.equal(fit1$coef, fit2$coef, tolerance=tol) [1] TRUE > all.equal(fit1$loglik[2], fit2$loglik[2], tolerance=tol) [1] TRUE > > fit3 <- survreg(Surv(time,status) ~ age + ph.karno, lung, robust=TRUE) > fit4 <- survreg(Surv(time,status) ~ age + ph.karno, lung, + scale=fit1$scale, robust=TRUE) > > # penalized models > fit1 <- survreg(Surv(time, status) ~ pspline(age), lung) > fit2 <- survreg(Surv(time, status) ~ pspline(age), lung, scale=fit1$scale) > all.equal(fit1$coef, fit2$coef, tolerance=tol) [1] TRUE > all.equal(fit1$loglik[2], fit2$loglik[2], tolerance=tol) [1] TRUE > > fit3 <- survreg(Surv(time,status) ~ pspline(age) + ph.karno, lung, robust=TRUE) > fit4 <- survreg(Surv(time,status) ~ pspline(age) + ph.karno, lung, + scale=fit1$scale, robust=TRUE) > > > > proc.time() user system elapsed 0.304 0.044 0.344 survival/tests/fr_rat1.R0000644000175100001440000000116412466142446015001 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # Tests using the rats data # # (Female rats, from Mantel et al, Cancer Research 37, # 3863-3868, November 77) rfit <- coxph(Surv(time,status) ~ rx + frailty(litter), rats, method='breslow', subset= (sex=='f')) names(rfit) rfit rfit$iter rfit$df rfit$history[[1]] rfit1 <- coxph(Surv(time,status) ~ rx + frailty(litter, theta=1), rats, method='breslow', subset=(sex=="f")) rfit1 rfit2 <- coxph(Surv(time,status) ~ frailty(litter), rats, subset=(sex=='f')) rfit2 survival/tests/book5.Rout.save0000644000175100001440000001604512656732513016154 0ustar hornikusers R Under development (unstable) (2016-01-29 r70039) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > > # Tests of the weighted Cox model > # This is section 1.3 of my appendix -- not yet found in the book > # though, it awaits the next edition > # > # Similar data set to test1, but add weights, > # a double-death/censor tied time > # a censored last subject > # The latter two are cases covered only feebly elsewhere. > # > # The data set testw2 has the same data, but done via replication > # > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > testw1 <- data.frame(time= c(1,1,2,2,2,2,3,4,5), + status= c(1,0,1,1,1,0,0,1,0), + x= c(2,0,1,1,0,1,0,1,0), + wt = c(1,2,3,4,3,2,1,2,1)) > xx <- testw1$wt > testw2 <- data.frame(time= rep(c(1,1,2,2,2,2,3,4,5), xx), + status= rep(c(1,0,1,1,1,0,0,1,0), xx), + x= rep(c(2,0,1,1,0,1,0,1,0), xx), + id= rep(1:9, xx)) > indx <- match(1:9, testw2$id) > > # Breslow estimate > byhand <- function(beta, newx=0) { + r <- exp(beta) + loglik <- 11*beta - (log(r^2 + 11*r +7) + 10*log(11*r +5) +2*log(2*r+1)) + hazard <- c(1/(r^2 + 11*r +7), 10/(11*r +5), 2/(2*r+1)) + xbar <- c((2*r^2 + 11*r)*hazard[1], 11*r/(11*r +5), r*hazard[3]) + U <- 11- (xbar[1] + 10*xbar[2] + 2*xbar[3]) + imat <- (4*r^2 + 11*r)*hazard[1] - xbar[1]^2 + + 10*(xbar[2] - xbar[2]^2) + 2*(xbar[3] - xbar[3]^2) + + temp <- cumsum(hazard) + risk <- c(r^2, 1,r,r,1,r,1,r,1) + expected <- risk* temp[c(1,1,2,2,2,2,2,3,3)] + + # The matrix of weights, one row per obs, one col per death + # deaths at 1,2,2,2, and 4 + riskmat <- matrix(c(1,1,1,1,1,1,1,1,1, + 0,0,1,1,1,1,1,1,1, + 0,0,1,1,1,1,1,1,1, + 0,0,1,1,1,1,1,1,1, + 0,0,0,0,0,0,0,1,1), ncol=5) + wtmat <- diag(c(r^2, 2, 3*r, 4*r, 3, 2*r, 1, 2*r, 1)) %*% riskmat + + x <- c(2,0,1,1,0,1,0,1,0) + status <- c(1,0,1,1,1,0,0,1,0) + wt <- c(1,2,3,4,3,2,1,2,1) + # Table of sums for score and Schoenfeld resids + hazmat <- riskmat %*% diag(c(1,3,4,3,2)/colSums(wtmat)) + dM <- -risk*hazmat #Expected part + dM[1,1] <- dM[1,1] +1 # deaths at time 1 + for (i in 2:4) dM[i+1, i] <- dM[i+1,i] +1 + dM[8,5] <- dM[8,5] +1 + mart <- rowSums(dM) + resid <-dM * outer(x, xbar[c(1,2,2,2,3)] ,'-') + + # Increments to the variance of the hazard + var.g <- cumsum(hazard^2/ c(1,10,2)) + var.d <- cumsum((xbar-newx)*hazard) + + list(loglik=loglik, U=U, imat=imat, hazard=hazard, xbar=xbar, + mart=c(1,0,1,1,1,0,0,1,0)-expected, expected=expected, + score=rowSums(resid), schoen=c(2,1,1,0,1) - xbar[c(1,2,2,2,3)], + varhaz=(var.g + var.d^2/imat)* exp(2*beta*newx)) + } > > aeq(byhand(0)$expected, c(1/19, 1/19, rep(103/152, 5), rep(613/456,2))) #verify [1] TRUE > > fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt, + method='breslow', iter=0) > fit0b <- coxph(Surv(time, status) ~x, testw2, method='breslow', iter=0) > fit <- coxph(Surv(time, status) ~x, testw1, weights=wt, method='breslow') > fitb <- coxph(Surv(time, status) ~x, testw2, method='breslow') > > aeq(resid(fit0, type='mart'), (resid(fit0b, type='mart'))[indx]) [1] TRUE > aeq(resid(fit0, type='scor'), (resid(fit0b, type='scor'))[indx]) [1] TRUE > aeq(unique(resid(fit0, type='scho')), unique(resid(fit0b, type='scho'))) [1] TRUE > > truth0 <- byhand(0,pi) > aeq(fit0$loglik[1], truth0$loglik) [1] TRUE > aeq(1/truth0$imat, fit0$var) [1] TRUE > aeq(truth0$mart, fit0$resid) [1] TRUE > aeq(truth0$scho, resid(fit0, 'schoen')) [1] TRUE > aeq(truth0$score, resid(fit0, 'score')) [1] TRUE > sfit <- survfit(fit0, list(x=pi), censor=FALSE) > aeq(sfit$std.err^2, truth0$var) [1] TRUE > aeq(-log(sfit$surv), cumsum(truth0$haz)) [1] TRUE > > truth <- byhand(0.85955744, .3) > aeq(truth$loglik, fit$loglik[2]) [1] TRUE > aeq(1/truth$imat, fit$var) [1] TRUE > aeq(truth$mart, fit$resid) [1] TRUE > aeq(truth$scho, resid(fit, 'schoen')) [1] TRUE > aeq(truth$score, resid(fit, 'score')) [1] TRUE > > sfit <- survfit(fit, list(x=.3), censor=FALSE) > aeq(sfit$std.err^2, truth$var) [1] TRUE > aeq(-log(sfit$surv), (cumsum(truth$haz)* exp(fit$coef*.3))) [1] TRUE > > > fit0 Call: coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt, method = "breslow", iter = 0) coef exp(coef) se(coef) z p x 0.000 1.000 0.586 0 1 Likelihood ratio test=0 on 1 df, p=1 n= 9, number of events= 5 > summary(fit) Call: coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt, method = "breslow") n= 9, number of events= 5 coef exp(coef) se(coef) z Pr(>|z|) x 0.8596 2.3621 0.7131 1.205 0.228 exp(coef) exp(-coef) lower .95 upper .95 x 2.362 0.4233 0.5839 9.556 Concordance= 0.638 (se = 0.159 ) Rsquare= 0.171 (max possible= 0.999 ) Likelihood ratio test= 1.69 on 1 df, p=0.1932 Wald test = 1.45 on 1 df, p=0.2281 Score (logrank) test = 1.52 on 1 df, p=0.217 > resid(fit0, type='score') 1 2 3 4 5 6 1.24653740 0.03601108 0.10056700 0.10056700 -0.22180142 -0.21193300 7 8 9 0.46569858 -0.10082189 0.91014302 > resid(fit0, type='scho') 1 2 2 2 4 1.3157895 0.3125000 0.3125000 -0.6875000 0.3333333 > > resid(fit, type='score') 1 2 3 4 5 6 0.88681615 0.02497653 0.03608964 0.03608964 -0.54297652 -0.12528780 7 8 9 0.29564605 -0.09476911 0.58400064 > resid(fit, type='scho') 1 2 2 2 4 1.0368337 0.1613774 0.1613774 -0.8386226 0.1746960 > aeq(resid(fit, type='mart'), (resid(fitb, type='mart'))[indx]) [1] TRUE > aeq(resid(fit, type='scor'), (resid(fitb, type='scor'))[indx]) [1] TRUE > aeq(unique(resid(fit, type='scho')), unique(resid(fitb, type='scho'))) [1] TRUE > rr1 <- resid(fit, type='mart') > rr2 <- resid(fit, type='mart', weighted=T) > aeq(rr2/rr1, testw1$wt) [1] TRUE > > rr1 <- resid(fit, type='score') > rr2 <- resid(fit, type='score', weighted=T) > aeq(rr2/rr1, testw1$wt) [1] TRUE > > > proc.time() user system elapsed 0.228 0.012 0.236 survival/tests/r_lung.R0000644000175100001440000000300711732700061014713 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) lfit2 <- survreg(Surv(time, status) ~ age + ph.ecog + strata(sex), lung) lfit3 <- survreg(Surv(time, status) ~ sex + (age+ph.ecog)*strata(sex), lung) lfit4 <- survreg(Surv(time, status) ~ age + ph.ecog , lung, subset=(sex==1)) lfit5 <- survreg(Surv(time, status) ~ age + ph.ecog , lung, subset=(sex==2)) if (exists('censorReg')) { lfit1 <- censorReg(censor(time, status) ~ age + ph.ecog + strata(sex),lung) aeq(lfit4$coef, lfit1[[1]]$coef) aeq(lfit4$scale, lfit1[[1]]$scale) aeq(c(lfit4$scale, lfit5$scale), sapply(lfit1, function(x) x$scale)) } aeq(c(lfit4$scale, lfit5$scale), lfit3$scale ) # # Test out ridge regression and splines # lfit0 <- survreg(Surv(time, status) ~1, lung) lfit1 <- survreg(Surv(time, status) ~ age + ridge(ph.ecog, theta=5), lung) lfit2 <- survreg(Surv(time, status) ~ sex + ridge(age, ph.ecog, theta=1), lung) lfit3 <- survreg(Surv(time, status) ~ sex + age + ph.ecog, lung) lfit0 lfit1 lfit2 lfit3 xx <- pspline(lung$age, nterm=3, theta=.3) xx <- matrix(unclass(xx), ncol=ncol(xx)) # the raw matrix lfit4 <- survreg(Surv(time, status) ~xx, lung) lfit5 <- survreg(Surv(time, status) ~age, lung) lfit6 <- survreg(Surv(time, status)~pspline(age, df=2), lung) lfit7 <- survreg(Surv(time, status) ~ offset(lfit6$lin), lung) lfit4 lfit5 lfit6 signif(lfit7$coef,6) survival/tests/detail.Rout.save0000644000175100001440000000655711732700061016371 0ustar hornikusers R version 2.11.0 (2010-04-22) Copyright (C) 2010 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # A short test on coxph.detail, to ensure that the computed hazard is > # equal to the theoretical value > library(survival) Loading required package: splines > aeq <- function(a,b) all.equal(as.vector(a), as.vector(b)) > > # taken from book4.R > test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), + stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), + event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), + x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) > > byhand <- function(beta, newx=0) { + r <- exp(beta) + loglik <- 4*beta - (log(r+1) + log(r+2) + 2*log(3*r+2) + 2*log(3*r+1) + + log(2*r +2)) + u <- 1/(r+1) + 1/(3*r+1) + 2*(1/(3*r+2) + 1/(2*r+2)) - + ( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1)) + imat <- r*(1/(r+1)^2 + 2/(r+2)^2 + 6/(3*r+2)^2 + + 6/(3*r+1)^2 + 6/(3*r+2)^2 + 4/(2*r +2)^2) + + hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), + 1/(3*r+2), 1/(2*r +2) ) + + + # The matrix of weights, one row per obs, one col per time + # deaths at 2,3,6,7,8,9 + wtmat <- matrix(c(1,0,0,0,1, 0, 0,0,0,0, + 0,1,0,1,1, 0, 0,0,0,0, + 0,0,1,1,1, 0, 1,1,0,0, + 0,0,0,1,1, 0, 1,1,0,0, + 0,0,0,0,1, 1, 1,1,0,0, + 0,0,0,0,0, 1, 1,1,1,1, + 0,0,0,0,0,.5,.5,1,1,1), ncol=7) + wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat + + x <- c(1,0,0,1,0,1,1,1,0,0) + status <- c(1,1,1,1,1,1,1,0,0,0) + xbar <- colSums(wtmat*x)/ colSums(wtmat) + n <- length(x) + + # Table of sums for score and Schoenfeld resids + hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time + dM <- -hazmat #Expected part + for (i in 1:5) dM[i,i] <- dM[i,i] +1 #observed + dM[6:7,6:7] <- dM[6:7,6:7] +.5 # observed + mart <- rowSums(dM) + + # Table of sums for score and Schoenfeld resids + # Looks like the last table of appendix E.2.1 of the book + resid <- dM * outer(x, xbar, '-') + score <- rowSums(resid) + scho <- colSums(resid) + + # We need to add the ties back up (they are symmetric) + scho[6:7] <- rep(mean(scho[6:7]), 2) + + list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard* exp(beta*newx), + mart=mart, score=score, rmat=resid, + scho=scho) + } > > # The actual coefficient of the fit is close to zero. Using a larger > # number pushes the test harder, but it should still work without > # the init and iter arguments, i.e., for any coefficient. > fit1 <- coxph(Surv(start, stop, event) ~x, test2,init=-1, iter=0) > temp <- coxph.detail(fit1) > temp2 <- byhand(fit1$coef, fit1$means) > aeq(temp$haz, c(temp2$haz[1:5], sum(temp2$haz[6:7]))) [1] TRUE > > survival/tests/expected2.Rout.save0000644000175100001440000000233011732700061016773 0ustar hornikusers R version 2.11.1 (2010-05-31) Copyright (C) 2010 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > # > # A Cox model with a factor, followed by survexp. > # > pfit2 <- coxph(Surv(time, status > 0) ~ trt + log(bili) + + log(protime) + age + platelet + sex, data = pbc) > esurv <- survexp(~ trt, ratetable = pfit2, data = pbc) > > temp <- pbc > temp$sex2 <- factor(as.numeric(pbc$sex), levels=2:0, + labels=c("f", "m", "unknown")) > esurv2 <- survexp(~ trt, ratetable = pfit2, data = temp, + rmap=list(sex=sex2)) > > # The call components won't match, which happen to be first > all.equal(unclass(esurv)[-1], unclass(esurv2)[-1]) [1] TRUE > survival/tests/bladder.Rout.save0000644000175100001440000001422612656732454016535 0ustar hornikusers R Under development (unstable) (2016-01-29 r70039) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # Fit the models found in Wei et. al. > # > wfit <- coxph(Surv(stop, event) ~ (rx + size + number)* strata(enum) + + cluster(id), bladder, method='breslow') > wfit Call: coxph(formula = Surv(stop, event) ~ (rx + size + number) * strata(enum) + cluster(id), data = bladder, method = "breslow") coef exp(coef) se(coef) robust se z p rx -0.5176 0.5959 0.3158 0.3075 -1.68 0.0923 size 0.0679 1.0702 0.1012 0.0853 0.80 0.4260 number 0.2360 1.2662 0.0761 0.0721 3.27 0.0011 rx:strata(enum)enum=2 -0.1018 0.9032 0.5043 0.3265 -0.31 0.7552 rx:strata(enum)enum=3 -0.1823 0.8334 0.5579 0.3916 -0.47 0.6417 rx:strata(enum)enum=4 -0.1332 0.8753 0.6581 0.4968 -0.27 0.7887 size:strata(enum)enum=2 -0.1440 0.8659 0.1680 0.1119 -1.29 0.1981 size:strata(enum)enum=3 -0.2792 0.7564 0.2086 0.1511 -1.85 0.0647 size:strata(enum)enum=4 -0.2711 0.7626 0.2515 0.1856 -1.46 0.1442 number:strata(enum)enum=2 -0.0984 0.9063 0.1193 0.1144 -0.86 0.3895 number:strata(enum)enum=3 -0.0662 0.9360 0.1298 0.1167 -0.57 0.5708 number:strata(enum)enum=4 0.0928 1.0972 0.1466 0.1175 0.79 0.4298 Likelihood ratio test=29.4 on 12 df, p=0.00344 n= 340, number of events= 112 > > # Check the rx coefs versus Wei, et al, JASA 1989 > rx <- c(1,4,5,6) # the treatment coefs above > cmat <- diag(4); cmat[1,] <- 1; #contrast matrix > wfit$coef[rx] %*% cmat # the coefs in their paper (table 5) [,1] [,2] [,3] [,4] [1,] -0.5176209 -0.6194404 -0.6998771 -0.6507935 > t(cmat) %*% wfit$var[rx,rx] %*% cmat # var matrix (eqn 3.2) [,1] [,2] [,3] [,4] [1,] 0.09455501 0.06017669 0.05677331 0.0437777 [2,] 0.06017669 0.13242834 0.13011557 0.1160420 [3,] 0.05677331 0.13011557 0.17235879 0.1590865 [4,] 0.04377770 0.11604200 0.15908650 0.2398112 > > # Anderson-Gill fit > fita <- coxph(Surv(start, stop, event) ~ rx + size + number + cluster(id), + bladder2, method='breslow') > summary(fita) Call: coxph(formula = Surv(start, stop, event) ~ rx + size + number + cluster(id), data = bladder2, method = "breslow") n= 178, number of events= 112 coef exp(coef) se(coef) robust se z Pr(>|z|) rx -0.45979 0.63142 0.19996 0.25801 -1.782 0.07474 . size -0.04256 0.95833 0.06903 0.07555 -0.563 0.57317 number 0.17164 1.18726 0.04733 0.06131 2.799 0.00512 ** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 exp(coef) exp(-coef) lower .95 upper .95 rx 0.6314 1.5837 0.3808 1.047 size 0.9583 1.0435 0.8264 1.111 number 1.1873 0.8423 1.0528 1.339 Concordance= 0.634 (se = 0.03 ) Rsquare= 0.09 (max possible= 0.994 ) Likelihood ratio test= 16.77 on 3 df, p=0.000787 Wald test = 11.76 on 3 df, p=0.008256 Score (logrank) test = 18.57 on 3 df, p=0.0003355, Robust = 11.44 p=0.009588 (Note: the likelihood ratio and score tests assume independence of observations within a cluster, the Wald and robust score tests do not). > > # Prentice fits. Their model 1 a and b are the same > fit1p <- coxph(Surv(stop, event) ~ rx + size + number, bladder2, + subset=(enum==1), method='breslow') > fit2pa <- coxph(Surv(stop, event) ~ rx + size + number, bladder2, + subset=(enum==2), method='breslow') > fit2pb <- coxph(Surv(stop-start, event) ~ rx + size + number, bladder2, + subset=(enum==2), method='breslow') > fit3pa <- coxph(Surv(stop, event) ~ rx + size + number, bladder2, + subset=(enum==3), method='breslow') > #and etc. > fit1p Call: coxph(formula = Surv(stop, event) ~ rx + size + number, data = bladder2, subset = (enum == 1), method = "breslow") coef exp(coef) se(coef) z p rx -0.5176 0.5959 0.3158 -1.64 0.1012 size 0.0679 1.0702 0.1012 0.67 0.5025 number 0.2360 1.2662 0.0761 3.10 0.0019 Likelihood ratio test=9.66 on 3 df, p=0.0216 n= 85, number of events= 47 > fit2pa Call: coxph(formula = Surv(stop, event) ~ rx + size + number, data = bladder2, subset = (enum == 2), method = "breslow") coef exp(coef) se(coef) z p rx -0.42421 0.65428 0.40220 -1.05 0.29 size -0.12503 0.88247 0.11709 -1.07 0.29 number 0.00199 1.00199 0.09376 0.02 0.98 Likelihood ratio test=2.02 on 3 df, p=0.569 n= 46, number of events= 29 > fit2pb Call: coxph(formula = Surv(stop - start, event) ~ rx + size + number, data = bladder2, subset = (enum == 2), method = "breslow") coef exp(coef) se(coef) z p rx -0.25911 0.77174 0.40511 -0.64 0.52 size -0.11636 0.89015 0.11924 -0.98 0.33 number -0.00571 0.99431 0.09667 -0.06 0.95 Likelihood ratio test=1.27 on 3 df, p=0.735 n= 46, number of events= 29 > fit3pa Call: coxph(formula = Surv(stop, event) ~ rx + size + number, data = bladder2, subset = (enum == 3), method = "breslow") coef exp(coef) se(coef) z p rx -0.8985 0.4072 0.5535 -1.62 0.10 size 0.0850 1.0887 0.2086 0.41 0.68 number -0.0172 0.9830 0.1280 -0.13 0.89 Likelihood ratio test=4.16 on 3 df, p=0.245 n= 27, number of events= 22 > rm(rx, cmat, wfit, fita, fit1p, fit2pa, fit2pb, fit3pa) > > proc.time() user system elapsed 0.200 0.028 0.225 survival/tests/tmerge2.R0000644000175100001440000000171013054077667015013 0ustar hornikuserslibrary(survival) # This test is based on a user report that a 0/1 variable would not reset # to zero. It turned out to be a bug when data2 was not sorted baseline <- data.frame(idd=1:5, futime=c(20, 30, 40, 30, 20), status= c(0, 1, 0, 1, 0)) tests <- data.frame(idd = c(2,3,3,3,4,4,5), date = c(25, -1, 15, 23, 17, 19, 14), onoff= c( 1, 1, 0, 1, 1, 0, 1)) tests <- tests[c(7,2,6,3,4,1,5),] #scramble data2 mydata <- tmerge(baseline, baseline, id=idd, death=event(futime, status)) mydata <- tmerge(mydata, tests, id=idd, ondrug=tdc(date, onoff)) all.equal(mydata$ondrug, c(NA, NA,1, 1,0,1, NA, 1,0, NA, 1)) # Check out addition of a factor tests$ff <- factor(tests$onoff, 0:1, letters[4:5]) mydata <- tmerge(mydata, tests, id=idd, fgrp= tdc(date, ff), options=list(tdcstart="new")) all.equal(mydata$fgrp, factor(c(3,3,2,2,1,2,3,2,1,3,2), labels=c("d", "e", "new"))) survival/tests/infcox.Rout.save0000644000175100001440000000424012164375013016405 0ustar hornikusers R version 3.0.0 (2013-04-03) -- "Masked Marvel" Copyright (C) 2013 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # A test to exercise the "infinity" check on 2 variables > # > test3 <- data.frame(futime=1:12, fustat=c(1,0,1,0,1,0,0,0,0,0,0,0), + x1=rep(0:1,6), x2=c(rep(0,6), rep(1,6))) > > # This will produce a warning message, which is the point of the test. > # The variance is close to singular and gives different answers > # on different machines > fit3 <- coxph(Surv(futime, fustat) ~ x1 + x2, test3, iter=25) Warning message: In fitter(X, Y, strats, offset, init, control, weights = weights, : Loglik converged before variable 1,2 ; beta may be infinite. > > all(fit3$coef < -22) [1] TRUE > all.equal(round(fit3$log, 4),c(-6.8669, -1.7918)) [1] TRUE > > # > # Actual solution > # time 1, 12 at risk, 3 each of x1/x2 = 00, 01, 10, 11 > # time 2, 10 at risk, 2, 3, 2 , 3 > # time 5, 8 at risk, 1, 3, 1, 3 > # Let r1 = exp(beta1), r2= exp(beta2) > # loglik = -log(3 + 3r1 + 3r2 + 3 r1*r2) - log(2 + 2r1 + 3r2 + 3 r1*r2) - > # log(1 + r1 + 3r2 + 3 r1*r2) > true <- function(beta) { + r1 <- exp(beta[1]) + r2 <- exp(beta[2]) + loglik <- -log(3*(1+ r1+ r2+ r1*r2)) - log(2+ 2*r1 + 3*r2 + 3*r1*r2) - + log(1 + r1 + 3*r2 + 3*r1*r2) + loglik + } > > all.equal(fit3$loglik[2], true(fit3$coef), check.attributes=FALSE) [1] TRUE > > proc.time() user system elapsed 0.216 0.020 0.233 survival/tests/data.capacitor0000644000175100001440000000606511732700061016111 0ustar hornikusers 1 300.00 0 20 2 300.00 0 20 3 300.00 0 20 4 300.00 0 20 5 300.00 0 20 6 300.00 0 20 7 300.00 0 20 8 300.00 0 20 9 300.00 0 20 10 300.00 0 20 11 300.00 0 20 12 300.00 0 20 13 300.00 0 20 14 300.00 0 20 15 300.00 0 20 16 300.00 0 20 17 300.00 0 20 18 300.00 0 20 19 300.00 0 20 20 300.00 0 20 21 300.00 0 20 22 300.00 0 20 23 300.00 0 20 24 300.00 0 20 25 300.00 0 20 26 277.33 1 26 27 187.80 1 26 28 214.28 1 26 29 12.95 1 26 30 63.10 1 26 31 271.73 1 26 32 201.28 1 26 33 179.02 1 26 34 139.37 1 26 35 136.33 1 26 36 28.41 1 26 37 300.00 0 26 38 300.00 0 26 39 300.00 0 26 40 300.00 0 26 41 300.00 0 26 42 300.00 0 26 43 300.00 0 26 44 300.00 0 26 45 300.00 0 26 46 300.00 0 26 47 300.00 0 26 48 300.00 0 26 49 300.00 0 26 50 300.00 0 26 51 300.00 0 26 52 300.00 0 26 53 300.00 0 26 54 300.00 0 26 55 300.00 0 26 56 300.00 0 26 57 300.00 0 26 58 300.00 0 26 59 300.00 0 26 60 300.00 0 26 61 300.00 0 26 62 300.00 0 26 63 300.00 0 26 64 300.00 0 26 65 300.00 0 26 66 300.00 0 26 67 300.00 0 26 68 300.00 0 26 69 300.00 0 26 70 300.00 0 26 71 300.00 0 26 72 300.00 0 26 73 300.00 0 26 74 300.00 0 26 75 300.00 0 26 76 45.85 1 29 77 220.70 1 29 78 73.87 1 29 79 91.81 1 29 80 40.69 1 29 81 108.62 1 29 82 55.73 1 29 83 10.21 1 29 84 102.64 1 29 85 257.88 1 29 86 50.41 1 29 87 164.20 1 29 88 112.15 1 29 89 300.00 0 29 90 300.00 0 29 91 300.00 0 29 92 300.00 0 29 93 300.00 0 29 94 300.00 0 29 95 300.00 0 29 96 118.37 1 32 97 17.19 1 32 98 11.51 1 32 99 4.65 1 32 100 1.95 1 32 101 149.20 1 32 102 65.79 1 32 103 5.95 1 32 104 5.72 1 32 105 10.61 1 32 106 0.68 1 32 107 3.96 1 32 108 9.56 1 32 109 172.05 1 32 110 2.81 1 32 111 2.07 1 32 112 19.98 1 32 113 84.63 1 32 114 132.52 1 32 115 156.37 1 32 116 11.81 1 32 117 20.86 1 32 118 66.33 1 32 119 21.64 1 32 120 65.90 1 32 121 14.64 1 32 122 6.26 1 32 123 94.08 1 32 124 5.45 1 32 125 15.16 1 32 survival/tests/ties.rda0000644000175100001440000001365411732700061014747 0ustar hornikusers‹mZyœNeû·Ë¥¥RHÙ²e sÆ<3ó<çœ{;‰²EöHˆÒB e©PŠH!´ ½¶HZ(’l¯-’¤H‘%ï}Ÿïuæ÷Ïo>}¦™gÎrß×õÝ®[euhT²CÉ *P¨´ýWØ~[¤ýOAû¯„ýWtHï~5´ß”±ŸYN¢Òç#,:›‚ _=´|w’»FŸY4þQ’¢/W/n]äø>o˜˜]½,éÏ^7÷aI¹Óº'×>¦H½Qâ¦ÛÿAº×Ø«õ£HŒ:zo¹ß÷Qêš[Þ}ä»b¤'°XDú‰ÔàbÁYJÕ³—Ûó )wÛY½ÈÔš3»JÇÇI»Ë_û‰{Æ®;8 ùAf˦ž#Ùù­"wy?’ðëÂâ+JSÂÝæ¹r$[ÕþÖŠM¤–µë?nR9Rî1÷|Oâà€æUË'–|ºí›š’˾®”±£ ‰_Vg]Õç Rÿö-´µñQ[W÷He~ì^¨?©B+Ö¬Û˜ï/¤6œ£¼g‚³›ô%Y/zÒoŠwLí 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-óšc(ŸMðq<„ÎåúQ›ÑWq˜'ö3¯òá É>Ód7ôZ„SÙ\OŠÿßpˆfxª>®ë™8,a¢®DK Sò¸Nõ!„.mòb~ ü£w#ŒÌå°ÕŒdý¸ue¦p˜ó:ã•Wá£äCï³àpÃÔGˆeæcدÀ¿hZäñpG®ãC|x)U}¯9\4ç¡[Ã4†¼ð—cø£rÈ\aâ>/èáÐ)â|Ÿ)=öý†CP!¯æºˆ‡¾ŠÙ¨+Ð]úwø­ì|ÈbtgÈþÏgýªX‡š‡ÑOÁ2üÜÌǺ«¥È b¨YŸé,ø>ñ/뺫iÐ㊰/¼*Ò |6±?|Œýò|ä†õ£dÝ`zc¸¬ 4×»ùÅÂÞo‘(M'H³OJ„®¾ï#ɹF*ÂûAäÇøÒa~¬Ã5Þ1òáÉ<ª¯5óˆŠóö·)Þ¯€Q¥»cÝõõV³Ï6p$Õ|//@o¨ÑÐGš‡À†u‡áázZëŨ±8+ëÁ‡{<”бz•‡kŒ«ê!èg³“‡hŒSŠûG±?Mp-øÐ’a\ŠŸ_ñá@}ṎpýèŸá—÷“d~4¬tš92oľ38Î:|9ûÆðßzÂ|YŸË<̇“8ï‘ë8ØŒC ê= ¿ò‡7ìõ(„Ô¢²…äóýë+9x* XG+>T%ΠÕ0ä0Š‡nÆ]þï#¤‹Ã—Çè4ëÊÔÜOŽŽÄz4Öw’ÅøFšÝÁýxXÂx©gãpšæÃ’q"—M©òÐ#¢ö+µûä\D¾ÂyÙä/‚‡$I" öÙ!«$׿æ!šPȽM®p;S.gÒ7‚'$÷“©œÖ;0lÑçaãhCÈć‹Ö ÞÛó!¬qXñÐTòP$Íáv..ÓM8'ÃÏ.õ¿ÿ\ÍR¹q+survival/tests/coxsurv2.Rout.save0000644000175100001440000000562611732700061016716 0ustar hornikusers R version 2.11.1 (2010-05-31) Copyright (C) 2010 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > # > # Check that the survival curves from a Cox model with beta=0 > # match ordinary survival > # > # Aalen > surv1 <- survfit(Surv(time,status) ~ sex, data=lung, type='fleming', + error='tsiatis') > fit1 <- coxph(Surv(time, status) ~ age + strata(sex), data=lung, iter=0, + method='breslow') > fit1$var <- 0*fit1$var #sneaky, causes the extra term in the Cox variance > # calculation to be zero > surv2 <- survfit(fit1, type='aalen', vartype='tsiatis') > surv3 <- survfit(fit1) > > arglist <- c('n', 'time', 'n.risk','n.event', 'n.censor', 'surv', 'strata', + 'std.err', 'upper', 'lower') > all.equal(unclass(surv1)[arglist], unclass(surv2)[arglist]) [1] TRUE > all.equal(unclass(surv1)[arglist], unclass(surv3)[arglist]) [1] TRUE > > > # Efron method > surv1 <- survfit(Surv(time,status) ~ sex, data=lung, type='fh2', + error='tsiatis') > surv2 <- survfit(fit1, type='efron', vartype='efron') > all.equal(unclass(surv1)[arglist], unclass(surv2)[arglist]) [1] TRUE > > # Kaplan-Meier > surv1 <- survfit(Surv(time,status) ~ sex, data=lung) > surv2 <- survfit(fit1, type='kalb', vartype='green') > all.equal(unclass(surv1)[arglist], unclass(surv2)[arglist]) [1] TRUE > > > # Now add some random weights > rwt <- runif(nrow(lung), .5, 3) > surv1 <- survfit(Surv(time,status) ~ sex, data=lung, type='fleming', + error='tsiatis', weight=rwt) > fit1 <- coxph(Surv(time, status) ~ age + strata(sex), data=lung, iter=0, + method='breslow', weight=rwt) > fit1$var <- 0*fit1$var #sneaky > surv2 <- survfit(fit1, type='aalen', vartype='tsiatis') > surv3 <- survfit(fit1) > > all.equal(unclass(surv1)[arglist], unclass(surv2)[arglist]) [1] TRUE > all.equal(unclass(surv1)[arglist], unclass(surv3)[arglist]) [1] TRUE > > > # Efron method > surv1 <- survfit(Surv(time,status) ~ sex, data=lung, type='fh2', + error='tsiatis', weight=rwt) > surv2 <- survfit(fit1, type='efron', vartype='efron') > all.equal(unclass(surv1)[arglist], unclass(surv2)[arglist]) [1] TRUE > > # Kaplan-Meier > surv1 <- survfit(Surv(time,status) ~ sex, data=lung, weight=rwt) > surv2 <- survfit(fit1, type='kalb', vartype='green') > all.equal(unclass(surv1)[arglist], unclass(surv2)[arglist]) [1] TRUE > > survival/tests/surv.Rout.save0000644000175100001440000000455113070710415016117 0ustar hornikusers R Under development (unstable) (2017-03-17 r72360) -- "Unsuffered Consequences" Copyright (C) 2017 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # > library(survival) > > # Some simple tests of the Surv function > # The first two are motivated by a bug, pointed out by Kevin Buhr, > # where a mixture of NAs and invalid values didn't work right > # Even for the simplest things a test case is good. > # All but the third should produce warning messages > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > temp <- Surv(c(1, 10, 20, 30), c(2, NA, 0, 40), c(1,1,1,1)) Warning message: In Surv(c(1, 10, 20, 30), c(2, NA, 0, 40), c(1, 1, 1, 1)) : Stop time must be > start time, NA created > aeq(temp, c(1,10,NA,30, 2,NA,0,40, 1,1,1,1)) [1] TRUE > > temp <- Surv(c(1, 10, 20, 30), c(2, NA, 0, 40), type='interval2') Warning message: In Surv(c(1, 10, 20, 30), c(2, NA, 0, 40), type = "interval2") : Invalid interval: start > stop, NA created > aeq(temp, c(1,10,20,30, 2,1,1,40, 3,0,NA,3)) [1] TRUE > > #No error > temp <- Surv(1:5) > aeq(temp, c(1:5, 1,1,1,1,1)) [1] TRUE > > temp1 <- Surv(c(1,10,NA, 30, 30), c(1,NA,10,20, 40), type='interval2') Warning message: In Surv(c(1, 10, NA, 30, 30), c(1, NA, 10, 20, 40), type = "interval2") : Invalid interval: start > stop, NA created > temp2 <- Surv(c(1,10,10,30,30), c(9, NA, 5, 20,40), c(1, 0, 2,3,3), + type='interval') Warning message: In Surv(c(1, 10, 10, 30, 30), c(9, NA, 5, 20, 40), c(1, 0, 2, 3, : Invalid interval: start > stop, NA created > aeq(temp1, temp2) [1] TRUE > aeq(temp1, c(1,10,10,30,30, 1,1,1,1, 40, 1,0,2,NA,3)) [1] TRUE > > # Use of inf > temp1 <- Surv(c(1,10,NA, 30, 30), c(1,NA,10,30, 40), type='interval2') > temp2 <- Surv(c(1,10,-Inf, 30, 30), c(1,Inf,10,30, 40), type='interval2') > aeq(temp1, temp2) [1] TRUE > > proc.time() user system elapsed 1.388 0.060 1.448 survival/tests/doaml.Rout.save0000644000175100001440000001742112656731604016230 0ustar hornikusers R Under development (unstable) (2016-01-29 r70039) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > # > # These results can be found in Miller > # > fit <- coxph(Surv(aml$time, aml$status) ~ aml$x, method='breslow') > fit Call: coxph(formula = Surv(aml$time, aml$status) ~ aml$x, method = "breslow") coef exp(coef) se(coef) z p aml$xNonmaintained 0.904 2.470 0.512 1.77 0.078 Likelihood ratio test=3.3 on 1 df, p=0.0694 n= 23, number of events= 18 > resid(fit, type='mart') 1 2 3 4 5 6 0.86225539 0.79200985 -0.20799015 0.74818869 0.65652976 -0.39796610 7 8 9 10 11 12 0.45424957 0.25475051 -1.05400917 -0.55400917 -1.55400917 0.87844483 13 14 15 16 17 18 0.87844483 0.74006941 0.74006941 0.57677292 -0.51373647 0.15162716 19 20 21 22 23 0.01702219 -0.14897252 -0.56448258 -1.15185244 -1.60340676 > resid(fit, type='score') 1 2 3 4 5 6 -0.546856248 -0.492501830 0.141063944 -0.479907930 -0.447416819 0.268453990 7 8 9 10 11 12 -0.235908976 -0.072655945 0.640826596 0.640826596 0.640826596 0.237767767 13 14 15 16 17 18 0.237767767 0.232585063 0.232585063 0.203878910 -0.165307985 0.044923326 19 20 21 22 23 0.007079721 -0.039651990 -0.181184547 -0.395076175 -0.472116894 > resid(fit, type='scho') 5 5 8 8 9 12 13 0.2706690 0.2706690 0.3081229 0.3081229 -0.6423931 0.3360212 -0.6335658 18 23 23 27 30 31 33 -0.6494307 -0.6791937 0.3208063 0.3269751 0.3360212 -0.5970995 0.3505693 34 43 45 48 -0.5525731 0.3778334 0.5484457 0.0000000 > > # Test the drop of an itercept: should have no effect > fit2 <- coxph(Surv(time, status) ~ x -1, method='breslow', + data=aml) > aeq(fit$loglik, fit2$loglik) [1] TRUE > aeq(coef(fit), coef(fit2)) [1] TRUE > aeq(fit$var, fit2$var) [1] TRUE > > fit <- survfit(Surv(aml$time, aml$status) ~ aml$x) > fit Call: survfit(formula = Surv(aml$time, aml$status) ~ aml$x) n events median 0.95LCL 0.95UCL aml$x=Maintained 11 7 31 18 NA aml$x=Nonmaintained 12 11 23 8 NA > summary(fit) Call: survfit(formula = Surv(aml$time, aml$status) ~ aml$x) aml$x=Maintained time n.risk n.event survival std.err lower 95% CI upper 95% CI 9 11 1 0.909 0.0867 0.7541 1.000 13 10 1 0.818 0.1163 0.6192 1.000 18 8 1 0.716 0.1397 0.4884 1.000 23 7 1 0.614 0.1526 0.3769 0.999 31 5 1 0.491 0.1642 0.2549 0.946 34 4 1 0.368 0.1627 0.1549 0.875 48 2 1 0.184 0.1535 0.0359 0.944 aml$x=Nonmaintained time n.risk n.event survival std.err lower 95% CI upper 95% CI 5 12 2 0.8333 0.1076 0.6470 1.000 8 10 2 0.6667 0.1361 0.4468 0.995 12 8 1 0.5833 0.1423 0.3616 0.941 23 6 1 0.4861 0.1481 0.2675 0.883 27 5 1 0.3889 0.1470 0.1854 0.816 30 4 1 0.2917 0.1387 0.1148 0.741 33 3 1 0.1944 0.1219 0.0569 0.664 43 2 1 0.0972 0.0919 0.0153 0.620 45 1 1 0.0000 NaN NA NA > survdiff(Surv(aml$time, aml$status)~ aml$x) Call: survdiff(formula = Surv(aml$time, aml$status) ~ aml$x) N Observed Expected (O-E)^2/E (O-E)^2/V aml$x=Maintained 11 7 10.69 1.27 3.4 aml$x=Nonmaintained 12 11 7.31 1.86 3.4 Chisq= 3.4 on 1 degrees of freedom, p= 0.0653 > > # > # Test out the weighted K-M > # > # First, equal case weights- shouldn't change the survival, but will > # halve the variance > temp2 <-survfit(Surv(aml$time, aml$status)~1, type='kaplan', weight=rep(2,23)) > temp <-survfit(Surv(time, status)~1, aml) > aeq(temp$surv, temp2$surv) [1] TRUE > aeq(temp$std.err^2, 2*temp2$std.err^2) [1] TRUE > > # Risk weights-- use a null Cox model > tfit <- coxph(Surv(aml$time, aml$status) ~ offset(log(1:23))) > sfit <- survfit(tfit, type='aalen', censor=FALSE) > > # Now compute it by hand. The survfit program will produce a curve > # corresponding to the mean offset. This is a change on 7/2010, > # which caused S(new) = S(old)^exp(mean(log(1:23))). > # Ties are a nuisance > rscore <- exp(log(1:23) - mean(log(1:23)))[order(aml$time)] > atime <- sort(aml$time) > denom <- rev(cumsum(rev(rscore))) > denom <- denom[match(unique(atime), atime)] > deaths <- tapply(aml$status, aml$time, sum) > chaz <- cumsum(deaths/denom) > all.equal(sfit$surv, as.vector(exp(-chaz[deaths>0]))) [1] TRUE > cvar <- cumsum(deaths/denom^2) > all.equal(sfit$std^2, as.vector(cvar[deaths>0])) [1] TRUE > > # And the Efron result > summary(survfit(tfit)) Call: survfit(formula = tfit) time n.risk n.event survival std.err lower 95% CI upper 95% CI 5 23 2 0.932 0.0461 0.8463 1.000 8 21 2 0.863 0.0637 0.7467 0.997 9 19 1 0.827 0.0704 0.6999 0.977 12 18 1 0.793 0.0755 0.6576 0.955 13 17 1 0.757 0.0801 0.6152 0.931 18 14 1 0.719 0.0846 0.5709 0.905 23 13 2 0.645 0.0907 0.4893 0.849 27 11 1 0.607 0.0929 0.4496 0.819 30 9 1 0.565 0.0955 0.4054 0.787 31 8 1 0.519 0.0982 0.3579 0.752 33 7 1 0.474 0.0994 0.3140 0.715 34 6 1 0.423 0.1009 0.2649 0.675 43 5 1 0.373 0.1006 0.2198 0.633 45 4 1 0.312 0.1009 0.1657 0.588 48 2 1 0.199 0.1102 0.0674 0.589 > > # Lots of ties, so its a good test case > x1 <- coxph(Surv(time, status)~x, aml, method='efron') > x1 Call: coxph(formula = Surv(time, status) ~ x, data = aml, method = "efron") coef exp(coef) se(coef) z p xNonmaintained 0.916 2.498 0.512 1.79 0.074 Likelihood ratio test=3.38 on 1 df, p=0.0658 n= 23, number of events= 18 > x2 <- coxph(Surv(rep(0,23),time, status) ~x, aml, method='efron') > aeq(x1$coef, x2$coef) [1] TRUE > > > rm(x1, x2, atime, denom, deaths, chaz,cvar, tfit, sfit, temp, temp2, fit) > > proc.time() user system elapsed 0.204 0.036 0.236 survival/tests/r_resid.Rout.save0000644000175100001440000003557511732700061016560 0ustar hornikusers R version 2.7.1 (2008-06-23) Copyright (C) 2008 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > fit1 <- survreg(Surv(futime, fustat) ~ age + ecog.ps, ovarian) > fit4 <- survreg(Surv(log(futime), fustat) ~age + ecog.ps, ovarian, + dist='extreme') > > print(fit1) Call: survreg(formula = Surv(futime, fustat) ~ age + ecog.ps, data = ovarian) Coefficients: (Intercept) age ecog.ps 12.28496723 -0.09702669 0.09977342 Scale= 0.6032744 Loglik(model)= -90 Loglik(intercept only)= -98 Chisq= 15.98 on 2 degrees of freedom, p= 0.00034 n= 26 > summary(fit4) Call: survreg(formula = Surv(log(futime), fustat) ~ age + ecog.ps, data = ovarian, dist = "extreme") Value Std. Error z p (Intercept) 12.2850 1.5015 8.182 2.80e-16 age -0.0970 0.0235 -4.127 3.67e-05 ecog.ps 0.0998 0.3657 0.273 7.85e-01 Log(scale) -0.5054 0.2351 -2.149 3.16e-02 Scale= 0.603 Extreme value distribution Loglik(model)= -21.8 Loglik(intercept only)= -29.8 Chisq= 15.98 on 2 degrees of freedom, p= 0.00034 Number of Newton-Raphson Iterations: 5 n= 26 > > > # Hypothesis (and I'm fairly sure): censorReg shares the fault of many > # iterative codes -- it returns the loglik and variance for iteration k > # but the coef vector of iteration k+1. Hence the "all.equal" tests > # below don't come out perfect. > # > if (exists('censorReg')) { #true for Splus, not R + fit2 <- censorReg(censor(futime, fustat) ~ age + ecog.ps, ovarian) + fit3 <- survreg(Surv(futime, fustat) ~ age + ecog.ps, ovarian, + iter=0, init=c(fit2$coef, log(fit2$scale))) + + aeq(resid(fit2, type='working')[,1], resid(fit3, type='working')) + aeq(resid(fit2, type='response')[,1], resid(fit3, type='response')) + + temp <- sign(resid(fit3, type='working')) + aeq(resid(fit2, type='deviance')[,1], + temp*abs(resid(fit3, type='deviance'))) + aeq(resid(fit2, type='deviance')[,1], resid(fit3, type='deviance')) + } > # > # Now check fit1 and fit4, which should follow identical iteration paths > # These tests should all be true > # > aeq(fit1$coef, fit4$coef) [1] TRUE > > resid(fit1, type='working') 1 2 3 4 5 6 -4.5081778 -0.5909810 -2.4878519 0.6032744 -5.8993431 0.6032744 7 8 9 10 11 12 -1.7462937 -0.8102883 0.6032744 -1.6593962 -0.8235265 0.6032744 13 14 15 16 17 18 0.6032744 0.6032744 0.6032744 0.6032744 0.6032744 0.6032744 19 20 21 22 23 24 0.6032744 0.6032744 0.6032744 0.2572623 -31.8006867 -0.7426277 25 26 -0.2857597 0.6032744 > resid(fit1, type='response') 1 2 3 4 5 6 -155.14523 -58.62744 -262.03173 -927.79842 -1377.84908 -658.86626 7 8 9 10 11 12 -589.74449 -318.93436 4.50671 -686.83338 -434.39281 -1105.68733 13 14 15 16 17 18 -42.43371 -173.09223 -4491.29974 -3170.49394 -5028.31053 -2050.91373 19 20 21 22 23 24 -150.65033 -2074.09345 412.32400 76.35826 -3309.40331 -219.81579 25 26 -96.19691 -457.76731 > resid(fit1, type='deviance') 1 2 3 4 5 6 7 -1.5842290 -0.6132746 -1.2876971 0.5387840 -1.7148539 0.6682580 -1.1102921 8 9 10 11 12 13 14 -0.7460191 1.4253843 -1.0849419 -0.7531720 0.6648130 1.3526380 1.1954382 15 16 17 18 19 20 21 0.2962391 0.3916044 0.3278067 0.5929057 1.2747643 0.6171130 1.9857606 22 23 24 25 26 0.6125492 -2.4504208 -0.7080652 -0.3642424 0.7317955 > resid(fit1, type='dfbeta') (Intercept) age ecog.ps Log(scale) 1 0.43370970 -1.087867e-02 0.126322520 0.048379059 2 0.14426449 -5.144770e-03 0.088768478 -0.033939677 3 0.25768057 -3.066698e-03 -0.066578834 0.021817646 4 0.05772598 -5.068044e-04 -0.013121427 -0.007762466 5 -0.58773456 6.676156e-03 0.084189274 0.008064026 6 0.01499533 -7.881949e-04 0.026570173 -0.013513160 7 -0.17869321 4.126121e-03 -0.072760519 -0.015006956 8 -0.11851540 2.520303e-03 -0.045549628 -0.035686269 9 0.08327656 3.206404e-03 -0.141835350 0.024490806 10 -0.25083921 5.321702e-03 -0.073986269 -0.020648720 11 -0.21333934 4.155746e-03 -0.049832434 -0.040215681 12 0.13889770 -1.586136e-03 -0.019701151 -0.004686340 13 0.07892133 -2.706713e-03 0.085242459 0.007847879 14 0.29690157 -1.987141e-03 -0.085553120 0.017447343 15 0.04344618 -6.319243e-04 -0.001944285 -0.003533279 16 0.04866809 -1.068317e-03 0.012398602 -0.006340983 17 0.04368104 -9.248316e-04 0.009428718 -0.004869178 18 0.15684611 -2.081485e-03 -0.013068320 -0.003265399 19 0.48839511 -4.775829e-03 -0.093258090 0.032703354 20 0.17598922 -2.349254e-03 -0.014202966 -0.002486428 21 0.37869758 -8.442011e-03 0.163476417 0.100850775 22 -0.59761427 8.803638e-03 0.052784598 -0.053085234 23 -0.79017984 1.092304e-02 0.053690092 0.080780399 24 -0.02348526 8.331002e-04 -0.039028433 -0.032765737 25 -0.13948485 3.687927e-04 0.056781884 -0.055647859 26 0.05778937 3.766350e-06 -0.029232389 -0.008927920 > resid(fit1, type='dfbetas') [,1] [,2] [,3] [,4] 1 0.288846658 -0.4627232074 0.345395116 0.20574292 2 0.096078819 -0.2188323823 0.242713641 -0.14433617 3 0.171612884 -0.1304417700 -0.182041999 0.09278449 4 0.038444974 -0.0215568869 -0.035877029 -0.03301165 5 -0.391425795 0.2839697749 0.230193032 0.03429410 6 0.009986751 -0.0335258093 0.072649027 -0.05746778 7 -0.119008027 0.1755042532 -0.198944162 -0.06382048 8 -0.078930164 0.1072008799 -0.124543264 -0.15176395 9 0.055461420 0.1363841532 -0.387810796 0.10415271 10 -0.167056601 0.2263581990 -0.202295647 -0.08781336 11 -0.142082031 0.1767643342 -0.136253451 -0.17102630 12 0.092504589 -0.0674661531 -0.053867524 -0.01992972 13 0.052560878 -0.1151298322 0.233072686 0.03337488 14 0.197733705 -0.0845228882 -0.233922105 0.07419878 15 0.028934753 -0.0268788526 -0.005316126 -0.01502607 16 0.032412497 -0.0454407662 0.033900659 -0.02696647 17 0.029091172 -0.0393376416 0.025780305 -0.02070728 18 0.104458066 -0.0885357994 -0.035731824 -0.01388685 19 0.325266641 -0.2031395176 -0.254989284 0.13907843 20 0.117207199 -0.0999253459 -0.038834208 -0.01057410 21 0.252209096 -0.3590802699 0.446982501 0.42889079 22 -0.398005596 0.3744620571 0.144325354 -0.22575700 23 -0.526252483 0.4646108448 0.146801184 0.34353696 24 -0.015640965 0.0354358527 -0.106712804 -0.13934372 25 -0.092895624 0.0156865706 0.155254862 -0.23665514 26 0.038487186 0.0001602014 -0.079928144 -0.03796800 > resid(fit1, type='ldcase') 1 2 3 4 5 6 0.374432175 0.145690278 0.112678800 0.006399163 0.261176992 0.013280058 7 8 9 10 11 12 0.109842490 0.074103234 0.248285282 0.128482147 0.094038203 0.016111951 13 14 15 16 17 18 0.132812463 0.111857574 0.001698300 0.004730718 0.003131173 0.015840667 19 20 21 22 23 24 0.179925399 0.019071941 0.797119488 0.233096445 0.666613755 0.062959708 25 26 0.080117437 0.015922378 > resid(fit1, type='ldresp') 1 2 3 4 5 6 0.076910173 0.173810883 0.078356928 0.005310644 0.060742612 0.010002154 7 8 9 10 11 12 0.067356838 0.067065693 0.355103899 0.067043195 0.068142828 0.016740944 13 14 15 16 17 18 0.193444572 0.165021262 0.001494685 0.004083386 0.002767560 0.016400993 19 20 21 22 23 24 0.269571809 0.020129806 1.409736499 1.040266083 0.058637282 0.071819025 25 26 0.112702844 0.015105534 > resid(fit1, type='ldshape') 1 2 3 4 5 6 0.870628250 0.383362440 0.412503605 0.005534970 0.513991064 0.003310847 7 8 9 10 11 12 0.291860593 0.154910362 0.256160646 0.312329770 0.183191309 0.004184904 13 14 15 16 17 18 0.110215710 0.049299495 0.007678445 0.011633336 0.011588605 0.008641251 19 20 21 22 23 24 0.112967758 0.008271358 2.246729275 0.966929220 1.022043272 0.143857170 25 26 0.079754096 0.001606647 > resid(fit1, type='matrix') g dg ddg ds dds dsg 1 -1.74950763 -1.46198129 -0.32429540 0.88466493 -2.42358635 1.8800360 2 -0.68266980 -0.82027857 -1.38799493 -0.66206188 -0.57351872 1.3921043 3 -1.32369884 -1.33411374 -0.53625126 0.31503768 -1.83606321 1.8626973 4 -0.14514412 0.24059386 -0.39881329 -0.28013223 -0.26053084 0.2237590 5 -1.96497889 -1.50383619 -0.25491587 1.15700933 -2.68145423 1.8694717 6 -0.22328436 0.37012071 -0.61351964 -0.33477229 -0.16715487 0.1848047 7 -1.11099124 -1.23201028 -0.70550005 0.01052036 -1.48515401 1.8106760 8 -0.77288913 -0.95018808 -1.17265428 -0.51190170 -0.79753045 1.5525642 9 -1.01586016 1.68391053 -2.79128447 0.01598527 -0.01623681 -1.7104080 10 -1.08316634 -1.21566480 -0.73259465 -0.03052447 -1.43539383 1.7998987 11 -0.77825093 -0.95675178 -1.16177415 -0.50314979 -0.81016011 1.5600720 12 -0.22098818 0.36631452 -0.60721042 -0.33361394 -0.17002503 0.1866908 13 -0.91481479 1.51641567 -2.51364157 -0.08144930 0.07419757 -1.3814037 14 -0.71453621 1.18442981 -1.96333502 -0.24017106 0.15944438 -0.7863174 15 -0.04387880 0.07273440 -0.12056602 -0.13717935 -0.29168773 0.1546569 16 -0.07667699 0.12710134 -0.21068577 -0.19691828 -0.30879813 0.1993144 17 -0.05372862 0.08906165 -0.14763041 -0.15709224 -0.30221555 0.1713377 18 -0.17576861 0.29135764 -0.48296037 -0.30558900 -0.22570402 0.2151929 19 -0.81251205 1.34683655 -2.23254376 -0.16869744 0.13367171 -1.0672002 20 -0.19041424 0.31563454 -0.52320225 -0.31581218 -0.20797917 0.2078622 21 -1.97162252 3.26820173 -5.41743790 1.33844939 -2.24706488 -5.4868428 22 -0.68222519 1.23245193 -4.79064290 -0.58668577 -0.95209805 -2.8390386 23 -3.49689798 -1.62675999 -0.05115487 2.90949868 -4.20494743 1.7496975 24 -0.74529506 -0.91462436 -1.23160543 -0.55723389 -0.73139169 1.5108398 25 -0.56095318 -0.53280415 -1.86451840 -0.87536233 -0.22666819 0.9689667 26 -0.26776235 0.44384834 -0.73573207 -0.35281852 -0.11207472 0.1409908 > > aeq(resid(fit1, type='working'),resid(fit4, type='working')) [1] TRUE > #aeq(resid(fit1, type='response'), resid(fit4, type='response'))#should differ > aeq(resid(fit1, type='deviance'), resid(fit4, type='deviance')) [1] TRUE > aeq(resid(fit1, type='dfbeta'), resid(fit4, type='dfbeta')) [1] TRUE > aeq(resid(fit1, type='dfbetas'), resid(fit4, type='dfbetas')) [1] TRUE > aeq(resid(fit1, type='ldcase'), resid(fit4, type='ldcase')) [1] TRUE > aeq(resid(fit1, type='ldresp'), resid(fit4, type='ldresp')) [1] TRUE > aeq(resid(fit1, type='ldshape'), resid(fit4, type='ldshape')) [1] TRUE > aeq(resid(fit1, type='matrix'), resid(fit4, type='matrix')) [1] TRUE > # > # Some tests of the quantile residuals > # > motor <- read.table('data.motor', col.names=c('temp', 'time', 'status')) > > # These should agree exactly with Ripley and Venables' book > fit1 <- survreg(Surv(time, status) ~ temp, data=motor) > summary(fit1) Call: survreg(formula = Surv(time, status) ~ temp, data = motor) Value Std. Error z p (Intercept) 16.3185 0.62296 26.2 3.03e-151 temp -0.0453 0.00319 -14.2 6.74e-46 Log(scale) -1.0956 0.21480 -5.1 3.38e-07 Scale= 0.334 Weibull distribution Loglik(model)= -147.4 Loglik(intercept only)= -169.5 Chisq= 44.32 on 1 degrees of freedom, p= 2.8e-11 Number of Newton-Raphson Iterations: 7 n= 40 > > # > # The first prediction has the SE that I think is correct > # The third is the se found in an early draft of Ripley; fit1 ignoring > # the variation in scale estimate, except via it's impact on the > # upper left corner of the inverse information matrix. > # Numbers 1 and 3 differ little for this dataset > # > predict(fit1, data.frame(temp=130), type='uquantile', p=c(.5, .1), se=T) $fit [1] 10.306068 9.676248 $se.fit [1] 0.2135247 0.2202088 > > fit2 <- survreg(Surv(time, status) ~ temp, data=motor, scale=fit1$scale) > predict(fit2, data.frame(temp=130), type='uquantile', p=c(.5, .1), se=T) $fit [1] 10.306068 9.676248 $se.fit 1 1 0.2057964 0.2057964 > > fit3 <- fit2 > fit3$var <- fit1$var[1:2,1:2] > predict(fit3, data.frame(temp=130), type='uquantile', p=c(.5, .1), se=T) $fit [1] 10.306068 9.676248 $se.fit 1 1 0.2219959 0.2219959 > > pp <- seq(.05, .7, length=40) > xx <- predict(fit1, data.frame(temp=130), type='uquantile', se=T, + p=pp) > #matplot(pp, cbind(xx$fit, xx$fit+2*xx$se, xx$fit - 2*xx$se), type='l') > > > # > # Now try out the various combinations of strata, #predicted, and > # number of quantiles desired > # > fit1 <- survreg(Surv(time, status) ~ inst + strata(inst) + age + sex, lung) > qq1 <- predict(fit1, type='quantile', p=.3, se=T) > qq2 <- predict(fit1, type='quantile', p=c(.2, .3, .4), se=T) > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > aeq(qq1$fit, qq2$fit[,2]) [1] TRUE > aeq(qq1$se.fit, qq2$se.fit[,2]) [1] TRUE > > qq3 <- predict(fit1, type='quantile', p=c(.2, .3, .4), se=T, + newdata= lung[1:5,]) > aeq(qq3$fit, qq2$fit[1:5,]) [1] TRUE > > qq4 <- predict(fit1, type='quantile', p=c(.2, .3, .4), se=T, newdata=lung[7,]) > aeq(qq4$fit, qq2$fit[7,]) [1] TRUE > > qq5 <- predict(fit1, type='quantile', p=c(.2, .3, .4), se=T, newdata=lung) > aeq(qq2$fit, qq5$fit) [1] TRUE > aeq(qq2$se.fit, qq5$se.fit) [1] TRUE > survival/tests/pspline.Rout.save0000644000175100001440000000556112714102011016563 0ustar hornikusers R Under development (unstable) (2016-05-06 r70588) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > # > # Tests with the pspline function, to verify the prediction aspects > # > options(na.action=na.exclude) > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > spfit <- coxph(Surv(time, status) ~ pspline(age) + ph.ecog, lung) > > spfit2 <- coxph(Surv(time, status) ~ pspline(age) + ph.ecog, lung, x=TRUE) > x2 <- model.matrix(spfit) > all.equal(spfit2$x, x2) [1] TRUE > > keep <- (lung$age < 60) > x3 <- model.matrix(spfit, data=lung[keep,]) > attr(x3, 'assign') <- NULL #subscripting loses the assign attr below > all.equal(napredict(spfit$na.action,x2)[keep,], x3) [1] TRUE > > p2 <- predict(spfit, newdata=lung[keep,]) > aeq(p2, predict(spfit)[keep]) [1] TRUE > > > p3 <- survfit(spfit) > p4 <- survfit(spfit, newdata=lung[1:2,]) > temp <- scale(x2[1:2,], center=spfit$means, scale=FALSE)%*% coef(spfit) > aeq(p3$time, p4$time) [1] TRUE > aeq(outer(-log(p3$surv), exp(temp), '*'), -log(p4$surv)) [1] TRUE > > # Check out model.frame > spfit3 <- coxph(Surv(time, status) ~ pspline(age) + sex, lung, + model=TRUE) #avoid the missing value > m2 <- model.frame(spfit3, data=lung[keep,]) > all.equal(m2, spfit3$model[keep,], check.attributes=FALSE) [1] TRUE > > # > # Test of residuals, in response to a reported bug. The routines for > # m-resids of penalized models were separate from other m-resid calcs; > # refactored to change that. > # These are three progam paths that should all lead to the same C routine > fit <- coxph(Surv(tstart, tstop, status) ~ sex + treat + pspline(age), cgd) > fit2 <- coxph(Surv(tstart, tstop, status) ~ fit$linear, cgd, iter=0, init=1) > fit3 <- coxph(Surv(tstart, tstop, status) ~ offset(fit$linear), cgd) > all.equal(fit$resid, fit2$resid) [1] TRUE > all.equal(fit$resid, fit3$resid) [1] TRUE > > # > # Check using coxph.detail. The matrix multiply below only is > # valid for the breslow approximation. > fit4 <- coxph(Surv(tstart, tstop, status) ~ sex + treat + pspline(age), + cgd, ties='breslow') > dt <- coxph.detail(fit4, riskmat=TRUE) > rscore <- exp(fit4$linear) > exp4 <- (rscore *dt$riskmat) %*% dt$hazard > r4 <- cgd$status - exp4 > aeq(r4, fit4$resid) [1] TRUE > > proc.time() user system elapsed 1.296 0.032 1.323 survival/tests/clogit.Rout.save0000644000175100001440000000365411732700061016403 0ustar hornikusers R version 2.14.0 (2011-10-31) Copyright (C) 2011 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > # > # Test of the clogit function, and indirectly of the exact option > # > # Data set logan has the occupation of fathers, we create a > # multinomial response > # > nresp <- length(levels(logan$occupation)) > n <- nrow(logan) > indx <- rep(1:n, nresp) > logan2 <- data.frame(logan[indx,], + id = indx, + occ2 = factor(rep(levels(logan$occupation), each=n))) > logan2$y <- (logan2$occupation == logan2$occ2) > > #We expect two NA coefficients, so ignore the warning > fit1 <- clogit(y ~ occ2 + occ2:education + occ2:race + strata(id), logan2) Warning message: In coxph(formula = Surv(rep(1, 4190L), y) ~ occ2 + occ2:education + : X matrix deemed to be singular; variable 9 14 > > #since there is only one death per group, all methods are equal > dummy <- rep(1, nrow(logan2)) > fit2 <- coxph(Surv(dummy, y) ~ occ2 + occ2:education + occ2:race + strata(id), + logan2, method='breslow') Warning message: In coxph(Surv(dummy, y) ~ occ2 + occ2:education + occ2:race + strata(id), : X matrix deemed to be singular; variable 9 14 > > all.equal(fit1$coef, fit2$coef) [1] TRUE > all.equal(fit1$loglik, fit2$loglik) [1] TRUE > all.equal(fit1$var, fit2$var) [1] TRUE > all.equal(fit1$resid, fit2$resid) [1] TRUE > > survival/tests/summary_survfit.Rout.save0000644000175100001440000001312513065015015020372 0ustar hornikusers R Under development (unstable) (2017-03-17 r72360) -- "Unsuffered Consequences" Copyright (C) 2017 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > ## check that the scale option to summary.survfit works > ## Marc Schwartz reported this as a bug in 2.35-3. > library(survival) > fit <- survfit(Surv(futime, fustat) ~rx, data=ovarian) > temp1 <- summary(fit) > temp2 <- summary(fit, scale=365.25) > > all.equal(temp1$time/365.25, temp2$time) [1] TRUE > all.equal(temp1$rmean.endtime/365.25, temp2$rmean.endtime) [1] TRUE > all.equal(temp1$table[,5:6]/365.25, temp2$table[,5:6]) [1] TRUE > temp <- names(fit) > temp <- temp[!temp %in% c("time", "table", "rmean.endtime")] > all.equal(temp1[temp], temp2[temp]) [1] TRUE > > # Reprise, using the rmean option > temp1 <- summary(fit, rmean=300) > temp2 <- summary(fit, rmean=300, scale=365.25) > all.equal(temp1$time/365.25, temp2$time) [1] TRUE > all.equal(temp1$rmean.endtime/365.25, temp2$rmean.endtime) [1] TRUE > all.equal(temp1$table[,5:6]/365.25, temp2$table[,5:6]) [1] TRUE > all.equal(temp1[temp], temp2[temp]) [1] TRUE > > # Repeat using multi-state data. Time is in months for mgus2 > etime <- with(mgus2, ifelse(pstat==0, futime, ptime)) > event <- with(mgus2, ifelse(pstat==0, 2*death, 1)) > event <- factor(event, 0:2, labels=c("censor", "pcm", "death")) > mfit <- survfit(Surv(etime, event) ~ sex, mgus2) > temp1 <- summary(mfit) > temp2 <- summary(mfit, scale=12) > > all.equal(temp1$time/12, temp2$time) [1] TRUE > all.equal(temp1$rmean.endtime/12, temp2$rmean.endtime) [1] TRUE > all.equal(temp1$table[,3]/12, temp2$table[,3]) [1] TRUE > temp <- names(temp1) > temp <- temp[!temp %in% c("time", "table", "rmean.endtime")] > all.equal(temp1[temp], temp2[temp]) [1] TRUE > > # Reprise, using the rmean option > temp1 <- summary(mfit, rmean=240) > temp2 <- summary(mfit, rmean=240, scale=12) > all.equal(temp1$time/12, temp2$time) [1] TRUE > all.equal(temp1$rmean.endtime/12, temp2$rmean.endtime) [1] TRUE > all.equal(temp1$table[,3]/12, temp2$table[,3]) [1] TRUE > all.equal(temp1[temp], temp2[temp]) [1] TRUE > > > # The n.risk values from summary.survfit were off when there are multiple > # curves (version 2.39-2) > # Verify all components by subscripting > m1 <- mfit[1,] > m2 <- mfit[2,] > s1 <- summary(m1, times=c(0,100, 200, 300)) > s2 <- summary(m2, times=c(0,100, 200, 300)) > s3 <- summary(mfit, times=c(0,100, 200, 300)) > > tfun <- function(what) { + if (is.matrix(s3[[what]])) + all.equal(rbind(s1[[what]], s2[[what]]), s3[[what]]) + else all.equal(c(s1[[what]], s2[[what]]), s3[[what]]) + } > tfun('n') [1] TRUE > tfun("time") [1] TRUE > tfun("n.risk") [1] TRUE > tfun("n.event") [1] TRUE > tfun("n.censor") [1] TRUE > tfun("pstate") [1] TRUE > all.equal(rbind(s1$p0, s2$p0), s3$p0, check.attributes=FALSE) [1] TRUE > tfun("std.err") [1] TRUE > tfun("lower") [1] TRUE > tfun("upper") [1] TRUE > > # Check the cumulative sums > temp <- rbind(0, 0, + colSums(m1$n.event[m1$time <= 100,]), + colSums(m1$n.event[m1$time <= 200, ]), + colSums(m1$n.event[m1$time <= 300, ])) > all.equal(s1$n.event, apply(temp,2, diff)) [1] TRUE > > temp <- rbind(0, 0, + colSums(m2$n.event[m2$time <= 100,]), + colSums(m2$n.event[m2$time <= 200, ]), + colSums(m2$n.event[m2$time <= 300, ])) > all.equal(s2$n.event, apply(temp,2, diff)) [1] TRUE > > temp <- c(0, 0,sum(m1$n.censor[m1$time <= 100]), + sum(m1$n.censor[m1$time <= 200]), + sum(m1$n.censor[m1$time <= 300])) > all.equal(s1$n.censor, diff(temp)) [1] TRUE > > # check the same with survfit objects > s1 <- summary(fit[1], times=c(0, 200, 400, 600)) > s2 <- summary(fit[2], times=c(0, 200, 400, 600)) > s3 <- summary(fit, times=c(0, 200, 400, 600)) > tfun('n') [1] TRUE > tfun("time") [1] TRUE > tfun("n.risk") [1] TRUE > tfun("n.event") [1] TRUE > tfun("n.censor") [1] TRUE > tfun("surv") [1] TRUE > tfun("std.err") [1] TRUE > tfun("lower") [1] TRUE > tfun("upper") [1] TRUE > > f2 <- fit[2] > temp <- c(0, 0, sum(f2$n.event[f2$time <= 200]), + sum(f2$n.event[f2$time <= 400]), + sum(f2$n.event[f2$time <= 600])) > all.equal(s2$n.event, diff(temp)) [1] TRUE > > f1 <- fit[1] > temp <- c(0, 0,sum(f1$n.censor[f1$time <= 200]), + sum(f1$n.censor[f1$time <= 400]), + sum(f1$n.censor[f1$time <= 600])) > all.equal(s1$n.censor, diff(temp)) [1] TRUE > > # > # A check on the censor option > # > s1 <- summary(fit[1]) > s2 <- summary(fit[2]) > s3 <- summary(fit) > tfun('n') [1] TRUE > tfun("time") [1] TRUE > tfun("n.risk") [1] TRUE > tfun("n.event") [1] TRUE > tfun("n.censor") [1] TRUE > tfun("surv") [1] TRUE > tfun("std.err") [1] TRUE > tfun("lower") [1] TRUE > tfun("upper") [1] TRUE > > s1 <- summary(mfit[1]) > s2 <- summary(mfit[2]) > s3 <- summary(mfit) > tfun('n') [1] TRUE > tfun("time") [1] TRUE > tfun("n.risk") [1] TRUE > tfun("n.event") [1] TRUE > tfun("n.censor") [1] TRUE > tfun("surv") [1] TRUE > tfun("std.err") [1] TRUE > tfun("lower") [1] TRUE > tfun("upper") [1] TRUE > > proc.time() user system elapsed 1.468 0.068 1.533 survival/tests/book3.Rout.save0000644000175100001440000002375012701744412016143 0ustar hornikusers R Under development (unstable) (2016-03-23 r70368) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > > # > # Tests from the appendix of Therneau and Grambsch > # c. Data set 2 and Breslow estimate > # > test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), + stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), + event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), + x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) > fit0 <-coxph(Surv(start, stop, event) ~x, test2, iter=0, method='breslow') > > byhand <- function(beta, newx=0) { + r <- exp(beta) + loglik <- 4*beta - log(r+1) - log(r+2) - 3*log(3*r+2) - 2*log(3*r+1) + u <- 1/(r+1) + 1/(3*r+1) + 4/(3*r+2) - + ( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1)) + imat <- r/(r+1)^2 + 2*r/(r+2)^2 + 6*r/(3*r+2)^2 + + 3*r/(3*r+1)^2 + 3*r/(3*r+1)^2 + 12*r/(3*r+2)^2 + + hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), 2/(3*r+2) ) + xbar <- c(r/(r+1), r/(r+2), 3*r/(3*r+2), 3*r/(3*r+1), 3*r/(3*r+1), + 3*r/(3*r+2)) + + # The matrix of weights, one row per obs, one col per time + # deaths at 2,3,6,7,8,9 + wtmat <- matrix(c(1,0,0,0,1,0,0,0,0,0, + 0,1,0,1,1,0,0,0,0,0, + 0,0,1,1,1,0,1,1,0,0, + 0,0,0,1,1,0,1,1,0,0, + 0,0,0,0,1,1,1,1,0,0, + 0,0,0,0,0,1,1,1,1,1), ncol=6) + wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat + + x <- c(1,0,0,1,0,1,1,1,0,0) + status <- c(1,1,1,1,1,1,1,0,0,0) + xbar <- colSums(wtmat*x)/ colSums(wtmat) + n <- length(x) + + # Table of sums for score and Schoenfeld resids + hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time + dM <- -hazmat #Expected part + for (i in 1:6) dM[i,i] <- dM[i,i] +1 #observed + dM[7,6] <- dM[7,6] +1 # observed + mart <- rowSums(dM) + + # Table of sums for score and Schoenfeld resids + # Looks like the last table of appendix E.2.1 of the book + resid <- dM * outer(x, xbar, '-') + score <- rowSums(resid) + scho <- colSums(resid) + # We need to split the two tied times up, to match coxph + scho <- c(scho[1:5], scho[6]/2, scho[6]/2) + var.g <- cumsum(hazard*hazard /c(1,1,1,1,1,2)) + var.d <- cumsum( (xbar-newx)*hazard) + + surv <- exp(-cumsum(hazard) * exp(beta*newx)) + varhaz <- (var.g + var.d^2/imat)* exp(2*beta*newx) + + list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard, + mart=mart, score=score, rmat=resid, + scho=scho, surv=surv, var=varhaz) + } > > > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > fit0 <-coxph(Surv(start, stop, event) ~x, test2, iter=0, method='breslow') > truth0 <- byhand(0,0) > aeq(truth0$loglik, fit0$loglik[1]) [1] TRUE > aeq(1/truth0$imat, fit0$var) [1] TRUE > aeq(truth0$mart, fit0$resid) [1] TRUE > aeq(truth0$scho, resid(fit0, 'schoen')) [1] TRUE > aeq(truth0$score, resid(fit0, 'score')) [1] TRUE > sfit <- survfit(fit0, list(x=0), censor=FALSE) > aeq(sfit$std.err^2, truth0$var) [1] TRUE > aeq(sfit$surv, truth0$surv) [1] TRUE > > beta1 <- truth0$u/truth0$imat > fit1 <- coxph(Surv(start, stop, event) ~x, test2, iter=1, ties="breslow") > aeq(beta1, coef(fit1)) [1] TRUE > > truth <- byhand(-0.084526081, 0) > fit <- coxph(Surv(start, stop, event) ~x, test2, eps=1e-8, method='breslow') > aeq(truth$loglik, fit$loglik[2]) [1] TRUE > aeq(1/truth$imat, fit$var) [1] TRUE > aeq(truth$mart, fit$resid) [1] TRUE > aeq(truth$scho, resid(fit, 'schoen')) [1] TRUE > aeq(truth$score, resid(fit, 'score')) [1] TRUE > expect <- predict(fit, type='expected', newdata=test2) #force recalc > aeq(test2$event -fit$resid, expect) #tests the predict function [1] TRUE > > sfit <- survfit(fit, list(x=0), censor=FALSE) > aeq(sfit$std.err^2, truth$var) [1] TRUE > aeq(-log(sfit$surv), (cumsum(truth$haz))) [1] TRUE > > # Reprise the test, with strata > # offseting the times ensures that we will get the wrong risk sets > # if strata were not kept separate > test2b <- rbind(test2, test2, test2) > test2b$group <- rep(1:3, each= nrow(test2)) > test2b$start <- test2b$start + test2b$group > test2b$stop <- test2b$stop + test2b$group > fit0 <- coxph(Surv(start, stop, event) ~ x + strata(group), test2b, + iter=0, method="breslow") > aeq(3*truth0$loglik, fit0$loglik[1]) [1] TRUE > aeq(3*truth0$imat, 1/fit0$var) [1] TRUE > aeq(rep(truth0$mart,3), fit0$resid) [1] TRUE > aeq(rep(truth0$scho,3), resid(fit0, 'schoen')) [1] TRUE > aeq(rep(truth0$score,3), resid(fit0, 'score')) [1] TRUE > > fit1 <- coxph(Surv(start, stop, event) ~ x + strata(group), test2b, + iter=1, method="breslow") > aeq(fit1$coef, beta1) [1] TRUE > > fit3 <- coxph(Surv(start, stop, event) ~x + strata(group), + test2b, eps=1e-8, method='breslow') > aeq(3*truth$loglik, fit3$loglik[2]) [1] TRUE > aeq(3*truth$imat, 1/fit3$var) [1] TRUE > aeq(rep(truth$mart,3), fit3$resid) [1] TRUE > aeq(rep(truth$scho,3), resid(fit3, 'schoen')) [1] TRUE > aeq(rep(truth$score,3), resid(fit3, 'score')) [1] TRUE > > # > # Done with the formal test, now print out lots of bits > # > resid(fit) 1 2 3 4 5 6 0.52111895 0.65741078 0.78977654 0.24738772 -0.60629349 0.36902492 7 8 9 10 -0.06876579 -1.06876579 -0.42044692 -0.42044692 > resid(fit, 'scor') 1 2 3 4 5 6 0.27156496 -0.20696709 -0.45771743 -0.09586133 0.13608234 0.19288983 7 8 9 10 0.04655651 -0.37389040 0.24367131 0.24367131 > resid(fit, 'scho') 2 3 6 7 8 9 9 0.5211189 -0.3148216 -0.5795531 0.2661809 -0.7338191 0.4204469 0.4204469 > > predict(fit, type='lp') [1] -0.04226304 0.04226304 0.04226304 -0.04226304 0.04226304 -0.04226304 [7] -0.04226304 -0.04226304 0.04226304 0.04226304 > predict(fit, type='risk') [1] 0.9586176 1.0431688 1.0431688 0.9586176 1.0431688 0.9586176 0.9586176 [8] 0.9586176 1.0431688 1.0431688 > predict(fit, type='expected') 1 2 3 4 5 6 7 8 0.4788811 0.3425892 0.2102235 0.7526123 1.6062935 0.6309751 1.0687658 1.0687658 9 10 0.4204469 0.4204469 > predict(fit, type='terms') x 1 -0.04226304 2 0.04226304 3 0.04226304 4 -0.04226304 5 0.04226304 6 -0.04226304 7 -0.04226304 8 -0.04226304 9 0.04226304 10 0.04226304 attr(,"constant") [1] -0.04226304 > predict(fit, type='lp', se.fit=T) $fit 1 2 3 4 5 6 -0.04226304 0.04226304 0.04226304 -0.04226304 0.04226304 -0.04226304 7 8 9 10 -0.04226304 -0.04226304 0.04226304 0.04226304 $se.fit 1 2 3 4 5 6 7 8 0.3969086 0.3969086 0.3969086 0.3969086 0.3969086 0.3969086 0.3969086 0.3969086 9 10 0.3969086 0.3969086 > predict(fit, type='risk', se.fit=T) $fit 1 2 3 4 5 6 7 8 0.9586176 1.0431688 1.0431688 0.9586176 1.0431688 0.9586176 0.9586176 0.9586176 9 10 1.0431688 1.0431688 $se.fit 1 2 3 4 5 6 7 8 0.3886094 0.4053852 0.4053852 0.3886094 0.4053852 0.3886094 0.3886094 0.3886094 9 10 0.4053852 0.4053852 > predict(fit, type='expected', se.fit=T) $fit 1 2 3 4 5 6 7 8 0.4788811 0.3425892 0.2102235 0.7526123 1.6062935 0.6309751 1.0687658 1.0687658 9 10 0.4204469 0.4204469 $se.fit [1] 0.5182381 0.3982700 0.3292830 0.6266797 1.0255146 0.5852364 0.7341340 [8] 0.7341340 0.6268550 0.6268550 > predict(fit, type='terms', se.fit=T) $fit x 1 -0.04226304 2 0.04226304 3 0.04226304 4 -0.04226304 5 0.04226304 6 -0.04226304 7 -0.04226304 8 -0.04226304 9 0.04226304 10 0.04226304 attr(,"constant") [1] -0.04226304 $se.fit x 1 0.3969086 2 0.3969086 3 0.3969086 4 0.3969086 5 0.3969086 6 0.3969086 7 0.3969086 8 0.3969086 9 0.3969086 10 0.3969086 > > summary(survfit(fit)) Call: survfit(formula = fit) time n.risk n.event survival std.err lower 95% CI upper 95% CI 2 2 1 0.607 0.303 0.2279 1.000 3 3 1 0.437 0.262 0.1347 1.000 6 5 1 0.357 0.226 0.1034 1.000 7 4 1 0.277 0.188 0.0729 1.000 8 4 1 0.214 0.156 0.0514 0.894 9 5 2 0.143 0.112 0.0308 0.667 > summary(survfit(fit, list(x=2))) Call: survfit(formula = fit, newdata = list(x = 2)) time n.risk n.event survival std.err lower 95% CI upper 95% CI 2 2 1 0.644 0.444 0.16657 1 3 3 1 0.482 0.511 0.06055 1 6 5 1 0.404 0.504 0.03491 1 7 4 1 0.322 0.475 0.01801 1 8 4 1 0.258 0.437 0.00928 1 9 5 2 0.181 0.377 0.00302 1 > > proc.time() user system elapsed 0.364 0.028 0.392 survival/tests/frank.Rout.save0000644000175100001440000000302012164375045016220 0ustar hornikusers R version 3.0.0 (2013-04-03) -- "Masked Marvel" Copyright (C) 2013 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > # > # Check out intercept/interaction for Frank H > # > age2 <- lung$age - 50 > fit1 <- coxph(Surv(time, status) ~ age * strata(sex), lung) > fit2 <- coxph(Surv(time, status) ~ age2*strata(sex), lung) > > tdata <- data.frame(age=50:60, age2=0:10, sex=c(1,2,1,2,1,2,1,2,1,2,1)) > > surv1 <- survfit(fit1, tdata) > surv2 <- survfit(fit2, tdata) > # The call won't match, but the rest should > icall <- match("call", names(surv1)) > all.equal(unclass(surv1)[-icall], unclass(surv2)[-icall]) [1] TRUE > > > # It should match what I get with a single strata fit > > fit3 <- coxph(Surv(time, status) ~ age, data=lung, + init=fit1$coef[1], subset=(sex==1), iter=0) > surv1b <- survfit(fit3, newdata=list(age=c(50,52, 54))) > all.equal(c(surv1b$surv), surv1[c(1,3,5)]$surv) [1] TRUE > > > > > proc.time() user system elapsed 0.280 0.028 0.306 survival/tests/r_stanford.R0000644000175100001440000000511611732700061015571 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # The Stanford data from 1980 is used in Escobar and Meeker, Biometrics 1992. # t5 = T5 mismatch score # Their case numbers correspond to a data set sorted by age # aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) stanford2$t5 <- ifelse(stanford2$t5 <0, NA, stanford2$t5) stanford2 <- stanford2[order(stanford2$age, stanford2$time),] stanford2$time <- ifelse(stanford2$time==0, .5, stanford2$time) cage <- stanford2$age - mean(stanford2$age) fit1 <- survreg(Surv(time, status) ~ cage + I(cage^2), stanford2, dist='lognormal') fit1 ldcase <- resid(fit1, type='ldcase') ldresp <- resid(fit1, type='ldresp') # The ldcase and ldresp should be compared to table 1 in Escobar and # Meeker, Biometrics 1992, p519; the colums they label as (1/2) A_{ii} # They give data for selected cases, entered below as mdata mdata <- cbind(c(1,2,4,5,12,16,23,61,66,72,172,182,183,184), c(.035, .244, .141, .159, .194, .402, 0,0, .143, .403, .178, .033, .005, .015), c(.138, .145, .073, .076, .104, .159, 0,0, .109, .184, .116, .063, .103, .144)) dimnames(mdata) <- list(NULL, c("case#", "ldcase", "ldresp")) aeq(round(ldcase[mdata[,1]],3), mdata[,2]) aeq(round(ldresp[mdata[,1]],3), mdata[,3]) plot1 <- function() { # make their figure 1, 2, and 6 temp <- predict(fit1, type='quantile', p=c(.1, .5, .9)) plot(stanford2$age, stanford2$time, log='y', xlab="Age", ylab="Days", ylim=range(stanford2$time, temp)) matlines(stanford2$age, temp, lty=c(1,2,2), col=1) n <- length(ldcase) plot(1:n, ldcase, xlab="Case Number", ylab="(1/2) A", type='l') title (main="Case weight pertubations") plot(1:n, ldresp, xlab="Case Number", ylab="(1/2) A", ylim=c(0, .2), type='l') title(main="Response pertubations") indx <- which(ldresp > .07) text(indx, ldresp[indx]+ .005, indx%%10, cex=.6) } postscript('meekerplot.ps') plot1() dev.off() # # Stanford predictions in other ways # fit2 <- survreg(Surv(time, status) ~ poly(age,2), stanford2, dist='lognormal') p1 <- predict(fit1, type='response') p2 <- predict(fit2, type='response') aeq(p1, p2) p3 <- predict(fit2, type='terms', se=T) p4 <- predict(fit2, type='lp', se=T) p5 <- predict(fit1, type='lp', se=T) # aeq(p3$fit + attr(p3$fit, 'constant'), p4$fit) #R is missing the attribute aeq(p4$fit, p5$fit) aeq(p3$se.fit, p4$se.fit) #this one should be false aeq(p4$se.fit, p5$se.fit) #this one true survival/tests/infcox.R0000644000175100001440000000232112160143136014711 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # A test to exercise the "infinity" check on 2 variables # test3 <- data.frame(futime=1:12, fustat=c(1,0,1,0,1,0,0,0,0,0,0,0), x1=rep(0:1,6), x2=c(rep(0,6), rep(1,6))) # This will produce a warning message, which is the point of the test. # The variance is close to singular and gives different answers # on different machines fit3 <- coxph(Surv(futime, fustat) ~ x1 + x2, test3, iter=25) all(fit3$coef < -22) all.equal(round(fit3$log, 4),c(-6.8669, -1.7918)) # # Actual solution # time 1, 12 at risk, 3 each of x1/x2 = 00, 01, 10, 11 # time 2, 10 at risk, 2, 3, 2 , 3 # time 5, 8 at risk, 1, 3, 1, 3 # Let r1 = exp(beta1), r2= exp(beta2) # loglik = -log(3 + 3r1 + 3r2 + 3 r1*r2) - log(2 + 2r1 + 3r2 + 3 r1*r2) - # log(1 + r1 + 3r2 + 3 r1*r2) true <- function(beta) { r1 <- exp(beta[1]) r2 <- exp(beta[2]) loglik <- -log(3*(1+ r1+ r2+ r1*r2)) - log(2+ 2*r1 + 3*r2 + 3*r1*r2) - log(1 + r1 + 3*r2 + 3*r1*r2) loglik } all.equal(fit3$loglik[2], true(fit3$coef), check.attributes=FALSE) survival/tests/cancer.R0000644000175100001440000000212311745775414014700 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Test out all of the routines on a more complex data set # temp <- survfit(Surv(time, status) ~ ph.ecog, lung) summary(temp, times=c(30*1:11, 365*1:3)) print(temp[2:3]) temp <- survfit(Surv(time, status)~1, lung, type='fleming', conf.int=.9, conf.type='log-log', error='tsiatis') summary(temp, times=30 *1:5) temp <- survdiff(Surv(time, status) ~ inst, lung, rho=.5) print(temp, digits=6) temp <- coxph(Surv(time, status) ~ ph.ecog + ph.karno + pat.karno + wt.loss + sex + age + meal.cal + strata(inst), lung) summary(temp) cox.zph(temp) cox.zph(temp, transform='identity') coxph(Surv(rep(0,length(time)), time, status) ~ ph.ecog + ph.karno + pat.karno + wt.loss + sex + age + meal.cal + strata(inst), lung) # # Tests of using "." # fit1 <- coxph(Surv(time, status) ~ . - meal.cal - wt.loss - inst, lung) fit2 <- update(fit1, .~. - ph.karno) fit3 <- coxph(Surv(time, status) ~ age + sex + ph.ecog + pat.karno, lung) all.equal(fit2, fit3) survival/tests/detail.R0000644000175100001440000000515111732700061014671 0ustar hornikusers# A short test on coxph.detail, to ensure that the computed hazard is # equal to the theoretical value library(survival) aeq <- function(a,b) all.equal(as.vector(a), as.vector(b)) # taken from book4.R test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) byhand <- function(beta, newx=0) { r <- exp(beta) loglik <- 4*beta - (log(r+1) + log(r+2) + 2*log(3*r+2) + 2*log(3*r+1) + log(2*r +2)) u <- 1/(r+1) + 1/(3*r+1) + 2*(1/(3*r+2) + 1/(2*r+2)) - ( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1)) imat <- r*(1/(r+1)^2 + 2/(r+2)^2 + 6/(3*r+2)^2 + 6/(3*r+1)^2 + 6/(3*r+2)^2 + 4/(2*r +2)^2) hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), 1/(3*r+2), 1/(2*r +2) ) # The matrix of weights, one row per obs, one col per time # deaths at 2,3,6,7,8,9 wtmat <- matrix(c(1,0,0,0,1, 0, 0,0,0,0, 0,1,0,1,1, 0, 0,0,0,0, 0,0,1,1,1, 0, 1,1,0,0, 0,0,0,1,1, 0, 1,1,0,0, 0,0,0,0,1, 1, 1,1,0,0, 0,0,0,0,0, 1, 1,1,1,1, 0,0,0,0,0,.5,.5,1,1,1), ncol=7) wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat x <- c(1,0,0,1,0,1,1,1,0,0) status <- c(1,1,1,1,1,1,1,0,0,0) xbar <- colSums(wtmat*x)/ colSums(wtmat) n <- length(x) # Table of sums for score and Schoenfeld resids hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time dM <- -hazmat #Expected part for (i in 1:5) dM[i,i] <- dM[i,i] +1 #observed dM[6:7,6:7] <- dM[6:7,6:7] +.5 # observed mart <- rowSums(dM) # Table of sums for score and Schoenfeld resids # Looks like the last table of appendix E.2.1 of the book resid <- dM * outer(x, xbar, '-') score <- rowSums(resid) scho <- colSums(resid) # We need to add the ties back up (they are symmetric) scho[6:7] <- rep(mean(scho[6:7]), 2) list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard* exp(beta*newx), mart=mart, score=score, rmat=resid, scho=scho) } # The actual coefficient of the fit is close to zero. Using a larger # number pushes the test harder, but it should still work without # the init and iter arguments, i.e., for any coefficient. fit1 <- coxph(Surv(start, stop, event) ~x, test2,init=-1, iter=0) temp <- coxph.detail(fit1) temp2 <- byhand(fit1$coef, fit1$means) aeq(temp$haz, c(temp2$haz[1:5], sum(temp2$haz[6:7]))) survival/tests/fr_rat2.R0000644000175100001440000000411511732700061014765 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # From Gail, Sautner and Brown, Biometrics 36, 255-66, 1980 # 48 rats were injected with a carcinogen, and then randomized to either # drug or placebo. The number of tumors ranges from 0 to 13; all rats were # censored at 6 months after randomization. # Variables: rat, treatment (1=drug, 0=control), o # observation # within rat, # (start, stop] status # The raw data has some intervals of zero length, i.e., start==stop. # We add .1 to these times as an approximate solution # rat2 <- read.table('data.rat2', col.names=c('id', 'rx', 'enum', 'start', 'stop', 'status')) temp1 <- rat2$start temp2 <- rat2$stop for (i in 1:nrow(rat2)) { if (temp1[i] == temp2[i]) { temp2[i] <- temp2[i] + .1 if (i < nrow(rat2) && rat2$id[i] == rat2$id[i+1]) { temp1[i+1] <- temp1[i+1] + .1 if (temp2[i+1] <= temp1[i+1]) temp2[i+1] <- temp1[i+1] } } } rat2$start <- temp1 rat2$stop <- temp2 r2fit0 <- coxph(Surv(start, stop, status) ~ rx + cluster(id), rat2) r2fitg <- coxph(Surv(start, stop, status) ~ rx + frailty(id), rat2) r2fitm <- coxph(Surv(start, stop, status) ~ rx + frailty.gaussian(id), rat2) r2fit0 r2fitg r2fitm #This example is unusual: the frailties variances end up about the same, # but the effect on rx differs. Double check it # Because of different iteration paths, the coef won't be exactly the # same, but darn close. temp <- coxph(Surv(start, stop, status) ~ rx + offset(r2fitm$frail[id]), rat2) all.equal(temp$coef, r2fitm$coef[1], tolerance=1e-7) temp <- coxph(Surv(start, stop, status) ~ rx + offset(r2fitg$frail[id]), rat2) all.equal(temp$coef, r2fitg$coef[1], tolerance=1e-7) # # What do I get with AIC # r2fita1 <- coxph(Surv(start, stop, status) ~ rx + frailty(id, method='aic'), rat2) r2fita2 <- coxph(Surv(start, stop, status) ~ rx + frailty(id, method='aic', dist='gauss'), rat2) r2fita3 <- coxph(Surv(start, stop, status) ~ rx + frailty(id, dist='t'), rat2) r2fita1 r2fita2 r2fita3 survival/tests/data.peterson0000644000175100001440000000017711732700061016001 0ustar hornikusers1 4 1 1 7 1 1 12 1 2 3 0 2 10 0 2 22 1 2 21 1 2 11 0 2 12 0 6 18 1 6 9 1 3 12 0 3 19 1 3 16 0 3 5 0 3 14 0 3 20 1 4 2 1 5 6 1 survival/tests/frailty.Rout.save0000644000175100001440000000302011732700061016557 0ustar hornikusers R version 2.11.1 (2010-05-31) Copyright (C) 2010 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > # > # The constuction of a survival curve with sparse frailties > # > # In this case the coefficient vector is kept in two parts, the > # fixed coefs and the (often very large) random effects coefficients > # The survfit function treats the second set of coefficients as fixed > # values, to avoid an unmanagable variance matrix, and behaves like > # the second fit below. > > fit1 <- coxph(Surv(time, status) ~ age + frailty(inst), lung) > sfit1 <- survfit(fit1) > > # A parallel model with the frailties treated as fixed offsets > offvar <- fit1$frail[as.numeric(factor(lung$inst))] > fit2 <- coxph(Surv(time, status) ~ age + offset(offvar),lung) > fit2$var <- fit1$var #force variances to match > > all.equal(fit1$coef, fit2$coef) [1] TRUE > sfit2 <- survfit(fit2, newdata=list(age=fit1$means, offvar=0)) > all.equal(sfit1$surv, sfit2$surv) [1] TRUE > all.equal(sfit1$var, sfit2$var) [1] TRUE > survival/tests/tmerge.Rout.save0000644000175100001440000000712413055116030016376 0ustar hornikusers R Under development (unstable) (2017-02-21 r72241) -- "Unsuffered Consequences" Copyright (C) 2017 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > # Very simple tmerge example, for checking > data1 <- data.frame(idd = c(1,5,4,3,2,6), x1=1:6, age=50:55) > data2 <- data.frame(idd = c(2,5,1,2,1), x2=5:1, age=48:44) > test1 <- tmerge(data1, data1, id=idd, death=event(age)) > test2 <- tmerge(test1, data2, id=idd, zed=tdc(age, x2)) > all.equal(test2$id, c(1,1,1,5,5,4,3,2,2,2,6)) [1] TRUE > all.equal(test2$tstop, c(44, 46, 50, 47, 51, 52, 53, 45, 48, 54, 55)) [1] TRUE > all.equal(test2$death, c(0,0,1,0,1,1,1,0,0,1,1)) [1] TRUE > all.equal(test2$zed, c(NA, 1, 3,NA, 4, NA, NA, NA, 2, 5, NA)) [1] TRUE > > #add in a cumtdc variable and cumevent variable > data3 <- data.frame(idd=c(5,5,1,1,6,4,3,2), + age=c(45, 50, 44, 48, 53,-5,0,20), + x = c(1,5,2,3,7, 4,6,8)) > test3 <- tmerge(test2, data3, id=idd, x=cumtdc(age, x), + esum = cumevent(age)) > all.equal(test3$x, c(NA,2,2,5,NA, 1,1,6,4,6, NA, 8,8,8, NA,7)) [1] TRUE > all.equal(test3$esum, c(1,0,2,0,1,0,2,0,0,0,1,0,0,0,1,0)) [1] TRUE > > > # An example from Brendan Caroll > # It went wrong because the data is not sorted > > ages <- data.frame( id = c(1L, 2L, 5L, 6L, 9L, 10L, 12L, 13L, 14L, 15L, 16L, + 17L, 18L, 20L, 21L, 24L, 26L, 27L, 28L, 29L, 30L, 31L, 34L, 35L, 36L, 37L, + 38L, 39L, 40L, 42L, 45L, 46L, 43L, 48L, 49L, 50L, 51L, 52L, 54L, 55L, 57L, + 58L, 59L, 60L, 61L, 62L, 63L, 64L, 65L, 66L, 68L, 69L, 70L, 71L, 72L, 73L, + 74L, 75L, 8L, 19L, 22L, 23L, 33L, 41L), + age = c(13668, 21550, 15249, 21550, + 16045, 21550, 14976, 14976, 6574, 21550, 4463, 16927, 16927, 15706, 4567, + 21306, 17235, 22158, 19692, 17632, 17597, 4383, 5811, 7704, 5063, 17351, + 17015, 16801, 4383, 5080, 13185, 12604, 19784, 5310, 15369, 13239, 1638, + 21323, 10914, 21262, 7297, 17214, 17508, 14199, 14062, 2227, 8434, 4593, + 14429, 21323, 4782, 10813, 2667, 2853, 5709, 3140, 12237, 7882, 21550, + 15553, 16466, 16621, 19534, 21842)) > > transitions <- data.frame(id=c(2,2, 8, 19, 22, 23, 24, 31, + 33, 41, 43, 52, 55, 66, 6, 10, 43), + transition = c(18993, 13668, 15706, + 11609, 4023, 9316, 16193, 1461, + 4584, 17824, 11261, 16818, + 10670, 15479, 15249, 15887,3713)) > > # Unsorted > tdata <- tmerge(ages, ages, id=id, tstop=age) > newdata<- tmerge(tdata, transitions, id=id, enum=cumtdc(transition)) > > # sorted > test1 <- ages[order(ages$id),] > test2 <- tmerge(test1, test1, id=id, tstop=age) > tran2 <- transitions[order(transitions$id, transitions$transition),] > test3 <- tmerge(test2, tran2, id=id, enum=cumtdc(transition)) > all.equal(attr(newdata,'tcount'), attr(test3, 'tcount')) [1] TRUE > > test4 <- newdata[order(newdata$id, newdata$tstart),] > all.equal(test3, test4, check.attributes=FALSE) #rownames differ [1] TRUE > > > proc.time() user system elapsed 1.364 0.072 1.432 survival/tests/counting.R0000644000175100001440000000364311732700061015261 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # Create a "counting process" version of the simplest test data set # test1 <- data.frame(time= c(9, 3,1,1,6,6,8), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0)) test1b<- list(start= c(0, 3, 0, 0, 5, 0, 6,14, 0, 0, 10,20,30, 0), stop = c(3,10, 10, 5,20, 6,14,20, 30, 10,20,30,40, 10), status=c(0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), x= c(1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, NA), id = c(3, 3, 4, 5, 5, 6, 6, 6, 7, 1, 1, 1, 1, 2)) aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) # # Check out the various residuals under an Efron approximation # fit0 <- coxph(Surv(time, status)~ x, test1, iter=0) fit <- coxph(Surv(time, status) ~x, test1) fit0b <- coxph(Surv(start, stop, status) ~ x, test1b, iter=0) fitb <- coxph(Surv(start, stop, status) ~x, test1b) fitc <- coxph(Surv(time, status) ~ offset(fit$coef*x), test1) fitd <- coxph(Surv(start, stop, status) ~ offset(fit$coef*x), test1b) aeq(fit0b$coef, fit0$coef) aeq(resid(fit0), resid(fit0b, collapse=test1b$id)) aeq(resid(fit), resid(fitb, collapse=test1b$id)) aeq(resid(fitc), resid(fitd, collapse=test1b$id)) aeq(resid(fitc), resid(fit)) aeq(resid(fit0, type='score'), resid(fit0b, type='score', collapse=test1b$id)) aeq(resid(fit, type='score'), resid(fitb, type='score', collapse=test1b$id)) aeq(resid(fit0, type='scho'), resid(fit0b, type='scho', collapse=test1b$id)) aeq(resid(fit, type='scho'), resid(fitb, type='scho', collapse=test1b$id)) # The two survivals will have different censoring times # nrisk, nevent, surv, and std should be the same temp1 <- survfit(fit, list(x=1), censor=FALSE) temp2 <- survfit(fitb, list(x=1), censor=FALSE) all.equal(unclass(temp1)[c(3,4,6,8)], unclass(temp2)[c(3,4,6,8)]) survival/tests/testci.Rout.save0000644000175100001440000001302213004232520016375 0ustar hornikusers R version 3.2.3 (2015-12-10) -- "Wooden Christmas-Tree" Copyright (C) 2015 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > aeq <- function(x,y,...) all.equal(as.vector(x), as.vector(y),...) > > # > # Test out the survfit.ci function, which does competing risk > # estimates > # > # First trivial test > tdata <- data.frame(time=c(1,2,2,3,3,3,5,6), + status = c(0,1,0,1,0,1,0,1), + event = c(1,1,2,2,1,2,3,2), + grp = c(1,2,1,2,1,2,1,2)) > fit <- survfit(Surv(time, status*event, type='mstate') ~1, tdata) > > byhand <- function() { + #everyone starts in state 0 + p1 <- c(1,0,0) + + p2 <- c(6/7, 1/7, 0) # 0-1 transition at time 2 + u2 <- matrix(rep(c(1/49, -1/49, 0), each=8), ncol=3) #leverage matrix at time 2 + u2[1,] <- 0 #subject 1 is not present + u2[2,1:2] <- u2[2, 1:2] + c(-1/7, 1/7) + + p3 <- c((6/7)*(3/5), 1/7, 12/35) # 0-2 transition at time 3, 5 at risk + h3 <- matrix(c(3/5, 0, 2/5, 0,1,0, 0,1,0), byrow=T, ncol=3) #hazard mat + u3 <- u2 %*% h3 + u3[4:8,1] <- u3[4:8,1] + p2[1]*2/25 + u3[4:8,3] <- u3[4:8,3] -p2[1]*2/25 + u3[4,] <- u3[4,] + c(-p2[1]/5, 0, p2[1]/5) + u3[6,] <- u3[4,] + + p6 <- c(0, 1/7, 6/7) # 0-2 at time 6, 1 at risk + h6 <- matrix(c(-1,0,1,0,1,0,0,1,0), byrow=T, ncol=3) + u6 <- cbind(0, u3[,2], -u3[,2]) + + V <- rbind(0, colSums(u2^2), + colSums(u3^2), + colSums(u3^2), + colSums(u6^2)) + list(P=rbind(p1, p2, p3, p3, p6), u2=u2, u3=u3, u6=u6, V=V) + } > bfit <- byhand() > aeq(fit$pstate, bfit$P[,c(2,3,1)]) [1] TRUE > aeq(fit$n.risk[,3], c(8,7,5,2,1)) [1] TRUE > aeq(fit$n.event[,1:2], c(0,1,0,0,0, 0,0 ,2,0,1)) [1] TRUE > aeq(fit$std^2, bfit$V[,c(2,3,1)]) [1] TRUE > > # Times purposely has values that are before the start, exact, intermediate > # and after the end of the observed times > sfit <- summary(fit, times=c(0, 1, 3.5, 6, 7), extend=TRUE) > aeq(sfit$pstate, rbind(c(0,0,1), bfit$P[c(1,3,5,5), c(2,3,1)])) [1] TRUE > aeq(sfit$n.risk[,3], c(8,8, 2, 1, 0)) [1] TRUE > aeq(sfit$n.event, matrix(c(0,0,1,0,0, 0,0,2,1,0, 0,0,0,0,0), ncol=3)) [1] TRUE > > # > # For this we need the competing risks MGUS data set, first > # event > # > tdata <- mgus1[mgus1$enum==1,] > # Ensure the old-style call using "etype" works (backwards compatability) > fit1 <- survfit(Surv(stop, status) ~ 1, etype=event, tdata) > fit1b <-survfit(Surv(stop, event) ~1, tdata) > indx <- match("call", names(fit1)) > all.equal(unclass(fit1)[-indx], unclass(fit1b)[-indx]) [1] TRUE > > # Now get the overall survival, and the hazard for progression > fit2 <- survfit(Surv(stop, status) ~1, tdata) #overall to "first bad thing" > fit3 <- survfit(Surv(stop, status*(event=='pcm')) ~1, tdata, + type='fleming') > fit4 <- survfit(Surv(stop, status*(event=='death')) ~1, tdata, + type='fleming') > > aeq(fit1$n.risk[,3], fit2$n.risk) [1] TRUE > aeq(rowSums(fit1$n.event), fit2$n.event) [1] TRUE > > # Classic CI formula > # integral [hazard(t) S(t-0) dt], where S= "survival to first event" > haz1 <- diff(c(0, -log(fit3$surv))) #Aalen hazard estimate for progression > haz2 <- diff(c(0, -log(fit4$surv))) #Aalen estimate for death > tsurv <- c(1, fit2$surv[-length(fit2$surv)]) #lagged survival > ci1 <- cumsum(haz1 *tsurv) > ci2 <- cumsum(haz2 *tsurv) > aeq(cbind(ci1, ci2), fit1$pstate[,1:2]) [1] TRUE > > # > # Now, make sure that it works for subgroups > # > fit1 <- survfit(Surv(stop, event) ~ sex, tdata) > fit2 <- survfit(Surv(stop, event) ~ 1, tdata, + subset=(sex=='female')) > fit3 <- survfit(Surv(stop, event) ~ 1, tdata, + subset=(sex=='male')) > > aeq(fit2$pstate, fit1$pstate[1:fit1$strata[1],]) [1] TRUE > aeq(fit2$std, fit1$std[1:fit1$strata[1],]) [1] TRUE > aeq(fit3$pstate, fit1$pstate[-(1:fit1$strata[1]),]) [1] TRUE > > # A second test of cumulative incidence > # compare results to Bob Gray's functions > # The file gray1 is the result of > # library(cmprsk) > # tstat <- ifelse(tdata$status==0, 0, 1+ (tdata$event=='death')) > # gray1 <- cuminc(tdata$stop, tstat) > load("gray1.rda") > fit2 <- survfit(Surv(stop, event) ~ 1, tdata) > > if (FALSE) { + # lines of the two graphs should overlay + plot(gray1[[1]]$time, gray1[[1]]$est, type='l', + ylim=range(c(gray1[[1]]$est, gray1[[2]]$est)), + xlab="Time") + lines(gray1[[2]]$time, gray1[[2]]$est, lty=2) + matlines(fit2$time, fit2$pstate, col=2, lty=1:2, type='s') + } > # To formally match these is a bit of a nuisance. > # The cuminc function returns a full step function, and survfit only > # the bottoms of the steps. > temp1 <- tapply(gray1[[1]]$est, gray1[[1]]$time, max)[-1] #toss time 0 > indx1 <- match(names(temp1), fit2$time) > aeq(temp1, fit2$pstate[indx1,1]) [1] TRUE > > > proc.time() user system elapsed 1.317 0.065 1.391 survival/tests/data.fluid0000644000175100001440000000114711732700061015243 0ustar hornikusers 5.79 26kV 1579.52 26kV 2323.70 26kV 7.74 30kV 17.05 30kV 20.46 30kV 21.02 30kV 22.66 30kV 43.40 30kV 47.30 30kV 139.07 30kV 144.12 30kV 175.88 30kV 194.90 30kV 0.19 34kV 0.78 34kV 0.96 34kV 1.31 34kV 2.78 34kV 3.16 34kV 4.15 34kV 4.67 34kV 4.85 34kV 6.50 34kV 7.35 34kV 8.01 34kV 8.27 34kV 12.06 34kV 31.75 34kV 32.52 34kV 33.91 34kV 36.71 34kV 72.89 34kV 0.09 38kV 0.39 38kV 0.47 38kV 0.73 38kV 0.74 38kV 1.13 38kV 1.40 38kV 2.38 38kV survival/tests/r_lung.Rout.save0000644000175100001440000001206011732700061016377 0ustar hornikusers R version 2.14.0 (2011-10-31) Copyright (C) 2011 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: x86_64-unknown-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > lfit2 <- survreg(Surv(time, status) ~ age + ph.ecog + strata(sex), lung) > lfit3 <- survreg(Surv(time, status) ~ sex + (age+ph.ecog)*strata(sex), lung) > > lfit4 <- survreg(Surv(time, status) ~ age + ph.ecog , lung, + subset=(sex==1)) > lfit5 <- survreg(Surv(time, status) ~ age + ph.ecog , lung, + subset=(sex==2)) > > if (exists('censorReg')) { + lfit1 <- censorReg(censor(time, status) ~ age + ph.ecog + strata(sex),lung) + aeq(lfit4$coef, lfit1[[1]]$coef) + aeq(lfit4$scale, lfit1[[1]]$scale) + aeq(c(lfit4$scale, lfit5$scale), sapply(lfit1, function(x) x$scale)) + } > aeq(c(lfit4$scale, lfit5$scale), lfit3$scale ) [1] TRUE > > # > # Test out ridge regression and splines > # > lfit0 <- survreg(Surv(time, status) ~1, lung) > lfit1 <- survreg(Surv(time, status) ~ age + ridge(ph.ecog, theta=5), lung) > lfit2 <- survreg(Surv(time, status) ~ sex + ridge(age, ph.ecog, theta=1), lung) > lfit3 <- survreg(Surv(time, status) ~ sex + age + ph.ecog, lung) > > lfit0 Call: survreg(formula = Surv(time, status) ~ 1, data = lung) Coefficients: (Intercept) 6.034904 Scale= 0.7593936 Loglik(model)= -1153.9 Loglik(intercept only)= -1153.9 n= 228 > lfit1 Call: survreg(formula = Surv(time, status) ~ age + ridge(ph.ecog, theta = 5), data = lung) coef se(coef) se2 Chisq DF p (Intercept) 6.83082 0.42860 0.42860 254.0 1 0.00000 age -0.00783 0.00687 0.00687 1.3 1 0.25000 ridge(ph.ecog) -0.32032 0.08484 0.08405 14.2 1 0.00016 Scale= 0.738 Iterations: 1 outer, 5 Newton-Raphson Degrees of freedom for terms= 1 1 1 1 Likelihood ratio test=18.6 on 2 df, p=8.73e-05 n=227 (1 observation deleted due to missingness) > lfit2 Call: survreg(formula = Surv(time, status) ~ sex + ridge(age, ph.ecog, theta = 1), data = lung) coef se(coef) se2 Chisq DF p (Intercept) 6.27163 0.45280 0.45210 191.84 1 0.0e+00 sex 0.40096 0.12371 0.12371 10.50 1 1.2e-03 ridge(age) -0.00746 0.00675 0.00674 1.22 1 2.7e-01 ridge(ph.ecog) -0.33848 0.08329 0.08314 16.51 1 4.8e-05 Scale= 0.731 Iterations: 1 outer, 6 Newton-Raphson Degrees of freedom for terms= 1 1 2 1 Likelihood ratio test=30 on 3 df, p=1.37e-06 n=227 (1 observation deleted due to missingness) > lfit3 Call: survreg(formula = Surv(time, status) ~ sex + age + ph.ecog, data = lung) Coefficients: (Intercept) sex age ph.ecog 6.273435252 0.401090541 -0.007475439 -0.339638098 Scale= 0.731109 Loglik(model)= -1132.4 Loglik(intercept only)= -1147.4 Chisq= 29.98 on 3 degrees of freedom, p= 1.4e-06 n=227 (1 observation deleted due to missingness) > > > xx <- pspline(lung$age, nterm=3, theta=.3) > xx <- matrix(unclass(xx), ncol=ncol(xx)) # the raw matrix > lfit4 <- survreg(Surv(time, status) ~xx, lung) > lfit5 <- survreg(Surv(time, status) ~age, lung) > > lfit6 <- survreg(Surv(time, status)~pspline(age, df=2), lung) > > lfit7 <- survreg(Surv(time, status) ~ offset(lfit6$lin), lung) > > lfit4 Call: survreg(formula = Surv(time, status) ~ xx, data = lung) Coefficients: (Intercept) xx1 xx2 xx3 xx4 xx5 13.551290 -7.615741 -7.424565 -7.533378 -7.571272 -14.527489 Scale= 0.755741 Loglik(model)= -1150.1 Loglik(intercept only)= -1153.9 Chisq= 7.52 on 5 degrees of freedom, p= 0.19 n= 228 > lfit5 Call: survreg(formula = Surv(time, status) ~ age, data = lung) Coefficients: (Intercept) age 6.88712062 -0.01360829 Scale= 0.7587515 Loglik(model)= -1151.9 Loglik(intercept only)= -1153.9 Chisq= 3.91 on 1 degrees of freedom, p= 0.048 n= 228 > lfit6 Call: survreg(formula = Surv(time, status) ~ pspline(age, df = 2), data = lung) coef se(coef) se2 Chisq DF p (Intercept) 6.5918 0.63681 0.41853 107.15 1.00 0.000 pspline(age, df = 2), lin -0.0136 0.00687 0.00687 3.94 1.00 0.047 pspline(age, df = 2), non 0.78 1.06 0.400 Scale= 0.756 Iterations: 4 outer, 12 Newton-Raphson Theta= 0.926 Degrees of freedom for terms= 0.4 2.1 1.0 Likelihood ratio test=5.2 on 1.5 df, p=0.0441 n= 228 > signif(lfit7$coef,6) (Intercept) 1.47899e-09 > survival/tests/r_peterson.Rout.save0000644000175100001440000001005211732700061017270 0ustar hornikusers R version 2.14.0 Under development (unstable) (2011-04-10 r55401) Copyright (C) 2011 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: x86_64-unknown-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # Data courtesy of Bercedis Peterson, Duke University. > # v4 of survreg fails due to 2 groups that have only 1 subject; the coef > # for them easily gets out of hand. In fact, this data set is my toughest > # test of the minimizer. > # > # A shrinkage model for this coefficient is therefore interesting > > > peterson <- data.frame( + scan('data.peterson', what=list(grp=0, time=0, status=0))) Read 19 records > > fitp <- survreg(Surv(time, status) ~ factor(grp), peterson) > summary(fitp) Call: survreg(formula = Surv(time, status) ~ factor(grp), data = peterson) Value Std. Error z p (Intercept) 2.291 0.115 19.92 2.93e-88 factor(grp)2 0.786 0.177 4.44 8.79e-06 factor(grp)3 0.728 0.183 3.97 7.09e-05 factor(grp)4 -1.598 0.218 -7.32 2.48e-13 factor(grp)5 -0.500 0.218 -2.29 2.21e-02 factor(grp)6 0.475 0.170 2.79 5.23e-03 Log(scale) -1.684 0.257 -6.54 6.09e-11 Scale= 0.186 Weibull distribution Loglik(model)= -26.7 Loglik(intercept only)= -40.7 Chisq= 28.18 on 5 degrees of freedom, p= 3.4e-05 Number of Newton-Raphson Iterations: 9 n= 19 > > # Now a shrinkage model. Give the group coefficients > # about 1/2 the scale parameter of the original model, i.e., .18. > # > ffit <- survreg(Surv(time, status) ~ frailty(grp, theta=.1), peterson) > ffit Call: survreg(formula = Surv(time, status) ~ frailty(grp, theta = 0.1), data = peterson) coef se(coef) se2 Chisq DF p (Intercept) 2.62 0.172 0.0874 232.0 1.00 0.0000 frailty(grp, theta = 0.1) 10.4 2.15 0.0067 Scale= 0.301 Iterations: 1 outer, 6 Newton-Raphson Variance of random effect= 0.1 I-likelihood = -11.8 Degrees of freedom for terms= 0.3 2.2 0.7 Likelihood ratio test=13.8 on 1.1 df, p=0.00027 n= 19 > > # > # Try 3 degrees of freedom, since there are 6 groups > # compare them to the unconstrained ones. The frailty coefs are > # on a "sum to constant" constraint rather than "first coef=0", so > # some conversion is neccessary > # > ffit3 <- survreg(Surv(time, status) ~ frailty(grp, df=3), peterson) > print(ffit3) Call: survreg(formula = Surv(time, status) ~ frailty(grp, df = 3), data = peterson) coef se(coef) se2 Chisq DF p (Intercept) 2.54 0.187 0.0685 184.1 1.00 0.00000 frailty(grp, df = 3) 16.7 3.06 0.00088 Scale= 0.227 Iterations: 6 outer, 32 Newton-Raphson Variance of random effect= 0.17 I-likelihood = -10.1 Degrees of freedom for terms= 0.1 3.1 0.3 Likelihood ratio test=22.9 on 1.5 df, p=4.58e-06 n= 19 > > temp <- mean(c(0, fitp$coef[-1])) - mean(ffit3$frail) > temp2 <- c(fitp$coef[1] + temp, c(0,fitp$coef[-1]) - temp) > xx <- rbind(c(nrow(peterson), table(peterson$grp)), + temp2, + c(ffit3$coef, ffit3$frail)) > dimnames(xx) <- list(c("N", "factor", "frailty"), + c("Intercept", paste("grp", 1:6))) > signif(xx,3) Intercept grp 1 grp 2 grp 3 grp 4 grp 5 grp 6 N 19.00 3.000 6.000 6.000 1.00 1.000 2.000 factor 2.43 -0.137 0.649 0.591 -1.74 -0.636 0.338 frailty 2.54 -0.255 0.474 0.438 -1.21 -0.554 0.180 > > rm(ffit, ffit3, temp, temp2, xx, fitp) > survival/tests/mrtest.Rout.save0000644000175100001440000000312711732700061016433 0ustar hornikusers R version 2.7.1 (2008-06-23) Copyright (C) 2008 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > {if (is.R()) mdy.date <- function(m, d, y) { + y <- ifelse(y<100, y+1900, y) + as.Date(paste(m,d,y, sep='/'), "%m/%d/%Y") + } + else mdy.date <- function(m,d,y) { + y <- ifelse(y<100, y+1900, y) + timeDate(paste(y, m, d, sep='/'), in.format="%Y/%m/%d") + } + } > > # > # A test of the match.ratetable function, specifically the > # change to allow partial matching of strings > # Note that 10,000 days old is 27.4 years > # > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > temp1 <- data.frame(year=mdy.date(2,2,1960:1964), + age = 10000 + 1:5, + sex = c('M', 'fema', 'f', 'ma', 'F')) > > temp2 <- ratetable(year=temp1$year, age=temp1$age, sex=temp1$sex) > temp3 <- match.ratetable(temp2, survexp.us) > aeq(temp3$R[,2], c(1,2,2,1,2)) [1] TRUE > survival/tests/aareg.Rout.save0000644000175100001440000003011611732700061016172 0ustar hornikusers R version 2.14.0 Under development (unstable) (2011-04-10 r55401) Copyright (C) 2011 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: x86_64-unknown-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # Test aareg, for some simple data where the answers can be computed > # in closed form > # > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > test1 <- data.frame(time= c(4, 3,1,1,2,2,3), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0), + wt= c(1, 1:6)) > > tfit <- aareg(Surv(time, status) ~ x, test1) > aeq(tfit$times, c(1,2,2)) [1] TRUE > aeq(tfit$nrisk, c(6,4,4)) [1] TRUE > aeq(tfit$coefficient, matrix(c(0,0,1/3, 1/3, 1, -1/3), ncol=2)) [1] TRUE > aeq(tfit$tweight, matrix(c(3,3,3, 3/2, 3/4, 3/4), ncol=2)) [1] TRUE > aeq(tfit$test.statistic, c(1,1)) [1] TRUE > aeq(tfit$test.var, c(1, -1/4, -1/4, 1/4 + 9/16 + 1/16)) [1] TRUE > > tfit <- aareg(Surv(time, status) ~ x, test1, test='nrisk') > aeq(tfit$tweight, matrix(c(3,3,3, 3/2, 3/4, 3/4), ncol=2)) #should be as before [1] TRUE > aeq(tfit$test.statistic, c(4/3, 6/3+ 4 - 4/3)) [1] TRUE > aeq(tfit$test.var, c(16/9, -16/9, -16/9, 36/9 + 16 + 16/9)) [1] TRUE > > # In the 1-variable case, this is the same as the default Aalen weight > tfit <- aareg(Surv(time, status) ~ x, test1, test='variance') > aeq(tfit$test.statistic, c(1,1)) [1] TRUE > aeq(tfit$test.var, c(1, -1/4, -1/4, 1/4 + 9/16 + 1/16)) [1] TRUE > > # > # Repeat the above, with case weights > # > tfit <- aareg(Surv(time, status) ~x, test1, weights=wt) > aeq(tfit$times, c(1,2,2)) [1] TRUE > aeq(tfit$nrisk, c(21,16,16)) [1] TRUE > aeq(tfit$coefficient, matrix(c(0,0,5/12, 2/9, 1, -5/12), ncol=2)) [1] TRUE > aeq(tfit$tweight, matrix(c(12,12,12, 36/7, 3,3), ncol=2)) [1] TRUE > aeq(tfit$test.statistic, c(5, 72/63 + 3 - 15/12)) [1] TRUE > aeq(tfit$test.var, c(25, -25/4, -25/4, (72/63)^2 + 9 + (5/4)^2)) [1] TRUE > > tfit <- aareg(Surv(time, status) ~x, test1, weights=wt, test='nrisk') > aeq(tfit$test.statistic, c(20/3, 42/9 + 16 - 16*5/12)) [1] TRUE > aeq(tfit$test.var, c(400/9, -400/9, -400/9, + (42/9)^2 + 16^2 + (16*5/12)^2)) [1] TRUE > > # > # Make a test data set with no NAs, in sorted order, no ties, > # 15 observations > tdata <- lung[15:29, c('time', 'status', 'age', 'sex', 'ph.ecog')] > tdata$status <- tdata$status -1 > tdata <- tdata[order(tdata$time, tdata$status),] > row.names(tdata) <- 1:15 > tdata$status[8] <- 0 #for some variety > > afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, tdata, nmin=6) > # > # Now, do it "by hand" > cfit <- coxph(Surv(time, status) ~ age + sex + ph.ecog, tdata, iter=0, + method='breslow') > dt1 <- coxph.detail(cfit) > sch1 <- resid(cfit, type='schoen') > > # First estimate of Aalen: from the Cox computations, first 9 > # The first and last cols of the ninth are somewhat unstable (approx =0) > mine <- rbind(solve(dt1$imat[,,1], sch1[1,]), + solve(dt1$imat[,,2], sch1[2,]), + solve(dt1$imat[,,3], sch1[3,]), + solve(dt1$imat[,,4], sch1[4,]), + solve(dt1$imat[,,5], sch1[5,]), + solve(dt1$imat[,,6], sch1[6,]), + solve(dt1$imat[,,7], sch1[7,]), + solve(dt1$imat[,,8], sch1[8,]), + solve(dt1$imat[,,9], sch1[9,])) > mine <- diag(1/dt1$nrisk[1:9]) %*% mine > > aeq(mine, afit$coef[1:9, -1]) [1] TRUE > > rm(tfit, afit, mine, dt1, cfit, sch1) > > # > # Check out the dfbeta matrix from aareg > # Note that it is kept internally in time order, not data set order > # Those who want residuals should use the resid function! > > # > # First, the simple test case where I know the anwers > # > afit <- aareg(Surv(time, status) ~ x, test1, dfbeta=T) > temp <- c(rep(0,6), #intercepts at time 1 + c(2,-1,-1,0,0,0)/9, #alpha at time 1 + c(0,0,0,2, -1, -1)/9, #intercepts at time 2 + c(0,0,0,-2,1,1)/9) #alpha at time 2 > aeq(afit$dfbeta, temp) [1] TRUE > > # > #Now a multivariate data set > # > afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, lung, dfbeta=T) > > ord <- order(lung$time, -lung$status) > cfit <- coxph(Surv(time, status) ~ age + sex + ph.ecog, lung[ord,], + method='breslow', iter=0, x=T) > cdt <- coxph.detail(cfit, riskmat=T) > > # an arbitrary list of times > acoef <- rowsum(afit$coef, afit$times) #per death time coefs > indx <- match(cdt$time, afit$times) > for (i in c(2,5,27,54,101, 135)) { + lwho <- (cdt$riskmat[,i]==1) + lmx <- cfit$x[lwho,] + lmy <- 1*( cfit$y[lwho,2]==1 & cfit$y[lwho,1] == cdt$time[i]) + fit <- lm(lmy~ lmx) + cat("i=", i, "coef=", aeq(fit$coef, acoef[i,])) + + rr <- diag(resid(fit)) + zz <- cbind(1,lmx) + zzinv <- solve(t(zz) %*% zz) + cat(" twt=", aeq(1/(diag(zzinv)), afit$tweight[indx[i],])) + + df <- t(zzinv %*% t(zz) %*% rr) + cat(" dfbeta=", aeq(df, afit$dfbeta[lwho,,i]), "\n") + } i= 2 coef= TRUE twt= TRUE dfbeta= TRUE i= 5 coef= TRUE twt= TRUE dfbeta= TRUE i= 27 coef= TRUE twt= TRUE dfbeta= TRUE i= 54 coef= TRUE twt= TRUE dfbeta= TRUE i= 101 coef= TRUE twt= TRUE dfbeta= TRUE i= 135 coef= TRUE twt= TRUE dfbeta= TRUE > > rm(afit, cfit, cdt, lwho, lmx, lmy, fit, rr, zz, df) > > > # Repeat it with case weights > ww <- rep(1:5, length=nrow(lung))/ 3.0 > afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, lung, dfbeta=T, + weights=ww) > cfit <- coxph(Surv(time, status) ~ age + sex + ph.ecog, lung[ord,], + method='breslow', iter=0, x=T, weight=ww[ord]) > cdt <- coxph.detail(cfit, riskmat=T) > > acoef <- rowsum(afit$coef, afit$times) #per death time coefs > for (i in c(2,5,27,54,101, 135)) { + who <- (cdt$riskmat[,i]==1) + x <- cfit$x[who,] + y <- 1*( cfit$y[who,2]==1 & cfit$y[who,1] == cdt$time[i]) + w <- cfit$weight[who] + fit <- lm(y~x, weights=w) + cat("i=", i, "coef=", aeq(fit$coef, acoef[i,])) + + rr <- diag(resid(fit)) + zz <- cbind(1,x) + zzinv <- solve(t(zz)%*% (w*zz)) + cat(" twt=", aeq(1/(diag(zzinv)), afit$tweight[indx[i],])) + + df <- t(zzinv %*% t(zz) %*% (w*rr)) + cat(" dfbeta=", aeq(df, afit$dfbeta[who,,i]), "\n") + } i= 2 coef= TRUE twt= TRUE dfbeta= TRUE i= 5 coef= TRUE twt= TRUE dfbeta= TRUE i= 27 coef= TRUE twt= TRUE dfbeta= TRUE i= 54 coef= TRUE twt= TRUE dfbeta= TRUE i= 101 coef= TRUE twt= TRUE dfbeta= TRUE i= 135 coef= TRUE twt= TRUE dfbeta= TRUE > > rm(afit, cfit, cdt, who, x, y, fit, rr, zz, df) > rm(ord, acoef) > > # > # Check that the test statistic computed within aareg and > # the one recomputed within summary.aareg are the same. > # Of course, they could both be wrong, but at least they'll agree! > # If the maxtime argument is used in summary, it recomputes the test, > # even if we know that it wouldn't have had to. > # > # Because the 1-variable and >1 variable case have different code, test > # them both. > # > afit <- aareg(Surv(time, status) ~ age, lung, dfbeta=T) > asum <- summary(afit, maxtime=max(afit$times)) > aeq(afit$test.stat, asum$test.stat) [1] TRUE > aeq(afit$test.var, asum$test.var) [1] TRUE > aeq(afit$test.var2, asum$test.var2) [1] TRUE > > print(afit) Call: aareg(formula = Surv(time, status) ~ age, data = lung, dfbeta = T) n= 228 139 out of 139 unique event times used slope coef se(coef) robust se z p Intercept -0.000872 -0.000905 4.26e-03 4.13e-03 -0.219 0.8270 age 0.000110 0.000142 6.96e-05 6.75e-05 2.110 0.0351 Chisq=4.44 on 1 df, p=0.035; test weights=aalen > > afit <- aareg(Surv(time, status) ~ age, lung, dfbeta=T, test='nrisk') > asum <- summary(afit, maxtime=max(afit$times)) > aeq(afit$test.stat, asum$test.stat) [1] TRUE > aeq(afit$test.var, asum$test.var) [1] TRUE > aeq(afit$test.var2, asum$test.var2) [1] TRUE > > summary(afit) $table slope coef se(coef) robust se z Intercept -0.0009538483 -0.11693804 0.534885651 0.533148054 -0.219335 age 0.0001053024 0.01795521 0.008746523 0.008734005 2.055782 p Intercept 0.82638908 age 0.03980352 $test [1] "nrisk" $test.statistic Intercept age -19.29478 2.96261 $test.var [,1] [,2] [1,] 7789.1449 -126.055872 [2,] -126.0559 2.082758 $test.var2 [,1] [,2] [1,] 7738.6204 -125.5077 [2,] -125.5077 2.0768 $chisq [,1] [1,] 4.22624 $n [1] 228 139 139 attr(,"class") [1] "summary.aareg" > > # > # Mulitvariate > # > afit <- aareg(Surv(time, status) ~ age + sex + ph.karno + pat.karno, lung, + dfbeta=T) > asum <- summary(afit, maxtime=max(afit$times)) > aeq(afit$test.stat, asum$test.stat) [1] TRUE > aeq(afit$test.var, asum$test.var) [1] TRUE > aeq(afit$test.var2, asum$test.var2) [1] TRUE > > print(afit) Call: aareg(formula = Surv(time, status) ~ age + sex + ph.karno + pat.karno, data = lung, dfbeta = T) n=224 (4 observations deleted due to missingness) 132 out of 136 unique event times used slope coef se(coef) robust se z p Intercept 2.15e-02 0.025000 8.45e-03 7.72e-03 3.25 0.00117 age 3.09e-05 0.000076 7.32e-05 6.49e-05 1.17 0.24100 sex -2.96e-03 -0.004020 1.25e-03 1.23e-03 -3.27 0.00109 ph.karno -6.77e-05 -0.000083 6.69e-05 8.30e-05 -1.00 0.31700 pat.karno -1.01e-04 -0.000112 5.59e-05 5.70e-05 -1.96 0.05010 Chisq=23.36 on 4 df, p=0.00011; test weights=aalen > > afit <- aareg(Surv(time, status) ~ age + sex + ph.karno + pat.karno, lung, + dfbeta=T, test='nrisk') > asum <- summary(afit, maxtime=max(afit$times)) > aeq(afit$test.stat, asum$test.stat) [1] TRUE > aeq(afit$test.var, asum$test.var) [1] TRUE > aeq(afit$test.var2, asum$test.var2) [1] TRUE > > summary(afit) $table slope coef se(coef) robust se z Intercept 2.119015e-02 3.05872822 1.044992929 0.955953617 3.199662 age 3.181122e-05 0.01071085 0.009280348 0.008182931 1.308926 sex -2.985556e-03 -0.49368373 0.153217001 0.151559500 -3.257359 ph.karno -8.371983e-05 -0.01131957 0.007825769 0.009654398 -1.172478 pat.karno -8.501076e-05 -0.01328844 0.007241150 0.007669582 -1.732617 p Intercept 0.00137589 age 0.19055946 sex 0.00112454 ph.karno 0.24100515 pat.karno 0.08316385 $test [1] "nrisk" $test.statistic Intercept age sex ph.karno pat.karno 480.220330 1.681604 -77.508345 -1.777173 -2.086286 $test.var b0 b0 26916.95995 -177.3767597 -791.4141458 -103.5540756 -69.1210402 -177.37676 2.1228915 0.1752574 0.4055099 0.1622945 -791.41415 0.1752574 578.6463538 -0.9726495 -0.6320578 -103.55408 0.4055099 -0.9726495 1.5095704 -0.5793466 -69.12104 0.1622945 -0.6320578 -0.5793466 1.2924520 $test.var2 [,1] [,2] [,3] [,4] [,5] [1,] 22525.42254 -109.0376340 -1294.620657 -135.7477106 -24.1718358 [2,] -109.03763 1.6505060 2.562655 0.1774270 -0.1206339 [3,] -1294.62066 2.5626546 566.194480 7.4865489 -4.7691882 [4,] -135.74771 0.1774270 7.486549 2.2974694 -0.9877341 [5,] -24.17184 -0.1206339 -4.769188 -0.9877341 1.4499155 $chisq [,1] [1,] 22.3874 $n [1] 224 132 136 attr(,"class") [1] "summary.aareg" > > # Weights play no role in the final computation of the test statistic, given > # the coefficient matrix, nrisk, and dfbeta as inputs. (Weights do > # change the inputs). So there is no need to reprise the above with > # case weights. > survival/tests/surv.R0000644000175100001440000000204113070706637014435 0ustar hornikusers# library(survival) # Some simple tests of the Surv function # The first two are motivated by a bug, pointed out by Kevin Buhr, # where a mixture of NAs and invalid values didn't work right # Even for the simplest things a test case is good. # All but the third should produce warning messages aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) temp <- Surv(c(1, 10, 20, 30), c(2, NA, 0, 40), c(1,1,1,1)) aeq(temp, c(1,10,NA,30, 2,NA,0,40, 1,1,1,1)) temp <- Surv(c(1, 10, 20, 30), c(2, NA, 0, 40), type='interval2') aeq(temp, c(1,10,20,30, 2,1,1,40, 3,0,NA,3)) #No error temp <- Surv(1:5) aeq(temp, c(1:5, 1,1,1,1,1)) temp1 <- Surv(c(1,10,NA, 30, 30), c(1,NA,10,20, 40), type='interval2') temp2 <- Surv(c(1,10,10,30,30), c(9, NA, 5, 20,40), c(1, 0, 2,3,3), type='interval') aeq(temp1, temp2) aeq(temp1, c(1,10,10,30,30, 1,1,1,1, 40, 1,0,2,NA,3)) # Use of inf temp1 <- Surv(c(1,10,NA, 30, 30), c(1,NA,10,30, 40), type='interval2') temp2 <- Surv(c(1,10,-Inf, 30, 30), c(1,Inf,10,30, 40), type='interval2') aeq(temp1, temp2) survival/tests/factor.Rout.save0000644000175100001440000000342011732700061016367 0ustar hornikusers R version 2.14.0 (2011-10-31) Copyright (C) 2011 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > # > # Ensure that factors work in prediction > # > library(survival) Loading required package: splines > > options(na.action="na.exclude") # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > tfit <- coxph(Surv(time, status) ~ age + factor(ph.ecog), lung) > p1 <- predict(tfit, type='risk') > > # Testing NA handling is important too > keep <- (is.na(lung$ph.ecog) | lung$ph.ecog !=1) > lung2 <- lung[keep,] > p2 <- predict(tfit, type='risk', newdata=lung[keep,]) > aeq(p1[keep], p2) [1] TRUE > > # Same, for survreg > tfit <- survreg(Surv(time, status) ~ age + factor(ph.ecog), lung) > p1 <- predict(tfit, type='response') > p2 <- predict(tfit, type='response', newdata=lung2) > aeq(p1[keep], p2) [1] TRUE > > > # Now repeat it tossing the missings > options(na.action=na.omit) > keep2 <- (lung$ph.ecog[!is.na(lung$ph.ecog)] !=1) > > tfit2 <- survreg(Surv(time, status) ~ age + factor(ph.ecog), lung) > p3 <- predict(tfit2, type='response') > p4 <- predict(tfit2, type='response', newdata=lung2, na.action=na.omit) > aeq(p3[keep2] , p4) [1] TRUE > survival/tests/pyear.R0000644000175100001440000001643012701744412014556 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) {if (is.R()) mdy.date <- function(m, d, y) { y <- ifelse(y<100, y+1900, y) as.Date(paste(m,d,y, sep='/'), "%m/%d/%Y") } else mdy.date <- function(m,d,y) { y <- ifelse(y<100, y+1900, y) timeDate(paste(y, m, d, sep='/'), in.format="%Y/%m/%d") } } # # Simple case: a single male subject, born 6/6/36 and entered on study 6/6/55. # temp1 <- mdy.date(6,6,36) temp2 <- mdy.date(6,6,55)# Now compare the results from person-years # temp.age <- tcut(temp2-temp1, floor(c(-1, (18:31 * 365.24))), labels=c('0-18', paste(18:30, 19:31, sep='-'))) temp.yr <- tcut(temp2, mdy.date(1,1,1954:1965), labels=1954:1964) temp.time <- 3700 #total days of fu py1 <- pyears(temp.time ~ temp.age + temp.yr, scale=1) #output in days # The subject should appear in 20 cells # 6/6/55 - 12/31/55, 209 days, age 19-20, 1955 # 1/1/56 - 6/ 4/56, 156 days, age 19-20, 1956 # 6/5/56 - 12/31/56, 210 days, age 20-21, 1956 (a leap year, and his # birthday computes one day earlier) # 1/1/57 - 6/ 5/57, 156 days, age 20-21, 1957 # 6/6/57 - 12/31/57, 209 days, age 21-22, 1957 # and etc # with 203 days "off table", ie, beyond the last cell of the table # # It is a nuisance, but tcut follows 'cut' in that we give the ENDS of # the intervals, whereas the survival tables use the starts of intervals. # Thus this breakdown does not match that in doexpect.s # xx <- matrix(0, nrow=14, ncol=11) xx[cbind(3:11, 3:11)] <- 156 xx[cbind(3:12, 2:11)] <- c(209, 210, rep(c(209, 209, 209, 210),2)) dimnames(xx) <- list(temp.age= c('0-18', paste(18:30, 19:31, sep='-')), temp.yr = 1954:1964) all.equal(xx, py1$pyears) all.equal(203, py1$offtable) all.equal(1*(xx>0), py1$n) # # Now with expecteds # py2 <- pyears(temp.time ~ temp.age + temp.yr + ratetable(age=temp2-temp1, year=temp2, sex=1), scale=1, ratetable=survexp.us ) #output in days all.equal(xx, py2$pyears) all.equal(203, py2$offtable) all.equal(1*(xx>0), py2$n) py2b <- pyears(temp.time ~ temp.age + temp.yr, rmap = list(age=temp2-temp1, year=temp2, sex=1), scale=1, ratetable=survexp.us ) #output in days all.equal(xx, py2b$pyears) all.equal(203, py2b$offtable) all.equal(1*(xx>0), py2b$n) all.equal(py2$expected, py2b$expected) py3 <- pyears(temp.time ~ temp.age + temp.yr, rmap=list(age=temp2-temp1, year=temp2, sex=1), scale=1, ratetable=survexp.us , expect='pyears') all.equal(py2$n, py3$n) all.equal(py2$pyear, py3$pyear) all.equal(py3$n, 1*(py3$expect>0)) # Now, compute the py3 result "by hand". Since there is only one person # it can be derived from py2. # xx1 <- py2$expect[py2$n>0] # the hazard over each interval cumhaz <- cumsum(c(0, xx1[-length(xx1)])) # the cumulative hazard xx2 <- py3$expect[py3$n>0] # the expected number of person days xx3 <- py3$pyears[py3$n>0] # the potential number of person days # This is the integral of the curve "exp(-haz *t)" over the interval integral <- xx3 * exp(-cumhaz)* (1- exp(-xx1))/ xx1 # They might not be exactly equal, since the C code tracks changes in the # rate tables that occur -within- an interval. So try for 6 digits all.equal(round(integral,3), round(xx2,3)) # Cut off the bottom of the table, instead of the side temp.age <- tcut(temp2-temp1, floor(c(-1, (18:27 * 365.24))), labels=c('0-18', paste(18:26, 19:27, sep='-'))) py4 <- eval(py3$call) all.equal(py4$pyear, py3$pyear[1:10,]) all.equal(py4$expect, py3$expect[1:10,]) rm(temp.age, integral, xx1, xx2, xx3, cumhaz, py1, py2, py3, py4) rm(temp1, temp2, temp.yr, temp.time, xx) # # Simple case: a single male subject, born 6/6/36 and entered on study 6/6/55. # temp1 <- mdy.date(6,6,36) temp2 <- mdy.date(6,6,55)# Now compare the results from person-years # temp.age <- tcut(temp2-temp1, floor(c(-1, (18:31 * 365.24))), labels=c('0-18', paste(18:30, 19:31, sep='-'))) temp.yr <- tcut(temp2, mdy.date(1,1,1954:1965), labels=1954:1964) temp.time <- 3700 #total days of fu py1 <- pyears(temp.time ~ temp.age + temp.yr, scale=1) #output in days # The subject should appear in 20 cells # 6/6/55 - 12/31/55, 209 days, age 19-20, 1955 # 1/1/56 - 6/ 4/56, 156 days, age 19-20, 1956 # 6/5/56 - 12/31/56, 210 days, age 20-21, 1956 (a leap year, and his # birthday computes one day earlier) # 1/1/57 - 6/ 5/57, 156 days, age 20-21, 1957 # 6/6/57 - 12/31/57, 209 days, age 21-22, 1957 # and etc # with 203 days "off table", ie, beyond the last cell of the table # # It is a nuisance, but tcut follows 'cut' in that we give the ENDS of # the intervals, whereas the survival tables use the starts of intervals. # xx <- matrix(0, nrow=14, ncol=11) xx[cbind(3:11, 3:11)] <- 156 xx[cbind(3:12, 2:11)] <- c(209, 210, rep(c(209, 209, 209, 210),2)) dimnames(xx) <- list(temp.age= c('0-18', paste(18:30, 19:31, sep='-')), temp.yr = 1954:1964) all.equal(xx, py1$pyears) all.equal(203, py1$offtable) all.equal(1*(xx>0), py1$n) # # Now with expecteds # py2 <- pyears(temp.time ~ temp.age + temp.yr + ratetable(age=temp2-temp1, year=temp2, sex=1), scale=1, ratetable=survexp.us ) #output in days all.equal(xx, py2$pyears) all.equal(203, py2$offtable) all.equal(1*(xx>0), py2$n) py3 <- pyears(temp.time ~ temp.age + temp.yr + ratetable(age=temp2-temp1, year=temp2, sex=1), scale=1, ratetable=survexp.us , expect='pyears') all.equal(py2$n, py3$n) all.equal(py2$pyear, py3$pyear) all.equal(py3$n, 1*(py3$expect>0)) # Now, compute the py3 result "by hand". Since there is only one person # it can be derived from py2. # xx1 <- py2$expect[py2$n>0] # the hazard over each interval cumhaz <- cumsum(c(0, xx1[-length(xx1)])) # the cumulative hazard xx2 <- py3$expect[py3$n>0] # the expected number of person days xx3 <- py3$pyears[py3$n>0] # the potential number of person days # This is the integral of the curve "exp(-haz *t)" over the interval integral <- xx3 * exp(-cumhaz)* (1- exp(-xx1))/ xx1 # They might not be exactly equal, since the C code tracks changes in the # rate tables that occur -within- an interval. So try for 6 digits all.equal(round(integral,3), round(xx2,3)) # Cut off the bottom of the table, instead of the side temp.age <- tcut(temp2-temp1, floor(c(-1, (18:27 * 365.24))), labels=c('0-18', paste(18:26, 19:27, sep='-'))) py4 <- eval(py3$call) all.equal(py4$pyear, py3$pyear[1:10,]) all.equal(py4$expect, py3$expect[1:10,]) rm(temp.age, integral, xx1, xx2, xx3, cumhaz, py1, py2, py3, py4) rm(temp1, temp2, temp.yr, temp.time, xx) # # Create a "user defined" rate table, using the smoking data # temp <- scan("data.smoke")/100000 temp <- matrix(temp, ncol=8, byrow=T) smoke.rate <- c(rep(temp[,1],6), rep(temp[,2],6), temp[,3:8]) attributes(smoke.rate) <- list( dim=c(7,2,2,6,3), dimnames=list(c("45-49","50-54","55-59","60-64","65-69","70-74","75-79"), c("1-20", "21+"), c("Male","Female"), c("<1", "1-2", "3-5", "6-10", "11-15", ">=16"), c("Never", "Current", "Former")), dimid=c("age", "amount", "sex", "duration", "status"), factor=c(0,1,1,0,1), cutpoints=list(c(45,50,55,60,65,70,75),NULL, NULL, c(0,1,3,6,11,16),NULL), class='ratetable' ) rm(temp) is.ratetable(smoke.rate) summary(smoke.rate) print(smoke.rate) summary(smoke.rate[1:3,,1,,]) #test subscripting survival/tests/fr_resid.Rout.save0000644000175100001440000003651512656732304016734 0ustar hornikusers R Under development (unstable) (2016-01-29 r70039) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # > # The residual methods treat a sparse frailty as a fixed offset with > # no variance > # > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > kfit1 <- coxph(Surv(time, status) ~ age + sex + + frailty(id, dist='gauss'), kidney) > tempf <- predict(kfit1, type='terms')[,3] > temp <- kfit1$frail[match(kidney$id, sort(unique(kidney$id)))] > #all.equal(unclass(tempf), unclass(temp)) > all.equal(as.vector(tempf), as.vector(temp)) [1] TRUE > > # Now fit a model with explicit offset > kfitx <- coxph(Surv(time, status) ~ age + sex + offset(tempf),kidney, + eps=1e-7) > > # These are not always precisely the same, due to different iteration paths > aeq(kfitx$coef, kfit1$coef) [1] TRUE > > # This will make them identical > kfitx <- coxph(Surv(time, status) ~ age + sex + offset(temp),kidney, + iter=0, init=kfit1$coef) > aeq(resid(kfit1), resid(kfitx)) [1] TRUE > aeq(resid(kfit1, type='score'), resid(kfitx, type='score')) [1] TRUE > aeq(resid(kfit1, type='schoe'), resid(kfitx, type='schoe')) [1] TRUE > > # These are not the same, due to a different variance matrix > # The frailty model's variance is about 2x the naive "assume an offset" var > # Expect a value of about 0.5 > aeq(resid(kfit1, type='dfbeta'), resid(kfitx, type='dfbeta')) [1] "Mean relative difference: 0.5216263" > > # Force equality > zed <- kfitx > zed$var <- kfit1$var > aeq(resid(kfit1, type='dfbeta'), resid(zed, type='dfbeta')) [1] TRUE > > # The score residuals are equal, however. > > temp1 <- resid(kfit1, type='score') > temp2 <- resid(kfitx, type='score') > aeq(temp1, temp2) [1] TRUE > > # > # Now for some tests of predicted values > # > aeq(predict(kfit1, type='expected'), predict(kfitx, type='expected')) [1] TRUE > aeq(predict(kfit1, type='lp'), predict(kfitx, type='lp')) [1] TRUE > > temp1 <- predict(kfit1, type='terms', se.fit=T) > temp2 <- predict(kfitx, type='terms', se.fit=T) > aeq(temp1$fit[,1:2], temp2$fit) [1] TRUE > # the next is not equal, all.equal returns a character string in that case > is.character(aeq(temp1$se.fit[,1:2], temp2$se.fit)) [1] TRUE > mean(temp1$se.fit[,1:2]/ temp2$se.fit) [1] 1.433017 > aeq(as.vector(temp1$se.fit[,3])^2, + as.vector(kfit1$fvar[match(kidney$id, sort(unique(kidney$id)))])) [1] TRUE > > print(temp1) $fit age sex frailty(id, dist = "gauss") 1 -0.073981042 1.039553 0.59814468 2 -0.073981042 1.039553 0.59814468 3 0.020278123 -0.371269 0.38512389 4 0.020278123 -0.371269 0.38512389 5 -0.055129209 1.039553 0.20210998 6 -0.055129209 1.039553 0.20210998 7 -0.059842167 -0.371269 -0.55932015 8 -0.055129209 -0.371269 -0.55932015 9 -0.158814289 1.039553 0.28558387 10 -0.158814289 1.039553 0.28558387 11 -0.130536540 -0.371269 0.06628942 12 -0.125823582 -0.371269 0.06628942 13 0.034416998 1.039553 0.80505119 14 0.034416998 1.039553 0.80505119 15 0.053268830 -0.371269 -0.43834241 16 0.057981789 -0.371269 -0.43834241 17 0.119250245 -0.371269 -0.05631649 18 0.119250245 -0.371269 -0.05631649 19 0.034416998 1.039553 -0.49980572 20 0.039129956 1.039553 -0.49980572 21 0.001426290 -0.371269 -0.13028264 22 0.001426290 -0.371269 -0.13028264 23 -0.045703292 -0.371269 0.06377401 24 -0.045703292 -0.371269 0.06377401 25 -0.040990334 -0.371269 0.38815296 26 -0.040990334 -0.371269 0.38815296 27 -0.007999626 -0.371269 -0.47650510 28 -0.007999626 -0.371269 -0.47650510 29 -0.125823582 -0.371269 -0.66986830 30 -0.125823582 -0.371269 -0.66986830 31 0.076833621 1.039553 0.19359678 32 0.076833621 1.039553 0.19359678 33 0.076833621 -0.371269 -0.16483200 34 0.076833621 -0.371269 -0.16483200 35 -0.003286668 -0.371269 -0.15794998 36 0.001426290 -0.371269 -0.15794998 37 0.043842914 -0.371269 -0.46236014 38 0.043842914 -0.371269 -0.46236014 39 0.001426290 -0.371269 0.12603308 40 0.001426290 -0.371269 0.12603308 41 0.010852206 1.039553 -1.74303142 42 0.015565165 1.039553 -1.74303142 43 -0.064555125 -0.371269 -0.45211210 44 -0.064555125 -0.371269 -0.45211210 45 0.086259538 -0.371269 0.51574106 46 0.090972496 -0.371269 0.51574106 47 -0.007999626 -0.371269 0.09475123 48 -0.003286668 -0.371269 0.09475123 49 -0.003286668 1.039553 0.05790354 50 -0.003286668 1.039553 0.05790354 51 0.062694747 -0.371269 -0.37933234 52 0.067407705 -0.371269 -0.37933234 53 -0.158814289 -0.371269 0.11248891 54 -0.158814289 -0.371269 0.11248891 55 0.039129956 -0.371269 0.54791210 56 0.039129956 -0.371269 0.54791210 57 0.043842914 1.039553 0.45873482 58 0.043842914 1.039553 0.45873482 59 0.048555872 -0.371269 0.35639797 60 0.048555872 -0.371269 0.35639797 61 0.057981789 -0.371269 0.48803342 62 0.057981789 -0.371269 0.48803342 63 0.029704039 -0.371269 0.25597325 64 0.034416998 -0.371269 0.25597325 65 0.062694747 -0.371269 0.23054948 66 0.062694747 -0.371269 0.23054948 67 0.001426290 -0.371269 -0.13680005 68 0.006139248 -0.371269 -0.13680005 69 -0.102258791 -0.371269 0.51977995 70 -0.102258791 -0.371269 0.51977995 71 -0.007999626 -0.371269 -0.23878154 72 -0.007999626 -0.371269 -0.23878154 73 0.039129956 -0.371269 0.17174306 74 0.039129956 -0.371269 0.17174306 75 0.076833621 1.039553 -0.35822829 76 0.076833621 1.039553 -0.35822829 $se.fit age sex frailty(id, dist = "gauss") 1 0.195861829 0.3280279 0.6246430 2 0.195861829 0.3280279 0.6246430 3 0.053685514 0.1171528 0.6954922 4 0.053685514 0.1171528 0.6954922 5 0.145952360 0.3280279 0.5705340 6 0.145952360 0.3280279 0.5705340 7 0.158429727 0.1171528 0.4894541 8 0.145952360 0.1171528 0.4894541 9 0.420454437 0.3280279 0.6071455 10 0.420454437 0.3280279 0.6071455 11 0.345590234 0.1171528 0.5633997 12 0.333112867 0.1171528 0.5633997 13 0.091117615 0.3280279 0.6641707 14 0.091117615 0.3280279 0.6641707 15 0.141027084 0.1171528 0.5101890 16 0.153504451 0.1171528 0.5101890 17 0.315710223 0.1171528 0.5491569 18 0.315710223 0.1171528 0.5491569 19 0.091117615 0.3280279 0.5264083 20 0.103594982 0.3280279 0.5264083 21 0.003776045 0.1171528 0.5180953 22 0.003776045 0.1171528 0.5180953 23 0.120997626 0.1171528 0.6208806 24 0.120997626 0.1171528 0.6208806 25 0.108520259 0.1171528 0.5811421 26 0.108520259 0.1171528 0.5811421 27 0.021178689 0.1171528 0.6247779 28 0.021178689 0.1171528 0.6247779 29 0.333112867 0.1171528 0.5615987 30 0.333112867 0.1171528 0.5615987 31 0.203413919 0.3280279 0.6532405 32 0.203413919 0.3280279 0.6532405 33 0.203413919 0.1171528 0.5247227 34 0.203413919 0.1171528 0.5247227 35 0.008701322 0.1171528 0.5106606 36 0.003776045 0.1171528 0.5106606 37 0.116072349 0.1171528 0.6284328 38 0.116072349 0.1171528 0.6284328 39 0.003776045 0.1171528 0.6320009 40 0.003776045 0.1171528 0.6320009 41 0.028730780 0.3280279 0.5235228 42 0.041208147 0.3280279 0.5235228 43 0.170907094 0.1171528 0.5492095 44 0.170907094 0.1171528 0.5492095 45 0.228368654 0.1171528 0.6058686 46 0.240846021 0.1171528 0.6058686 47 0.021178689 0.1171528 0.6267998 48 0.008701322 0.1171528 0.6267998 49 0.008701322 0.3280279 0.5526664 50 0.008701322 0.3280279 0.5526664 51 0.165981818 0.1171528 0.5556706 52 0.178459185 0.1171528 0.5556706 53 0.420454437 0.1171528 0.5849825 54 0.420454437 0.1171528 0.5849825 55 0.103594982 0.1171528 0.6081780 56 0.103594982 0.1171528 0.6081780 57 0.116072349 0.3280279 0.6010279 58 0.116072349 0.3280279 0.6010279 59 0.128549717 0.1171528 0.5762113 60 0.128549717 0.1171528 0.5762113 61 0.153504451 0.1171528 0.5982501 62 0.153504451 0.1171528 0.5982501 63 0.078640248 0.1171528 0.6614053 64 0.091117615 0.1171528 0.6614053 65 0.165981818 0.1171528 0.5609510 66 0.165981818 0.1171528 0.5609510 67 0.003776045 0.1171528 0.5844921 68 0.016253412 0.1171528 0.5844921 69 0.270726031 0.1171528 0.6089631 70 0.270726031 0.1171528 0.6089631 71 0.021178689 0.1171528 0.6795741 72 0.021178689 0.1171528 0.6795741 73 0.103594982 0.1171528 0.6421784 74 0.103594982 0.1171528 0.6421784 75 0.203413919 0.3280279 0.5779661 76 0.203413919 0.3280279 0.5779661 > kfit1 Call: coxph(formula = Surv(time, status) ~ age + sex + frailty(id, dist = "gauss"), data = kidney) coef se(coef) se2 Chisq DF p age 0.00471 0.01248 0.00856 0.14267 1.0 0.7056 sex -1.41082 0.44518 0.31504 10.04319 1.0 0.0015 frailty(id, dist = "gauss 26.54461 14.7 0.0294 Iterations: 6 outer, 39 Newton-Raphson Variance of random effect= 0.569 Degrees of freedom for terms= 0.5 0.5 14.7 Likelihood ratio test=47.5 on 15.7 df, p=4.65e-05 n= 76 > kfitx Call: coxph(formula = Surv(time, status) ~ age + sex + offset(temp), data = kidney, init = kfit1$coef, iter = 0) coef exp(coef) se(coef) z p age 0.00471 1.00472 0.00875 0.54 0.59 sex -1.41082 0.24394 0.30916 -4.56 5e-06 Likelihood ratio test=0 on 2 df, p=1 n= 76, number of events= 58 > > rm(temp1, temp2, kfitx, zed, tempf) > # > # The special case of a single sparse frailty > # > > kfit1 <- coxph(Surv(time, status) ~ frailty(id, dist='gauss'), kidney) > tempf <- predict(kfit1, type='terms') > temp <- kfit1$frail[match(kidney$id, sort(unique(kidney$id)))] > all.equal(as.vector(tempf), as.vector(temp)) [1] TRUE > > # Now fit a model with explicit offset > kfitx <- coxph(Surv(time, status) ~ offset(tempf),kidney, eps=1e-7) > > aeq(resid(kfit1), resid(kfitx)) [1] TRUE > aeq(resid(kfit1, type='deviance'), resid(kfitx, type='deviance')) [1] TRUE > > # > # Some tests of predicted values > # > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > aeq(predict(kfit1, type='expected'), predict(kfitx, type='expected')) [1] TRUE > aeq(predict(kfit1, type='lp'), predict(kfitx, type='lp')) [1] TRUE > > temp1 <- predict(kfit1, type='terms', se.fit=T) > aeq(temp1$fit, kfitx$linear) [1] TRUE > aeq(temp1$se.fit^2, + kfit1$fvar[match(kidney$id, sort(unique(kidney$id)))]) [1] TRUE > > temp1 $fit [1] 0.696003729 0.696003729 0.244575316 0.244575316 0.494175549 [6] 0.494175549 -0.659248798 -0.659248798 0.521423106 0.521423106 [11] -0.114492938 -0.114492938 0.800127481 0.800127481 -0.488101282 [16] -0.488101282 -0.120396647 -0.120396647 0.131121515 0.131121515 [21] -0.214987009 -0.214987009 -0.054872789 -0.054872789 0.184657295 [26] 0.184657295 -0.510007747 -0.510007747 -0.790746805 -0.790746805 [31] 0.324674289 0.324674289 -0.239374060 -0.239374060 -0.264428564 [36] -0.264428564 -0.472698773 -0.472698773 0.006304049 0.006304049 [41] -0.873434085 -0.873434085 -0.530880840 -0.530880840 0.351411783 [46] 0.351411783 -0.037212138 -0.037212138 0.442049266 0.442049266 [51] -0.419206550 -0.419206550 -0.108012854 -0.108012854 0.346332076 [56] 0.346332076 0.659300205 0.659300205 0.197278585 0.197278585 [61] 0.304868889 0.304868889 0.139712997 0.139712997 0.093574024 [66] 0.093574024 -0.209690355 -0.209690355 0.302070834 0.302070834 [71] -0.278962288 -0.278962288 0.068599919 0.068599919 0.078493616 [76] 0.078493616 $se.fit [1] 0.6150025 0.6150025 0.6160184 0.6160184 0.5715622 0.5715622 0.4393615 [8] 0.4393615 0.5761369 0.5761369 0.4834244 0.4834244 0.6421184 0.6421184 [15] 0.4574824 0.4574824 0.4813578 0.4813578 0.5119792 0.5119792 0.4764145 [22] 0.4764145 0.5532477 0.5532477 0.5195437 0.5195437 0.5534327 0.5534327 [29] 0.4775572 0.4775572 0.6364522 0.6364522 0.4708988 0.4708988 0.4670896 [36] 0.4670896 0.5600672 0.5600672 0.5641880 0.5641880 0.4650576 0.4650576 [43] 0.4904715 0.4904715 0.5448430 0.5448430 0.5570120 0.5570120 0.5608187 [50] 0.5608187 0.4996021 0.4996021 0.4831697 0.4831697 0.5452255 0.5452255 [57] 0.6057428 0.6057428 0.5209402 0.5209402 0.5376594 0.5376594 0.5911350 [64] 0.5911350 0.5065368 0.5065368 0.5290283 0.5290283 0.5368433 0.5368433 [71] 0.5996077 0.5996077 0.5762814 0.5762814 0.5782753 0.5782753 > kfit1 Call: coxph(formula = Surv(time, status) ~ frailty(id, dist = "gauss"), data = kidney) coef se(coef) se2 Chisq DF p frailty(id, dist = "gauss 23 13.8 0.057 Iterations: 7 outer, 39 Newton-Raphson Variance of random effect= 0.458 Degrees of freedom for terms= 13.8 Likelihood ratio test=33.4 on 13.8 df, p=0.00234 n= 76 > > > > proc.time() user system elapsed 0.248 0.020 0.262 survival/tests/frailty.R0000644000175100001440000000152611732700061015103 0ustar hornikuserslibrary(survival) # # The constuction of a survival curve with sparse frailties # # In this case the coefficient vector is kept in two parts, the # fixed coefs and the (often very large) random effects coefficients # The survfit function treats the second set of coefficients as fixed # values, to avoid an unmanagable variance matrix, and behaves like # the second fit below. fit1 <- coxph(Surv(time, status) ~ age + frailty(inst), lung) sfit1 <- survfit(fit1) # A parallel model with the frailties treated as fixed offsets offvar <- fit1$frail[as.numeric(factor(lung$inst))] fit2 <- coxph(Surv(time, status) ~ age + offset(offvar),lung) fit2$var <- fit1$var #force variances to match all.equal(fit1$coef, fit2$coef) sfit2 <- survfit(fit2, newdata=list(age=fit1$means, offvar=0)) all.equal(sfit1$surv, sfit2$surv) all.equal(sfit1$var, sfit2$var) survival/tests/counting.Rout.save0000644000175100001440000000531611732700061016745 0ustar hornikusers R version 2.10.0 (2009-10-26) Copyright (C) 2009 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # Create a "counting process" version of the simplest test data set > # > test1 <- data.frame(time= c(9, 3,1,1,6,6,8), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0)) > > test1b<- list(start= c(0, 3, 0, 0, 5, 0, 6,14, 0, 0, 10,20,30, 0), + stop = c(3,10, 10, 5,20, 6,14,20, 30, 10,20,30,40, 10), + status=c(0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), + x= c(1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, NA), + id = c(3, 3, 4, 5, 5, 6, 6, 6, 7, 1, 1, 1, 1, 2)) > > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > # > # Check out the various residuals under an Efron approximation > # > fit0 <- coxph(Surv(time, status)~ x, test1, iter=0) > fit <- coxph(Surv(time, status) ~x, test1) > fit0b <- coxph(Surv(start, stop, status) ~ x, test1b, iter=0) > fitb <- coxph(Surv(start, stop, status) ~x, test1b) > fitc <- coxph(Surv(time, status) ~ offset(fit$coef*x), test1) > fitd <- coxph(Surv(start, stop, status) ~ offset(fit$coef*x), test1b) > > aeq(fit0b$coef, fit0$coef) [1] TRUE > > aeq(resid(fit0), resid(fit0b, collapse=test1b$id)) [1] TRUE > aeq(resid(fit), resid(fitb, collapse=test1b$id)) [1] TRUE > aeq(resid(fitc), resid(fitd, collapse=test1b$id)) [1] TRUE > aeq(resid(fitc), resid(fit)) [1] TRUE > > aeq(resid(fit0, type='score'), resid(fit0b, type='score', collapse=test1b$id)) [1] TRUE > aeq(resid(fit, type='score'), resid(fitb, type='score', collapse=test1b$id)) [1] TRUE > > aeq(resid(fit0, type='scho'), resid(fit0b, type='scho', collapse=test1b$id)) [1] TRUE > aeq(resid(fit, type='scho'), resid(fitb, type='scho', collapse=test1b$id)) [1] TRUE > > # The two survivals will have different censoring times > # nrisk, nevent, surv, and std should be the same > temp1 <- survfit(fit, list(x=1), censor=FALSE) > temp2 <- survfit(fitb, list(x=1), censor=FALSE) > all.equal(unclass(temp1)[c(3,4,6,8)], unclass(temp2)[c(3,4,6,8)]) [1] TRUE > > > survival/tests/tt.R0000644000175100001440000000316612325255713014072 0ustar hornikuserslibrary(survival) # A contrived example for the tt function # mkdata <- function(n, beta) { age <- runif(n, 20, 60) x <- rbinom(n, 1, .5) futime <- rep(40, n) # everyone has 40 years of follow-up status <- rep(0, n) dtime <- runif(n/2, 1, 40) # 1/2 of them die dtime <- sort(dtime) # The risk is set to beta[1]*x + beta[2]* f(current_age) # where f= 0 up to age 40, rises linear to age 70, flat after that for (i in 1:length(dtime)) { atrisk <- (futime >= dtime[i]) c.age <- age + dtime age2 <- pmin(30, pmax(0, c.age-40)) xbeta <- beta[1]*x + beta[2]*age2 # Select a death according to risk risk <- ifelse(atrisk, exp(xbeta), 0) dead <- sample(1:n, 1, prob=risk/sum(risk)) futime[dead] <- dtime[i] status[dead] <- 1 } data.frame(futime=futime, status=status, age=age, x=x, risk=risk) } tdata <- mkdata(500, c(log(1.5), 2/30)) fit1 <- coxph(Surv(futime, status) ~ x + pspline(age), tdata) fit2 <- coxph(Surv(futime, status) ~ x + tt(age), tdata, tt= function(x, t, ...) pspline(x+t)) dfit <- coxph(Surv(futime, status) ~ x + tt(age), tdata, tt= function(x, t, ...) x+t, iter=0, x=T) # # Check that cluster, weight, and offset were correctly expanded # tdata <- data.frame(tdata, grp=sample(1:100, 500, replace=TRUE), casewt = sample(1:5, 500, replace=TRUE), zz = rnorm(500)) dfit2 <- coxph(Surv(futime, status) ~ x + tt(age) + offset(zz) + cluster(grp), weight=casewt, data=tdata, tt= function(x, t, ...) x+t) survival/tests/fr_lung.Rout.save0000644000175100001440000000262011732700061016546 0ustar hornikusers R version 2.11.1 (2010-05-31) Copyright (C) 2010 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) Loading required package: splines > > # > # A test with the lung data > # This caused problems in one release > > # > # First, get rid of some missings > # > lung2 <- na.omit(lung[c('time', 'status', 'wt.loss')]) > > # > # Test the logliklihoods > # > fit <- coxph(Surv(time, status) ~ pspline(wt.loss,3), lung2, x=T) > fit0<- coxph(Surv(time, status) ~ 1, lung2) > fit1<- coxph(Surv(time, status) ~ fit$x, lung2, iter=0, init=fit$coef) > > all.equal(fit$loglik[1], fit0$loglik) [1] TRUE > all.equal(fit$loglik[2], fit1$loglik[2]) [1] TRUE > > # > # Check variances > # > imat <- solve(fit1$var) > var2 <- fit$var %*% imat %*% fit$var > all.equal(fit$var2, var2) [1] TRUE > survival/tests/testreg.R0000644000175100001440000000430211732700061015101 0ustar hornikusersoptions(na.action=na.exclude) #preserve length of missings library(survival) # # Run a test that can be verified using other packages (we used SAS) # test1 <- data.frame(time= c(9, 3,1,1,6,6,8), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0)) fit1w <- survreg(Surv(time, status) ~x, test1, dist='weibull') fit1w summary(fit1w) fit1e <- survreg(Surv(time, status) ~x, test1, dist='exponential') fit1e summary(fit1e) fit1l <- survreg(Surv(time, status) ~x, test1, dist='loglogistic') fit1l summary(fit1l) fit1g <- survreg(Surv(time, status) ~x, test1, dist='lognormal') summary(fit1g) # # Do a test with the ovarian data # fitfw <- survreg(Surv(futime, fustat) ~ age + ecog.ps, ovarian, dist='weibull') fitfw fitfl <- survreg(Surv(futime, fustat) ~ age + ecog.ps, ovarian, dist='loglogistic') fitfl #test out interval censoring, using some dummy time values idat <- read.table('data.interval', skip=3, header=T, sep=',') flsurv<- Surv(idat$ltime, idat$rtime, type='interval2') fitfw2 <- survreg(flsurv ~ age + ecog.ps, idat, dist='weibull') summary(fitfw2) fitfl2 <- survreg(flsurv ~ age + ecog.ps, idat, dist='loglogistic') summary(fitfl2) fitfg2 <- survreg(flsurv ~ age + ecog.ps, idat, dist='lognormal') summary(fitfg2) logt <- c(survreg.distributions$t, survreg.distributions$weibull[c('trans', 'itrans', 'dtrans')]) logt$name <- 'log(t)' fitft2 <- survreg(Surv(ltime, rtime, type='interval2') ~ age + ecog.ps, idat, dist=logt, parm=100) summary(fitft2) #should be quite close to fitfg2 # # Check out the survreg density and probability functions # # Gaussian x <- -10:10 p <- seq(.1, .95, length=25) all.equal(dsurvreg(x, 1, 5, 'gaussian'), dnorm(x, 1, 5)) all.equal(psurvreg(x, 1, 5, 'gaussian'), pnorm(x, 1, 5)) all.equal(qsurvreg(p, 1, 5, 'gaussian'), qnorm(p, 1, 5)) # Lognormal x <- 1:10 all.equal(dsurvreg(x, 1, 5, 'lognormal'), dlnorm(x, 1, 5)) all.equal(psurvreg(x, 1, 5, 'lognormal'), plnorm(x, 1, 5)) all.equal(qsurvreg(p, 1, 5, 'lognormal'), qlnorm(p, 1, 5)) # Weibull lambda <- exp(-2) rho <- 1/3 temp <- (lambda*x)^rho all.equal(psurvreg(x, 2, 3), 1- exp(-temp)) all.equal(dsurvreg(x, 2, 3), lambda*rho*(lambda*x)^(rho-1)*exp(-temp)) survival/tests/tmerge2.Rout.save0000644000175100001440000000334113054103376016465 0ustar hornikusers R Under development (unstable) (2017-02-21 r72241) -- "Unsuffered Consequences" Copyright (C) 2017 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > > # This test is based on a user report that a 0/1 variable would not reset > # to zero. It turned out to be a bug when data2 was not sorted > > baseline <- data.frame(idd=1:5, futime=c(20, 30, 40, 30, 20), + status= c(0, 1, 0, 1, 0)) > tests <- data.frame(idd = c(2,3,3,3,4,4,5), + date = c(25, -1, 15, 23, 17, 19, 14), + onoff= c( 1, 1, 0, 1, 1, 0, 1)) > tests <- tests[c(7,2,6,3,4,1,5),] #scramble data2 > > mydata <- tmerge(baseline, baseline, id=idd, death=event(futime, status)) > mydata <- tmerge(mydata, tests, id=idd, ondrug=tdc(date, onoff)) > > all.equal(mydata$ondrug, c(NA, NA,1, 1,0,1, NA, 1,0, NA, 1)) [1] TRUE > > > # Check out addition of a factor > tests$ff <- factor(tests$onoff, 0:1, letters[4:5]) > mydata <- tmerge(mydata, tests, id=idd, fgrp= tdc(date, ff), + options=list(tdcstart="new")) > > all.equal(mydata$fgrp, + factor(c(3,3,2,2,1,2,3,2,1,3,2), labels=c("d", "e", "new"))) [1] TRUE > > proc.time() user system elapsed 1.352 0.072 1.419 survival/tests/book5.R0000644000175100001440000001076212650522315014456 0ustar hornikuserslibrary(survival) options(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type # Tests of the weighted Cox model # This is section 1.3 of my appendix -- not yet found in the book # though, it awaits the next edition # # Similar data set to test1, but add weights, # a double-death/censor tied time # a censored last subject # The latter two are cases covered only feebly elsewhere. # # The data set testw2 has the same data, but done via replication # aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) testw1 <- data.frame(time= c(1,1,2,2,2,2,3,4,5), status= c(1,0,1,1,1,0,0,1,0), x= c(2,0,1,1,0,1,0,1,0), wt = c(1,2,3,4,3,2,1,2,1)) xx <- testw1$wt testw2 <- data.frame(time= rep(c(1,1,2,2,2,2,3,4,5), xx), status= rep(c(1,0,1,1,1,0,0,1,0), xx), x= rep(c(2,0,1,1,0,1,0,1,0), xx), id= rep(1:9, xx)) indx <- match(1:9, testw2$id) # Breslow estimate byhand <- function(beta, newx=0) { r <- exp(beta) loglik <- 11*beta - (log(r^2 + 11*r +7) + 10*log(11*r +5) +2*log(2*r+1)) hazard <- c(1/(r^2 + 11*r +7), 10/(11*r +5), 2/(2*r+1)) xbar <- c((2*r^2 + 11*r)*hazard[1], 11*r/(11*r +5), r*hazard[3]) U <- 11- (xbar[1] + 10*xbar[2] + 2*xbar[3]) imat <- (4*r^2 + 11*r)*hazard[1] - xbar[1]^2 + 10*(xbar[2] - xbar[2]^2) + 2*(xbar[3] - xbar[3]^2) temp <- cumsum(hazard) risk <- c(r^2, 1,r,r,1,r,1,r,1) expected <- risk* temp[c(1,1,2,2,2,2,2,3,3)] # The matrix of weights, one row per obs, one col per death # deaths at 1,2,2,2, and 4 riskmat <- matrix(c(1,1,1,1,1,1,1,1,1, 0,0,1,1,1,1,1,1,1, 0,0,1,1,1,1,1,1,1, 0,0,1,1,1,1,1,1,1, 0,0,0,0,0,0,0,1,1), ncol=5) wtmat <- diag(c(r^2, 2, 3*r, 4*r, 3, 2*r, 1, 2*r, 1)) %*% riskmat x <- c(2,0,1,1,0,1,0,1,0) status <- c(1,0,1,1,1,0,0,1,0) wt <- c(1,2,3,4,3,2,1,2,1) # Table of sums for score and Schoenfeld resids hazmat <- riskmat %*% diag(c(1,3,4,3,2)/colSums(wtmat)) dM <- -risk*hazmat #Expected part dM[1,1] <- dM[1,1] +1 # deaths at time 1 for (i in 2:4) dM[i+1, i] <- dM[i+1,i] +1 dM[8,5] <- dM[8,5] +1 mart <- rowSums(dM) resid <-dM * outer(x, xbar[c(1,2,2,2,3)] ,'-') # Increments to the variance of the hazard var.g <- cumsum(hazard^2/ c(1,10,2)) var.d <- cumsum((xbar-newx)*hazard) list(loglik=loglik, U=U, imat=imat, hazard=hazard, xbar=xbar, mart=c(1,0,1,1,1,0,0,1,0)-expected, expected=expected, score=rowSums(resid), schoen=c(2,1,1,0,1) - xbar[c(1,2,2,2,3)], varhaz=(var.g + var.d^2/imat)* exp(2*beta*newx)) } aeq(byhand(0)$expected, c(1/19, 1/19, rep(103/152, 5), rep(613/456,2))) #verify fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt, method='breslow', iter=0) fit0b <- coxph(Surv(time, status) ~x, testw2, method='breslow', iter=0) fit <- coxph(Surv(time, status) ~x, testw1, weights=wt, method='breslow') fitb <- coxph(Surv(time, status) ~x, testw2, method='breslow') aeq(resid(fit0, type='mart'), (resid(fit0b, type='mart'))[indx]) aeq(resid(fit0, type='scor'), (resid(fit0b, type='scor'))[indx]) aeq(unique(resid(fit0, type='scho')), unique(resid(fit0b, type='scho'))) truth0 <- byhand(0,pi) aeq(fit0$loglik[1], truth0$loglik) aeq(1/truth0$imat, fit0$var) aeq(truth0$mart, fit0$resid) aeq(truth0$scho, resid(fit0, 'schoen')) aeq(truth0$score, resid(fit0, 'score')) sfit <- survfit(fit0, list(x=pi), censor=FALSE) aeq(sfit$std.err^2, truth0$var) aeq(-log(sfit$surv), cumsum(truth0$haz)) truth <- byhand(0.85955744, .3) aeq(truth$loglik, fit$loglik[2]) aeq(1/truth$imat, fit$var) aeq(truth$mart, fit$resid) aeq(truth$scho, resid(fit, 'schoen')) aeq(truth$score, resid(fit, 'score')) sfit <- survfit(fit, list(x=.3), censor=FALSE) aeq(sfit$std.err^2, truth$var) aeq(-log(sfit$surv), (cumsum(truth$haz)* exp(fit$coef*.3))) fit0 summary(fit) resid(fit0, type='score') resid(fit0, type='scho') resid(fit, type='score') resid(fit, type='scho') aeq(resid(fit, type='mart'), (resid(fitb, type='mart'))[indx]) aeq(resid(fit, type='scor'), (resid(fitb, type='scor'))[indx]) aeq(unique(resid(fit, type='scho')), unique(resid(fitb, type='scho'))) rr1 <- resid(fit, type='mart') rr2 <- resid(fit, type='mart', weighted=T) aeq(rr2/rr1, testw1$wt) rr1 <- resid(fit, type='score') rr2 <- resid(fit, type='score', weighted=T) aeq(rr2/rr1, testw1$wt) survival/tests/data.smoke0000644000175100001440000000304511732700061015255 0ustar hornikusers 186.0 439.2 234.4 365.8 159.6 216.9 167.4 159.5 255.6 702.7 544.7 431.0 454.8 349.7 214.0 250.4 448.9 1132.4 945.2 728.8 729.4 590.2 447.3 436.6 733.7 1981.1 1177.7 1589.2 1316.5 1266.9 875.6 703.0 1119.4 3003.0 2244.9 3380.3 2374.9 1820.2 1669.1 1159.2 2070.5 4697.5 4255.3 5083.0 4485.0 3888.7 3184.3 2194.9 3675.3 7340.6 5882.4 6597.2 7707.5 4945.1 5618.0 4128.9 186.0 610.0 497.5 251.7 417.5 122.6 198.3 193.4 255.6 915.6 482.8 500.7 488.9 402.9 393.9 354.3 448.9 1391.0 1757.1 953.5 1025.8 744.0 668.5 537.8 733.7 2393.4 1578.4 1847.2 1790.1 1220.7 1100.0 993.3 1119.4 3497.9 2301.8 3776.6 2081.0 2766.4 2268.1 1230.7 2070.5 5861.3 3174.6 2974.0 3712.9 3988.8 3268.6 2468.9 3675.3 6250.0 4000.0 4424.8 7329.8 6383.0 7666.1 5048.1 125.7 225.6 0 433.9 212.0 107.2 135.9 91.0 177.3 353.8 116.8 92.1 289.5 200.9 121.3 172.1 244.8 542.8 287.4 259.5 375.9 165.8 202.2 247.2 397.7 858.0 1016.3 365.0 650.9 470.8 570.6 319.7 692.1 1496.2 1108.0 1348.5 1263.2 864.8 586.6 618.0 1160.0 2084.8 645.2 1483.1 1250.0 1126.3 1070.5 1272.1 2070.8 3319.5 0 2580.6 2590.7 3960.4 1666.7 1861.5 125.7 277.9 266.7 102.7 178.6 224.7 142.1 138.8 177.3 517.9 138.7 466.8 270.1 190.2 116.8 83.0 244.8 823.5 473.6 602.0 361.0 454.5 412.2 182.1 397.7 1302.9 1114.8 862.1 699.6 541.7 373.1 356.4 692.1 1934.9 2319.6 1250.0 1688.0 828.7 797.9 581.5 1160.0 2827.0 4635.8 2517.2 1687.3 2848.7 1621.2 1363.4 2070.8 4273.1 2409.6 5769.2 3125.0 2978.7 2803.7 2195.4 survival/tests/concordance.Rout.save0000644000175100001440000001245011732700061017372 0ustar hornikusers R version 2.12.2 (2011-02-25) Copyright (C) 2011 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: x86_64-unknown-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) Loading required package: splines > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > > # > # Simple tests of concordance. These numbers were derived in multiple > # codes. > # > aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) > > grank <- function(x, time, grp, wt) + unlist(tapply(x, grp, rank)) > grank2 <- function(x, time, grp, wt) { #for case weights + if (length(wt)==0) wt <- rep(1, length(x)) + z <- double(length(x)) + for (i in unique(grp)) { + indx <- which(grp==i) + temp <- tapply(wt[indx], x[indx], sum) + temp <- temp/2 + c(0, cumsum(temp)[-length(temp)]) + z[indx] <- temp[match(x[indx], names(temp))] + } + z + } > > > tdata <- aml[aml$x=='Maintained',] > tdata$y <- c(1,6,2,7,3,7,3,8,4,4,5) > tdata$wt <- c(1,2,3,2,1,2,3,4,3,2,1) > fit <- survConcordance(Surv(time, status) ~y, tdata) > aeq(fit$stats[1:4], c(14,24,2,0)) [1] TRUE > cfit <- coxph(Surv(time, status) ~ tt(y), tdata, tt=grank, method='breslow', + iter=0, x=T) > cdt <- coxph.detail(cfit) > aeq(4*sum(cdt$imat),fit$stats[5]^2) [1] TRUE > aeq(2*sum(cdt$score), diff(fit$stats[2:1])) [1] TRUE > > > # Lots of ties > tempx <- Surv(c(1,2,2,2,3,4,4,4,5,2), c(1,0,1,0,1,0,1,1,0,1)) > tempy <- c(5,5,4,4,3,3,7,6,5,4) > fit2 <- survConcordance(tempx ~ tempy) > aeq(fit2$stats[1:4], c(13,13,5,2)) [1] TRUE > cfit2 <- coxph(tempx ~ tt(tempy), tt=grank, method='breslow', iter=0) > aeq(4/cfit2$var, fit2$stats[5]^2) [1] TRUE > > # Bigger data > fit3 <- survConcordance(Surv(time, status) ~ age, lung) > aeq(fit3$stats[1:4], c(10717, 8706, 591, 28)) [1] TRUE > cfit3 <- coxph(Surv(time, status) ~ tt(age), lung, + iter=0, method='breslow', tt=grank, x=T) > cdt <- coxph.detail(cfit3) > aeq(4*sum(cdt$imat),fit3$stats[5]^2) [1] TRUE > aeq(2*sum(cdt$score), diff(fit3$stats[2:1])) [1] TRUE > > > # More ties > fit4 <- survConcordance(Surv(time, status) ~ ph.ecog, lung) > aeq(fit4$stats[1:4], c(8392, 4258, 7137, 28)) [1] TRUE > cfit4 <- coxph(Surv(time, status) ~ tt(ph.ecog), lung, + iter=0, method='breslow', tt=grank) > aeq(4/cfit4$var, fit4$stats[5]^2) [1] TRUE > > # Case weights > fit5 <- survConcordance(Surv(time, status) ~ y, tdata, weight=wt) > fit6 <- survConcordance(Surv(time, status) ~y, tdata[rep(1:11,tdata$wt),]) > aeq(fit5$stats[1:4], c(70, 91, 7, 0)) # checked by hand [1] TRUE > aeq(fit5$stats[1:3], fit6$stats[1:3]) #spurious "tied on time" value, ignore [1] TRUE > aeq(fit5$std, fit6$std) [1] TRUE > cfit5 <- coxph(Surv(time, status) ~ tt(y), tdata, weight=wt, + iter=0, method='breslow', tt=grank2) > cfit6 <- coxph(Surv(time, status) ~ tt(y), tdata[rep(1:11,tdata$wt),], + iter=0, method='breslow', tt=grank) > aeq(4/cfit6$var, fit6$stats[5]^2) [1] TRUE > aeq(cfit5$var, cfit6$var) [1] TRUE > > # Start, stop simplest cases > fit7 <- survConcordance(Surv(rep(0,11), time, status) ~ y, tdata) > aeq(fit7$stats, fit$stats) [1] TRUE > aeq(fit7$std.err, fit$std.err) [1] TRUE > fit7 <- survConcordance(Surv(rep(0,11), time, status) ~ y, tdata, weight=wt) > aeq(fit5$stats, fit7$stats) [1] TRUE > > # Multiple intervals for some, but same risk sets as tdata > tdata2 <- data.frame(time1=c(0,3, 5, 6,7, 0, 4,17, 7, 0,16, 2, 0, + 0,9, 5), + time2=c(3,9, 13, 7,13, 18, 17,23, 28, 16,31, 34, 45, + 9,48, 60), + status=c(0,1, 1, 0,0, 1, 0,1, 0, 0,1, 1, 0, 0,1, 0), + y = c(1,1, 6, 2,2, 7, 3,3, 7, 3,3, 8, 4, 4,4, 5), + wt= c(1,1, 2, 3,3, 2, 1,1, 2, 3,3, 4, 3, 2,2, 1)) > fit8 <- survConcordance(Surv(time1, time2, status) ~y, tdata2, weight=wt) > aeq(fit5$stats, fit8$stats) [1] TRUE > aeq(fit5$std.err, fit8$std.err) [1] TRUE > cfit8 <- coxph(Surv(time1, time2, status) ~ tt(y), tdata2, weight=wt, + iter=0, method='breslow', tt=grank2) > aeq(4/cfit8$var, fit8$stats[5]^2) [1] TRUE > aeq(fit8$stats[5]/(2*sum(fit8$stats[1:3])), fit8$std.err) [1] TRUE > > # Stratified > tdata3 <- data.frame(time1=c(tdata2$time1, rep(0, nrow(lung))), + time2=c(tdata2$time2, lung$time), + status = c(tdata2$status, lung$status -1), + x = c(tdata2$y, lung$ph.ecog), + wt= c(tdata2$wt, rep(1, nrow(lung))), + grp=rep(1:2, c(nrow(tdata2), nrow(lung)))) > fit9 <- survConcordance(Surv(time1, time2, status) ~x + strata(grp), + data=tdata3, weight=wt) > aeq(fit9$stats[1,], fit5$stats) [1] TRUE > aeq(fit9$stats[2,], fit4$stats) [1] TRUE > survival/tests/pyear.Rout.save0000644000175100001440000004146112701744412016245 0ustar hornikusers R Under development (unstable) (2016-03-23 r70368) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > {if (is.R()) mdy.date <- function(m, d, y) { + y <- ifelse(y<100, y+1900, y) + as.Date(paste(m,d,y, sep='/'), "%m/%d/%Y") + } + else mdy.date <- function(m,d,y) { + y <- ifelse(y<100, y+1900, y) + timeDate(paste(y, m, d, sep='/'), in.format="%Y/%m/%d") + } + } > > # > # Simple case: a single male subject, born 6/6/36 and entered on study 6/6/55. > # > > temp1 <- mdy.date(6,6,36) > temp2 <- mdy.date(6,6,55)# Now compare the results from person-years > # > temp.age <- tcut(temp2-temp1, floor(c(-1, (18:31 * 365.24))), + labels=c('0-18', paste(18:30, 19:31, sep='-'))) > temp.yr <- tcut(temp2, mdy.date(1,1,1954:1965), labels=1954:1964) > temp.time <- 3700 #total days of fu > py1 <- pyears(temp.time ~ temp.age + temp.yr, scale=1) #output in days > > # The subject should appear in 20 cells > # 6/6/55 - 12/31/55, 209 days, age 19-20, 1955 > # 1/1/56 - 6/ 4/56, 156 days, age 19-20, 1956 > # 6/5/56 - 12/31/56, 210 days, age 20-21, 1956 (a leap year, and his > # birthday computes one day earlier) > # 1/1/57 - 6/ 5/57, 156 days, age 20-21, 1957 > # 6/6/57 - 12/31/57, 209 days, age 21-22, 1957 > # and etc > # with 203 days "off table", ie, beyond the last cell of the table > # > # It is a nuisance, but tcut follows 'cut' in that we give the ENDS of > # the intervals, whereas the survival tables use the starts of intervals. > # Thus this breakdown does not match that in doexpect.s > # > xx <- matrix(0, nrow=14, ncol=11) > xx[cbind(3:11, 3:11)] <- 156 > xx[cbind(3:12, 2:11)] <- c(209, 210, rep(c(209, 209, 209, 210),2)) > dimnames(xx) <- list(temp.age= c('0-18', paste(18:30, 19:31, sep='-')), + temp.yr = 1954:1964) > all.equal(xx, py1$pyears) [1] TRUE > all.equal(203, py1$offtable) [1] TRUE > all.equal(1*(xx>0), py1$n) [1] TRUE > > # > # Now with expecteds > # > py2 <- pyears(temp.time ~ temp.age + temp.yr + + ratetable(age=temp2-temp1, year=temp2, sex=1), + scale=1, ratetable=survexp.us ) #output in days > all.equal(xx, py2$pyears) [1] TRUE > all.equal(203, py2$offtable) [1] TRUE > all.equal(1*(xx>0), py2$n) [1] TRUE > > py2b <- pyears(temp.time ~ temp.age + temp.yr, + rmap = list(age=temp2-temp1, year=temp2, sex=1), + scale=1, ratetable=survexp.us ) #output in days > all.equal(xx, py2b$pyears) [1] TRUE > all.equal(203, py2b$offtable) [1] TRUE > all.equal(1*(xx>0), py2b$n) [1] TRUE > all.equal(py2$expected, py2b$expected) [1] TRUE > > > > py3 <- pyears(temp.time ~ temp.age + temp.yr, + rmap=list(age=temp2-temp1, year=temp2, sex=1), + scale=1, ratetable=survexp.us , expect='pyears') > all.equal(py2$n, py3$n) [1] TRUE > all.equal(py2$pyear, py3$pyear) [1] TRUE > all.equal(py3$n, 1*(py3$expect>0)) [1] TRUE > > # Now, compute the py3 result "by hand". Since there is only one person > # it can be derived from py2. > # > xx1 <- py2$expect[py2$n>0] # the hazard over each interval > cumhaz <- cumsum(c(0, xx1[-length(xx1)])) # the cumulative hazard > xx2 <- py3$expect[py3$n>0] # the expected number of person days > xx3 <- py3$pyears[py3$n>0] # the potential number of person days > > # This is the integral of the curve "exp(-haz *t)" over the interval > integral <- xx3 * exp(-cumhaz)* (1- exp(-xx1))/ xx1 > # They might not be exactly equal, since the C code tracks changes in the > # rate tables that occur -within- an interval. So try for 6 digits > all.equal(round(integral,3), round(xx2,3)) [1] TRUE > > # Cut off the bottom of the table, instead of the side > temp.age <- tcut(temp2-temp1, floor(c(-1, (18:27 * 365.24))), + labels=c('0-18', paste(18:26, 19:27, sep='-'))) > > py4 <- eval(py3$call) > all.equal(py4$pyear, py3$pyear[1:10,]) [1] TRUE > all.equal(py4$expect, py3$expect[1:10,]) [1] TRUE > > > rm(temp.age, integral, xx1, xx2, xx3, cumhaz, py1, py2, py3, py4) > rm(temp1, temp2, temp.yr, temp.time, xx) > > > > > # > # Simple case: a single male subject, born 6/6/36 and entered on study 6/6/55. > # > > temp1 <- mdy.date(6,6,36) > temp2 <- mdy.date(6,6,55)# Now compare the results from person-years > # > temp.age <- tcut(temp2-temp1, floor(c(-1, (18:31 * 365.24))), + labels=c('0-18', paste(18:30, 19:31, sep='-'))) > temp.yr <- tcut(temp2, mdy.date(1,1,1954:1965), labels=1954:1964) > temp.time <- 3700 #total days of fu > py1 <- pyears(temp.time ~ temp.age + temp.yr, scale=1) #output in days > > # The subject should appear in 20 cells > # 6/6/55 - 12/31/55, 209 days, age 19-20, 1955 > # 1/1/56 - 6/ 4/56, 156 days, age 19-20, 1956 > # 6/5/56 - 12/31/56, 210 days, age 20-21, 1956 (a leap year, and his > # birthday computes one day earlier) > # 1/1/57 - 6/ 5/57, 156 days, age 20-21, 1957 > # 6/6/57 - 12/31/57, 209 days, age 21-22, 1957 > # and etc > # with 203 days "off table", ie, beyond the last cell of the table > # > # It is a nuisance, but tcut follows 'cut' in that we give the ENDS of > # the intervals, whereas the survival tables use the starts of intervals. > # > xx <- matrix(0, nrow=14, ncol=11) > xx[cbind(3:11, 3:11)] <- 156 > xx[cbind(3:12, 2:11)] <- c(209, 210, rep(c(209, 209, 209, 210),2)) > dimnames(xx) <- list(temp.age= c('0-18', paste(18:30, 19:31, sep='-')), + temp.yr = 1954:1964) > all.equal(xx, py1$pyears) [1] TRUE > all.equal(203, py1$offtable) [1] TRUE > all.equal(1*(xx>0), py1$n) [1] TRUE > > # > # Now with expecteds > # > py2 <- pyears(temp.time ~ temp.age + temp.yr + + ratetable(age=temp2-temp1, year=temp2, sex=1), + scale=1, ratetable=survexp.us ) #output in days > all.equal(xx, py2$pyears) [1] TRUE > all.equal(203, py2$offtable) [1] TRUE > all.equal(1*(xx>0), py2$n) [1] TRUE > > > py3 <- pyears(temp.time ~ temp.age + temp.yr + + ratetable(age=temp2-temp1, year=temp2, sex=1), + scale=1, ratetable=survexp.us , expect='pyears') > all.equal(py2$n, py3$n) [1] TRUE > all.equal(py2$pyear, py3$pyear) [1] TRUE > all.equal(py3$n, 1*(py3$expect>0)) [1] TRUE > > # Now, compute the py3 result "by hand". Since there is only one person > # it can be derived from py2. > # > xx1 <- py2$expect[py2$n>0] # the hazard over each interval > cumhaz <- cumsum(c(0, xx1[-length(xx1)])) # the cumulative hazard > xx2 <- py3$expect[py3$n>0] # the expected number of person days > xx3 <- py3$pyears[py3$n>0] # the potential number of person days > > # This is the integral of the curve "exp(-haz *t)" over the interval > integral <- xx3 * exp(-cumhaz)* (1- exp(-xx1))/ xx1 > # They might not be exactly equal, since the C code tracks changes in the > # rate tables that occur -within- an interval. So try for 6 digits > all.equal(round(integral,3), round(xx2,3)) [1] TRUE > > # Cut off the bottom of the table, instead of the side > temp.age <- tcut(temp2-temp1, floor(c(-1, (18:27 * 365.24))), + labels=c('0-18', paste(18:26, 19:27, sep='-'))) > > py4 <- eval(py3$call) > all.equal(py4$pyear, py3$pyear[1:10,]) [1] TRUE > all.equal(py4$expect, py3$expect[1:10,]) [1] TRUE > > > rm(temp.age, integral, xx1, xx2, xx3, cumhaz, py1, py2, py3, py4) > rm(temp1, temp2, temp.yr, temp.time, xx) > > > > > # > # Create a "user defined" rate table, using the smoking data > # > temp <- scan("data.smoke")/100000 Read 224 items > temp <- matrix(temp, ncol=8, byrow=T) > smoke.rate <- c(rep(temp[,1],6), rep(temp[,2],6), temp[,3:8]) > attributes(smoke.rate) <- list( + dim=c(7,2,2,6,3), + dimnames=list(c("45-49","50-54","55-59","60-64","65-69","70-74","75-79"), + c("1-20", "21+"), + c("Male","Female"), + c("<1", "1-2", "3-5", "6-10", "11-15", ">=16"), + c("Never", "Current", "Former")), + dimid=c("age", "amount", "sex", "duration", "status"), + factor=c(0,1,1,0,1), + cutpoints=list(c(45,50,55,60,65,70,75),NULL, NULL, + c(0,1,3,6,11,16),NULL), + class='ratetable' + ) > rm(temp) > > is.ratetable(smoke.rate) [1] TRUE > summary(smoke.rate) Rate table with 5 dimensions: age ranges from 45 to 75; with 7 categories amount has levels of: 1-20 21+ sex has levels of: Male Female duration ranges from 0 to 16; with 6 categories status has levels of: Never Current Former > print(smoke.rate) Rate table with dimension(s): age amount sex duration status , , Male, <1, Never 1-20 21+ 45-49 0.001860 0.001860 50-54 0.002556 0.002556 55-59 0.004489 0.004489 60-64 0.007337 0.007337 65-69 0.011194 0.011194 70-74 0.020705 0.020705 75-79 0.036753 0.036753 , , Female, <1, Never 1-20 21+ 45-49 0.001257 0.001257 50-54 0.001773 0.001773 55-59 0.002448 0.002448 60-64 0.003977 0.003977 65-69 0.006921 0.006921 70-74 0.011600 0.011600 75-79 0.020708 0.020708 , , Male, 1-2, Never 1-20 21+ 45-49 0.001860 0.001860 50-54 0.002556 0.002556 55-59 0.004489 0.004489 60-64 0.007337 0.007337 65-69 0.011194 0.011194 70-74 0.020705 0.020705 75-79 0.036753 0.036753 , , Female, 1-2, Never 1-20 21+ 45-49 0.001257 0.001257 50-54 0.001773 0.001773 55-59 0.002448 0.002448 60-64 0.003977 0.003977 65-69 0.006921 0.006921 70-74 0.011600 0.011600 75-79 0.020708 0.020708 , , Male, 3-5, Never 1-20 21+ 45-49 0.001860 0.001860 50-54 0.002556 0.002556 55-59 0.004489 0.004489 60-64 0.007337 0.007337 65-69 0.011194 0.011194 70-74 0.020705 0.020705 75-79 0.036753 0.036753 , , Female, 3-5, Never 1-20 21+ 45-49 0.001257 0.001257 50-54 0.001773 0.001773 55-59 0.002448 0.002448 60-64 0.003977 0.003977 65-69 0.006921 0.006921 70-74 0.011600 0.011600 75-79 0.020708 0.020708 , , Male, 6-10, Never 1-20 21+ 45-49 0.001860 0.001860 50-54 0.002556 0.002556 55-59 0.004489 0.004489 60-64 0.007337 0.007337 65-69 0.011194 0.011194 70-74 0.020705 0.020705 75-79 0.036753 0.036753 , , Female, 6-10, Never 1-20 21+ 45-49 0.001257 0.001257 50-54 0.001773 0.001773 55-59 0.002448 0.002448 60-64 0.003977 0.003977 65-69 0.006921 0.006921 70-74 0.011600 0.011600 75-79 0.020708 0.020708 , , Male, 11-15, Never 1-20 21+ 45-49 0.001860 0.001860 50-54 0.002556 0.002556 55-59 0.004489 0.004489 60-64 0.007337 0.007337 65-69 0.011194 0.011194 70-74 0.020705 0.020705 75-79 0.036753 0.036753 , , Female, 11-15, Never 1-20 21+ 45-49 0.001257 0.001257 50-54 0.001773 0.001773 55-59 0.002448 0.002448 60-64 0.003977 0.003977 65-69 0.006921 0.006921 70-74 0.011600 0.011600 75-79 0.020708 0.020708 , , Male, >=16, Never 1-20 21+ 45-49 0.001860 0.001860 50-54 0.002556 0.002556 55-59 0.004489 0.004489 60-64 0.007337 0.007337 65-69 0.011194 0.011194 70-74 0.020705 0.020705 75-79 0.036753 0.036753 , , Female, >=16, Never 1-20 21+ 45-49 0.001257 0.001257 50-54 0.001773 0.001773 55-59 0.002448 0.002448 60-64 0.003977 0.003977 65-69 0.006921 0.006921 70-74 0.011600 0.011600 75-79 0.020708 0.020708 , , Male, <1, Current 1-20 21+ 45-49 0.004392 0.006100 50-54 0.007027 0.009156 55-59 0.011324 0.013910 60-64 0.019811 0.023934 65-69 0.030030 0.034979 70-74 0.046975 0.058613 75-79 0.073406 0.062500 , , Female, <1, Current 1-20 21+ 45-49 0.002256 0.002779 50-54 0.003538 0.005179 55-59 0.005428 0.008235 60-64 0.008580 0.013029 65-69 0.014962 0.019349 70-74 0.020848 0.028270 75-79 0.033195 0.042731 , , Male, 1-2, Current 1-20 21+ 45-49 0.004392 0.006100 50-54 0.007027 0.009156 55-59 0.011324 0.013910 60-64 0.019811 0.023934 65-69 0.030030 0.034979 70-74 0.046975 0.058613 75-79 0.073406 0.062500 , , Female, 1-2, Current 1-20 21+ 45-49 0.002256 0.002779 50-54 0.003538 0.005179 55-59 0.005428 0.008235 60-64 0.008580 0.013029 65-69 0.014962 0.019349 70-74 0.020848 0.028270 75-79 0.033195 0.042731 , , Male, 3-5, Current 1-20 21+ 45-49 0.004392 0.006100 50-54 0.007027 0.009156 55-59 0.011324 0.013910 60-64 0.019811 0.023934 65-69 0.030030 0.034979 70-74 0.046975 0.058613 75-79 0.073406 0.062500 , , Female, 3-5, Current 1-20 21+ 45-49 0.002256 0.002779 50-54 0.003538 0.005179 55-59 0.005428 0.008235 60-64 0.008580 0.013029 65-69 0.014962 0.019349 70-74 0.020848 0.028270 75-79 0.033195 0.042731 , , Male, 6-10, Current 1-20 21+ 45-49 0.004392 0.006100 50-54 0.007027 0.009156 55-59 0.011324 0.013910 60-64 0.019811 0.023934 65-69 0.030030 0.034979 70-74 0.046975 0.058613 75-79 0.073406 0.062500 , , Female, 6-10, Current 1-20 21+ 45-49 0.002256 0.002779 50-54 0.003538 0.005179 55-59 0.005428 0.008235 60-64 0.008580 0.013029 65-69 0.014962 0.019349 70-74 0.020848 0.028270 75-79 0.033195 0.042731 , , Male, 11-15, Current 1-20 21+ 45-49 0.004392 0.006100 50-54 0.007027 0.009156 55-59 0.011324 0.013910 60-64 0.019811 0.023934 65-69 0.030030 0.034979 70-74 0.046975 0.058613 75-79 0.073406 0.062500 , , Female, 11-15, Current 1-20 21+ 45-49 0.002256 0.002779 50-54 0.003538 0.005179 55-59 0.005428 0.008235 60-64 0.008580 0.013029 65-69 0.014962 0.019349 70-74 0.020848 0.028270 75-79 0.033195 0.042731 , , Male, >=16, Current 1-20 21+ 45-49 0.004392 0.006100 50-54 0.007027 0.009156 55-59 0.011324 0.013910 60-64 0.019811 0.023934 65-69 0.030030 0.034979 70-74 0.046975 0.058613 75-79 0.073406 0.062500 , , Female, >=16, Current 1-20 21+ 45-49 0.002256 0.002779 50-54 0.003538 0.005179 55-59 0.005428 0.008235 60-64 0.008580 0.013029 65-69 0.014962 0.019349 70-74 0.020848 0.028270 75-79 0.033195 0.042731 , , Male, <1, Former 1-20 21+ 45-49 0.002344 0.004975 50-54 0.005447 0.004828 55-59 0.009452 0.017571 60-64 0.011777 0.015784 65-69 0.022449 0.023018 70-74 0.042553 0.031746 75-79 0.058824 0.040000 , , Female, <1, Former 1-20 21+ 45-49 0.000000 0.002667 50-54 0.001168 0.001387 55-59 0.002874 0.004736 60-64 0.010163 0.011148 65-69 0.011080 0.023196 70-74 0.006452 0.046358 75-79 0.000000 0.024096 , , Male, 1-2, Former 1-20 21+ 45-49 0.003658 0.002517 50-54 0.004310 0.005007 55-59 0.007288 0.009535 60-64 0.015892 0.018472 65-69 0.033803 0.037766 70-74 0.050830 0.029740 75-79 0.065972 0.044248 , , Female, 1-2, Former 1-20 21+ 45-49 0.004339 0.001027 50-54 0.000921 0.004668 55-59 0.002595 0.006020 60-64 0.003650 0.008621 65-69 0.013485 0.012500 70-74 0.014831 0.025172 75-79 0.025806 0.057692 , , Male, 3-5, Former 1-20 21+ 45-49 0.001596 0.004175 50-54 0.004548 0.004889 55-59 0.007294 0.010258 60-64 0.013165 0.017901 65-69 0.023749 0.020810 70-74 0.044850 0.037129 75-79 0.077075 0.073298 , , Female, 3-5, Former 1-20 21+ 45-49 0.002120 0.001786 50-54 0.002895 0.002701 55-59 0.003759 0.003610 60-64 0.006509 0.006996 65-69 0.012632 0.016880 70-74 0.012500 0.016873 75-79 0.025907 0.031250 , , Male, 6-10, Former 1-20 21+ 45-49 0.002169 0.001226 50-54 0.003497 0.004029 55-59 0.005902 0.007440 60-64 0.012669 0.012207 65-69 0.018202 0.027664 70-74 0.038887 0.039888 75-79 0.049451 0.063830 , , Female, 6-10, Former 1-20 21+ 45-49 0.001072 0.002247 50-54 0.002009 0.001902 55-59 0.001658 0.004545 60-64 0.004708 0.005417 65-69 0.008648 0.008287 70-74 0.011263 0.028487 75-79 0.039604 0.029787 , , Male, 11-15, Former 1-20 21+ 45-49 0.001674 0.001983 50-54 0.002140 0.003939 55-59 0.004473 0.006685 60-64 0.008756 0.011000 65-69 0.016691 0.022681 70-74 0.031843 0.032686 75-79 0.056180 0.076661 , , Female, 11-15, Former 1-20 21+ 45-49 0.001359 0.001421 50-54 0.001213 0.001168 55-59 0.002022 0.004122 60-64 0.005706 0.003731 65-69 0.005866 0.007979 70-74 0.010705 0.016212 75-79 0.016667 0.028037 , , Male, >=16, Former 1-20 21+ 45-49 0.001595 0.001934 50-54 0.002504 0.003543 55-59 0.004366 0.005378 60-64 0.007030 0.009933 65-69 0.011592 0.012307 70-74 0.021949 0.024689 75-79 0.041289 0.050481 , , Female, >=16, Former 1-20 21+ 45-49 0.000910 0.001388 50-54 0.001721 0.000830 55-59 0.002472 0.001821 60-64 0.003197 0.003564 65-69 0.006180 0.005815 70-74 0.012721 0.013634 75-79 0.018615 0.021954 > > summary(smoke.rate[1:3,,1,,]) #test subscripting Rate table with 4 dimensions: age ranges from 45 to 55; with 3 categories amount has levels of: 1-20 21+ duration ranges from 0 to 16; with 6 categories status has levels of: Never Current Former > > proc.time() user system elapsed 0.416 0.032 0.446 survival/tests/stratatest.R0000644000175100001440000000314111732700061015622 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Trivial test of stratified residuals # Make a second strata = replicate of the first, and I should get the # exact same answers test1 <- data.frame(time= c(9, 3,1,1,6,6,8), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0)) test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) temp <- as.matrix(test1) n <- nrow(temp) ndead<- sum(test1$status[!is.na(test1$status)]) temp <- data.frame(rbind(temp, temp)) #later releases of S have rbind.data.frame tstrat <- rep(1:2, c(n,n)) fit1 <- coxph(Surv(time, status) ~x, test1) fit2 <- coxph(Surv(time, status) ~x + strata(tstrat), temp) all.equal(resid(fit1) , (resid(fit2))[1:n]) all.equal(resid(fit1, type='score') , (resid(fit2, type='score'))[1:n]) all.equal(resid(fit1, type='schoe') , (resid(fit2, type='schoe'))[1:ndead]) #AG model temp <- as.matrix(test2) n <- nrow(temp) ndead<- sum(test2$event[!is.na(test2$event)]) temp <- data.frame(rbind(temp, temp)) tstrat <- rep(1:2, c(n,n)) fit1 <- coxph(Surv(start, stop, event) ~x, test2) fit2 <- coxph(Surv(start, stop, event) ~x + strata(tstrat), temp) all.equal(resid(fit1) , (resid(fit2))[1:n]) all.equal(resid(fit1, type='score') , (resid(fit2, type='score'))[1:n]) all.equal(resid(fit1, type='schoe') , (resid(fit2, type='schoe'))[1:ndead]) survival/tests/survfit2.R0000644000175100001440000000070212470201064015207 0ustar hornikuserslibrary(survival) # # Check out the Dory&Korn confidence interval option # tdata <- data.frame(time= 1:10, status=c(1,0,1,0,1,0,0,0,1,0)) fit1 <- survfit(Surv(time, status) ~1, tdata, conf.lower='modified') fit2 <- survfit(Surv(time, status) ~1, tdata) stdlow <- fit2$std * sqrt(c(1, 10/9, 1, 8/7, 1, 6/5, 6/4, 6/3, 1, 2/1)) lower <- exp(log(fit2$surv) - qnorm(.975)*stdlow) all.equal(fit1$lower, lower, check.attributes=FALSE) survival/tests/doweight.R0000644000175100001440000001760711741355257015267 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # Tests of the weighted Cox model # # Similar data set to test1, but add weights, # a double-death/censor tied time # a censored last subject # The latter two are cases covered only feebly elsewhere. # # The data set testw2 has the same data, but done via replication # aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) testw1 <- data.frame(time= c(1,1,2,2,2,2,3,4,5), status= c(1,0,1,1,1,0,0,1,0), x= c(2,0,1,1,0,1,0,1,0), wt = c(1,2,3,4,3,2,1,2,1)) xx <- c(1,2,3,4,3,2,1,2,1) testw2 <- data.frame(time= rep(c(1,1,2,2,2,2,3,4,5), xx), status= rep(c(1,0,1,1,1,0,0,1,0), xx), x= rep(c(2,0,1,1,0,1,0,1,0), xx), id= rep(1:9, xx)) indx <- match(1:9, testw2$id) testw2 <- data.frame(time= rep(c(1,1,2,2,2,2,3,4,5), xx), status= rep(c(1,0,1,1,1,0,0,1,0), xx), x= rep(c(2,0,1,1,0,1,0,1,0), xx), id= rep(1:9, xx)) indx <- match(1:9, testw2$id) fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt, method='breslow', iter=0) fit0b <- coxph(Surv(time, status) ~x, testw2, method='breslow', iter=0) fit <- coxph(Surv(time, status) ~x, testw1, weights=wt, method='breslow') fitb <- coxph(Surv(time, status) ~x, testw2, method='breslow') texp <- function(beta) { # expected, Breslow estimate r <- exp(beta) temp <- cumsum(c(1/(r^2 + 11*r +7), 10/(11*r +5), 2/(2*r+1))) c(r^2, 1,r,r,1,r,1,r,1)* temp[c(1,1,2,2,2,2,2,3,3)] } aeq(texp(0), c(1/19, 1/19, rep(103/152, 5), rep(613/456,2))) #verify texp() xbar <- function(beta) { # xbar, Breslow estimate r <- exp(beta) temp <- r* rep(c(2*r + 11, 11/10, 1), c(2, 5, 2)) temp * texp(beta) } fit0 summary(fit) aeq(resid(fit0), testw1$status - texp(0)) resid(fit0, type='score') resid(fit0, type='scho') aeq(resid(fit0, type='mart'), (resid(fit0b, type='mart'))[indx]) aeq(resid(fit0, type='scor'), (resid(fit0b, type='scor'))[indx]) aeq(unique(resid(fit0, type='scho')), unique(resid(fit0b, type='scho'))) aeq(resid(fit, type='mart'), testw1$status - texp(fit$coef)) resid(fit, type='score') resid(fit, type='scho') aeq(resid(fit, type='mart'), (resid(fitb, type='mart'))[indx]) aeq(resid(fit, type='scor'), (resid(fitb, type='scor'))[indx]) aeq(unique(resid(fit, type='scho')), unique(resid(fitb, type='scho'))) rr1 <- resid(fit, type='mart') rr2 <- resid(fit, type='mart', weighted=T) aeq(rr2/rr1, testw1$wt) rr1 <- resid(fit, type='score') rr2 <- resid(fit, type='score', weighted=T) aeq(rr2/rr1, testw1$wt) fit <- coxph(Surv(time, status) ~x, testw1, weights=wt, method='efron') fit resid(fit, type='mart') resid(fit, type='score') resid(fit, type='scho') # Tests of the weighted Cox model, AG form of the data # Same solution as doweight1.s # testw3 <- data.frame(id = c( 1, 1, 2, 3, 3, 3, 4, 5, 5, 6, 7, 8, 8, 9), begin= c( 0, 5, 0, 0,10,15, 0, 0,14, 0, 0, 0,23, 0), time= c( 5,10,10,10,15,20,20,14,20,20,30,23,40,50), status= c( 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0), x= c( 2, 2, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0), wt = c( 1, 1, 2, 3, 3, 3, 4, 3, 3, 2, 1, 2, 2, 1)) fit0 <- coxph(Surv(begin,time, status) ~x, testw3, weights=wt, method='breslow', iter=0) fit <- coxph(Surv(begin,time, status) ~x, testw3, weights=wt, method='breslow') fit0 summary(fit) resid(fit0, type='mart', collapse=testw3$id) resid(fit0, type='score', collapse=testw3$id) resid(fit0, type='scho') resid(fit, type='mart', collapse=testw3$id) resid(fit, type='score', collapse=testw3$id) resid(fit, type='scho') fit0 <- coxph(Surv(begin, time, status) ~x,testw3, weights=wt, iter=0) resid(fit0, 'mart', collapse=testw3$id) resid(coxph(Surv(begin, time, status) ~1, testw3, weights=wt) , collapse=testw3$id) #Null model fit <- coxph(Surv(begin,time, status) ~x, testw3, weights=wt, method='efron') fit resid(fit, type='mart', collapse=testw3$id) resid(fit, type='score', collapse=testw3$id) resid(fit, type='scho') # # Check out the impact of weights on the dfbetas # Am I computing them correctly? # wtemp <- rep(1,26) wtemp[c(5,10,15)] <- 2:4 fit <- coxph(Surv(futime, fustat) ~ age + ecog.ps, ovarian, weights=wtemp) rr <- resid(fit, 'dfbeta') fit1 <- coxph(Surv(futime, fustat) ~ age + ecog.ps, ovarian, weights=wtemp, subset=(-5)) fit2 <- coxph(Surv(futime, fustat) ~ age + ecog.ps, ovarian, weights=wtemp, subset=(-10)) fit3 <- coxph(Surv(futime, fustat) ~ age + ecog.ps, ovarian, weights=wtemp, subset=(-15)) # # Effect of case weights on expected survival curves post Cox model # fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt, method='breslow', iter=0) fit0b <- coxph(Surv(time, status) ~x, testw2, method='breslow', iter=0) surv1 <- survfit(fit0, newdata=list(x=0)) surv2 <- survfit(fit0b, newdata=list(x=0)) aeq(surv1$surv, surv2$surv) # # Check out the Efron approx. # fit0 <- coxph(Surv(time, status) ~x,testw1, weights=wt, iter=0) fit <- coxph(Surv(time, status) ~x,testw1, weights=wt) resid(fit0, 'mart') resid(coxph(Surv(time, status) ~1, testw1, weights=wt)) #Null model # lfun is the known log-likelihood for this data set, worked out in the # appendix of Therneau and Grambsch # ufun is the score vector and ifun the information matrix lfun <- function(beta) { r <- exp(beta) a <- 7*r +3 b <- 4*r +2 11*beta - ( log(r^2 + 11*r +7) + (10/3)*(log(a+b) + log(2*a/3 +b) + log(a/3 +b)) + 2*log(2*r +1)) } aeq(fit0$log[1], lfun(0)) aeq(fit$log[2], lfun(fit$coef)) ufun <- function(beta, efron=T) { #score statistic r <- exp(beta) xbar1 <- (2*r^2+11*r)/(r^2+11*r +7) xbar2 <- 11*r/(11*r +5) xbar3 <- 2*r/(2*r +1) xbar2b<- 26*r/(26*r+12) xbar2c<- 19*r/(19*r + 9) temp <- 11 - (xbar1 + 2*xbar3) if (efron) temp - (10/3)*(xbar2 + xbar2b + xbar2c) else temp - 10*xbar2 } print(ufun(fit$coef) < 1e-4) # Should be true ifun <- function(beta, efron=T) { # information matrix r <- exp(beta) xbar1 <- (2*r^2+11*r)/(r^2+11*r +7) xbar2 <- 11*r/(11*r +5) xbar3 <- 2*r/(2*r +1) xbar2b<- 26*r/(26*r+12) xbar2c<- 19*r/(19*r + 9) temp <- ((4*r^2 + 11*r)/(r^2+11*r +7) - xbar1^2) + 2*(xbar3 - xbar3^2) if (efron) temp + (10/3)*((xbar2- xbar2^2) + (xbar2b - xbar2b^2) + (xbar2c -xbar2c^2)) else temp + 10 * (xbar2- xbar2^2) } aeq(fit0$var, 1/ifun(0)) aeq(fit$var, 1/ifun(fit$coef)) # Make sure that the weights pass through the residuals correctly rr1 <- resid(fit, type='mart') rr2 <- resid(fit, type='mart', weighted=T) aeq(rr2/rr1, testw1$wt) rr1 <- resid(fit, type='score') rr2 <- resid(fit, type='score', weighted=T) aeq(rr2/rr1, testw1$wt) # # Look at the individual components # dt0 <- coxph.detail(fit0) dt <- coxph.detail(fit) aeq(sum(dt$score), ufun(fit$coef)) #score statistic aeq(sum(dt0$score), ufun(0)) aeq(dt0$hazard, c(1/19, (10/3)*(1/16 + 1/(6+20/3) + 1/(6+10/3)), 2/3)) rm(fit, fit0, rr1, rr2, dt, dt0) # # Effect of weights on the robust variance # test1 <- data.frame(time= c(9, 3,1,1,6,6,8), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0), wt= c(3,0,1,1,1,1,1), id= 1:7) testx <- data.frame(time= c(4,4,4,1,1,2,2,3), status=c(1,1,1,1,0,1,1,0), x= c(0,0,0,1,1,1,0,0), wt= c(1,1,1,1,1,1,1,1), id= 1:8) fit1 <- coxph(Surv(time, status) ~x + cluster(id), test1, method='breslow', weights=wt) fit2 <- coxph(Surv(time, status) ~x + cluster(id), testx, method='breslow') db1 <- resid(fit1, 'dfbeta', weighted=F) db1 <- db1[-2] #toss the missing db2 <- resid(fit2, 'dfbeta') aeq(db1, db2[3:8]) W <- c(3,1,1,1,1,1) #Weights, after removal of the missing value aeq(fit2$var, sum(db1*db1*W)) aeq(fit1$var, sum(db1*db1*W*W)) survival/tests/tiedtime.Rout.save0000644000175100001440000000343113054045730016723 0ustar hornikusers R version 3.3.2 (2016-10-31) -- "Sincere Pumpkin Patch" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: x86_64-apple-darwin13.4.0 (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > library(survival) > > # > # The survival code was failing for certain data sets when called as > # survfit(Surv(time2-time1, status) ~ ...... > # The issue was how tied floating point numbers are handled, and the > # fact that unique(x), factor(x) and tapply(x) are not guarranteed to > # all be the same. > # This test fails in survival 2.36-5, fixed in 2.36-6. Data sets that > # can cause it are few and far between. > # > > load('ties.rda') > x <- time2 -time1 > > # Here is the heart of the old problem > # length(unique(x))== length(table(x)) > # And the prior fix which worked ALMOST always > # x <- round(x, 15) > # length(unique(round(x,15)))== length(table(round(x,15))) > > fit1 <- survfit(Surv(x) ~1) > length(fit1$time) == length(fit1$surv) [1] TRUE > > > # a second test, once "rounding.R" > > tdata <- data.frame(time=c(1,2, sqrt(2)^2, 2, sqrt(2)^2), + status=rep(1,5), + group=c(1,1,1,2,2)) > fit <- survfit(Surv(time, status) ~ group, data=tdata) > > all.equal(sum(fit$strata), length(fit$time)) [1] TRUE > > proc.time() user system elapsed 0.733 0.053 0.802 survival/tests/coxsurv3.R0000644000175100001440000000742411732700061015230 0ustar hornikuserslibrary(survival) aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) # One more test on coxph survival curves, to test out the individual # option. First fit a model with a time dependent covariate # test2 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) # True hazard function, from the validation document lambda <- function(beta, x=0, method='efron') { r <- exp(beta) lambda <- c(1/(r+1), 1/(r+2), 1/(3*r +2), 1/(3*r+1), 1/(3*r+1), 1/(3*r+2) + 1/(2*r +2)) if (method == 'breslow') lambda[9] <- 2/(3*r +2) list(time=c(2,3,6,7,8,9), lambda=lambda) } fit <- coxph(Surv(start, stop, event) ~x, test2) # A curve for someone who never changes surv1 <-survfit(fit, newdata=list(x=0), censor=FALSE) true <- lambda(fit$coef, 0) aeq(true$time, surv1$time) aeq(-log(surv1$surv), cumsum(true$lambda)) # Reprise it with a time dependent subject who doesn't change data2 <- data.frame(start=c(0, 4, 9, 11), stop=c(4, 9, 11, 17), event=c(0,0,0,0), x=c(0,0,0,0)) surv2 <- survfit(fit, newdata=data2, individual=TRUE, censor=FALSE) aeq(surv2$surv, surv1$surv) # # Now a more complex data set with multiple strata # test3 <- data.frame(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17, 1:11), event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0,1), x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 2, 3, 2, 1, 1, 1, 0, 2, 1,0), grp = c(rep('a', 10), rep('b', 11))) fit2 <- coxph(Surv(start, stop, event) ~ x + strata(grp), test3) # The above tests show the program works for a simple case, use it to # get a true baseline for strata 2 fit2b <- coxph(Surv(start, stop, event) ~x, test3, subset=(grp=='b'), init=fit2$coef, iter=0) temp <- survfit(fit2b, newdata=list(x=0), censor=F) true2 <- list(time=temp$time, lambda=diff(c(0, -log(temp$surv)))) true1 <- lambda(fit2$coef, x=0) # Separate strata, one value surv3 <- survfit(fit2, list(x=0), censor=FALSE) aeq(true1$time, (surv3[1])$time) aeq(-log(surv3[1]$surv), cumsum(true1$lambda)) data4 <- data.frame(start=c(0, 4, 9, 11), stop=c(4, 9, 11, 17), event=c(0,0,0,0), x=c(0,0,0,0), grp=rep('a', 4)) surv4a <- survfit(fit2, newdata=data4, individual=T, censor=FALSE) aeq(-log(surv4a$surv), cumsum(true1$lambda)) data4$grp <- rep('b',4) surv4b <- survfit(fit2, newdata=data4, individual=T, censor=FALSE) aeq(-log(surv4b$surv), cumsum(true2$lambda)) # Now for something more complex # Subject 1 skips day 4. Since there were no events that day the survival # will be the same, but the times will be different. # Subject 2 spends some time in strata 1, some in strata 2, with # moving covariates # data5 <- data.frame(start=c(0,5,9,11, 0, 4, 3), stop =c(4,9,11,17, 4,8,7), event=rep(0,7), x=c(1,1,1,1, 0,1,2), grp=c('a', 'a', 'a', 'a', 'a', 'a', 'b'), subject=c(1,1,1,1, 2,2,2)) surv5 <- survfit(fit2, newdata=data5, censor=FALSE, id=subject) aeq(surv5[1]$time, c(2,3,5,6,7,8)) #surv1 has 2, 3, 6, 7, 8, 9 aeq(surv5[1]$surv, surv3[1]$surv ^ exp(fit2$coef)) tlam <- c(true1$lambda[1:2]* exp(fit2$coef * data5$x[5]), true1$lambda[3:5]* exp(fit2$coef * data5$x[6]), true2$lambda[3:4]* exp(fit2$coef * data5$x[7])) aeq(-log(surv5[2]$surv), cumsum(tlam)) survival/tests/book7.R0000644000175100001440000000337612030334160014452 0ustar hornikuserslibrary(survival) options(na.action=na.exclude) options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type # # Tests from the appendix of Therneau and Grambsch # Data set 1 + exact method test1 <- data.frame(time= c(9, 3,1,1,6,6,8), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0)) byhand7 <- function(beta) { r <- exp(beta) loglik <- 2*(beta - log(3*r + 3)) u <- 2/(r+1) imat <- 2*r/(r+1)^2 haz <- c(1/(3*r+3), 2/(r+3), 0, 1 ) ties <- c(1,1,2,2,3,4) wt <- c(r,r,r,1,1,1) mart <- c(1,0,1,1,0,1) - wt* (cumsum(haz))[ties] #martingale residual list(loglik=loglik, u=u, imat=imat, mart=mart) } aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) fit0 <-coxph(Surv(time, status) ~x, test1, iter=0, method='exact') truth0 <- byhand7(0) aeq(truth0$loglik, fit0$loglik[1]) aeq(1/truth0$imat, fit0$var) aeq(truth0$mart, fit0$resid[c(2:6,1)]) fit1 <- coxph(Surv(time, status) ~x, test1, iter=1, method='exact') aeq(fit1$coef, truth0$u*fit0$var) truth1 <- byhand7(fit1$coef) aeq(fit1$loglik[2], truth1$loglik) aeq(1/truth1$imat, fit1$var) aeq(truth1$mart, resid(fit1)[c(3:7,1)]) # Beta is infinite for this model, so we will get a warning message fit2 <- coxph(Surv(time, status) ~x, test1, method='exact') aeq(resid(fit2)[-2], c(0, 2/3, -1/3, -4/3, 1, 0)) #values from the book # # Now a multivariate case: start/stop data uses a different C routine # zz <- rep(0, nrow(lung)) fit1 <- coxph(Surv(time, status) ~ age + ph.ecog + sex, lung, method="exact") fit2 <- coxph(Surv(zz, time, status) ~ age + ph.ecog + sex, lung, method="exact") aeq(fit1$loglik, fit2$loglik) aeq(fit1$var, fit2$var) aeq(fit1$score, fit2$score) aeq(fit1$resid, fit2$resid) survival/tests/data.turbine0000644000175100001440000000217311732700061015610 0ustar hornikusersNA 4 0 4 NA 39 NA 10 4 10 NA 49 NA 14 2 14 NA 31 NA 18 7 18 NA 66 NA 22 5 22 NA 25 NA 26 9 26 NA 30 NA 30 9 30 NA 33 NA 34 6 34 NA 7 NA 38 22 38 NA 12 NA 42 21 42 NA 19 NA 46 21 46 NA 15 survival/tests/coxsurv.R0000644000175100001440000000416013054045730015143 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # # Test out subscripting in the case of a coxph survival curve # aeq <- function(x,y, ...) all.equal(as.vector(x), as.vector(y), ...) fit <- coxph(Surv(time, status) ~ age + sex + meal.cal + strata(ph.ecog), data=cancer) surv1 <- survfit(fit) temp <- surv1[2:3] which <- cumsum(surv1$strata) zed <- (which[1]+1):(which[3]) aeq(surv1$surv[zed], temp$surv) aeq(surv1$time[zed], temp$time) # This call should not create a model frame in the code -- so same # answer but a different path through the underlying code fit <- coxph(Surv(time, status) ~ age + sex + meal.cal + strata(ph.ecog), x=T, data=cancer) surv2 <- survfit(fit) all.equal(surv1, surv2) # # Now a result with a matrix of survival curves # dummy <- data.frame(age=c(30,40,60), sex=c(1,2,2), meal.cal=c(500, 1000, 1500)) surv2 <- survfit(fit, newdata=dummy) zed <- 1:which[1] aeq(surv2$surv[zed,1], surv2[1,1]$surv) aeq(surv2$surv[zed,2], surv2[1,2]$surv) aeq(surv2$surv[zed,3], surv2[1,3]$surv) aeq(surv2$surv[zed, ], surv2[1,1:3]$surv) aeq(surv2$surv[zed], (surv2[1]$surv)[,1]) aeq(surv2$surv[zed, ], surv2[1, ]$surv) # And the depreciated form - call with a named vector as 'newdata' # the resulting $call component won't match so delete it before comparing surv3 <- survfit(fit, c(age=40, sex=2, meal.cal=1000)) all.equal(unclass(surv2[,2])[-length(surv3)], unclass(surv3)[-length(surv3)]) # Test out offsets, which have recently become popular due to a Langholz paper fit1 <- coxph(Surv(time, status) ~ age + ph.ecog, lung) fit2 <- coxph(Surv(time, status) ~ age + offset(ph.ecog * fit1$coef[2]), lung) surv1 <- survfit(fit1, newdata=data.frame(age=50, ph.ecog=1)) surv2 <- survfit(fit2, newdata=data.frame(age=50, ph.ecog=1)) all.equal(surv1$surv, surv2$surv) # # Check out the start.time option # surv3 <- survfit(fit1, newdata=data.frame(age=50, ph.ecog=1), start.time=100) index <- match(surv3$time, surv1$time) rescale <- summary(surv1, time=100)$surv all.equal(surv3$surv, surv1$surv[index]/rescale) survival/tests/doweight.Rout.save0000644000175100001440000003570612656731554016760 0ustar hornikusers R Under development (unstable) (2016-01-29 r70039) -- "Unsuffered Consequences" Copyright (C) 2016 The R Foundation for Statistical Computing Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > options(na.action=na.exclude) # preserve missings > options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type > library(survival) > > # Tests of the weighted Cox model > # > # Similar data set to test1, but add weights, > # a double-death/censor tied time > # a censored last subject > # The latter two are cases covered only feebly elsewhere. > # > # The data set testw2 has the same data, but done via replication > # > aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) > > testw1 <- data.frame(time= c(1,1,2,2,2,2,3,4,5), + status= c(1,0,1,1,1,0,0,1,0), + x= c(2,0,1,1,0,1,0,1,0), + wt = c(1,2,3,4,3,2,1,2,1)) > xx <- c(1,2,3,4,3,2,1,2,1) > testw2 <- data.frame(time= rep(c(1,1,2,2,2,2,3,4,5), xx), + status= rep(c(1,0,1,1,1,0,0,1,0), xx), + x= rep(c(2,0,1,1,0,1,0,1,0), xx), + id= rep(1:9, xx)) > indx <- match(1:9, testw2$id) > testw2 <- data.frame(time= rep(c(1,1,2,2,2,2,3,4,5), xx), + status= rep(c(1,0,1,1,1,0,0,1,0), xx), + x= rep(c(2,0,1,1,0,1,0,1,0), xx), + id= rep(1:9, xx)) > indx <- match(1:9, testw2$id) > > fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt, + method='breslow', iter=0) > fit0b <- coxph(Surv(time, status) ~x, testw2, method='breslow', iter=0) > fit <- coxph(Surv(time, status) ~x, testw1, weights=wt, method='breslow') > fitb <- coxph(Surv(time, status) ~x, testw2, method='breslow') > > texp <- function(beta) { # expected, Breslow estimate + r <- exp(beta) + temp <- cumsum(c(1/(r^2 + 11*r +7), 10/(11*r +5), 2/(2*r+1))) + c(r^2, 1,r,r,1,r,1,r,1)* temp[c(1,1,2,2,2,2,2,3,3)] + } > aeq(texp(0), c(1/19, 1/19, rep(103/152, 5), rep(613/456,2))) #verify texp() [1] TRUE > > xbar <- function(beta) { # xbar, Breslow estimate + r <- exp(beta) + temp <- r* rep(c(2*r + 11, 11/10, 1), c(2, 5, 2)) + temp * texp(beta) + } > > fit0 Call: coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt, method = "breslow", iter = 0) coef exp(coef) se(coef) z p x 0.000 1.000 0.586 0 1 Likelihood ratio test=0 on 1 df, p=1 n= 9, number of events= 5 > summary(fit) Call: coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt, method = "breslow") n= 9, number of events= 5 coef exp(coef) se(coef) z Pr(>|z|) x 0.8596 2.3621 0.7131 1.205 0.228 exp(coef) exp(-coef) lower .95 upper .95 x 2.362 0.4233 0.5839 9.556 Concordance= 0.638 (se = 0.159 ) Rsquare= 0.171 (max possible= 0.999 ) Likelihood ratio test= 1.69 on 1 df, p=0.1932 Wald test = 1.45 on 1 df, p=0.2281 Score (logrank) test = 1.52 on 1 df, p=0.217 > aeq(resid(fit0), testw1$status - texp(0)) [1] TRUE > resid(fit0, type='score') 1 2 3 4 5 6 1.24653740 0.03601108 0.10056700 0.10056700 -0.22180142 -0.21193300 7 8 9 0.46569858 -0.10082189 0.91014302 > resid(fit0, type='scho') 1 2 2 2 4 1.3157895 0.3125000 0.3125000 -0.6875000 0.3333333 > > aeq(resid(fit0, type='mart'), (resid(fit0b, type='mart'))[indx]) [1] TRUE > aeq(resid(fit0, type='scor'), (resid(fit0b, type='scor'))[indx]) [1] TRUE > aeq(unique(resid(fit0, type='scho')), unique(resid(fit0b, type='scho'))) [1] TRUE > > > aeq(resid(fit, type='mart'), testw1$status - texp(fit$coef)) [1] TRUE > resid(fit, type='score') 1 2 3 4 5 6 0.88681615 0.02497653 0.03608964 0.03608964 -0.54297652 -0.12528780 7 8 9 0.29564605 -0.09476911 0.58400064 > resid(fit, type='scho') 1 2 2 2 4 1.0368337 0.1613774 0.1613774 -0.8386226 0.1746960 > aeq(resid(fit, type='mart'), (resid(fitb, type='mart'))[indx]) [1] TRUE > aeq(resid(fit, type='scor'), (resid(fitb, type='scor'))[indx]) [1] TRUE > aeq(unique(resid(fit, type='scho')), unique(resid(fitb, type='scho'))) [1] TRUE > rr1 <- resid(fit, type='mart') > rr2 <- resid(fit, type='mart', weighted=T) > aeq(rr2/rr1, testw1$wt) [1] TRUE > > rr1 <- resid(fit, type='score') > rr2 <- resid(fit, type='score', weighted=T) > aeq(rr2/rr1, testw1$wt) [1] TRUE > > fit <- coxph(Surv(time, status) ~x, testw1, weights=wt, method='efron') > fit Call: coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt, method = "efron") coef exp(coef) se(coef) z p x 0.873 2.393 0.713 1.22 0.22 Likelihood ratio test=1.75 on 1 df, p=0.186 n= 9, number of events= 5 > resid(fit, type='mart') 1 2 3 4 5 6 0.85334536 -0.02560716 0.32265266 0.32265266 0.71696234 -1.07772629 7 8 9 -0.45034077 -0.90490339 -0.79598658 > resid(fit, type='score') 1 2 3 4 5 6 0.88116056 0.02477248 0.06057806 0.06057806 -0.59724033 -0.16737066 7 8 9 0.38040295 -0.13750290 0.66631324 > resid(fit, type='scho') 1 2 2 2 4 1.0325955 0.1621759 0.1621759 -0.8378241 0.1728229 > > # Tests of the weighted Cox model, AG form of the data > # Same solution as doweight1.s > # > testw3 <- data.frame(id = c( 1, 1, 2, 3, 3, 3, 4, 5, 5, 6, 7, 8, 8, 9), + begin= c( 0, 5, 0, 0,10,15, 0, 0,14, 0, 0, 0,23, 0), + time= c( 5,10,10,10,15,20,20,14,20,20,30,23,40,50), + status= c( 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0), + x= c( 2, 2, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0), + wt = c( 1, 1, 2, 3, 3, 3, 4, 3, 3, 2, 1, 2, 2, 1)) > > fit0 <- coxph(Surv(begin,time, status) ~x, testw3, weights=wt, + method='breslow', iter=0) > fit <- coxph(Surv(begin,time, status) ~x, testw3, weights=wt, method='breslow') > fit0 Call: coxph(formula = Surv(begin, time, status) ~ x, data = testw3, weights = wt, method = "breslow", iter = 0) coef exp(coef) se(coef) z p x 0.000 1.000 0.586 0 1 Likelihood ratio test=0 on 1 df, p=1 n= 14, number of events= 5 > summary(fit) Call: coxph(formula = Surv(begin, time, status) ~ x, data = testw3, weights = wt, method = "breslow") n= 14, number of events= 5 coef exp(coef) se(coef) z Pr(>|z|) x 0.8596 2.3621 0.7131 1.205 0.228 exp(coef) exp(-coef) lower .95 upper .95 x 2.362 0.4233 0.5839 9.556 Concordance= 0.638 (se = 0.159 ) Rsquare= 0.114 (max possible= 0.991 ) Likelihood ratio test= 1.69 on 1 df, p=0.1932 Wald test = 1.45 on 1 df, p=0.2281 Score (logrank) test = 1.52 on 1 df, p=0.217 > resid(fit0, type='mart', collapse=testw3$id) 1 2 3 4 5 6 0.94736842 -0.05263158 0.32236842 0.32236842 0.32236842 -0.67763158 7 8 9 -0.67763158 -0.34429825 -1.34429825 > resid(fit0, type='score', collapse=testw3$id) 1 2 3 4 5 6 1.24653740 0.03601108 0.10056700 0.10056700 -0.22180142 -0.21193300 7 8 9 0.46569858 -0.10082189 0.91014302 > resid(fit0, type='scho') 10 20 20 20 40 1.3157895 0.3125000 0.3125000 -0.6875000 0.3333333 > > resid(fit, type='mart', collapse=testw3$id) 1 2 3 4 5 6 0.85531186 -0.02593169 0.17636221 0.17636221 0.65131344 -0.82363779 7 8 9 -0.34868656 -0.64894181 -0.69807852 > resid(fit, type='score', collapse=testw3$id) 1 2 3 4 5 6 0.88681615 0.02497653 0.03608964 0.03608964 -0.54297652 -0.12528780 7 8 9 0.29564605 -0.09476911 0.58400064 > resid(fit, type='scho') 10 20 20 20 40 1.0368337 0.1613774 0.1613774 -0.8386226 0.1746960 > fit0 <- coxph(Surv(begin, time, status) ~x,testw3, weights=wt, iter=0) > resid(fit0, 'mart', collapse=testw3$id) 1 2 3 4 5 6 0.94736842 -0.05263158 0.44454887 0.44454887 0.44454887 -0.88126566 7 8 9 -0.88126566 -0.54793233 -1.54793233 > resid(coxph(Surv(begin, time, status) ~1, testw3, weights=wt) + , collapse=testw3$id) #Null model 1 2 3 4 5 6 0.94736842 -0.05263158 0.44454887 0.44454887 0.44454887 -0.88126566 7 8 9 -0.88126566 -0.54793233 -1.54793233 > > fit <- coxph(Surv(begin,time, status) ~x, testw3, weights=wt, method='efron') > fit Call: coxph(formula = Surv(begin, time, status) ~ x, data = testw3, weights = wt, method = "efron") coef exp(coef) se(coef) z p x 0.873 2.393 0.713 1.22 0.22 Likelihood ratio test=1.75 on 1 df, p=0.186 n= 14, number of events= 5 > resid(fit, type='mart', collapse=testw3$id) 1 2 3 4 5 6 0.85334536 -0.02560716 0.32265266 0.32265266 0.71696234 -1.07772629 7 8 9 -0.45034077 -0.90490339 -0.79598658 > resid(fit, type='score', collapse=testw3$id) 1 2 3 4 5 6 0.88116056 0.02477248 0.06057806 0.06057806 -0.59724033 -0.16737066 7 8 9 0.38040295 -0.13750290 0.66631324 > resid(fit, type='scho') 10 20 20 20 40 1.0325955 0.1621759 0.1621759 -0.8378241 0.1728229 > # > # Check out the impact of weights on the dfbetas > # Am I computing them correctly? > # > wtemp <- rep(1,26) > wtemp[c(5,10,15)] <- 2:4 > fit <- coxph(Surv(futime, fustat) ~ age + ecog.ps, ovarian, weights=wtemp) > rr <- resid(fit, 'dfbeta') > > fit1 <- coxph(Surv(futime, fustat) ~ age + ecog.ps, ovarian, weights=wtemp, + subset=(-5)) > fit2 <- coxph(Surv(futime, fustat) ~ age + ecog.ps, ovarian, weights=wtemp, + subset=(-10)) > fit3 <- coxph(Surv(futime, fustat) ~ age + ecog.ps, ovarian, weights=wtemp, + subset=(-15)) > > # > # Effect of case weights on expected survival curves post Cox model > # > fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt, method='breslow', + iter=0) > fit0b <- coxph(Surv(time, status) ~x, testw2, method='breslow', iter=0) > > surv1 <- survfit(fit0, newdata=list(x=0)) > surv2 <- survfit(fit0b, newdata=list(x=0)) > aeq(surv1$surv, surv2$surv) [1] TRUE > # > # Check out the Efron approx. > # > > fit0 <- coxph(Surv(time, status) ~x,testw1, weights=wt, iter=0) > fit <- coxph(Surv(time, status) ~x,testw1, weights=wt) > resid(fit0, 'mart') 1 2 3 4 5 6 0.94736842 -0.05263158 0.44454887 0.44454887 0.44454887 -0.88126566 7 8 9 -0.88126566 -0.54793233 -1.54793233 > resid(coxph(Surv(time, status) ~1, testw1, weights=wt)) #Null model 1 2 3 4 5 6 0.94736842 -0.05263158 0.44454887 0.44454887 0.44454887 -0.88126566 7 8 9 -0.88126566 -0.54793233 -1.54793233 > > # lfun is the known log-likelihood for this data set, worked out in the > # appendix of Therneau and Grambsch > # ufun is the score vector and ifun the information matrix > lfun <- function(beta) { + r <- exp(beta) + a <- 7*r +3 + b <- 4*r +2 + 11*beta - ( log(r^2 + 11*r +7) + + (10/3)*(log(a+b) + log(2*a/3 +b) + log(a/3 +b)) + 2*log(2*r +1)) + } > aeq(fit0$log[1], lfun(0)) [1] TRUE > aeq(fit$log[2], lfun(fit$coef)) [1] TRUE > > ufun <- function(beta, efron=T) { #score statistic + r <- exp(beta) + xbar1 <- (2*r^2+11*r)/(r^2+11*r +7) + xbar2 <- 11*r/(11*r +5) + xbar3 <- 2*r/(2*r +1) + xbar2b<- 26*r/(26*r+12) + xbar2c<- 19*r/(19*r + 9) + temp <- 11 - (xbar1 + 2*xbar3) + if (efron) temp - (10/3)*(xbar2 + xbar2b + xbar2c) + else temp - 10*xbar2 + } > print(ufun(fit$coef) < 1e-4) # Should be true x TRUE > > ifun <- function(beta, efron=T) { # information matrix + r <- exp(beta) + xbar1 <- (2*r^2+11*r)/(r^2+11*r +7) + xbar2 <- 11*r/(11*r +5) + xbar3 <- 2*r/(2*r +1) + xbar2b<- 26*r/(26*r+12) + xbar2c<- 19*r/(19*r + 9) + temp <- ((4*r^2 + 11*r)/(r^2+11*r +7) - xbar1^2) + + 2*(xbar3 - xbar3^2) + if (efron) temp + (10/3)*((xbar2- xbar2^2) + (xbar2b - xbar2b^2) + + (xbar2c -xbar2c^2)) + else temp + 10 * (xbar2- xbar2^2) + } > > aeq(fit0$var, 1/ifun(0)) [1] TRUE > aeq(fit$var, 1/ifun(fit$coef)) [1] TRUE > > > > # Make sure that the weights pass through the residuals correctly > rr1 <- resid(fit, type='mart') > rr2 <- resid(fit, type='mart', weighted=T) > aeq(rr2/rr1, testw1$wt) [1] TRUE > rr1 <- resid(fit, type='score') > rr2 <- resid(fit, type='score', weighted=T) > aeq(rr2/rr1, testw1$wt) [1] TRUE > > # > # Look at the individual components > # > dt0 <- coxph.detail(fit0) > dt <- coxph.detail(fit) > aeq(sum(dt$score), ufun(fit$coef)) #score statistic [1] TRUE > aeq(sum(dt0$score), ufun(0)) [1] TRUE > aeq(dt0$hazard, c(1/19, (10/3)*(1/16 + 1/(6+20/3) + 1/(6+10/3)), 2/3)) [1] TRUE > > > > rm(fit, fit0, rr1, rr2, dt, dt0) > # > # Effect of weights on the robust variance > # > test1 <- data.frame(time= c(9, 3,1,1,6,6,8), + status=c(1,NA,1,0,1,1,0), + x= c(0, 2,1,1,1,0,0), + wt= c(3,0,1,1,1,1,1), + id= 1:7) > testx <- data.frame(time= c(4,4,4,1,1,2,2,3), + status=c(1,1,1,1,0,1,1,0), + x= c(0,0,0,1,1,1,0,0), + wt= c(1,1,1,1,1,1,1,1), + id= 1:8) > > fit1 <- coxph(Surv(time, status) ~x + cluster(id), test1, method='breslow', + weights=wt) > fit2 <- coxph(Surv(time, status) ~x + cluster(id), testx, method='breslow') > > db1 <- resid(fit1, 'dfbeta', weighted=F) > db1 <- db1[-2] #toss the missing > db2 <- resid(fit2, 'dfbeta') > aeq(db1, db2[3:8]) [1] TRUE > > W <- c(3,1,1,1,1,1) #Weights, after removal of the missing value > aeq(fit2$var, sum(db1*db1*W)) [1] TRUE > aeq(fit1$var, sum(db1*db1*W*W)) [1] TRUE > > > proc.time() user system elapsed 0.268 0.032 0.296 survival/tests/expected.R0000644000175100001440000002300412257335007015234 0ustar hornikusersoptions(na.action=na.exclude) # preserve missings options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type library(survival) # Tests of expected survival aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) # # This makes several scripts easier # Certain tests depended in the now-depreciated date library {if (is.R()) mdy.date <- function(m, d, y) { y <- ifelse(y<100, y+1900, y) as.Date(paste(m,d,y, sep='/'), "%m/%d/%Y") } else mdy.date <- function(m,d,y) { y <- ifelse(y<100, y+1900, y) timeDate(paste(y, m, d, sep='/'), in.format="%Y/%m/%d") } } # This function takes a single subject and walks down the rate table # Input: the vector of starting points, futime, and a ratetable # Output: the full history of walking through said table. Let n= #unique # rates that were used # cell = n by #dims of the table: index of the table cell # days = time spent in cell # hazard= accumulated hazard = days * rate # This does not do date or factor conversions -- start has to be numeric # ratewalk <- function(start, futime, ratetable=survexp.us) { if (!is.ratetable(ratetable)) stop("Bad rate table") ratedim <- dim(ratetable) nvar <- length(ratedim) if (length(start) != nvar) stop("Wrong length for start") if (futime <=0) stop("Invalid futime") attR <- attributes(ratetable) discrete <- (attR$type ==1) #discrete categories maxn <- sum(!discrete)*prod(ratedim[!discrete]) #most cells you can hit cell <- matrix(0, nrow=maxn, ncol=nvar) days <- hazard <- double(maxn) eps <- 1e-8 #Avoid round off error n <- 0 while (futime >0) { n <- n+1 #what cell am I in? # Note that at the edges of the rate table, we use the edge: if # it only goes up the the year 2000, year 2000 is used for any # dates beyond. This effectively eliminates one boundary cell[n,discrete] <- start[discrete] edge <- futime #time to nearest edge, or finish for (j in which(!discrete)) { indx <- sum(start[j] >= attR$cutpoints[[j]]-eps) cell[n, j] <- max(1, indx) if (indx < ratedim[j]) edge <- min(edge, (attR$cutpoints[[j]])[indx+1] - start[j]) } days[n] <- edge #this many days in the cell # using a matrix as a subscript is so handy sometimes hazard[n] <- edge * (as.matrix(ratetable))[cell[n,,drop=F]] futime <- futime - edge #amount of time yet to account for start[!discrete] <- start[!discrete] + edge #walk forward in time } list(cell=cell[1:n,], days=days[1:n], hazard=hazard[1:n]) } # Simple test of ratewalk: 20 years old, start on 7Sep 1960 (day 250) # 116 days at the 1960, 20 year old male rate, through the end of the day # on 12/31/1960, then 84 days at the 1961 rate. # The decennial q for 1960 males is .00169. zz <- ratewalk(c(20.4*365.25, 1, 250), 200) all.equal(zz$hazard[1], -(116/365.25)*log(1-.00169)) all.equal(zz$days, c(116,84)) # # Simple case 1: a single male subject, born 1/1/36 and entered on study 1/2/55 # # Compute the 1, 5, 10 and 12 year expected survival temp1 <- mdy.date(1,1,36) temp2 <- mdy.date(1,2,55) exp1 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=1, race='white'), ratetable=survexp.usr,times=c(366, 1827, 3653, 4383)) tyear <- as.numeric(temp2 - mdy.date(1,1,1960)) h1 <- ratewalk(c(temp2-temp1, 1, 1, tyear), 366, survexp.usr) h2 <- ratewalk(c(temp2-temp1, 1, 1, tyear), 1827, survexp.usr) h3 <- ratewalk(c(temp2-temp1, 1, 1, tyear), 3653, survexp.usr) h4 <- ratewalk(c(temp2-temp1, 1, 1, tyear), 4383, survexp.usr) aeq(-log(exp1$surv), c(sum(h1$hazard), sum(h2$hazard), sum(h3$hazard), sum(h4$hazard))) # Just a little harder: # Born 3/1/25 and entered the study on 6/10/55. The code creates shifted # dates to align with US rate tables - entry is 59 days earlier (days from # 1/1/25 to 3/1/25). # temp1 <- mdy.date(3,1,25) temp2 <- mdy.date(6,10,55) exp1 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=2, race='black'), ratetable=survexp.usr,times=c(366, 1827, 3653, 4383)) tyear <- as.numeric(temp2 - mdy.date(1,1,1960)) - 59 h1 <- ratewalk(c(temp2-temp1, 2, 2, tyear), 366, survexp.usr) h2 <- ratewalk(c(temp2-temp1, 2, 2, tyear), 1827, survexp.usr) h3 <- ratewalk(c(temp2-temp1, 2, 2, tyear), 3653, survexp.usr) h4 <- ratewalk(c(temp2-temp1, 2, 2, tyear), 4383, survexp.usr) aeq(-log(exp1$surv), c(sum(h1$hazard), sum(h2$hazard), sum(h3$hazard), sum(h4$hazard))) # # Simple case 2: make sure that the averages are correct, for Ederer method # # Compute the 1, 5, 10 and 12 year expected survival temp1 <- mdy.date(1:6,6:11,1890:1895) temp2 <- mdy.date(6:1,11:6,c(55:50)) temp3 <- c(1,2,1,2,1,2) age <- temp2 - temp1 exp1 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=temp3), times=c(366, 1827, 3653, 4383)) exp2 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=temp3) + I(1:6), times=c(366, 1827, 3653, 4383)) exp3 <- exp2$surv for (i in 1:length(temp1)){ exp3[,i] <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=temp3), times=c(366, 1827, 3653, 4383), subset=i)$surv } print(aeq(exp2$surv, exp3)) print(all.equal(exp1$surv, apply(exp2$surv, 1, mean))) # They agree, but are they right? # for (i in 1:length(temp1)) { offset <- as.numeric(temp1[i] - mdy.date(1,1, 1889+i)) tyear = (as.numeric(temp2[i] - mdy.date(1,1,1960))) - offset haz1 <- ratewalk(c((temp2-temp1)[i], temp3[i], tyear), 366) haz2 <- ratewalk(c((temp2-temp1)[i], temp3[i], tyear), 1827) haz3 <- ratewalk(c((temp2-temp1)[i], temp3[i], tyear), 3653) haz4 <- ratewalk(c((temp2-temp1)[i], temp3[i], tyear), 4383) print(aeq(-log(exp2$surv[,i]), c(sum(haz1$hazard), sum(haz2$hazard), sum(haz3$hazard), sum(haz4$hazard)))) } # # Check that adding more time points doesn't change things # exp4 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=temp3) + I(1:6), times=sort(c(366, 1827, 3653, 4383, 30*(1:100)))) aeq(exp4$surv[match(exp2$time, exp4$time),], exp2$surv) exp4 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=temp3), times=sort(c(366, 1827, 3653, 4383, 30*(1:100)))) aeq(exp1$surv, exp4$surv[match(exp1$time, exp4$time, nomatch=0)]) # # Now test Hakulinen's method, assuming an analysis date of 3/1/57 # futime <- mdy.date(3,1,57) - temp2 xtime <- sort(c(futime, 30, 60, 185, 365)) exp1 <- survexp(futime ~ ratetable(year=temp2, age=(temp2-temp1), sex=1), times=xtime, conditional=F) exp2 <- survexp(~ratetable(year=temp2, age=(temp2-temp1), sex=1) + I(1:6), times=futime) wt <- rep(1,6) con <- double(6) for (i in 1:6) { con[i] <- sum(exp2$surv[i,i:6])/sum(wt[i:6]) wt <- exp2$surv[i,] } exp1$surv[match(futime, xtime)] aeq(exp1$surv[match(futime, xtime)], cumprod(con)) # # Now for the conditional method # exp1 <- survexp(futime ~ ratetable(year=temp2, age=(temp2-temp1), sex=1), times=xtime, conditional=T) cond <- exp2$surv for (i in 6:2) cond[i,] <- (cond[i,]/cond[i-1,]) #conditional survival for (i in 1:6) con[i] <- exp(mean(log(cond[i, i:6]))) all.equal(exp1$surv[match(futime, xtime)], cumprod(con)) cumprod(con) # # Test out expected survival, when the parent pop is another Cox model # test1 <- data.frame(time= c(4, 3,1,1,2,2,3), status=c(1,NA,1,0,1,1,0), x= c(0, 2,1,1,1,0,0)) fit <- coxph(Surv(time, status) ~x, test1, method='breslow') dummy <- data.frame(time=c(.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5), status=c(1,0,1,0,1,0,1,1,1), x=(-4:4)/2) efit <- survexp(time ~ ratetable(x=x), dummy, ratetable=fit, cohort=F) # # Now, compare to the true answer, which is known to us # ss <- exp(fit$coef) haz <- c( 1/(3*ss+3), 2/(ss+3), 1) #truth at time 0,1,2,4+ chaz <- cumsum(c(0,haz)) chaz2 <- chaz[c(1,2,2,3,3,3,3,4,4)] risk <- exp(fit$coef*dummy$x) efit2 <- exp(-risk*chaz2) all.equal(as.vector(efit), as.vector(efit2)) #ignore mismatched name attrib # # Now test the direct-adjusted curve (Ederer) # efit <- survexp( ~ ratetable(x=x), dummy, ratetable=fit, se=F) direct <- survfit(fit, newdata=dummy, censor=FALSE)$surv chaz <- chaz[-1] #drop time 0 d2 <- exp(outer(-chaz, risk)) all.equal(as.vector(direct), as.vector(d2)) #this tests survfit all.equal(as.vector(efit$surv), as.vector(apply(direct,1,mean))) #direct # Check out the "times" arg of survexp efit2 <- survexp( ~ ratetable(x=x), dummy, ratetable=fit, se=F, times=c(.5, 2, 3.5,6)) aeq(efit2$surv, c(1, efit$surv[c(2,2,3)])) # # Now test out the Hakulinen method (Bonsel's method) # By construction, we have a large correlation between x and censoring # # In theory, hak1 and hak2 would be the same. In practice, like a KM and # F-H, they differ when n is small. # efit <- survexp( time ~ ratetable(x=x), dummy, ratetable=fit, se=F) surv <- wt <- rep(1,9) tt <- c(1,2,4) hak1 <- hak2 <- NULL for (i in 1:3) { wt[dummy$time < tt[i]] <- 0 hak1 <- c(hak1, exp(-sum(haz[i]*risk*surv*wt)/sum(surv*wt))) hak2 <- c(hak2, sum(exp(-haz[i]*risk)*surv*wt)/sum(surv*wt)) surv <- surv * exp(-haz[i]*risk) } all.equal(as.vector(efit$surv), as.vector(cumprod(hak1))) # # Now do the conditional estimate # efit <- survexp( time ~ ratetable(x=x), dummy, ratetable=fit, se=F, conditional=T) wt <- rep(1,9) cond <- NULL for (i in 1:3) { wt[dummy$time < tt[i]] <- 0 cond <- c(cond, exp(-sum(haz[i]*risk*wt)/sum(wt))) } all.equal(as.vector(efit$surv), as.vector(cumprod(cond))) survival/src/0000755000175100001440000000000013070714004012726 5ustar hornikuserssurvival/src/pystep.c0000755000175100001440000000571013070714004014424 0ustar hornikusers/* $Id: pystep.c 11166 2008-11-24 22:10:34Z therneau $ */ /* ** Returns the amount of time that will be spent in the current "cell", ** along with the index of the cell (treating a multi-way array as linear). ** This is a basic calculation in all of the person-years work. ** ** Input ** nc: number of categories ** data[nc] start points, for the data values ** fac[nc] 1: category is a factor, 0: it is continuous ** >=2: special handling for "years" dim of US rate tables ** dims[nc] the extent of each category ** cuts[nc,dims+1] ragged array, containing the start for each interval ** step the amount of time remaining for the subject. ** edge if =0, then the cuts contain +1 obs, and we are strict ** about out-of-range cells. If it is a 1, then the ** table is assummed to extend infinitly at the edges. ** ** Output ** *index linear index into the array ** if *index == -1, then the returned amount of time is "off table"; ** if one of the dimensions has fac >1 -- ** *index2 second index for linear interpolation ** *wt a number between 0 and 1, amount of wt for the first index ** this will be 1 if none of the dims have fac >1 ** ** Return value amount of time in indexed cell. */ #include "survS.h" #include "survproto.h" double pystep(int nc, int *index, int *index2, double *wt, double *data, Sint *fac, Sint *dims, double **cuts, double step, int edge) { int i,j; double maxtime; double shortfall; double temp; int kk, dtemp; kk=1; *index =0; *index2=0; *wt =1; shortfall =0; maxtime = step; for (i=0; i1) dtemp = 1 + (fac[i]-1)*dims[i]; else dtemp = dims[i]; for (j=0; j shortfall) { if (temp > step) shortfall = step; else shortfall = temp; } if (temp < maxtime) maxtime = temp; } else if (j==dtemp){ /*bigger than last cutpoint */ if (edge==0) { temp = cuts[i][j] - data[i]; /* time to upper limit */ if (temp <=0) shortfall = step; else if (temp < maxtime) maxtime = temp; } if (fac[i] >1) j = dims[i] -1; /*back to normal indices */ else j--; } else { temp = cuts[i][j] - data[i]; /* time to next cutpoint */ if (temp < maxtime) maxtime = temp; j--; if (fac[i] >1) { /*interpolate the year index */ *wt = 1.0 - (j%fac[i])/ (double)fac[i]; j /= fac[i]; *index2 = kk; } } *index += j*kk; } kk *= dims[i]; } *index2 += *index; if (shortfall ==0) return(maxtime); else { *index = -1; return(shortfall); } } survival/src/survfit4.c0000755000175100001440000000205313070714004014663 0ustar hornikusers/* $Id: survfit4.c 11166 2008-11-24 22:10:34Z therneau $ */ /* ** C routine to do a small computation that is hard in Splus ** ** n = number of observations ** d = number of deaths ** x1, x2 = ingredients in the sums ** ** If d=0, then new x1 = new x2 =1 (fill in value) ** d=1, new x1 = 1/x1, ** new x2 = (1/x1)^2 ** d=2, new x1 = (1/2) [ 1/x1 + 1/(x1 - x2/2)] ** new x2 = (1/2) [ same terms, squared] ** d=3 new x1 = (1/3) [ 1/x1 + 1/(x1 - x2/3) + 1/(x1 - 2*x2/3)] ** etc. */ #include "survS.h" void survfit4(Sint *n, Sint *dd, double *x1, double *x2) { double temp, temp1, temp2; int i,j; double d; for (i=0; i< *n; i++) { d = dd[i]; if (d==0) { x1[i] =1; x2[i] =1; } else if (d==1){ temp = 1/x1[i]; x1[i] = temp; x2[i] = temp*temp; } else { temp1 = 1/x1[i]; temp2 = temp1 * temp1; for (j=1; j= dtime; istart++) nrisk--; for(j= i+1; j=dtime; istart++) { atrisk[sort1[istart]]=0; nrisk--; } for (j=1; j0) { matrix[i][i] = 1/matrix[i][i]; /*this line inverts D */ for (j= (i+1); j #include "survS.h" #include "survproto.h" /* my habit is to name a S object "charlie2" and the pointer ** to the contents of the object "charlie"; the latter is ** used in the computations */ SEXP pyears3b(SEXP death2, SEXP efac2, SEXP edims2, SEXP ecut2, SEXP expect2, SEXP grpx2, SEXP x2, SEXP y2, SEXP times2, SEXP ngrp2) { int i,j,k; int n, death, edim, ngrp, ntime; double **x; double *data2; double **ecut, *etemp; double hazard, /*cum hazard over an interval */ cumhaz; /*total hazard to date for the subject */ double timeleft, thiscell, etime, time, et2; int index, indx, indx2; double wt; double *wvec; /* vector of weights needed for unconditional surv */ int group; int *efac, *edims, *grpx; double *expect, *y, *times; SEXP esurv2, nsurv2, rlist, rlistnames; double *esurv; int *nsurv; /* ** copies of input arguments */ death = asInteger(death2); ngrp = asInteger(ngrp2); efac = INTEGER(efac2); edims = INTEGER(edims2); edim = LENGTH(edims2); expect= REAL(expect2); grpx = INTEGER(grpx2); n = LENGTH(y2); x = dmatrix(REAL(x2), n, edim); y = REAL(y2); times = REAL(times2); ntime = LENGTH(times2); /* scratch space */ data2 = (double *)ALLOC(edim+1, sizeof(double)); wvec = (double *)ALLOC(ntime*ngrp, sizeof(double)); for (j=0; j1) etemp += 1 + (efac[i]-1)*edims[i]; } /* ** Create output arrays */ PROTECT(esurv2 = allocVector(REALSXP, ntime*ngrp)); esurv = REAL(esurv2); PROTECT(nsurv2 = allocVector(INTSXP, ntime*ngrp)); nsurv = INTEGER(nsurv2); for (i=0; i<(ntime*ngrp); i++) { esurv[i] =0.; nsurv[i] =0; } /* compute */ for (i=0; i0; j++) { thiscell = times[j] - time; if (thiscell > timeleft) thiscell = timeleft; index =j + ntime*group; /* expected calc ** The wt parameter only comes into play for older style US rate ** tables, where pystep does interpolation. ** Each call to pystep moves up to the next 'boundary' in the ** expected table, data2 contains our current position therein */ etime = thiscell; hazard =0; while (etime >0) { et2 = pystep(edim, &indx, &indx2, &wt, data2, efac, edims, ecut, etime, 1); if (wt <1) hazard+= et2*(wt*expect[indx] +(1-wt)*expect[indx2]); else hazard+= et2* expect[indx]; for (k=0; k0) { if (death==0) esurv[i] /= wvec[i]; else esurv[i] = exp(-esurv[i]/wvec[i]); } else if (death!=0) esurv[i] = exp(-esurv[i]); } /* ** package the output */ PROTECT(rlist = allocVector(VECSXP, 2)); SET_VECTOR_ELT(rlist,0, esurv2); SET_VECTOR_ELT(rlist,1, nsurv2); PROTECT(rlistnames= allocVector(STRSXP, 2)); SET_STRING_ELT(rlistnames, 0, mkChar("surv")); SET_STRING_ELT(rlistnames, 1, mkChar("n")); setAttrib(rlist, R_NamesSymbol, rlistnames); unprotect(4); return(rlist); } survival/src/survS.h0000755000175100001440000000073713070714004014233 0ustar hornikusers/* ** This file started out with support for Splus, then morphed to allow ** either R or Splus (based on ifdef lines), and now is R only. */ #include "R.h" #include "Rinternals.h" #include /* typedef int Sint; */ /* no longer needed */ /* ** Memory defined with ALLOC is removed automatically by S. ** That with "Calloc" I have to remove myself. Use the ** latter for objects that need to to persist between calls. */ #define ALLOC(a,b) R_alloc(a,b) survival/src/chsolve2.c0000755000175100001440000000163013070714004014622 0ustar hornikusers/* $Id: chsolve2.c 11376 2009-12-14 22:53:57Z therneau $ ** ** Solve the equation Ab = y, where the cholesky decomposition of A and y ** are the inputs. ** ** Input **matrix, which contains the chol decomp of an n by n ** matrix in its lower triangle. ** y[n] contains the right hand side ** ** y is overwriten with b ** ** Terry Therneau */ #include "survS.h" #include "survproto.h" void chsolve2(double **matrix, int n, double *y) { register int i,j; register double temp; /* ** solve Fb =y */ for (i=0; i=0; i--) { if (matrix[i][i]==0) y[i] =0; else { temp = y[i]/matrix[i][i]; for (j= i+1; j #include "survS.h" #include "survproto.h" void agmart2(Sint *n, Sint *method, double *start, double *stop, Sint *event, Sint *nstrat, Sint *strata, Sint *sort1, Sint *sort2, double *score, double *wt, double *resid, double *haz) { int i, j, k, ksave; int p, istrat, indx2; double deaths, denom, e_denom; double hazard, e_hazard; double temp, time; double wtsum, *dtimes; int nused, ndeath; int person; int strata_start; nused = *n; j=0; for (i=0; i=strata_start; k--) { /*non-deaths */ p = sort1[k]; if (stop[p] > time) break; resid[p] -= score[p]*hazard; } for (; person= stop[p]; k++); for (j=k; j #include "survS.h" #define SMALL -200 /* exp(-200) is a really small loglik */ double survregc2(int n, int nvar, int nstrat, int whichcase, double *beta, int dist, Sint *strat, double *offset, double *time1, double *time2, double *status, double *wt, double **covar, double **imat, double **JJ, double *u, SEXP expr, SEXP rho, double *z, int nf, Sint *frail, double *fdiag, double *jdiag ) { int person, i,j,k; int nvar2; int strata; double eta, sigma; int icount; /* running count of # of interval censored */ int fgrp =0; /* the =0 to quiet a compiler warning */ double loglik, temp; double temp1, temp2; double sz, zz, zu; double sig2; /* add "=0" to keep the compiler from worrying about uninitialized vars */ /* double g, dg, ddg, dsig, ddsig, dsg; */ double g=0, dg=0, ddg=0, dsig=0, ddsig=0, dsg=0; SEXP rmat; double *funs[5]; double w; nvar2 = nvar + nstrat; loglik=0; if (whichcase==0) { for (i=0; i1) { strata= strat[person] -1; /*S likes to start counting at 1 */ sigma = exp(beta[strata+nvar+nf]); } eta =0; for (i=0; i0){ fgrp = frail[person] -1; eta += beta[fgrp]; } z[person] = (time1[person] - eta)/sigma; if (status[person]==3) { z[icount] = (time2[person] - eta)/sigma; icount++; } } /* ** The result of the eval will be a matrix of 5 rows and n colums, which ** we re-index for convenience. Note that the parent routine has given ** us the address of z WITHIN the evaluation frame rho, we just keep ** replacing the values it contains; expr then acts like a function of ** z. ** Actually, if there were any interval censored obs they take up 2 cols; ** icount from above contains the actual number of columns used. */ PROTECT(rmat = eval(expr, rho)); funs[0] = REAL(rmat); for (i=0; i<4; i++) funs[i+1] = funs[i] + icount; /* ** calculate the first and second derivative wrt eta, ** then the derivatives of the loglik (u, imat, JJ) */ icount =n; for (person=0; person1) { strata= strat[person] -1; /*S likes to start counting at 1 */ sigma = exp(beta[strata+nvar]); sig2 = 1/(sigma*sigma); } zz = z[person]; sz = zz * sigma; j = status[person]; /*convert to integer */ switch(j) { case 1: /* exact */ if (funs[2][person] <=0) { /* off the probability scale -- avoid log(0), and set the ** derivatives to gaussian limits (almost any deriv will ** do, since the function value triggers step-halving). */ g = SMALL; dg = -zz/sigma; ddg = -1/sigma; dsig =0; ddsig=0; dsg=0; } else { g = log(funs[2][person]) - log(sigma); temp1 = funs[3][person]/sigma; temp2 = funs[4][person]*sig2; dg = -temp1; dsig= -(sz*temp1 +1); ddg= temp2 - dg*dg; dsg = sz * temp2 - dg*(1- sz*temp1); ddsig = sz*sz*temp2 + sz*temp1*(1- sz*temp1); } break; case 0: /* right censored */ if (funs[1][person] <=0) { g = SMALL; dg = zz/sigma; ddg =0; dsig =0; ddsig=0; dsg=0; } else { g = log(funs[1][person]); temp1 = -funs[2][person]/(funs[1][person]*sigma); temp2 = -funs[3][person]*funs[2][person]*sig2/ funs[1][person]; dg = -temp1; dsig= -sz * temp1; ddg= temp2 - dg*dg; dsg = sz * temp2 - dg*(1+dsig); ddsig = sz*sz*temp2 - dsig*(1+dsig); } break; case 2: /* left censored */ if (funs[2][person] <=0) { /* off the probability scale -- avoid log(0) */ g = SMALL; dg = -zz/sigma; dsig =0; ddsig=0; dsg=0; ddg =0; } else { g = log(funs[0][person]); temp1 = funs[2][person]/(funs[0][person]*sigma); temp2 = funs[3][person]*funs[2][person]*sig2/ funs[0][person]; dg= -temp1; dsig= -sz * temp1; ddg= temp2 - dg*dg; dsg = sz * temp2 - dg*(1+dsig); ddsig = sz*sz*temp2 - dsig*(1+dsig); } break; case 3: /* interval censored */ zu = z[icount]; /*stop roundoff in tails*/ if (zz>0) temp = funs[1][person] - funs[1][icount]; else temp = funs[0][icount] - funs[0][person]; if (temp <=0) { /* off the probability scale -- avoid log(0) */ g = SMALL; dg = 1; ddg =0; dsig =0; ddsig=0; dsg=0; } else { funs[3][icount] *= funs[2][icount]; /*f', not f'/f */ funs[3][person] *= funs[2][person]; g = log(temp); dg = -(funs[2][icount] -funs[2][person])/(temp*sigma); ddg = (funs[3][icount] -funs[3][person])*sig2/temp - dg*dg; dsig = (zz*funs[2][person] - zu*funs[2][icount])/temp; ddsig= (zu*zu*funs[3][icount] - zz*zz*funs[3][person]) /temp - dsig*(1+dsig); dsg = (zu*funs[3][icount] - zz*funs[3][person])/ (temp*sigma) - dg *(1+dsig); } icount++; break; } loglik += g * wt[person]; /* ** Now the derivs wrt loglik */ if (whichcase==1) continue; /*only needed the loglik */ w = wt[person]; if (nf>0) { fgrp = frail[person] -1; u[fgrp] += dg * w; fdiag[fgrp] -= ddg * w; jdiag[fgrp] += dg*dg *w; } for (i=0; i0) { imat[i][fgrp] -= covar[i][person] * ddg * w; JJ [i][fgrp] += temp * dg; } } if (nstrat!=0) { /* need derivative wrt log sigma */ k = strata+nvar; u[k+nf] += w* dsig; for (i=0; i0) { imat[k][fgrp] -= dsg * w; JJ [k][fgrp] += dsig *dg *w; } } } UNPROTECT(1); /* release the memory pointed to by funs[] */ return(loglik); } survival/src/coxexact.c0000644000175100001440000003516713070714004014724 0ustar hornikusers/* Automatically generated from the noweb directory */ #include #include "survS.h" #include "survproto.h" #include double coxd0(int d, int n, double *score, double *dmat, int dmax) { double *dn; if (d==0) return(1.0); dn = dmat + (n-1)*dmax + d -1; /* pointer to dmat[d,n] */ if (*dn ==0) { /* still to be computed */ *dn = score[n-1]* coxd0(d-1, n-1, score, dmat, dmax); if (d1) d1[indx] += score[n-1]* coxd1(d-1, n-1, score, dmat, d1, covar, dmax); } return(d1[indx]); } double coxd2(int d, int n, double *score, double *dmat, double *d1j, double *d1k, double *d2, double *covarj, double *covark, int dmax) { int indx; indx = (n-1)*dmax + d -1; /*index to the current array member d1[d,n]*/ if (d2[indx] ==0) { /*still to be computed */ d2[indx] = coxd0(d-1, n-1, score, dmat, dmax)*score[n-1] * covarj[n-1]* covark[n-1]; if (d1) d2[indx] += score[n-1] * ( coxd2(d-1, n-1, score, dmat, d1j, d1k, d2, covarj, covark, dmax) + covarj[n-1] * coxd1(d-1, n-1, score, dmat, d1k, covark, dmax) + covark[n-1] * coxd1(d-1, n-1, score, dmat, d1j, covarj, dmax)); } return(d2[indx]); } SEXP coxexact(SEXP maxiter2, SEXP y2, SEXP covar2, SEXP offset2, SEXP strata2, SEXP ibeta, SEXP eps2, SEXP toler2) { int i,j,k; int iter; double **covar, **imat; /*ragged arrays */ double *time, *status; /* input data */ double *offset; int *strata; int sstart; /* starting obs of current strata */ double *score; double *oldbeta; double zbeta; double newlk=0; double temp; int halving; /*are we doing step halving at the moment? */ int nrisk; /* number of subjects in the current risk set */ int dsize, /* memory needed for one coxc0, coxc1, or coxd2 array */ dmemtot, /* amount needed for all arrays */ ndeath; /* number of deaths at the current time point */ double maxdeath; /* max tied deaths within a strata */ double dtime; /* time value under current examiniation */ double *dmem0, **dmem1, *dmem2; /* pointers to memory */ double *dtemp; /* used for zeroing the memory */ double *d1; /* current first derivatives from coxd1 */ double d0; /* global sum from coxc0 */ /* copies of scalar input arguments */ int nused, nvar, maxiter; double eps, toler; /* returned objects */ SEXP imat2, beta2, u2, loglik2; double *beta, *u, *loglik; SEXP rlist, rlistnames; int nprotect; /* number of protect calls I have issued */ nused = LENGTH(offset2); nvar = ncols(covar2); maxiter = asInteger(maxiter2); eps = asReal(eps2); /* convergence criteria */ toler = asReal(toler2); /* tolerance for cholesky */ /* ** Set up the ragged array pointer to the X matrix, ** and pointers to time and status */ covar= dmatrix(REAL(covar2), nused, nvar); time = REAL(y2); status = time +nused; strata = INTEGER(PROTECT(duplicate(strata2))); offset = REAL(offset2); /* temporary vectors */ score = (double *) R_alloc(nused+nvar, sizeof(double)); oldbeta = score + nused; /* ** create output variables */ PROTECT(beta2 = duplicate(ibeta)); beta = REAL(beta2); PROTECT(u2 = allocVector(REALSXP, nvar)); u = REAL(u2); PROTECT(imat2 = allocVector(REALSXP, nvar*nvar)); imat = dmatrix(REAL(imat2), nvar, nvar); PROTECT(loglik2 = allocVector(REALSXP, 5)); /* loglik, sctest, flag,maxiter*/ loglik = REAL(loglik2); nprotect = 5; strata[0] =1; /* in case the parent forgot */ temp = 0; /* temp variable for dsize */ maxdeath =0; j=0; /* start of the strata */ for (i=0; i0) { /* If maxdeath <2 leave the strata alone at it's current value of 1 */ if (maxdeath >1) strata[j] = maxdeath; j = i; if (maxdeath*nrisk > temp) temp = maxdeath*nrisk; } maxdeath =0; /* max tied deaths at any time in this strata */ nrisk=0; ndeath =0; } dtime = time[i]; ndeath =0; /*number tied here */ while (time[i] ==dtime) { nrisk++; ndeath += status[i]; i++; if (i>=nused || strata[i] >0) break; /*tied deaths don't cross strata */ } if (ndeath > maxdeath) maxdeath=ndeath; } if (maxdeath*nrisk > temp) temp = maxdeath*nrisk; if (maxdeath >1) strata[j] = maxdeath; /* Now allocate memory for the scratch arrays Each per-variable slice is of size dsize */ dsize = temp; temp = temp * ((nvar*(nvar+1))/2 + nvar + 1); dmemtot = dsize * ((nvar*(nvar+1))/2 + nvar + 1); if (temp != dmemtot) { /* the subscripts will overflow */ error("(number at risk) * (number tied deaths) is too large"); } dmem0 = (double *) R_alloc(dmemtot, sizeof(double)); /*pointer to memory */ dmem1 = (double **) R_alloc(nvar, sizeof(double*)); dmem1[0] = dmem0 + dsize; /*points to the first derivative memory */ for (i=1; i0) { /* first obs of a new strata */ maxdeath= strata[i]; dtemp = dmem0; for (j=0; j=nused || strata[i] >0) break; } /* We have added up over the death time, now process it */ if (ndeath >0) { /* Add to the loglik */ d0 = coxd0(ndeath, nrisk, score+sstart, dmem0, maxdeath); R_CheckUserInterrupt(); newlk -= log(d0); dmem2 = dmem0 + (nvar+1)*dsize; /*start for the second deriv memory */ for (j=0; j 3) R_CheckUserInterrupt(); u[j] -= d1[j]; for (k=0; k<= j; k++) { /* second derivative*/ temp = coxd2(ndeath, nrisk, score+sstart, dmem0, dmem1[j], dmem1[k], dmem2, covar[j] + sstart, covar[k] + sstart, maxdeath); if (ndeath > 5) R_CheckUserInterrupt(); imat[k][j] += temp/d0 - d1[j]*d1[k]; dmem2 += dsize; } } } } loglik[0] = newlk; /* save the loglik for iteration zero */ loglik[1] = newlk; /* and it is our current best guess */ /* ** update the betas and compute the score test */ for (i=0; i0) { /* first obs of a new strata */ maxdeath= strata[i]; dtemp = dmem0; for (j=0; j=nused || strata[i] >0) break; } /* We have added up over the death time, now process it */ if (ndeath >0) { /* Add to the loglik */ d0 = coxd0(ndeath, nrisk, score+sstart, dmem0, maxdeath); R_CheckUserInterrupt(); newlk -= log(d0); dmem2 = dmem0 + (nvar+1)*dsize; /*start for the second deriv memory */ for (j=0; j 3) R_CheckUserInterrupt(); u[j] -= d1[j]; for (k=0; k<= j; k++) { /* second derivative*/ temp = coxd2(ndeath, nrisk, score+sstart, dmem0, dmem1[j], dmem1[k], dmem2, covar[j] + sstart, covar[k] + sstart, maxdeath); if (ndeath > 5) R_CheckUserInterrupt(); imat[k][j] += temp/d0 - d1[j]*d1[k]; dmem2 += dsize; } } } } /* am I done? ** update the betas and test for convergence */ loglik[3] = cholesky2(imat, nvar, toler); if (fabs(1-(loglik[1]/newlk))<= eps && halving==0) { /* all done */ loglik[1] = newlk; loglik[4] = iter; chinv2(imat, nvar); for (i=1; i #include "survS.h" #include "survproto.h" void survdiff2(Sint *nn, Sint *nngroup, Sint *nstrat, double *rho, double *time, Sint *status, Sint *group, Sint *strata, double *obs, double *exp, double *var, double *risk, double *kaplan) { register int i,j,k; int kk; int n, ngroup, ntot; int istart, koff; double km, nrisk, wt, tmp; double deaths; ntot = *nn; ngroup = *nngroup; istart=0; koff=0; for (i=0; i< ngroup*ngroup; i++) var[i]=0; for (i=0; i< *nstrat*ngroup; i++) { obs[i]=0; exp[i]=0; } while (istart < ntot) { /* loop over the strata */ for (i=0; i=istart; i--) { if (*rho ==0) wt=1; else wt= pow(kaplan[i], *rho); deaths = 0; for (j=i; j>=istart && time[j]==time[i]; j--) { k = group[j]-1; deaths += status[j]; risk[k] += 1; obs[k + koff] += status[j] *wt; } i= j +1; nrisk = n-i; if (deaths>0) { /* a death time */ for (k=0; k=2 special handling for US "calendar year" ** edims[edim] the number of rows, columns, etc ** ecut[ ] the starting points for each non-factor dimension, ** strung together. ** expect the actual table of expected rates ** edata[edim, n] the subject data-- where each indexes into the ** expected table, at time 0. ** ** output table's description ** odim number of dimensions ** ofac[odim] 1=is a factor, 0=continuous (time based) ** odims[odim] the number of rows, columns, etc ** ocut[] for each non-factor dimension, the odim[i]+1 cutpoints ** that define the intervals; concatonated. ** odata[odim, n] the subject data-- where each indexes into the ** expected table, at time 0. ** ** Output: ** pyears output table of person years ** pn number of observations that contribute to each cell ** pcount number of events ** pexpect expected number of events ** offtable total person years that did not fall into the output table ** ** Scratch -- allocated on the fly ** scratch[edim + odim] */ #include #include "survS.h" #include "survproto.h" /* names that begin with "s" will be re-declared in the main body */ void pyears1(Sint *sn, Sint *sny, Sint *sdoevent, double *sy, double *weight, Sint *sedim, Sint *efac, Sint *edims, double *secut, double *expect, double *sedata, Sint *sodim, Sint *ofac, Sint *odims, double *socut, Sint *smethod, double *sodata, double *pyears, double *pn, double *pcount, double *pexpect, double *offtable) { int i,j; int n, ny, doevent, method, edim, odim; double *start, *stop, *event, **ecut, **ocut, **edata, **odata; double *data, *data2; double timeleft, thiscell, etime, et2; int index, indx, indx2; double lwt; /*this variable is returned by pystep, and controls the "on the fly" linear interpolation done for the calandar year dimension of rate tables */ int dostart; double hazard, cumhaz; double temp, lambda; double eps; /* protection against accumulated round off */ n = *sn; ny= *sny; doevent = *sdoevent; method = *smethod; edim = *sedim; odim = *sodim; start = sy; if (ny==3 || (ny==2 && doevent==0)) { stop = sy +n; dostart =1; } else { stop = sy; dostart =0; } event = stop +n; edata = dmatrix(sedata, n, edim); odata = dmatrix(sodata, n, odim); i=edim + odim; data = (double *) ALLOC(i, sizeof(double)); data2 = data + odim; /* ** ecut and ocut will be ragged arrays */ ecut = (double **)ALLOC(edim, sizeof(double *)); for (i=0; i1) secut += 1 + (efac[i]-1)*edims[i]; } ocut = (double **)ALLOC(odim, sizeof(double *)); for (i=0; i0]) * 1e-8 ** The events are counted in the last cell to which person years are ** added in the while() loop below. We don't want to "spill over" into ** a next (incorrect) cell due to accumulated round off, in the case ** that a subjects fu time exactly matches one of the cell boundaries. */ eps =0; /* guard against the rare case that all(time==0) */ for (i=0; i0) { eps = timeleft; break; } } for (; i0 && timeleft < eps) eps = timeleft; } eps *= 1e-8; *offtable =0; for (i=0; i eps) { thiscell = pystep(odim, &index, &indx2, &lwt, data, ofac, odims, ocut, timeleft, 0); if (index >=0) { pyears[index] += thiscell * weight[i]; pn[index] += 1; /* expected calc */ etime = thiscell; hazard=0; temp =0; while (etime >0) { /* ** The hazard or survival curve (temp) calculated within ** this loop don't depend on the case weight --- the ** whole loop is only for one person, and hazard is a ** function of time alone. Once computed, however, the ** total hazard added into the expected table ** is weighted. */ et2 = pystep(edim, &indx, &indx2, &lwt, data2, efac, edims, ecut, etime, 1); if (lwt <1) lambda = (lwt*expect[indx] + (1-lwt)*expect[indx2]); else lambda = expect[indx]; if (method==0) temp += exp(-hazard)*(1-exp(-lambda*et2))/ lambda; hazard += lambda * et2; for (j=0; j=0 && doevent) pcount[index] += event[i] * weight[i]; } } survival/src/coxmart2.c0000755000175100001440000000370513070714004014641 0ustar hornikusers/* ** Compute the martingale residual for a Cox model. ** This routine does the same work as coxmart, except ** it expects data in inverse time order ** only does the Breslow method ** exists for the sake of coxexact.fit ** ** Input ** n number of subjects ** time vector of times ** status vector of status values ** score the vector of subject scores, i.e., exp(beta*z) ** strata is =1 for the first obs of a strata ** wt case weights ** Output ** the residual for each subject */ #include "survS.h" #include "survproto.h" void coxmart2(Sint *sn, double *time, Sint *status, Sint * strata, double *score, double *wt, double *resid) { int i,j; int n; double deaths, denom; double expected, hazard; n = *sn; /* ** Accumulate the weighted score in reverse time order (data order) ** Temporarily save the resulting hazard in the residual vector */ denom =0; for (i=0; i=0; i--) { expected += resid[i]; resid[i] = status[i] - score[i]*expected; if (strata[i] ==1) expected=0; /* last obs of a strata */ } } survival/src/coxfit5.c0000755000175100001440000004311113070714004014456 0ustar hornikusers/* A reentrant version of the Coxfit program, for random effects modeling ** with reasonable efficiency (I hope). The important arrays are saved ** from call to call so as to speed up the process. The x-matrix itself ** is the most important of these. ** ** coxfit5_a: Entry and intial iteration step for beta=initial, theta=0 ** (no frailty) ** Most of the same arguments as coxfit2. ** Allocate and save arrays in static locations. ** coxfit5_b: Iterate to convergence given an initial value. ** coxfit5_c: Compute residuals and release the saved memory. ** ** McGilchrist's method for frailty with a fixed theta, but for ** space savings I assume that many elements of imat are zero ** ** the input parameters are ** ** maxiter :number of iterations ** nused :number of people ** nvar :number of covariates ** y[2,n] :row 1: time of event or censoring for person i ** :row 2: status for the ith person 1=dead , 0=censored ** covar(nv,n) :covariates for person i. ** Note that S sends this in column major order. ** strata(nstrat):sizes of the strata, cumulative ** sort : sort order for the obs, last to first within strata ** offset(n) :offset for the linear predictor ** weights(n) :case weights ** eps :tolerance for convergence. Iteration continues until ** the percent change in loglikelihood is <= eps. ** tolerch :tolerance for the Cholesky routines ** method : Method 0=Breslow, 1=Efron ** ptype : 1 or 3 -- there is a sparse term ** : 2 or 3 -- there is a non-sparse term in the model ** nfrail : number of frailty groups (sparse terms), 0 if there are ** none ** frail : a vector containing the frailty groups ** fbeta : initial frailty estimates ** pdiag : if 0, then for the non-sparse terms only the diagonal ** of the variance matrix is penalized, otherwise the ** full matrix is used. ** ** returned parameters ** means(nv) : vector of column means of X ** beta(nv) : the vector of answers (at start contains initial est) ** u(nv) : score vector ** imat(nv,nv) : the variance matrix at beta=final ** if flag<0, imat is undefined upon return ** loglik :loglik at beta=final ** flag :success flag 1000 did not converge ** 1 to nvar: rank of the solution ** maxiter :actual number of iterations used ** fbeta(nfrail): fitted frailty values ** fdiag(nfrail + nvar): diagonal of cholesky of the full inverse ** jmat : inverse of the cholesky ** imat : cholesky of the information matrix ** expect : contains the "expected" for each subject ** ** work arrays ** mark(n) ** wtave(n) ** score(n) ** a(nvar+ nfrail), a2(nvar+nfrail) ** cmat(nvar,nvar+nfrail) ragged array ** cmat2(nvar,nvar+nfrail) ** fdiag the diagonal of the sparse information ** oldbeta(nvar + nfrail) always contains the "last iteration" ** ** the work arrays are passed as a single ** vector of storage, and then broken out. ** ** calls functions: cholesky3, chsolve3, chinv2 ** ** the data must be sorted by ascending time within strata */ #include #include #include "survS.h" #include "survproto.h" static double **covar, **cmat, **cmat2; static double *mark, *wtave; static double *a, *oldbeta, *a2; static double *offset, *weights; static int *status, *frail=NULL, *sort; static double *score, *ttime; /* Hp-UX really doesn't like "time" as a var */ static double *tmean; static int ptype, pdiag; static double *ipen, *upen, logpen; static Sint *zflag; static double **cmatrix(double *, int, int); void coxfit5_a(Sint *nusedx, Sint *nvarx, double *yy, double *covar2, double *offset2, double *weights2, Sint *strata, Sint *sorted, double *means, double *beta, double *u, double *loglik, Sint *methodx, Sint *ptype2, Sint *pdiag2, Sint *nfrail, Sint *frail2, void *fexpr1, void *fexpr2, void *rho) { int i,j,k, p, istrat; int ii; int nused, nvar; int nf, nvar2; double denom, zbeta, risk; double temp, temp2; double ndead; double d2, efron_wt; double method; nused = *nusedx; nvar = *nvarx; nf= *nfrail; method= *methodx; nvar2 = nvar + nf; ptype = *ptype2; pdiag = *pdiag2; /* ** Allocate storage for the arrays and vectors ** Since they will be used later, sizes are based on what will be ** needed with the frailty terms. */ if (nvar >0) { covar= cmatrix(covar2, nused, nvar); cmat = cmatrix(0, nvar2, nvar+1); cmat2= cmatrix(0, nvar2, nvar+1); } a = Calloc(4*nvar2 + 6*nused, double); oldbeta = a + nvar2; a2 = oldbeta + nvar2; mark = a2 + nvar2; wtave= mark + nused; weights = wtave+ nused; offset = weights + nused; score = offset + nused; tmean = score + nused; ttime = tmean + nvar2; status = Calloc(2*nused, int); sort = status + nused; for (i=0; i nvar) i=nf; else i=nvar; if (nf > nvar*nvar) j=nf; else j=nvar*nvar; if (pdiag==0) upen = Calloc(2*i, double); else upen = Calloc(i+j, double); ipen = upen + i; if (ptype>1) zflag = Calloc(nvar, Sint); else zflag = Calloc(2, Sint); if (nf>0) { frail = Calloc(nused, int); for (i=0; i0) { /* once per unique death time */ /* ** Trick: when 'method==0' then temp=0, giving Breslow's method */ ndead = mark[p]; for (k=0; k0) { imat = dmatrix(imat2, nvar2, nvar); jmat = dmatrix(jmat2, nvar2, nvar); } else { imat = 0; /*never used, but passed as dummy to chol */ jmat = 0; } for (i=0; i0) { fgrp = frail[p] -1; zbeta = offset[p] + fbeta[fgrp]; } else zbeta = offset[p]; for (i=0; i0) a[fgrp] += risk; for (i=0; i0) cmat[i][fgrp] += risk*covar[i][p]; for (j=0; j<=i; j++) cmat[i][j+nf] += risk*covar[i][p]*covar[j][p]; } if (status[p]==1) { efron_wt += risk; newlk += weights[p] *zbeta; if (nf>0) { u[fgrp] += weights[p]; a2[fgrp] += risk; } for (i=0; i0) cmat2[i][fgrp] += risk*covar[i][p]; for (j=0; j<=i; j++) cmat2[i][j+nf] += risk*covar[i][p]*covar[j][p]; } } if (mark[p] >0) { /* once per unique death time */ ndead = mark[p]; for (k=0; k0 && newlk < *loglik) { /*it is not converging ! */ halving =1; for (i=0; i0) { /* ** Compute the size of the hazard jump at this point, with the ** total jump saved (temporarily) in "expect", and the Efron ** amount in "weights". It applies to deaths at this point. */ ndead = mark[p]; temp2 = 0; efron_wt =0; for (j=0; j=0; ) { p = sort[ip]; if (status[p] >0) { ndead = mark[p]; temp = expect[p]; hazard2 =weights[p]; for (j=0; j 0) { cmatrix_free(cmat2); cmatrix_free(cmat); cmatrix_free(covar); } } survival/src/agfit4.c0000644000175100001440000006326313070714004014262 0ustar hornikusers/* Automatically generated from the noweb directory */ #include #include "survS.h" #include "survproto.h" SEXP agfit4(SEXP surv2, SEXP covar2, SEXP strata2, SEXP weights2, SEXP offset2, SEXP ibeta2, SEXP sort12, SEXP sort22, SEXP method2, SEXP maxiter2, SEXP eps2, SEXP tolerance2, SEXP doscale2) { int i,j,k, person; int indx1, istrat, p, p1; int nrisk; int nused, nvar; int rank, rank2, fail; double **covar, **cmat, **imat; /*ragged array versions*/ double *a, *oldbeta; double *scale; double *a2, **cmat2; double *eta; double denom, zbeta, risk; double dtime; double temp, temp2; double newlk =0; int halving; /*are we doing step halving at the moment? */ double tol_chol, eps; double meanwt; int deaths; double denom2, etasum; int *keep; /* marker for useless obs */ /* inputs */ double *start, *tstop, *event; double *weights, *offset; int *sort1, *sort2, maxiter; int *strata, nstrat; double method; /* saving this as double forces some double arithmetic */ int doscale; /* returned objects */ SEXP imat2, beta2, u2, loglik2; double *beta, *u, *loglik; SEXP sctest2, flag2, iter2; double *sctest; int *flag, *iter; SEXP rlist; static const char *outnames[]={"coef", "u", "imat", "loglik", "sctest", "flag", "iter", ""}; int nprotect; /* number of protect calls I have issued */ /* get sizes and constants */ nused = nrows(covar2); nvar = ncols(covar2); method= asInteger(method2); eps = asReal(eps2); tol_chol = asReal(tolerance2); maxiter = asInteger(maxiter2); doscale = asInteger(doscale2); nstrat = LENGTH(strata2); /* input arguments */ start = REAL(surv2); tstop = start + nused; event = tstop + nused; weights = REAL(weights2); offset = REAL(offset2); sort1 = INTEGER(sort12); sort2 = INTEGER(sort22); strata = INTEGER(strata2); /* ** scratch space ** nvar: a, a2, oldbeta, scale ** nvar*nvar: cmat, cmat2 ** nused: eta, keep */ eta = (double *) R_alloc(nused + 4*nvar + 2*nvar*nvar, sizeof(double)); a = eta + nused; a2= a + nvar; scale = a2 + nvar; oldbeta = scale + nvar; keep = (int *) R_alloc(nused, sizeof(int)); /* ** Set up the ragged arrays ** covar2 might not need to be duplicated, even though ** we are going to modify it, due to the way this routine was ** was called. In this case NAMED(covar2) will =0 */ PROTECT(imat2 = allocVector(REALSXP, nvar*nvar)); nprotect =1; if (NAMED(covar2)>0) { PROTECT(covar2 = duplicate(covar2)); nprotect++; } covar= dmatrix(REAL(covar2), nused, nvar); imat = dmatrix(REAL(imat2), nvar, nvar); cmat = dmatrix(oldbeta+ nvar, nvar, nvar); cmat2= dmatrix(oldbeta+ nvar + nvar*nvar, nvar, nvar); /* ** create the output structures */ PROTECT(rlist = mkNamed(VECSXP, outnames)); nprotect++; beta2 = SET_VECTOR_ELT(rlist, 0, duplicate(ibeta2)); beta = REAL(beta2); u2 = SET_VECTOR_ELT(rlist, 1, allocVector(REALSXP, nvar)); u = REAL(u2); SET_VECTOR_ELT(rlist, 2, imat2); loglik2 = SET_VECTOR_ELT(rlist, 3, allocVector(REALSXP, 2)); loglik = REAL(loglik2); sctest2 = SET_VECTOR_ELT(rlist, 4, allocVector(REALSXP, 1)); sctest = REAL(sctest2); flag2 = SET_VECTOR_ELT(rlist, 5, allocVector(INTSXP, 3)); flag = INTEGER(flag2); for (i=0; i<3; i++) flag[i]=0; iter2 = SET_VECTOR_ELT(rlist, 6, allocVector(INTSXP, 1)); iter = INTEGER(iter2); /* ** Subtract the mean from each covar, as this makes the variance ** computation much more stable. The mean is taken per stratum, ** the scaling is overall. */ if (nvar==1) doscale =0; /* scaling has no impact, so skip it */ for (i=0; i0) temp = temp2/temp; /* 1/scale */ else temp = 1.0; /* rare case of a constant covariate */ scale[i] = temp; for (person=0; person 200) { flag[1]++; /* a count, for debugging/profiling purposes */ temp = etasum/nrisk; for (i=0; i0) { nrisk++; etasum += eta[p]; denom += risk; for (i=0; i 200) { flag[1]++; /* a count, for debugging/profiling purposes */ temp = etasum/nrisk; for (i=0; i1) { /* on iteration 1 the cholesky has already been done */ rank2 = cholesky2(imat, nvar, tol_chol); /* Are we done? */ fail = isnan(newlk) + isinf(newlk) + abs(rank-rank2); if (fail ==0 && halving ==0 && fabs(1-(loglik[1]/newlk)) <= eps) break; } /* Update coefficients */ if (fail >0 || newlk < loglik[1]) { /*never true on iteration 1 */ /* ** The routine has not made progress past the last good value. */ halving =1; flag[2]++; for (i=0; i 200) { flag[1]++; /* a count, for debugging/profiling purposes */ temp = etasum/nrisk; for (i=0; i0) { nrisk++; etasum += eta[p]; denom += risk; for (i=0; i 200) { flag[1]++; /* a count, for debugging/profiling purposes */ temp = etasum/nrisk; for (i=0; i1: estimate multiple scales (strata) ** strat - if nstrat>0, contains the strata number for each subject ** eps - tolerance for convergence. Iteration continues until the ** relative change in the deviance is <= eps. ** tol_chol- tolerance for Cholesky decomposition ** dist - 1=extreme value, 2=logistic, 3=gaussian, 4=callback ** debug - >0 causes tracing information. Can be removed ** expr - for callback, the expression to be evaluated ** rho - for callback, the environment (R) or frame (Splus) in which ** to do the evaluation. ** Output ** beta - the final coef vector ** iter - the number of iterations consumed ** imat - the information matrix ** loglik - the final log-liklihood ** flag - success flag 0 =ok ** -1= did not converge ** u - the score vector ** ** Work arrays ** newbeta(nvar)- always contains the "next iteration" ** JJ = the approx variance matrix J'J, guarranteed non-singular */ #include "survS.h" #include "survproto.h" SEXP survreg6(SEXP maxiter2, SEXP nvarx, SEXP y, SEXP ny2, SEXP covar2, SEXP wtx, SEXP offset2, SEXP beta2, SEXP nstratx, SEXP stratax, SEXP epsx, SEXP tolx, SEXP dist, SEXP dexpr, SEXP rho) { int i,j; int n, maxiter, ny; double *newbeta; int halving, iter; double newlk; double *loglik, eps, tol_chol; double *beta; Sint *flag; SEXP out_beta; int nvar, nvar2, nstrat; double **covar; Sint *strat ; double *time2, *time1, *status; double *offset; double **imat, **JJ; double *u, *wt, *usave; double (*dolik)(); /* will be pointed to survregc1 or survregc2 */ SEXP z; double *zptr = NULL; SEXP out_iter, out_loglik, out_imat, out_flag; SEXP out_u; SEXP rlist, rlistnames; Sint *iter2; int nprotect; /* ** The only input arg that is overwritten is beta */ out_beta = PROTECT(duplicate(beta2)); beta = REAL(out_beta); maxiter = asInteger(maxiter2); n = LENGTH(wtx); ny = asInteger(ny2); nvar = asInteger(nvarx); offset = REAL(offset2); nstrat = asInteger(nstratx); strat = INTEGER(stratax); wt = REAL(wtx); eps = asReal(epsx); tol_chol= asReal(tolx); covar = dmatrix(REAL(covar2), n, nvar); /* ** nvar = # of "real" x variables, for iteration ** nvar2= # of parameters to maximize = nvar + nstrat ** nstrat= # of strata, where 0== fixed sigma */ nvar2 = nvar + nstrat; /* number of coefficients */ /* ** Create the output variables */ PROTECT(out_imat = allocVector(REALSXP, nvar2*nvar2)); imat = dmatrix(REAL(out_imat), nvar2, nvar2); PROTECT(out_iter = allocVector(INTSXP, 1)); iter2 = INTEGER(out_iter); PROTECT(out_loglik = allocVector(REALSXP, 1)); loglik = REAL(out_loglik); PROTECT(out_flag = allocVector(INTSXP, 1)); flag = INTEGER(out_flag); PROTECT(out_u = allocVector(REALSXP, nvar2)); usave = REAL(out_u); nprotect = 6; /* Create scratch variables ** u = working version of score vector, overwritten with u H-inv during ** Newton steps ** usave = a copy of u, after each Newton step. Returned to the S ** parent routine, and also used to "backtrack" when we need to fail ** over to a Fisher step after NR + halving didn't work */ newbeta = (double *) Calloc(LENGTH(beta2) + nvar2 + nvar2*nvar2, double); u = newbeta + length(beta2); JJ = dmatrix(u +nvar2, nvar2, nvar2); /* ** fixed scale parameters were tacked onto the end of beta at input ** copy them to to the end of newbeta as well (survregc1/c2 expects em) */ for (i=nvar; i0 when in the midst of "step halving" */ newlk = (*dolik)(n, nvar, nstrat, 0, newbeta,asInteger(dist), strat, offset, time1, time2, status, wt, covar, imat, JJ, u, dexpr, rho, zptr, 0, NULL, NULL, NULL); for (i=0; i10, in which ** case step halving isn't quite enough. Make sure the new ** try differs from the last good one by no more than 1/3 ** approx log(3) = 1.1 ** Step halving isn't enough of a "back away" when a ** log(sigma) goes from 0.5 to -3, or has become singular. */ if (halving==1) { /* only the first time */ for (i=0; i 1.1) newbeta[nvar+i] = beta[nvar+i] - 1.1; } } newlk = (*dolik)(n, nvar, nstrat, 1, newbeta,asInteger(dist), strat, offset, time1, time2, status, wt, covar, imat, JJ, u, dexpr, rho, zptr, 0, NULL, NULL, NULL); } } else { /* take a standard NR step */ halving=0; *loglik = newlk; *flag = cholesky3(imat, nvar2, 0, NULL, tol_chol); if (*flag < 0) { i = cholesky3(JJ, nvar2, 0, NULL, tol_chol); chsolve2(JJ, nvar2, u); } else chsolve2(imat,nvar2,u); for (i=0; i #include "survS.h" #include "survproto.h" void agscore(Sint *nx, Sint *nvarx, double *y, double *covar2, Sint *strata, double *score, double *weights, Sint *method, double *resid2, double *a) { int i,k; int n, nvar; int person; double denom, time; double *a2, *mean; double e_denom; double risk; double hazard, meanwt; double deaths, downwt; int dd; double *start, *stop, *event; double **covar, **resid; double temp1, temp2, d2; double *mh1, *mh2, *mh3; n = *nx; nvar = *nvarx; start =y; stop = y+n; event = y+(n+n); /* ** Set up the ragged arrays */ covar= dmatrix(covar2, n, nvar); resid = dmatrix(resid2, n, nvar); a2 = a+nvar; mean= a2 + nvar; mh1 = mean + nvar; mh2 = mh1 + nvar; mh3 = mh2 + nvar; for (person=0; person0) { /* ** This happens when a penalty is infinite. (Which itself ** is often how a penalty routine signals that it was given ** an illegal value for a parameter). In this case the ** updated value of beta will have already been set to 0 ** via cptr1 above, which is of course the correct solution, ** but the U and H use for the parent routine's Newton-Raphson ** step are infinite as well. We force the u and ** hmat matrices to dummy values that will cause no update ** (none needed) and more importantly no infinte/infinite ** arithmetic errors: u=0 and H = identity. (Only the ** relevant columns of each, of course). */ for (i=0; i 1) { /* ** Get the penalty for the dense part of the matrix ** Note that penalties never apply to the variance terms, ** which means that indices go to nvar, not nvar2 */ for (i=0; i=0; ) { ndeath =0; if (status[i]==1) { /* process all tied deaths at this point */ for (j=i; j>=0 && status[j]==1 && time[j]==time[i]; j--) { ndeath += wt[j]; index = indx[j]; for (k=i; k>j; k--) count[3] += wt[j]*wt[k]; /* tied on time */ count[2] += wt[j] * nwt[index]; /* tied on x */ child = (2*index) +1; /* left child */ if (child < ntree) count[0] += wt[j] * twt[child]; /*left children */ child++; if (child < ntree) count[1] += wt[j] * twt[child]; /*right children */ while (index >0) { /* walk up the tree */ parent = (index-1)/2; if (index & 1) /* I am the left child */ count[1] += wt[j] * (twt[parent] - twt[index]); else count[0] += wt[j] * (twt[parent] - twt[index]); index = parent; } } } else j = i-1; /* Add the weights for these obs into the tree and update variance*/ for (; i>j; i--) { wsum1=0; oldmean = twt[0]/2; index = indx[i]; nwt[index] += wt[i]; twt[index] += wt[i]; wsum2 = nwt[index]; child = 2*index +1; /* left child */ if (child < ntree) wsum1 += twt[child]; while (index >0) { parent = (index-1)/2; twt[parent] += wt[i]; if (!(index&1)) /* I am a right child */ wsum1 += (twt[parent] - twt[index]); index=parent; } wsum3 = twt[0] - (wsum1 + wsum2); /* sum of weights above */ lmean = wsum1/2; umean = wsum1 + wsum2 + wsum3/2; /* new upper mean */ newmean = twt[0]/2; myrank = wsum1 + wsum2/2; vss += wsum1*(newmean+ oldmean - 2*lmean) * (newmean - oldmean); vss += wsum3*(newmean+ oldmean+ wt[i]- 2*umean) *(oldmean-newmean); vss += wt[i]* (myrank -newmean)*(myrank -newmean); } count[4] += ndeath * vss/twt[0]; } UNPROTECT(1); return(count2); } SEXP concordance2(SEXP y, SEXP wt2, SEXP indx2, SEXP ntree2, SEXP sortstop, SEXP sortstart) { int i, j, k, index; int child, parent; int n, ntree; int istart, iptr, jptr; double *time1, *time2, *status, dtime; double *twt, *nwt, *count; int *sort1, *sort2; double vss, myrank; double wsum1, wsum2, wsum3; /*sum of wts below, tied, above*/ double lmean, umean, oldmean, newmean; double ndeath; SEXP count2; double *wt; int *indx; n = nrows(y); ntree = asInteger(ntree2); wt = REAL(wt2); indx = INTEGER(indx2); sort2 = INTEGER(sortstop); sort1 = INTEGER(sortstart); time1 = REAL(y); time2 = time1 + n; status= time2 + n; PROTECT(count2 = allocVector(REALSXP, 5)); count = REAL(count2); twt = (double *) R_alloc(2*ntree, sizeof(double)); nwt = twt + ntree; for (i=0; i< 2*ntree; i++) twt[i] =0.0; for (i=0; i<5; i++) count[i]=0.0; vss =0; istart = 0; /* where we are with start times */ for (i=0; i= dtime; istart++) { wsum1 =0; oldmean = twt[0]/2; jptr = sort1[istart]; index = indx[jptr]; nwt[index] -= wt[jptr]; twt[index] -= wt[jptr]; wsum2 = nwt[index]; child = 2*index +1; /* left child */ if (child < ntree) wsum1 += twt[child]; while (index >0) { parent = (index-1)/2; twt[parent] -= wt[jptr]; if (!(index&1)) /* I am a right child */ wsum1 += (twt[parent] - twt[index]); index=parent; } wsum3 = twt[0] - (wsum1 + wsum2); lmean = wsum1/2; umean = wsum1 + wsum2 + wsum3/2; /* new upper mean */ newmean = twt[0]/2; myrank = wsum1 + wsum2/2; vss += wsum1*(newmean+ oldmean - 2*lmean) * (newmean-oldmean); oldmean -= wt[jptr]; /* the z in equations above */ vss += wsum3*(newmean+ oldmean -2*umean) * (newmean-oldmean); vss -= wt[jptr]* (myrank -newmean)*(myrank -newmean); } /* Process deaths */ for (j=i; j 0) { /* walk up the tree */ parent = (index-1)/2; if (index &1) /* I am the left child */ count[1] += wt[jptr] * (twt[parent] - twt[index]); else count[0] += wt[jptr] * (twt[parent] - twt[index]); index = parent; } } } else j = i+1; /* Add the weights for these obs into the tree and compute variance */ for (; i0) { parent = (index-1)/2; twt[parent] += wt[iptr]; if (!(index&1)) /* I am a right child */ wsum1 += (twt[parent] - twt[index]); index=parent; } wsum3 = twt[0] - (wsum1 + wsum2); lmean = wsum1/2; umean = wsum1 + wsum2 + wsum3/2; /* new upper mean */ newmean = twt[0]/2; myrank = wsum1 + wsum2/2; vss += wsum1*(newmean+ oldmean - 2*lmean) * (newmean-oldmean); vss += wsum3*(newmean+ oldmean +wt[iptr] - 2*umean) * (oldmean-newmean); vss += wt[iptr]* (myrank -newmean)*(myrank -newmean); } count[4] += ndeath * vss/twt[0]; } UNPROTECT(1); return(count2); } survival/src/coxmart.c0000755000175100001440000000443413070714004014557 0ustar hornikusers/* $Id: coxmart.c 11166 2008-11-24 22:10:34Z therneau $ */ /* ** Compute the martingale residual for a Cox model ** ** Input ** n number of subjects ** method will be ==1 for the Efron method ** time vector of times ** status vector of status values ** score the vector of subject scores, i.e., exp(beta*z) ** strata is =1 for the last obs of a strata ** mark carried forward from the coxfit routine ** ** Output ** expected the expected number of events for the subject ** ** The martingale residual is more of a nuisance for the Efron method ** */ #include #include "survS.h" #include "survproto.h" void coxmart(Sint *sn, Sint *method, double *time, Sint *status, Sint * strata, double *score, double *wt, double *expect) { register int i,j; int lastone; int n; double deaths, denom=0, e_denom=0; double hazard; double temp, wtsum; double downwt; n = *sn; strata[n-1] =1; /* Failsafe */ /* Pass 1-- store the risk denominator in 'expect' */ for (i= n -1; i>=0; i--) { if (strata[i]==1) denom =0; denom += score[i]*wt[i]; if (i==0 || strata[i-1]==1 || time[i-1]!=time[i]) expect[i] = denom; else expect[i] =0; } /* Pass 2-- now do the work */ deaths=0; wtsum =0; e_denom=0; hazard =0; lastone = 0; for (i= 0; i #include "survS.h" #include "survproto.h" SEXP coxfit6(SEXP maxiter2, SEXP time2, SEXP status2, SEXP covar2, SEXP offset2, SEXP weights2, SEXP strata2, SEXP method2, SEXP eps2, SEXP toler2, SEXP ibeta, SEXP doscale2) { int i,j,k, person; double **covar, **cmat, **imat; /*ragged arrays */ double wtave; double *a, *newbeta; double *a2, **cmat2; double *scale; double denom=0, zbeta, risk; double temp, temp2; int ndead; /* number of death obs at a time point */ double tdeath=0; /* ndead= total at a given time point, tdeath= all */ double newlk=0; double dtime; double deadwt; /*sum of case weights for the deaths*/ double denom2; /* sum of weighted risk scores for the deaths*/ int halving; /*are we doing step halving at the moment? */ int nrisk; /* number of subjects in the current risk set */ /* copies of scalar input arguments */ int nused, nvar, maxiter; int method; double eps, toler; int doscale; /* vector inputs */ double *time, *weights, *offset; int *status, *strata; /* returned objects */ SEXP imat2, means2, beta2, u2, loglik2; double *beta, *u, *loglik, *means; SEXP sctest2, flag2, iter2; double *sctest; int *flag, *iter; SEXP rlist, rlistnames; int nprotect; /* number of protect calls I have issued */ /* get local copies of some input args */ nused = LENGTH(offset2); nvar = ncols(covar2); method = asInteger(method2); maxiter = asInteger(maxiter2); eps = asReal(eps2); /* convergence criteria */ toler = asReal(toler2); /* tolerance for cholesky */ doscale = asInteger(doscale2); time = REAL(time2); weights = REAL(weights2); offset= REAL(offset2); status = INTEGER(status2); strata = INTEGER(strata2); /* ** Set up the ragged arrays and scratch space ** Normally covar2 does not need to be duplicated, even though ** we are going to modify it, due to the way this routine was ** was called. In this case NAMED(covar2) will =0 */ nprotect =0; if (NAMED(covar2)>0) { PROTECT(covar2 = duplicate(covar2)); nprotect++; } covar= dmatrix(REAL(covar2), nused, nvar); PROTECT(imat2 = allocVector(REALSXP, nvar*nvar)); nprotect++; imat = dmatrix(REAL(imat2), nvar, nvar); a = (double *) R_alloc(2*nvar*nvar + 4*nvar, sizeof(double)); newbeta = a + nvar; a2 = newbeta + nvar; scale = a2 + nvar; cmat = dmatrix(scale + nvar, nvar, nvar); cmat2= dmatrix(scale + nvar +nvar*nvar, nvar, nvar); /* ** create output variables */ PROTECT(beta2 = duplicate(ibeta)); beta = REAL(beta2); PROTECT(means2 = allocVector(REALSXP, nvar)); means = REAL(means2); PROTECT(u2 = allocVector(REALSXP, nvar)); u = REAL(u2); PROTECT(loglik2 = allocVector(REALSXP, 2)); loglik = REAL(loglik2); PROTECT(sctest2 = allocVector(REALSXP, 1)); sctest = REAL(sctest2); PROTECT(flag2 = allocVector(INTSXP, 1)); flag = INTEGER(flag2); PROTECT(iter2 = allocVector(INTSXP, 1)); iter = INTEGER(iter2); nprotect += 7; /* ** Subtract the mean from each covar, as this makes the regression ** much more stable. */ tdeath=0; temp2=0; for (i=0; i 0) temp = temp2/temp; /* scaling */ else temp=1.0; /* rare case of a constant covariate */ scale[i] = temp; for (person=0; person=0; ) { if (strata[person] == 1) { nrisk =0 ; denom = 0; for (i=0; i=0 &&time[person]==dtime) { /* walk through the this set of tied times */ nrisk++; zbeta = offset[person]; /* form the term beta*z (vector mult) */ for (i=0; i=0 && strata[person]==1) break; /*ties don't cross strata */ } if (ndead >0) { /* we need to add to the main terms */ if (method==0) { /* Breslow */ denom += denom2; loglik[1] -= deadwt* log(denom); for (i=0; i=0; ) { if (strata[person] == 1) { /* rezero temps for each strata */ denom = 0; nrisk =0; for (i=0; i=0 && time[person]==dtime) { nrisk++; zbeta = offset[person]; for (i=0; i0 && strata[person]==1) break; /*tied times don't cross strata*/ } if (ndead >0) { /* add up terms*/ if (method==0) { /* Breslow */ denom += denom2; newlk -= deadwt* log(denom); for (i=0; i maxbeta[i]) { newbeta[i] = maxbeta[i]; } else if (newbeta[i] < -maxbeta[i]) newbeta[i] = -maxbeta[i]; */ } } } /* return for another iteration */ /* ** We end up here only if we ran out of iterations */ loglik[1] = newlk; chinv2(imat, nvar); for (i=0; i newtime and id=nid. */ for (k=0; k eps) eps = matrix[i][i]; for (j=(i+1); j=0; i--) { if (matrix[i][i+m]==0) y[i+m] =0; else { temp = y[i+m]/matrix[i][i+m]; for (j= i+1; j=0; i--) { if (diag[i] == 0) y[i] =0; else { temp = y[i] / diag[i]; for (j=0; j0) df++; /* count up the df */ for (i=0; i< *ntest; i++) { for (j=0; j0]) * 1e-8 ** The events are counted in the last cell to which person years are ** added in the while() loop below. We don't want to "spill over" into ** a next (incorrect) cell due to accumulated round off, in the case ** that a subjects fu time exactly matches one of the cell boundaries. */ eps =0; /* guard against the rare case that all(time==0) */ for (i=0; i0) { eps = timeleft; /* starting guess for min = first non-zero value*/ break; } } for (; i0) && (timeleft < eps)) eps = timeleft; } eps *= 1e-8; *offtable =0; for (i=0; i eps) { thiscell = pystep(odim, &index, &d1, &d2, data, ofac, odims, ocut, timeleft, 0); if (index >=0) { pyears[index] += thiscell * wt[i]; pn[index] += 1; } else *offtable += thiscell * wt[i]; for (j=0; j=0 && doevent) pcount[index] += event[i] * wt[i]; } } survival/src/finegray.c0000755000175100001440000000651413070714004014707 0ustar hornikusers/* ** Do the indexing for a Fine-Gray model ** input: (tstart, tstop] the time interval for each obs ** ctime, cprob: the underlying survival curve ** the interval that ends at ctime has probability cprob ** extend: should this observation be extended? ** keep: output the interval from ctime[i] to ctime[i+1]? ** ** output: row = which row of the original data, for each row of the new ** (start, end] = the new time intervals ** wt = probability weight for the interval. This is 1.0 ** for all but the extended intervals. */ #include "survS.h" #include "survproto.h" #include SEXP finegray(SEXP tstart2, SEXP tstop2, SEXP ctime2, SEXP cprob2, SEXP extend2, SEXP keep2) { int i,j, k, iadd, extra; int n; /* number of observations */ int ncut; /* number of censoring intervals */ int n2; /* number of new obs */ double tempwt; double *tstart, *tstop; double *ctime, *cprob; int *extend, *keep; /* returned objects */ SEXP row2, start2, end2, wt2, add2, rlist; double *start, *end, *wt; int *row, *add; static const char *outnames[]={"row", "start", "end", "wt", "add", ""}; n = LENGTH(tstart2); ncut = LENGTH(cprob2); tstart = REAL(tstart2); tstop = REAL(tstop2); extend= LOGICAL(extend2); keep = LOGICAL(keep2); ctime = REAL(ctime2); cprob = REAL(cprob2); /* ** how many obs will I need? NA inputs are left alone. ** Extend observations have weight 1 up to the next cutpoint after their ** max, and an extra for any cutpoints after that. */ extra =0; for (i=0; i #include "survS.h" #include "survproto.h" void coxdetail(Sint *nusedx, Sint *nvarx, Sint *ndeadx, double *y, double *covar2, Sint *strata, double *score, double *weights, double *means2, double *u2, double *var, Sint *rmat, double *nrisk2, double *work) { int i,j,k,person; int nused, nvar; int nrisk, ndead; double **covar, **cmat; /*ragged arrays */ double **means; double **u; double *a; double *a2, **cmat2; double *wmeans; double denom; double time; double temp, temp2, temp3; double method; double hazard; double varhaz; int itemp, deaths; int ideath; double efron_wt, d2; double risk; double meanwt; double wdeath; double *start, *stop, *event; int rflag; nused = *nusedx; nvar = *nvarx; method= *means2; ndead = *ndeadx; rflag = 1- rmat[0]; /* ** Set up the ragged arrays */ covar= dmatrix(covar2, nused, nvar); means= dmatrix(means2, ndead, nvar); u = dmatrix(u2, ndead, nvar); cmat = dmatrix(work, nvar, nvar); cmat2= dmatrix(work + nvar*nvar, nvar, nvar); a = work + 2*nvar*nvar; a2= a+nvar; wmeans = a2+nvar; start =y; stop =y + nused; event =y + nused +nused; /* ** Subtract the mean from each covar, as this makes the variance calc ** much more stable */ for (i=0; i0 ** isurv[n] -- individual survival curves ** ** cx and cy must be sorted by (event before censor) within stop time */ #include #include "survS.h" #include "survproto.h" static double *y, *nscore, **newx, **surv, **vsurv, *isurv, **used, **tvar; static int *strata; static double ttime, /* Some HP compilers choke on "time" as a variable */ **imat, *mean; static int death, ncurve, se, nvar, n; static void addup(); void agsurv3(Sint *sn, Sint *snvar, Sint *sncurve, Sint *snpt, Sint *sse, double *score, double *sy, Sint *grpx, double *r, double *coef, double *var, double *xmean, Sint *scn, double *cy, double *cx, double *ssurv, double *varh, double *sused, Sint *smethod) { int i,j,k,l; double *start, *stop, *event; int cn; int npt, nvar2, method; int kk=0, psave; int itime; int person; int deaths, nrisk; int need; double *a=0, *a2=0; double weight=0, e_denom, denom; double inc, sumt, km =0; double temp, downwt, d2; double haz, varhaz; double **oldx =0; n = *sn; nvar = *snvar; cn = *scn; npt = *snpt; se = *sse; ncurve = *sncurve; method = *smethod; death = method/10; method = method - death*10; y = sy; start = cy; stop = cy+ cn; event = cy+ cn+ cn; strata = grpx; /* ** scratch space */ need = 2*n + se*nvar*(2+ n*(n+1)/2) + nvar; nscore = (double *) ALLOC(need, sizeof(double)); for (i=0; i0) vsurv[i][itime]=0; } return; } /* ** Note that the subjects are sorted in strata order */ pstart=0; for (ic=0; ic= ttime) { temp = -haz*nscore[i]; /*increment to the individual hazard*/ if (death==0) { wt += isurv[i]; totsurv += exp(temp) * isurv[i]; } else { wt += 1; totsurv += temp; } isurv[i] *= exp(temp); } /* ** The variance is computed as though it were the Ederer est, always */ if (se==1) { /* Do the variance term (nasty) */ for (j=pstart; j<=i; j++) { temp =0; for (k=0; k #include "survS.h" #include "survproto.h" void coxscho(Sint *nusedx, Sint *nvarx, double *y, double *covar2, double *score, Sint *strata, Sint *method2, double *work) { int i,k,person; int nused, nvar; double **covar; double *a; double *a2; double *mean; double denom, weight; double time; double temp; double method; double deaths; double efron_wt; double *start, *stop, *event; nused = *nusedx; nvar = *nvarx; method= *method2; /* ** Set up the ragged arrays */ covar= dmatrix(covar2, nused, nvar); a = work; a2= a+nvar; mean = a2+nvar; start =y; stop =y + nused; event =y + nused +nused; /* ** Now walk through the data */ for (person=0; person #include "survS.h" #include "survproto.h" void agexact(Sint *maxiter, Sint *nusedx, Sint *nvarx, double *start, double *stop, Sint *event, double *covar2,double *offset, Sint *strata, double *means, double *beta, double *u, double *imat2, double loglik[2], Sint *flag, double *work, Sint *work2, double *eps, double *tol_chol, double *sctest) { int i,j,k, l, person; int iter; int n, nvar; double **covar, **cmat, **imat; /*ragged array versions*/ double *a, *newbeta; double *score, *newvar; double denom, zbeta, weight; double time; double temp; double newlk =0; int halving; /*are we doing step halving at the moment? */ int nrisk, deaths; int *index, *atrisk; n = *nusedx; nvar = *nvarx; /* ** Set up the ragged arrays */ covar= dmatrix(covar2, n, nvar); imat = dmatrix(imat2, nvar, nvar); cmat = dmatrix(work, nvar, nvar); a = work + nvar*nvar; newbeta = a + nvar; score = newbeta + nvar; newvar = score + n; index = (int *) work2; atrisk= index+n; /* ** Subtract the mean from each covar, as this makes the regression ** much more stable */ for (i=0; i=0) { for (i=0; i=0) { for (i=0; i #define SMALL -200 /* what to use for log(f(x)) when f(x) gives a zero, i.e., the calling made a really bad guess for beta */ static void exvalue_d(double z, double ans[4], int j); static void logistic_d(double z, double ans[4], int j); static void gauss_d(double z, double ans[4], int j); static void (*sreg_gg)(); #define SPI 2.506628274631001 /* sqrt(2*pi) */ #define ROOT_2 1.414213562373095 double survregc1(int n, int nvar, int nstrat, int whichcase, double *beta, int dist, Sint *strat, double *offset, double *time1, double *time2, double *status, double *wt, double **covar, double **imat, double **JJ, double *u, SEXP expr, SEXP rho, double *dummy, int nf, Sint *frail, double *fdiag, double *jdiag ) { int person, i,j,k; int nvar2; /* nvar + nstrat */ int nvar3; /* nvar2 + nf */ int strata; double eta, sigma; double z, zu, loglik, temp, temp2; double sz; double sig2; double funs[4], ufun[4]; int fgrp =0; /* the =0 to quiet a compiler warning */ double w; /* add "=0" to keep the compiler from worrying about uninitialized vars */ double g=0, dg=0, ddg=0, dsig=0, ddsig=0, dsg=0; switch(dist) { case 1: sreg_gg = exvalue_d; break; case 2: sreg_gg = logistic_d; break; case 3: sreg_gg = gauss_d; break; } nvar2 = nvar + nstrat; nvar3 = nvar2 + nf; loglik =0; if (whichcase==0) { for (i=0; i1) { /* ** multiple scales: pick the right sigma for this obs ** The more common case of a single scale is set 6 lines above */ strata= strat[person] -1; /*S likes to start counting at 1 */ sigma = exp(beta[strata+nvar+nf]); sig2 = 1/(sigma*sigma); } eta =0; for (i=0; i0){ fgrp = frail[person] -1; eta += beta[fgrp]; } sz = (time1[person] - eta); /* sigma * z */ z = sz /sigma; j = status[person]; /*convert to integer */ switch(j) { case 1: /* exact */ (*sreg_gg)(z, funs,1); if (funs[1] <=0) { /* off the probability scale -- avoid log(0), and set the ** derivatives to gaussian limits (almost any deriv will ** do, since the function value triggers step-halving). */ g = SMALL; dg = -z/sigma; ddg = -1/sigma; dsig =0; ddsig=0; dsg=0; } else { g = log(funs[1]) - log(sigma); temp = funs[2]/sigma; temp2= funs[3]*sig2; dg = -temp; dsig= -temp*sz; ddg= temp2 - dg*dg; dsg = sz * temp2 - dg*(dsig +1); ddsig = sz*sz* temp2 - dsig*(1+dsig); dsig -= 1; } break; case 0: /* right censored */ (*sreg_gg)(z, funs,2); if (funs[1] <=0) { g = SMALL; dg = z/sigma; ddg =0; dsig =0; ddsig=0; dsg=0; } else { g = log(funs[1]); temp = -funs[2]/(funs[1]*sigma); temp2= -funs[3]*sig2/funs[1]; dg = -temp; dsig= -temp*sz; ddg= temp2 - dg*dg; dsg = sz * temp2 - dg*(dsig +1); ddsig = sz*sz* temp2 - dsig*(1+dsig); } break; case 2: /* left censored */ (*sreg_gg)(z, funs,2); if (funs[0] <=0) { /* off the probability scale -- avoid log(0) */ g = SMALL; dg = -z/sigma; dsig =0; ddsig=0; dsg=0; ddg =0; } else { g = log(funs[0]); temp = funs[2]/(funs[0]*sigma); temp2= funs[3]*sig2/funs[0]; dg = -temp; dsig= -temp*sz; ddg= temp2 - dg*dg; dsg = sz * temp2 - dg*(dsig +1); ddsig = sz*sz* temp2 - dsig*(1+dsig); } break; case 3: /* interval censored */ zu = (time2[person] - eta)/sigma; /*upper endpoint */ (*sreg_gg)(z, funs, 2); (*sreg_gg)(zu,ufun ,2); if (z>0) temp = funs[1] - ufun[1]; /*stop roundoff in tails*/ else temp = ufun[0] - funs[0]; if (temp <=0) { /* off the probability scale -- avoid log(0) */ g = SMALL; dg = 1; ddg =0; dsig =0; ddsig=0; dsg=0; } else { g = log(temp); dg = -(ufun[2] - funs[2])/(temp*sigma); ddg = (ufun[3] - funs[3])*sig2/temp - dg*dg; dsig = (z*funs[2] - zu*ufun[2])/temp; ddsig= ((zu*zu*ufun[3] - z*z*funs[3])/temp) - dsig*(1+dsig); dsg = ((zu*ufun[3] - z*funs[3])/ (temp*sigma)) - dg * (dsig +1); } break; } loglik += g * wt[person]; /*if (person<8) fprintf(stderr, "i=%d, g=%g, dg=%g, ddg=%g, dsg=%g\n", person, g, dg, ddg, dsg);*/ /* ** Now the derivs wrt loglik ** Remember that the "x" for a sparse term is 1 */ if (whichcase==1) continue; /*only needed the loglik */ w = wt[person]; if (nf>0) { u[fgrp] += dg * w; fdiag[fgrp] -= ddg * w; jdiag[fgrp] += dg*dg *w; } for (i=0; i0) { imat[i][fgrp] -= covar[i][person] * ddg * w; JJ [i][fgrp] += temp * dg; } } if (nstrat!=0) { /* need derivative wrt log sigma */ k = strata+nvar; u[k+nf] += w* dsig; for (i=0; i0) { imat[k][fgrp] -= dsg * w; JJ [k][fgrp] += dsig *dg *w; } } } return(loglik); } /* ** Case ans[0] ans[1] ans[2] ans[3] ** 1 f f'/f f''/ f ** 2 F 1-F f f' ** ** We do both F and 1-F to avoid the error in (1-F) for F near 1 */ static void logistic_d(double z, double ans[4], int j) { double w, temp; int sign, ii; /* ** The symmetry of the logistic allows me to be careful, and never take ** exp(large number). This routine should be very accurate. */ if (z>0) { w = exp(-z); sign = -1; ii=0; } else { w = exp(z); sign = 1; ii=1; } temp = 1+w; switch(j) { case 1: ans[1] = w/(temp*temp); ans[2] = sign*(1-w)/temp; ans[3] = (w*w -4*w +1)/(temp*temp); break; case 2: ans[1-ii] = w/temp; ans[ii] = 1/temp; ans[2] = w/(temp*temp); ans[3] = sign*ans[2]*(1-w)/temp; break; } } static void gauss_d(double z, double ans[4], int j) { double f; f = exp(-z*z/2) /SPI; switch(j) { case 1: ans[1] =f; ans[2] = -z; ans[3] = z*z -1; break; case 2: if (z>0) { ans[0] = (1 + erf(z/ROOT_2))/2; ans[1] = erfc(z/ROOT_2) /2; } else { ans[1] = (1 + erf(-z/ROOT_2))/2; ans[0] = erfc(-z/ROOT_2) /2; } ans[2] = f; ans[3] = -z*f; break; } } /* ** In the Gaussian and logistic cases, I could avoid numeric disaster by only ** evaluating exp(x) for x<0. By symmetry, I got what I need for ** x >0. The extreme value dist, howerver, is asymmetric, and I don't yet ** see the appropriate numeric tricks. ** Perhaps a Taylor series will could be used for large z. */ static void exvalue_d(double z, double ans[4], int j) { double temp; double w; if (z < SMALL) w= exp(SMALL); else if (-z < SMALL) w = exp(-SMALL); /* stop infinite answers */ else w = exp(z); temp = exp(-w); switch(j) { case 1: ans[1] = w*temp; ans[2] = 1-w; ans[3] = w*(w-3) +1; break; case 2: ans[0] = 1-temp; ans[1] = temp; ans[2] = w*temp; ans[3] = w*temp*(1-w); break; } } survival/src/survsplit.c0000755000175100001440000000501613070714004015152 0ustar hornikusers/* ** Do the indexing for survSplit ** input: (tstart, tstop] the time interval for each obs ** cut: the vector of new cutpoints ** output: row = which row of the original data, for each row of the new ** (start, end] = the new time intervals ** censor = the new should be censored (new end point) */ #include "survS.h" #include "survproto.h" #include SEXP survsplit(SEXP tstart2, SEXP tstop2, SEXP cut2) { int i,j, k, extra; int n; /* number of observations */ int ncut; /* number of cuts */ int n2; /* number of new obs */ double *tstart, *tstop, *cut; /* returned objects */ SEXP row2, interval2, start2, end2, censor2, rlist; double *start, *end; int *row, *censor, *interval; static const char *outnames[]={"row", "interval", "start", "end", "censor", ""}; n = LENGTH(tstart2); ncut = LENGTH(cut2); tstart = REAL(tstart2); tstop = REAL(tstop2); cut = REAL(cut2); /* ** how many obs will I need? Each cutpoint strictly within an interal ** generates an extra line. NA inputs are left alone. */ extra =0; for (i=0; i tstart[i] && cut[j] < tstop[i]) extra++; } /* allocate output */ n2 = n + extra; PROTECT(rlist = mkNamed(VECSXP, outnames)); row2 = SET_VECTOR_ELT(rlist, 0, allocVector(INTSXP, n2)); row = INTEGER(row2); interval2 = SET_VECTOR_ELT(rlist, 1, allocVector(INTSXP, n2)); interval = INTEGER(interval2); start2 = SET_VECTOR_ELT(rlist, 2, allocVector(REALSXP, n2)); start = REAL(start2); end2 = SET_VECTOR_ELT(rlist, 3, allocVector(REALSXP, n2)); end = REAL(end2); censor2= SET_VECTOR_ELT(rlist, 4, allocVector(LGLSXP, n2)); censor = LOGICAL(censor2); /* do the work */ k =0; for (i=0; i tstart[i]) { end[k] = cut[j]; censor[k] =1; k++; start[k] = cut[j]; row[k] =i+1; interval[k] = j+1; } } end[k] = tstop[i]; censor[k] =0; k++; } } UNPROTECT(1); return(rlist); } survival/src/doloop.c0000755000175100001440000000362413070714004014376 0ustar hornikusers/* $Id: doloop.c 11357 2009-09-04 15:22:46Z therneau $ ** ** Program to mimic a set of nested do loops ** ** Usual calling sequence would be ** init_doloop(min,max); ** while (doloop(nloops, index) >=min) { ** some calculations ** } ** ** The result of this is as though the code had been written for "nloops" ** nested for loops: ** ** for (index[0]=min; index[0]= (minval+i)) return (minval+i-1); else return (minval-1); } nloops--; index[nloops]++; /*increment the lastmost index */ if (index[nloops] <= (maxval-depth)) return(index[nloops]); else if (nloops ==0) return(minval - depth); else { depth++; index[nloops] = doloop(nloops, index) +1; depth--; return(index[nloops]); } } survival/src/survfitci.c0000644000175100001440000002444613070714004015122 0ustar hornikusers/* Automatically generated from the noweb directory */ #include "survS.h" #include "survproto.h" #include SEXP survfitci(SEXP ftime2, SEXP sort12, SEXP sort22, SEXP ntime2, SEXP status2, SEXP cstate2, SEXP wt2, SEXP id2, SEXP p2, SEXP i02, SEXP sefit2) { int i, j, k, kk; /* generic loop indices */ int ck, itime, eptr; /*specific indices */ double ctime; /*current time of interest, in the main loop */ int oldstate, newstate; /*when changing state */ double temp, *temp2; /* scratch double, and vector of length nstate */ double *dptr; /* reused in multiple contexts */ double *p; /* current prevalence vector */ double **hmat; /* hazard matrix at this time point */ double **umat; /* per subject leverage at this time point */ int *atrisk; /* 1 if the subject is currently at risk */ int *ns; /* number curently in each state */ int *nev; /* number of events at this time, by state */ double *ws; /* weighted count of number state */ double *wtp; /* case weights indexed by subject */ double wevent; /* weighted number of events at current time */ int nstate; /* number of states */ int n, nperson; /*number of obs, subjects*/ double **chaz; /* cumulative hazard matrix */ /* pointers to the R variables */ int *sort1, *sort2; /*sort index for entry time, event time */ double *entry,* etime; /*entry time, event time */ int ntime; /* number of unique event time values */ int *status; /*0=censored, 1,2,... new states */ int *cstate; /* current state for each subject */ int *dstate; /* the next state, =cstate if not an event time */ double *wt; /* weight for each observation */ double *i0; /* initial influence */ int *id; /* for each obs, which subject is it */ int sefit; /* returned objects */ SEXP rlist; /* the returned list and variable names of same */ const char *rnames[]= {"nrisk","nevent","ncensor", "p", "cumhaz", "std", "influence", ""}; SEXP setemp; double **pmat, **vmat, *cumhaz, *usave; int *ncensor, **nrisk, **nevent; ntime= asInteger(ntime2); nperson = LENGTH(cstate2); /* number of unique subjects */ n = LENGTH(sort12); /* number of observations in the data */ PROTECT(cstate2 = duplicate(cstate2)); cstate = INTEGER(cstate2); entry= REAL(ftime2); etime= entry + n; sort1= INTEGER(sort12); sort2= INTEGER(sort22); status= INTEGER(status2); wt = REAL(wt2); id = INTEGER(id2); PROTECT(p2 = duplicate(p2)); /*copy of initial prevalence */ p = REAL(p2); nstate = LENGTH(p2); /* number of states */ i0 = REAL(i02); sefit = asInteger(sefit2); /* allocate space for the output objects ** Ones that are put into a list do not need to be protected */ PROTECT(rlist=mkNamed(VECSXP, rnames)); setemp = SET_VECTOR_ELT(rlist, 0, allocMatrix(INTSXP, ntime, nstate)); nrisk = imatrix(INTEGER(setemp), ntime, nstate); /* time by state */ setemp = SET_VECTOR_ELT(rlist, 1, allocMatrix(INTSXP, ntime, nstate)); nevent = imatrix(INTEGER(setemp), ntime, nstate); /* time by state */ setemp = SET_VECTOR_ELT(rlist, 2, allocVector(INTSXP, ntime)); ncensor = INTEGER(setemp); /* total at each time */ setemp = SET_VECTOR_ELT(rlist, 3, allocMatrix(REALSXP, ntime, nstate)); pmat = dmatrix(REAL(setemp), ntime, nstate); setemp = SET_VECTOR_ELT(rlist, 4, allocVector(REALSXP, nstate*nstate*ntime)); cumhaz = REAL(setemp); if (sefit >0) { setemp = SET_VECTOR_ELT(rlist, 5, allocMatrix(REALSXP, ntime, nstate)); vmat= dmatrix(REAL(setemp), ntime, nstate); } if (sefit >1) { setemp = SET_VECTOR_ELT(rlist, 6, allocVector(REALSXP, n*nstate*(ntime+1))); usave = REAL(setemp); } /* allocate space for scratch vectors */ ws = (double *) R_alloc(2*nstate, sizeof(double)); /*weighted number in state */ temp2 = ws + nstate; ns = (int *) R_alloc(2*nstate, sizeof(int)); nev = ns + nstate; atrisk = (int *) R_alloc(2*nperson, sizeof(int)); dstate = atrisk + nperson; wtp = (double *) R_alloc(nperson, sizeof(double)); hmat = (double**) dmatrix((double *)R_alloc(nstate*nstate, sizeof(double)), nstate, nstate); chaz = (double**) dmatrix((double *)R_alloc(nstate*nstate, sizeof(double)), nstate, nstate); if (sefit >0) umat = (double**) dmatrix((double *)R_alloc(nperson*nstate, sizeof(double)), nstate, nperson); /* R_alloc does not zero allocated memory */ for (i=0; i1) { /* copy influence, and save it */ dptr = i0; for (j=0; j0) { newstate = status[k] -1; /* 0 based subscripts */ oldstate = cstate[id[k]]; if (oldstate != newstate) { /* A "move" to the same state does not count */ dstate[id[k]] = newstate; nev[newstate]++; wevent += wt[k]; hmat[oldstate][newstate] += wt[k]; } } else ncensor[itime]++; } else break; } if (wevent > 0) { /* there was at least one move with weight > 0 */ /* finish computing H */ for (j=0; j0) { temp =0; for (k=0; k0) { if (sefit >0) { /* Update U, part 1 U = U %*% H -- matrix multiplication */ for (j=0; j0) { temp =0; for (k=0; k 1) for (k=0; k0) cstate[id[j]] = status[j]-1; /*new state */ atrisk[id[j]] =0; } else break; } itime++; } /* return a list */ UNPROTECT(3); return(rlist); } survival/src/init.c0000755000175100001440000000554313070714004014047 0ustar hornikusers/* ** This file causes the entry points of my .C routines to be preloaded ** Added at the request of R-core. ** It adds one more layer of protection by declaring the number of arguments, ** and perhaps a tiny bit of speed */ #include "survS.h" #include "R_ext/Rdynload.h" #include "Rversion.h" #include "survproto.h" static const R_CMethodDef Centries[] = { {"Cagfit5a", (DL_FUNC) &agfit5a, 20}, {"Cagfit5b", (DL_FUNC) &agfit5b, 19}, {"Cagfit5c", (DL_FUNC) &agfit5c, 1}, {"Cagsurv3", (DL_FUNC) &agsurv3, 19}, {"Cagsurv4", (DL_FUNC) &agsurv4, 6}, {"Cagsurv5", (DL_FUNC) &agsurv5, 10}, {"Cagexact", (DL_FUNC) &agexact, 20}, {"Cagmart", (DL_FUNC) &agmart, 9}, {"Cagmart2", (DL_FUNC) &agmart2, 13}, {"Cagscore", (DL_FUNC) &agscore, 10}, {"Ccoxdetail", (DL_FUNC) &coxdetail, 14}, {"Ccoxfit5a", (DL_FUNC) &coxfit5_a, 20}, {"Ccoxfit5b", (DL_FUNC) &coxfit5_b, 19}, {"Ccoxfit5c", (DL_FUNC) &coxfit5_c, 5}, {"Ccoxmart", (DL_FUNC) &coxmart, 8}, {"Ccoxmart2", (DL_FUNC) &coxmart2, 7}, {"Ccoxph_wtest",(DL_FUNC) &coxph_wtest,6}, {"Ccoxscho", (DL_FUNC) &coxscho, 8}, {"Ccoxscore", (DL_FUNC) &coxscore, 10}, {"Cpyears1", (DL_FUNC) &pyears1, 22}, {"Cpyears2", (DL_FUNC) &pyears2, 14}, {"Csurvdiff2", (DL_FUNC) &survdiff2, 13}, {"Csurvfit4", (DL_FUNC) &survfit4, 4}, {NULL, NULL, 0} }; static const R_CallMethodDef Callentries[] = { {"Cagfit4", (DL_FUNC) &agfit4, 13}, {"Cagmart3", (DL_FUNC) &agmart3, 6}, {"Cconcordance1", (DL_FUNC) &concordance1, 4}, {"Cconcordance2", (DL_FUNC) &concordance2, 6}, {"Ccoxcount1", (DL_FUNC) &coxcount1, 2}, {"Ccoxcount2", (DL_FUNC) &coxcount2, 4}, {"Ccoxexact", (DL_FUNC) &coxexact, 8}, {"Ccoxfit6", (DL_FUNC) &coxfit6, 12}, {"Cfinegray", (DL_FUNC) &finegray, 6}, {"Cpyears3b", (DL_FUNC) &pyears3b, 10}, {"Csurvfitci", (DL_FUNC) &survfitci, 11}, {"Csurvreg6", (DL_FUNC) &survreg6, 15}, {"Csurvreg7", (DL_FUNC) &survreg7, 21}, {"Csurvsplit", (DL_FUNC) &survsplit, 3}, {"Ctmerge", (DL_FUNC) &tmerge, 7}, {NULL, NULL, 0} }; void R_init_survival(DllInfo *dll){ R_registerRoutines(dll, Centries, Callentries, NULL, NULL); /* The following line makes only those routines defined above available to outside packages, i.e., internal things like dmatrix() are now invisible. */ R_useDynamicSymbols(dll, FALSE); /* ** This line makes them only be available via the symbols above ** i.e., .Call("tmerge", ) won't work but .Call(Ctmerge, ) will ** This feature was added in version 2.16 */ #if defined(R_VERSION) && R_VERSION >= R_Version(2, 16, 0) R_forceSymbols(dll, TRUE); #endif } survival/src/survConcordance.c0000755000175100001440000001166213070714004016241 0ustar hornikusers/* ** $Id: survConcordance.c 11166 2008-11-24 22:10:34Z therneau $ ** ** For each observation, we want to know, for the subset of observations ** with longer survival (and only those) ** number with smaller, bigger, and tied x values ** ** The input data is sorted, largest survival to smallest survival ** ** n number of time/status/x values ** time ** status needed to keep track of tied survival times ** x vector of scores ** n2 number of unique x values ** x2 sorted vector of unique x values, smallest to largest ** ** temp scratch vector of length 2* n2 ** ** returned ** result number concordant, discordant, tied survival, tied x but ** not tied survival, and incomparable times ** (bigger survival + smaller risk score = concordant) */ #include "survS.h" #include void survConcordance(Sint *np, double *time, Sint *status, double *x, Sint *n2p, double *x2, Sint *temp,Sint *result) { int i, j, k=0; int start, end; int n, n2; Sint *count1, *count2, *count; int tdeath; int nright, nsame; n = *np; n2= *n2p; count1 = &(temp[0]); count2 = &(temp[n2]); for (i=0; i<5; i++) result[i] =0; /* redundant I think */ for (i=0; i x2[k]. (Draw a picture). ** The root of the tree is element k= floor((n2-1)/2), with value x2[k]. ** In general, for any subtree that "owns" elements i to j, the root ** of that subtree is element k= floor((i+j)/2), whose left subtree ** owns elements i to k-1 of the tree, and right subtree owns elements ** k+1 to j. ** ** As we update, count[i] will be the number of data values in this ** node and all nodes below. ** ** We walk through the data one survival time at at time, comparing each ** to all the survival times above it. ** If the time is censored, all those above are "incomparable". ** Otherwise, we need to find the position of x[i], among x[1: (i-1)] ** We do this by updating the counts in the binary tree. The count ** vector contains the number of x[0 to i] that are in or below any ** given node k of the binary tree. ** ** Tied death times are a nuisance; we have to refrain from updating ** the counts until the end of each set of them. Thus a vector ** count1 (up to date) and count2 (lagged). ** nright = sum(# values to the right, each time I take a left branch) */ tdeath =0; /* current count of tied deaths */ for (i=0; i 0) { /* ** Walk the tree a first time, to count this observation's ** position */ nright = 0; start = 0; end= n2-1; /*start to end of sublist being looked at */ if (tdeath==0) count=count1; /* use the appropriate count */ else count=count2; while(start <= end) { k = (start+end)/2; if (x[i] == x2[k]) break; if (x[i] < x2[k]) { /* take the left branch (smaller numbers) */ end = k-1; nright = nright + (count[k] - count[(start+end)/2]); } else start = k+1; /*right branch */ } /* ** At this point x[i] = x2[k]; we've found the number in the ** x2 list */ nsame = count[k]; /*provisional */ if (k start) /* there is a left hand branch below here */ nsame = nsame - count[(start+k-1)/2]; result[3] += nsame; result[1] += nright; /* # values bigger than x[i] */ result[0] += i - (tdeath + nsame + nright); /* # smaller */ /* Is the next survival time tied with this one? */ if (i<(n-1) && status[i+1]>0 &&(time[i] == time[i+1])) { tdeath += 1; /* Yes it is */ if (tdeath==1) { for (j=0; j #include "survS.h" #include "survproto.h" SEXP agmart3(SEXP surv2, SEXP score2, SEXP weight2, SEXP strata2, SEXP sortx, SEXP method2) { int k, ksave; int p, istrat, indx2; double deaths, denom, e_denom; double hazard, e_hazard, cumhaz; double temp, time; double wtsum; int n, person; /* pointers to the input data */ double *start, *stop, *event; double *weight, *score; int *sort1, *sort2, *strata; int method; /* integer version of input */ /* output */ SEXP resid2; double *resid; n = nrows(surv2); method = asInteger(method2); start = REAL(surv2); stop = start +n; event = stop +n; weight= REAL(weight2); score = REAL(score2); sort1 = INTEGER(sortx); sort2 = sort1 + n; strata= INTEGER(strata2); PROTECT(resid2 = allocVector(REALSXP, n)); resid = REAL(resid2); /* ** 'person' walks through the the data from 1 to n, ** sort1[0] points to the largest stop time, sort1[1] the next, ... ** 'time' is a scratch variable holding the time of current interest ** 'indx2' walks through the start times. It will be smaller than ** 'person': if person=27 that means that 27 subjects have stop >=time, ** and are thus potential members of the risk set. If 'indx2' =9, ** that means that 9 subjects have start >=time and thus are NOT part ** of the risk set. (stop > start for each subject guarrantees that ** the 9 are a subset of the 27). ** Basic algorithm: move 'person' forward, adding the new subject into ** the risk set. If this is a new, unique death time, take selected ** old obs out of the sums, add in obs tied at this time, then update ** the cumulative hazard. Everything resets at the end of a stratum. ** The sort order is from large time to small, so we encounter a subject's ** ending time first, then their start time. ** The martingale residual for a subject is ** status - (cumhaz at end of their interval - cumhaz at start)*score */ istrat=0; indx2 =0; denom =0; cumhaz =0; for (person=0; person #include #include "survS.h" #include "survproto.h" static double **covar, **cmat, **cmat2; static double *a, *oldbeta, *a2; static double *offset, *weights; static int *event, *frail = NULL; static double *score, *start, *stop; static int *sort1, *sort2; static double *tmean; static int ptype, pdiag; static double *ipen, *upen, logpen; static Sint *zflag; static double **cmatrix(double *, int, int); void agfit5a(Sint *nusedx, Sint *nvarx, double *yy, double *covar2, double *offset2, double *weights2, Sint *strata, Sint *sort, double *means, double *beta, double *u, double *loglik, Sint *methodx, Sint *ptype2, Sint *pdiag2, Sint *nfrail, Sint *frail2, void *fexpr1, void *fexpr2, void *rho) { int i,j,k, person; int nused, nvar; int nf, nvar2; int deaths, itemp; int istrat, indx2, p, ksave; double denom, zbeta, risk; double temp; double d2, efron_wt; double method; double meanwt, time; nused = *nusedx; nvar = *nvarx; nf= *nfrail; method= *methodx; nvar2 = nvar + nf; ptype = *ptype2; pdiag = *pdiag2; /* ** Allocate storage for the arrays and vectors ** Since they will be used later, sizes are based on what will be ** needed with the frailty terms. */ if (nvar >0) { covar= cmatrix(covar2, nused, nvar); cmat = cmatrix(0, nvar2, nvar+1); cmat2= cmatrix(0, nvar2, nvar+1); } a = Calloc(4*nvar2 + 5*nused , double); oldbeta = a + nvar2; a2 = oldbeta + nvar2; weights = a2+ nvar2; offset = weights + nused; score = offset + nused; tmean = score + nused; start = tmean + nvar2; stop = start + nused; event = Calloc(3*nused, int); sort1 = event + nused; sort2 = sort1 + nused; for (i=0; i nvar) i=nf; else i=nvar; if (nf > nvar*nvar) j=nf; else j=nvar*nvar; if (pdiag==0) upen = Calloc(2*i, double); else upen = Calloc(i+j, double); ipen = upen + i; if (ptype>1) zflag = Calloc(nvar, Sint); else zflag = Calloc(2, Sint); if (nf>0) { frail = Calloc(nused, int); for (i=0; i=time, ** and are thus potential members of the risk set. If 'indx2' =9, ** that means that 9 subjects have start >=time and thus are NOT part ** of the risk set. (stop > start for each subject guarrantees that ** the 9 are a subset of the 27). ** Basic algorithm: move 'person' forward, adding the new subject into ** the risk set. If this is a new, unique death time, take selected ** old obs out of the sums, add in obs tied at this time, then ** add terms to the loglik, etc. */ istrat=0; indx2 =0; denom =0; for (person=0; person0) { imat = dmatrix(imat2, nvar2, nvar); jmat = dmatrix(jmat2, nvar2, nvar); } else { imat = 0; /*never used, but passed as dummy to chol */ jmat = 0; } for (i=0; i0) { fgrp = frail[person] -1; zbeta = offset[person] + fbeta[fgrp]; } else zbeta = offset[person]; for (i=0; i 20 && *maxiter >1) { /* ** If the above happens, then ** 1. There is a real chance for catastrophic cancellation ** in the computation of "denom", which leads to ** numeric failure via log(neg number) -> inf loglik ** 2. A risk score for one person of exp(20) > 400 million ** is either an infinite beta, in which case any ** reasonable coefficient will do, or a big overreach ** in the Newton-Raphson step. ** In either case, a good solution is step halving. However, ** if the user asked for exactly 1 iteration, we should ** just return what they asked. ** ** Why 20? Most machines have about 16 digits of precision, ** and this preserves approx 7 digits in the subtraction ** when a high risk score person leaves the risk set. ** (Because of centering, the average risk score is about 0). ** Second, if eps is small and beta is infinite, we rarely ** get a value above 16. So a 20 is usually a NR overshoot. ** A data set with zbeta=54 on iter 1 led to this fix, the ** true final solution had max values of 4.47. */ halving=1; for (i=0; i0) fgrp = frail[p] -1; else fgrp = -1; if (event[p]==0){ risk = exp(score[p]) * weights[p]; denom += risk; if (fgrp >=0) a[fgrp] += risk; for (i=0; i=0) cmat[i][fgrp] += risk * covar[i][p]; for (j=0; j<=i; j++) cmat[i][j+nf] += risk*covar[i][p]*covar[j][p]; } person++; } else { time = stop[p]; /* ** subtract out the subjects whose start time is to the right */ for (; indx20) fgrp = frail[p] - 1; else fgrp = -1; if (fgrp >=0) a[fgrp] -= risk; for (i=0; i=0) cmat[i][fgrp] -= risk* covar[i][p]; for (j=0; j<=i; j++) cmat[i][j+nf] -= risk*covar[i][p]*covar[j][p]; } } /* ** compute the averages over this death time (a2 & c2) */ efron_wt =0; meanwt =0; for (i=0; i0) { fgrp = frail[p] -1; if (fgrp>=0) a[fgrp] += risk; } else fgrp = -1; for (i=0; i=0) cmat[i][fgrp] += risk*covar[i][p]; for (j=0; j<=i; j++) cmat[i][j+nf] += risk*covar[i][p]*covar[j][p]; } if (event[p]==1) { deaths += event[p]; efron_wt += risk* weights[p]; meanwt += weights[p]; if (fgrp >= 0) { u[fgrp] += weights[p]; a2[fgrp] += risk; } for (i=0; i=0) cmat2[i][fgrp] += risk*covar[i][p]; for (j=0; j<=i; j++) cmat2[i][j+nf] += risk*covar[i][p]*covar[j][p]; } } } ksave =k; /* add results into u and imat */ itemp = -1; meanwt /= deaths; for (; person0 && newlk < *loglik) { /*it is not converging ! */ halving =1; for (i=0; i 0) { cmatrix_free(cmat2); cmatrix_free(cmat); cmatrix_free(covar); } } survival/src/cholesky3.c0000755000175100001440000000506013070714004015002 0ustar hornikusers/* $Id: cholesky3.c 11166 2008-11-24 22:10:34Z therneau $ */ /* ** subroutine to do Cholesky decompostion on a matrix: C = FDF' ** where F is lower triangular with 1's on the diagonal, and D is diagonal ** This is a specialized form for the frailty problem. The matric C in this ** case has C[1:m, 1:m] diagonal and C[(m+1):n, 1:n)] is dense. ** ** arguments are: ** n the size of the matrix to be factored ** m the size of the diagonal upper portion ** diag the diagonal upper portion ** **matrix a ragged array containing the dense portion ** toler tolerance for detecting singularity ** ** The diagonal portion of the matrix is unchanged by the factorization. ** For the dense portion, D occupies the diagonal (of the full matrix). ** The factorization is returned in the lower triangle. ** The upper triangle of the matrix is entirely unused by the process (but ** because of the compressed storage, this isn't much space). ** ** Return value: the rank of the matrix (non-negative definite), or -rank ** if not non-negative definite ** ** If a column is deemed to be redundant, then that diagonal is set to zero. ** ** Terry Therneau */ #include "survS.h" #include "survproto.h" int cholesky3(double **matrix, int n, int m, double *diag, double toler) { double temp; int i,j,k; double eps, pivot; int rank; int n2; int nonneg; n2 = n-m; /* number of full covariates */ nonneg=1; eps =0; for (i=0; i eps) eps = matrix[i][i+m]; eps *= toler; rank =0; /* pivot out the diagonal elements */ for (i=0; i #include "survS.h" #include "survproto.h" void coxscore(Sint *nx, Sint *nvarx, double *y, double *covar2, Sint *strata, double *score, double *weights, Sint *method, double *resid2, double *scratch) { int i,j, k; double temp; int n, nvar; double deaths; int dd; double *time, *status; double *a, *a2; double denom=0, e_denom; double risk; double **covar; double **resid; double hazard, meanwt; double downwt, temp2; double mean; n = *nx; nvar = *nvarx; time = y; status = y+n; a = scratch; a2 = a+nvar; /* ** Set up the ragged array */ covar= dmatrix(covar2, n, nvar); resid= dmatrix(resid2, n, nvar); e_denom=0; deaths=0; meanwt=0; for (i=0; i=0; i--) { if (strata[i]==1) { denom =0; for (j=0; j0 && (i==0 || strata[i-1]==1 || time[i]!=time[i-1])){ /* last obs of a set of tied death times */ if (deaths <2 || *method==0) { hazard = meanwt/denom; for (j=0; j LARGE) return(LARGE); return (x); } survival/src/dmatrix.c0000755000175100001440000000150113070714004014542 0ustar hornikusers/* ** set up the indices so that C code can use x[i][j] notation for R ** matrices. Remember that R sees matrices in column order and C in ** row order, so every reference in the C code will be x[col][row]. ** ** array = pointer to the data ** nrow, ncol = number of rows and colums, from R's point of view. */ #include "survS.h" #include "survproto.h" double **dmatrix(double *array, int nrow, int ncol) { int i; double **pointer; pointer = (double **) ALLOC(ncol, sizeof(double *)); for (i=0; i0){ fdiag[i] = 1/fdiag[i]; /* this line inverts D */ for (j=0; j0) { matrix[i][ii] = 1/matrix[i][ii]; /*this line inverts D */ for (j= (i+1); j #include "survS.h" #include "survproto.h" void agmart(Sint *n, Sint *method, double *start, double *stop, Sint *event, double *score, double *wt, Sint *strata, double *resid) { int i,k; double deaths, denom, e_denom; double hazard, e_hazard; double temp, time; double wtsum; int nused; int person; nused = *n; strata[nused-1] =1; /* Failsafe */ for (i=0; i1: estimate multiple scales (strata) ** strat - if nstrat>0, contains the strata number for each subject ** eps - tolerance for convergence. Iteration continues until the ** relative change in the deviance is <= eps. ** tol_chol- tolerance for Cholesky decomposition ** dist - 1=extreme value, 2=logistic, 3=gaussian, 4=callback ** dexpr - for callback, the expression to be evaluated that evaluates ** the distribution function of the random effect ** rho - for callback, the environment (R) or frame (Splus) in which ** to do evaluations ** ptype - 1= sparse penalties, 2=dense penalties, 1+2 = both, 0=none ** pdiag - 0 = the penalty matrix is diagonal ** nfrail - number of levels of the sparse term (0 = no sparse term) ** fgrp - which frailty group each subject is in ** pexpr1 - for callback, the expression to eval for sparse penalties ** pexpr2 - the expression for dense penalties ** ** Output ** beta - the final coef vector ** iter - the number of iterations consumed ** hmat - the cholesky of the penalized information matrix ** hinv - the cholesky of the inverse of hmat ** hdiag - diagonal portion of hinv ** loglik - the final log-liklihood ** u - the final score vector. Usually =0 at convergence, but ** useful in other cases for a score test. ** flag - success flag 0 =ok ** -1= did not converge ** ** Work arrays ** newbeta(nvar)- always contains the "next iteration" ** u(nvar) - first deriv of the loglik ** JJ = the approx variance matrix J'J, guarranteed non-singular ** ** Notes on hmat: H will be p=(nfrail+ nvar + nstrat) square, but the ** upper left nfrail*nfrail corner is a diagonal matrix. It is stored ** as "hdiag", which "hmat" contains the remaining dense portion. If ** H = LDL' (see cholesky3), then H-inverse = (L-inv)' (Dinv) (L-inv) ** where D is diagonal and L is lower-triangular with ones on the diagonal, ** and L[1:nfrail, 1:nfrail] is the identity. ** The return parts are hmat = L[(nfrail+1):p, 1:p], hinv L-inverse[ same], ** and g=hdiag = D-inverse. See coxpenal.df for more. */ #include "survS.h" #include "survproto.h" SEXP survreg7(SEXP maxiter2, SEXP nvarx, SEXP y, SEXP ny2, SEXP covar2, SEXP wtx, SEXP offset2, SEXP beta2, SEXP nstratx, SEXP stratax, SEXP epsx, SEXP tolx, SEXP dist, SEXP dexpr, SEXP rho, SEXP ptype2, SEXP pdiag2, SEXP nfrail2, SEXP fgrp2, SEXP pexpr1, SEXP pexpr2) { /* local variables */ int i,j; int nvar, nvar2, nvar3, nstrat; int iter; double newlk =0; double (*dolik)(); /* will point to (*dolik) or survregc2 */ double x1, x2, x3, x4; double y1, y2, y3; int golden, goright; double newpen; /* pointers for the data regions of the input arguments */ double **covar; Sint *strat ; double *time2, *time1, *status; double *offset; Sint *fgrp; double *wt; /* copies of the scalar input arguments */ double eps, tol_chol; int n, maxiter, ny; int nfrail, ptype, pdiag; /* Variables allocated in this routine */ double *jdiag, *newbeta, *u; /* variables for the callback code */ SEXP coef1, coef2; double *cptr1=NULL, *cptr2 =NULL; /* stop a gcc warning */ double **JJ; SEXP z; double *zptr = NULL; /* structures and pointers for the returned list object */ SEXP out_iter, out_loglik, out_hmat, out_hinv, out_flag, out_beta; SEXP out_penalty; SEXP out_hdiag, out_u; double *loglik, *usave; double **hmat, **hinv, *beta, *hdiag; double *penalty; SEXP rlist, rlistnames; Sint *iter2, *flag; int nprotect; /* number of PROTECT calls that I have issued */ /* ** The only input arg that is rewritten is beta, so no need to duplicate */ maxiter = asInteger(maxiter2); n = LENGTH(wtx); ny = asInteger(ny2); nvar = asInteger(nvarx); offset = REAL(offset2); nstrat = asInteger(nstratx); strat = INTEGER(stratax); wt = REAL(wtx); eps = asReal(epsx); tol_chol= asReal(tolx); covar = dmatrix(REAL(covar2), n, nvar); nfrail = asInteger(nfrail2); ptype = asInteger(ptype2); pdiag = asInteger(pdiag2); fgrp = INTEGER(fgrp2); /* ** nvar = # of "real" x variables, found in the coefficient matrix ** nvar2= size of the dense portion of hmat = nvar + nstrat ** nvar3= #coefficients = nfrail + nvar2 ** nstrat= # of strata, where 0== fixed sigma */ nvar2 = nvar + nstrat; /* number of coefficients */ nvar3 = nvar2 + nfrail; /* ** Create the output variables */ PROTECT(out_beta = duplicate(beta2)); beta = REAL(out_beta); PROTECT(out_hmat = allocVector(REALSXP, nvar3*nvar2)); hmat = dmatrix(REAL(out_hmat), nvar3, nvar2); PROTECT(out_hinv = allocVector(REALSXP, nvar3*nvar2)); hinv = dmatrix(REAL(out_hinv), nvar3, nvar2); PROTECT(out_hdiag = allocVector(REALSXP, nvar3)); hdiag = REAL(out_hdiag); PROTECT(out_iter = allocVector(INTSXP, 1)); iter2 = INTEGER(out_iter); PROTECT(out_loglik = allocVector(REALSXP, 1)); loglik = REAL(out_loglik); PROTECT(out_flag = allocVector(INTSXP, 1)); flag = INTEGER(out_flag); PROTECT(out_u = allocVector(REALSXP, nvar3)); usave = REAL(out_u); /* the working vector 'u' gets destroyed in chsolve*/ PROTECT(out_penalty= allocVector(REALSXP, 1)); penalty = REAL(out_penalty); nprotect =9; /* Create the scratch vectors ** u = working version of score vector, overwritten with u H-inv during ** Newton steps ** usave = a copy of u, after each Newton step. Returned to the S ** parent routine, and also used to "backtrack" when we need to fail ** over to a Fisher step instead of an NR step */ newbeta = Calloc(LENGTH(beta2) + nvar3 + nfrail + nvar2*nvar3, double); jdiag = newbeta + length(beta2); u = jdiag + nfrail; JJ = dmatrix(u + nvar3, nvar3, nvar2); /* ** fixed scale parameters were tacked onto the end of beta at input ** copy them to to the end of newbeta as well ((*dolik) expects them) */ for (i=nvar; i1) { /* ** There is a penalty on the non-sparse terms ** Create the vector coef2 in the contained data frame ** (pexpr2 is implicitly a function of 'coef2') ** Since scale parameters are never panalized, only the first ** nvar of the coefficients are passed in. */ PROTECT(coef2 = allocVector(REALSXP, nvar)); defineVar(install("coef2"), coef2, rho); cptr2 = REAL(coef2); nprotect++; } /* ** Get the loglik, score, and hessian for the initial parameters */ *loglik = (*dolik)(n, nvar, nstrat, 0, beta, asInteger(dist), strat, offset, time1, time2, status, wt, covar, hmat, JJ, u, dexpr, rho, zptr, nfrail, fgrp, hdiag, jdiag); survpenal(0, nfrail, nvar, hmat, JJ, hdiag, jdiag, u, beta, penalty, ptype, pdiag, pexpr1, cptr1, pexpr2, cptr2, rho); *loglik += *penalty; for (i=0; i y3) { x4 = x3; x3 = x1; x1 = x3 - (x4-x3)/.618; y3 = y1; for (i=0; i y2) { /* toss away the interval from x1 to x2 */ x1=x2; x2=x3; x3 = .618*x4 + .382*x1; y2 =y3; for (i=0; i *loglik || y3 > *loglik) { /* Success - keep the better guess & compute derivatives */ if (y2 > y3) { for (i=0; i 1) *flag= 1000; /* no "non convergence" for 0 or 1 iter */ *iter2 = iter; /* ** Put together the return list */ alldone: *flag = cholesky3(hmat, nvar3, nfrail, hdiag, tol_chol); for (i=0; i>= cmatrix <- function(model, formula, type=c("full", "linear", "linear2") { # If any of the parts I need are missing, then likely the first are # is not a model if (missing(model)) stop("a model argument is required") Terms <- try(terms(model), silent=TRUE) if (class(Terms) =="try-error") stop("the model does not have a terms structure") else Terms <- delete.response(Terms) # y is not needed Tatt <- attributes(Terms) if (missing(formula) || ! is.formula(formula)) stop("a formula argument is required") fterm <- delete.response(terms(formula)) fatt <- attributes(fterm) indx <- match(fatt$term.labels, Tatt$term.labels) if (any(is.na(indx))) { temp <- fatt$term.labels[is.na(indx)] stop("formula component not found ", temp) } # match these up with the columns via the assign attribute assign <- model$assign if (missing(assign)) stop("the model is missing an assign component") if (is.list(assign)) { # old style assign as used in Splus, and still used in coxph assign <- rep(1:length(assign), sapply(assign, length)) } ncoef <- length(assign) whichcol <- which(assign %in% indx) # any coefficients that are NA are ignored whichcol <- whichcol[!is.na(coef(fit))] ntest <- length(whichcol) # Now build the matrix <> # return the result cmat @ Building the contrast matrix is very easy for type=full; it is simply a test of ``are all these coefficients zero''. The ``linear'' is of interest for terms that have more than one column; the two most common cases are a factor variable or a spline. The ``linear2'' form returns a pair of tests, one for the linear and one for the nonlinear part. For non-linear functions such as splines we need some notion of the range of the data, since we want to be linear over the entire range. If the test is for only a single column then all tests are the same. <>= test <- match.arg(test) if (test== "full") { cmat <- matrix(0., nrow= ntest, ncol=ncoef) for (i in 1:ntest) cmat[i, whichcol[i]] <- 1 return(cmat) } # All of the other transformations require a single term, no interactions tlab <- fatt$term.labels if (length(tlab) > 1) stop(test, " tests must be for a single term") # is it a factor? isfac <- (exists(model$xlevels) && !is.na(match(tlab, names(model$xlevels)))) if (test == "pairwise") { if (!isfac) stop("pairwise tests are only valid for categorical predictors") if (is.null(model$contrasts)) stop("model has no contrasts component") # The test is a simple linear one, in the order of the factor cmat <- matrix(0., nrow=1, ncol=coef) cmat[whichcol] <- 1:whichcol if (test == "linear2") { cmat <- list(linear=cmat) @ First are two helper routines, followed by simple contrasts. Formulas are from chapter 5 of Searle. The sums of squares only makes sense within a linear model. <>= gsolve <- function(mat, y, eps=sqrt(.Machine$double.eps)) { # solve using a generalized inverse # this is very similar to the ginv function of MASS temp <- svd(mat, nv=0) dd <- ifelse(temp$d > temp$d[1]*eps, 1/temp$d, 0) dpos <- (dd >0) # all the parentheses save a tiny bit of time if y is a vector drop(temp$u[,dpos] %*%(dd[dpos] * (t(temp$u[,dpos, drop=FALSE]) %*% y))) } qform <- function(var, beta) # quadratic form b' (V-inverse) b sum(beta * gsolve(var, beta)) cfun <- function(cmat, fit) { varmat <- vcov(fit) if (class(fit) == "lm") sigma2 <- summary(fit)$sigma^2 else sigma2 <- 1 # for the Cox model case beta <- coef(fit) if (!is.matrix(cmat)) cmat <- matrix(cmat, nrow=1) if (ncol(cmat) != length(beta)) stop("wrong dimension for contrast") estimate <- drop(cmat %*% beta) #vector of contrasts ss <- qform(cmat %*% varmat %*% t(cmat), estimate) *sigma2 list(estimate=estimate, ss=ss, var=drop(cmat %*% varmat %*% t(cmat))) } @ Here is the primary pair of functions. The contrast function is simply a way to call the yates function with population=``none''. In that case the method argument has no effect. The population can be one of the keywords below, or it can be a data set. <>= contrast <- function(object, test, population="none", ...) yates(object, test, population, ...) yates <- function(object, test, population=c("none", "data", "uniform", "sas"), method=c("direct", "glm", "nstt"), ...) { Terms <- delete.response(terms(object)) beta <- coef(object) vmat <- vcov(object) assign <- object$assign term.label <- attr(Terms, "term.labels") # a function that allows them to refer to terms by name or by number matchterm <- function(x) { nlab <- length(term.label) index <- pmatch(x, c(term.label, 1:nlab), nomatch=0) index <- ifelse(index > nlab, index-nlab, index) c("", term.label)[1+index] } # pick up any labels on the contrast argument if (!missing(contrast)) { if (!is.list(contrast)) contrast <- list(contrast) cname <- matchterm(names(contrast)) } else cname <- NULL if (missing(term)) { if (length(cname) ==0) term <- unique(assign) } else { # terms were specified if (is.formula(term)) { temp <- delete.response(terms(term)) term <- temp$term.labels } if (!is.numeric(term) && !is.character(term)) stop("invalid 'term' argument") tname <- matchterm(term) if (any(tname=="")) stop(paste("term", paste(term.labels[tname==""], collaspe=" "), "not found in the model")) if (length(cname)) cname <- match.arg(cname, tname) } else stop("invalid 'term' argument") } term <- unique(term) #in case of duplicates in the user argument @ Here is first function for simple contrasts. We first make sure that the object is a model fit and that various helper function return the bits we need. <>= contrast <- function(object, test, ...) Terms <- delete.response(terms(object)) beta <- coef(object) vmat <- vcov(object) assign <- object$assign term.label <- attr(Terms, "term.labels") # a function that allows them to refer to terms by name or by number matchterm <- function(x) { nlab <- length(term.label) index <- pmatch(x, c(term.label, 1:nlab), nomatch=0) index <- ifelse(index > nlab, index-nlab, index) c("", term.label)[1+index] } # pick up any labels on the contrast argument if (!missing(contrast)) { if (!is.list(contrast)) contrast <- list(contrast) cname <- matchterm(names(contrast)) } else cname <- NULL if (missing(term)) { if (length(cname) ==0) term <- unique(assign) } else { # terms were specified if (is.formula(term)) { temp <- delete.response(terms(term)) term <- temp$term.labels } if (!is.numeric(term) && !is.character(term)) stop("invalid 'term' argument") tname <- matchterm(term) if (any(tname=="")) stop(paste("term", paste(term.labels[tname==""], collaspe=" "), "not found in the model")) if (length(cname)) cname <- match.arg(cname, tname) } else stop("invalid 'term' argument") } term <- unique(term) #in case of duplicates in the user argument term if (!missing(contrast) && !missing(population)) stop("only one of 'contrast' or 'population' can be specified") <> <> class(rval) <- "yates" rval } @ If a contast argument was specified if should be a vector, matrix, or list. If more than 1 term is requested it must be a list, each element of which is a vector or matrix. Check all elements for being the right length. It is possible to simply name the contrasts and skip the term argument. <>= if (!missing(contrast)) { if (length(term) ==1 && !is.list(contrast)) contrast <- list(contrast) # match each contrast to the right term cname <- names(contrast) if (is.null(cname)) cname <- term.labels[term] else { if (an @ The yates function is survival/noweb/survfitKM.Rnw0000644000175100001440000004231013026501446015700 0ustar hornikusers\subsection{Kaplan-Meier} Note -- this chunk is in development. We still use ../R/survfitKM.S This routine has been rewritten more times than any other in the package, as we trade off simplicty of the code with execution speed. This version does all of the oranizational work in S and calls a C routine for each separate curve. The first did everything in C but was too hard to maintain and the most recent did nearly everything in S; introduction of robust variance prompted a movement of more of the code into C since that is computationally intensive. <>= survfitKM <- function(x, y, casewt=rep(1,length(x)), type=c('kaplan-meier', 'fleming-harrington', 'fh2'), error=c('greenwood', "aalen", "robust", "tsiatis"), se.fit=TRUE, conf.int= .95, conf.type=c('log', 'log-log', 'plain', 'none'), conf.lower=c('usual', 'peto', 'modified'), start.time, new.time) { type <- match.arg(type) method <- match(type, c("kaplan-meier", "fleming-harrington", "fh2")) if (missing(error) & any(casewt != floor(casewt)) error <- 'robust' else error <- match.arg(error) error.int <- match(error, c("greenwood", "aalen", "robust", "tsiatis")) if (error.int==4) error.int <- 2 # these are synonyms conf.type <- match.arg(conf.type) conf.lower<- match.arg(conf.lower) if (is.logical(conf.int)) { # A common error is for users to use "conf.int = FALSE" # it's illegal, but allow it if (!conf.int) conf.type <- "none" conf.int <- .95 } if (!is.Surv(y)) stop("y must be a Surv object") if (!is.factor(x)) stop("x must be a factor") if (attr(y, 'type') != 'right' && attr(y, 'type') != 'counting') stop("Can only handle right censored or counting data") ny <- ncol(y) # Will be 2 for right censored, 3 for counting xlev <- levels(x) # Will supply names for the curves x <- as.numeric(x) # keep only the levels # Allow "new.time" as a synonym for start.time if (missing(start.time) && !missing(new.time)) start.time <- new.time if (!missing(start.time)) { n.all <- c(table(x)) # remember the original data size # remove any obs whose end time is <= start.time keep <- (y[,ny-1] >= start.time) if (all(keep==FALSE)) stop(paste("start.time =", start.time, "is greater than all time points.")) x <- x[keep] y <- y[keep,,drop=FALSE] #make sure y remains a matrix casewt <- casewt[keep] } n.used <- as.vector(table(x)) # This is for the printout nstrat <- length(n.used) # number of curves <> <> } @ The computation creates a list with one survival curve per element. Since the number of curves is usually small the outer "for" loop is no particular worry. One of the odder things we do is to use as.numeric(factor(y)) as the response variable instead of y itself. The problem is that if two times are within machine precision then [[unique]], [[factor]], [[table]] and [[==]] can all do different things. We have been burned by this in the past. <>= survlist <- vector("list", nstrat) xint <- as.numeric(x) for (i in 1:nstrat) { who <- which(xint==i) if (ny==2) { ftime <- factor(y[who,1]) indx <- order(ftime, -status[who]) #censors after deaths survlist[[i]] <- c(list(time=type.convert(levels(ftime), as.is=TRUE, dec=getOption("OutDec")), .Call("survkm1", as.integer(ftime[indx]), as.integer(y[who[indx],2]), as.double(wt[who[indx]]), method, error, length(levels(ftime))) } else { ftime <- factor(y[who, 1:2]) # Be careful that no one person has overlapping time intervals if (error==4) { <> } survlist[[i]] <- c(list(time=as.numeric(levels(ftime))), .Call("survkm2", as.integer(ftime), as.integer(y[who,3]), method, error, length(levels(ftime)), id[who])) } } @ indx <- order(id, Y[,2]) #ordered event times within subject indx1 <- c(NA, indx) #a pair of lagged indices indx2 <- c(indx, NA) same <- (id[indx1] == id[indx2] & !is.na(indx1) & !is.na(indx2)) #indx1, indx2= same id? if (any(same & X[indx1] != X[indx2])) { who <- 1 + min(which(same & X[indx1] != X[indx2])) stop("subject is in two different groups, id ", (id[indx1])[who]) } if (any(same & Y[indx1,2] != Y[indx2,1])) { who <- 1 + min(which(same & Y[indx1,2] != Y[indx2,1])) stop("gap in follow-up, id ", (id[indx1])[who]) } if (any(Y[,1] == Y[,2])) stop("cannot have start time == stop time") if (any(same & Y[indx1,3] == Y[indx2,3] & Y[indx1,3] !=0)) { who <- 1 + min(which(same & Y[indx1,1] != Y[indx2,2])) stop("subject changes to the same state, id ", (id[indx1])[who]) } if (any(same & weights[indx1] != weights[indx2])) { who <- 1 + min(which(same & weights[indx1] != weights[indx2])) stop("subject changes case weights, id ", (id[indx1])[who]) } Now for the real work using C routines. My standard for a variable named ``zed'' is to use zed2 for the S object and zed for the data part of the object; the latter is what the C code works with. <>= /* -*- c -*- */ #include #include "survS.h #include "survproto.h" SEXP survkm1(SEXP itime2, SEXP status2, SEXP wt2, SEXP method2, SEXP error2, SEXP ntime2 { int i, j, k; int n; /* number of observations */ /* Data passed in */ int ntime; /* number of unique times = length of output vectors */ int method, error; int *itime, *status; double *wt; /* ** output vectors */ SEXP nrisk2, nevent2, ncensor2, surv, cumhaz; double *nrisk, *nevent, *ncensor, *surv, *cumhaz; SEXP ievent2, icensor2; /* integer counts, in case of weights */ int *ievent, *icensor; const char *rnames[]={"nrisk", "nevent", "ncensor", "surv", "cumhaz", "std", "ievent", "icensor", ""}; /* ** Get copies of the input data */ ntime = asInteger(ntime2); method= asInteger(method2); error = asInteger(error2); itime = INTEGER(itime2); status= INTEGER(status2); wt = REAL(wt2); if (method==4) id = INTEGER(id2); n = LENGTH(itime); /* ** create output objects */ PROTECT(nrisk2 = allocVector(REALSXP, ntime)); nrisk = REAL(nrisk2); PROTECT(nevent2 = allocVector(REALSXP, ntime)); nevent = REAL(nevent2); PROTECT(ncensor2 = allocVector(REALSXP, ntime)); ncensor = REAL(ncensor2); PROTECT(surv2 = allocVector(REALSXP, ntime)); surv = REAL(surv2); PROTECT(cumhaz2 = allocVector(REALSXP, ntime)); cumhaz = REAL(cumhaz2); PROTECT(ievent2 = allocVector(INTSXP, ntime)); ievent = INTEGER(ivent2); PROTECT(icensor2 = allocVector(INTSXP, ntime)); icensor = INTEGER(icensor2); if (error=0) PROTECT(var2 = allocVector(REALSXP, 1));/* no std wanted */ else PROTECT(var2= allocVector(REALSXP, ntime)); var = REAL(var2); /* ** first pass, from largest time to smallest, count up ** number events, number at risk, number censored */ i = n -1; temp =0; /* accumulates number at risk */ for (j=ntime-1; j>=0; j--) { nevent[j] = 0; ievent[j]=0; ncensor[j]= 0; icensor[j]=0; ctime = itime[i]; /* current time of interest */ while(itime[i]== ctime && i>=0) { temp += wt[i]; if (status[i]==1){ nevent[j] += wt[i]; ievent[j]++; } else{ ncensor[j] += wt[i]; icensor[j]++; } i--; } nrisk[j] = temp; } /* ** Second pass, from smallest time to largest, accumulate ** the cumulative hazard and survival */ <> if (error >0) { <> } /* ** create the output structure */ PROTECT(rlist = mkNamed(VEXSXP, rnames)); SET_VECTOR_ELT(rlist, 0, nrisk2); SET_VECTOR_ELT(rlist, 1, nevent2); SET_VECTOR_ELT(rlist, 2, ncensor2); SET_VECTOR_ELT(rlist, 3, surv2); SET_VECTOR_ELT(rlist, 4, cumhaz2); SET_VECTOR_ELT(rlist, 5, var2); SET_VECTOR_ELT(rlist, 1, ievent2); SET_VECTOR_ELT(rlist, 2, icensor2); UNPROTECT(9); /*once there is NO chance of a memory allocation, we let go*/ return(rlist); } @ Let $Y_i(t)=1$ if observation $i$ is at risk at time $t$ and 0 otherwise, $s_i(t)$ be 1 at the point of an event for subject $i$ (status of 1), $w_i$ be the case weight for observation $i$, and $u_j$ $j=1,2, \ldots$ be the unique death times. Define \begin{center} \begin{tabular}{r@{=}rl} $r_j$& $\sum Y_i(u_j) w_i$ & weighted number at risk \\ $d_j$& $\sum s_i(u_j) w__i$ & weighted number of events \\ $c_j)$& $\sum (Y_i(u_j)-s_i(u_j)) w_i$ & weighted number of censored values \end{tabular} \end{center} For (start, stop] data there will also be $e_j$ which counts the number of subjects who enter at time $t$. Also, let $f_j$ be the total number of failures (deaths) at time $t$, not weighted. The cumulative hazard estimates are the Nelson-Aalen-Breslow (same estimate, three different papers in three places) or the Fleming-Harrington. \begin{align*} \Lambda_A(t) &\ \sum{u_j \le t} d_j/r_j \\ \Lambda_{FH}(t) &= \sum{u_j \le t} \frac{d_j} {(1/f_j) \sum_{k=0}^{f_j-1} (r_j - kd_j/f_j)} \end{align*} To understand the Fleming-Harrington estimate, suppose that at some time point we had three deaths out of 10 at risk. The Aalen estimate gives a hazard estimate of 3/10. The FH estimate assumes that the deaths didn't actually all happen at once, even though rounding in the data collection process makes it appear that way, so the better estimate is 1/10 + 1/9 + 1/8. The third person to die, whoever that was, would have had only 8 at risk when thier event happened. The estimate of survival is either the Kaplan-Meier or the exponential of the hazard. \begin{equation*} KM(t) = \prod_{u_j \le t} \frac{r_j - d_j}{r_j} \end{equation*} <>= tempc =0; /*accumulates the chaz */ temps =1; /*accumulates the survival */ tempv =0; /*accumulates the variance */ if (method==1) { /*KM survival and Aalen hazard, 99% of the calls */ for (j=0; j0) { temps *= (nrisk[j] - nevent[j])/nevent[j]; tempc += nevent[j]/nrisk[j]; } surv[j] = temps; chaz[j] = tempc; } } else if (method==2) { /*Aalen hazard and exponent for survival */ for (j=0; j0) tempc += nevent[j]/nrisk[j]; chaz[j] = tempc; surv[j] = exp(-tempc); } } else { /* FH hazard, rarest call */ for (j=0; j0) { temp <- nevent[j]/ievent[j]; for (k=0; i>= temp =0; if (error==1) { /* Greenwood */ for (j=0; j0) temp += nevent[j]/(nrisk[j] * (nrisk[j]-nevent[j])); var[j] = temp; } else if (error==2) { /* Aalen */ for (j=0; j0) temp += nevent[j]/(nrisk[j] * nrisk[j]); var[j] = temp; } else { inf = (double *) Ralloc(n, sizeof(double)); /* scratch space */ for (i=0; i0) { /*nothing changes at non-event times */ ctime = time[i]; /*current event time */ if (method <3) { /* variance of the Aalen hazard */ for (;i>= /* -*- c -*- */ #include #include "survS.h #include "survproto.h" SEXP survkm2(SEXP itime2, SEXP status2, SEXP wt2, SEXP method2, SEXP error2, SEXP ntime2, SEXP id2, SEXP nid2, SEXP sort1) { int i, j, k; int n; /* number of observations */ int nid; /* number of unique id values */ /* Data passed in */ int ntime; /* number of unique times = length of output vectors */ int method, error; int *start, *stop, *status, *id; double *wt; /* ** output vectors */ SEXP nrisk2, nevent2, ncensor2, surv, cumhaz; double *nrisk, *nevent, *ncensor, *surv, *cumhaz; SEXP ievent2, icensor2; /* integer counts, in case of weights */ int *ievent, *icensor; const char *rnames[]={"nrisk", "nevent", "ncensor", "surv", "cumhaz", "std", "ievent", "icensor", ""}; /* ** Get copies of the input data */ ntime = asInteger(ntime2); n = LENGTH(itime); nid= asInteger(nid); method= asInteger(method2); error = asInteger(error2); start = INTEGER(itime2); stop = start + n; status= INTEGER(status2); wt = REAL(wt2); if (method==4) id = INTEGER(id2); n = LENGTH(itime); id = INTEGER(id2); nid= asInteger(nid); /* ** create output objects */ PROTECT(nrisk2 = allocVector(REALSXP, ntime)); nrisk = REAL(nrisk2); PROTECT(nevent2 = allocVector(REALSXP, ntime)); nevent = REAL(nevent2); PROTECT(ncensor2 = allocVector(REALSXP, ntime)); ncensor = REAL(ncensor2); PROTECT(surv2 = allocVector(REALSXP, ntime)); surv = REAL(surv2); PROTECT(cumhaz2 = allocVector(REALSXP, ntime)); cumhaz = REAL(cumhaz2); PROTECT(ievent2 = allocVector(INTSXP, ntime)); ievent = INTEGER(ivent2); PROTECT(icensor2 = allocVector(INTSXP, ntime)); icensor = INTEGER(icensor2); if (error=0) PROTECT(var2 = allocVector(REALSXP, 1));/* no std wanted */ else PROTECT(var2= allocVector(REALSXP, ntime)); var = REAL(var2); /* ** first pass, from largest time to smallest, count up ** number events, number at risk, number censored */ i = n -1; temp =0; /* accumulates number at risk */ for (j=ntime-1; j>=0; j--) { nevent[j] = 0; ievent[j]=0; ncensor[j]= 0; icensor[j]=0; ctime = itime[i]; /* current time of interest */ while(itime[i]== ctime && i>=0) { temp += wt[i]; if (status[i]==1){ nevent[j] += wt[i]; ievent[j]++; } else{ ncensor[j] += wt[i]; icensor[j]++; } i--; } nrisk[j] = temp; } /* ** Second pass, from smallest time to largest, accumulate ** the cumulative hazard and survival */ <> if (error >0) { <> } /* ** create the output structure */ PROTECT(rlist = mkNamed(VEXSXP, rnames)); SET_VECTOR_ELT(rlist, 0, nrisk2); SET_VECTOR_ELT(rlist, 1, nevent2); SET_VECTOR_ELT(rlist, 2, ncensor2); SET_VECTOR_ELT(rlist, 3, surv2); SET_VECTOR_ELT(rlist, 4, cumhaz2); SET_VECTOR_ELT(rlist, 5, var2); SET_VECTOR_ELT(rlist, 1, ievent2); SET_VECTOR_ELT(rlist, 2, icensor2); UNPROTECT(9); /*once there is NO chance of a memory allocation, we let go*/ return(rlist); } @ survival/noweb/Makefile0000644000175100001440000000371413070714004014716 0ustar hornikusersPARTS = main.Rnw \ coxph.Rnw \ exact.nw \ agreg.Rnw \ coxsurv.Rnw \ coxsurv2.Rnw \ finegray.Rnw \ predict.coxph.Rnw \ concordance.Rnw \ survexp.Rnw \ pyears.Rnw pyears2.Rnw \ residuals.survreg.Rnw \ survfit.Rnw \ survfitCI.Rnw \ msurv.nw \ survfitms.Rnw \ plot.Rnw \ statefig.Rnw\ tmerge.Rnw\ tail # coxdetail.nw SFUN = agreg.fit.R \ agsurv.R \ coxph.R \ finegray.R \ model.matrix.coxph.R \ plot.survfit.R \ predict.coxph.R \ pyears.R \ print.pyears.R \ residuals.survreg.R\ statefig.R \ survConcordance.R \ survConcordance.fit.R \ survexp.R \ survfit.R \ survfitCI.R \ survfit.coxph.R \ survfitcoxph.fit.R \ survfitms.R\ tmerge.R CFUN = agsurv4.c agsurv5.c concordance1.c coxcount1.c \ agfit4.c \ coxexact.c \ survfitci.c # coxdetail2.c RDIR = ../R RFUN = $(SFUN:%=$(RDIR)/%) CFUN2= $(CFUN:%=../src/%) DOCDIR= ../inst/doc all: noweb.sty doc fun doc: code.pdf code.pdf: code.tex noweb.sty pdflatex code.tex pdflatex code.tex code.nw: $(PARTS) cat $(PARTS) > code.nw code.tex: code.nw echo "library(noweb); noweave('code.nw')" | R --slave $(SFUN): code.nw $(CFUN): code.nw $(CFUN2): code.nw $(RFUN): code.nw .PHONY: fun clean doc all fun: $(RFUN) $(CFUN2) noweb.sty test: $(RFUN) echo $(RFUN) %.R: echo "# Automatically generated from the noweb directory" > $@ echo "require(noweb); notangle('code.nw', target='$(*F)', out='zz')" | R --slave cat zz >> $@ rm zz %.S: echo "# Automatically generated from the noweb directory" > $@ echo "require(noweb); notangle('code.nw', target='$(*F)', out='zz')" | R --slave cat zz >> $@ rm zz %.c: echo "/* Automatically generated from the noweb directory */" > $@ echo "require(noweb); notangle('code.nw', target='$(*F)', out='zz')" | R --slave cat zz >> $@ rm zz clean: -rm code.nw code.log code.aux code.toc code.tex code.bbl code.blg code.out -rm noweb.sty noweb.sty: echo 'library(noweb); data(noweb); cat(noweb.sty, sep="\n", file="noweb.sty")' | R --slave survival/noweb/agreg.Rnw0000644000175100001440000010062113062563353015040 0ustar hornikusers\subsection{Anderson-Gill fits} When the survival data set has (start, stop] data a couple of computational issues are added. A primary one is how to do this compuation efficiently. At each event time we need to compute 3 quantities, each of them added up over the current risk set. \begin{itemize} \item The weighted sum of the risk scores $\sum w_i r_i$ where $r_i = \exp(\eta_i)$ and $\eta_i = x_{i1}\beta_1 + x_{i2}\beta_2 +\ldots$ is the current linear predictor. \item The weighted mean of the covariates $x$, with weight $w_i r_i$. \item The weighted variance-covariance matrix of $x$. \end{itemize} The current risk set at some event time $t$ is the set of all (start, stop] intervals that overlap $t$, and are part of the same strata. The round/square brackets in the prior sentence are important: for an event time $t=20$ the interval $(5,20]$ is considered to overlap $t$ and the interval $(20,55]$ does not overlap $t$. Our routine for the simple right censored Cox model computes these efficiently by keeping a cumulative sum. Starting with the longest survival move backwards through time, adding and subtracting subject from the sum as we go. The code below creates two sort indices, one orders the data by reverse stop time and the other by reverse start time, each within strata. For the first events are sorted before censors for a computational reason detailed later. The fit routine is called by the coxph function with arguments \begin{description} \item[x] matrix of covariates \item[y] three column matrix containing the start time, stop time, and event for each observation \item[strata] for stratified fits, the strata of each subject \item[offset] the offset, usually a vector of zeros \item[init] initial estimate for the coefficients \item[control] results of the coxph.control function \item[weights] case weights, often a vector of ones. \item[method] how ties are handled: 1=Breslow, 2=Efron \item[rownames] used to label the residuals \end{description} <>= agreg.fit <- function(x, y, strata, offset, init, control, weights, method, rownames) { n <- nrow(y) nvar <- ncol(x) event <- y[,3] if (all(event==0)) stop("Can't fit a Cox model with 0 failures") # Sort the data (or rather, get a list of sorted indices) # For both stop and start times, the indices go from last to first if (length(strata)==0) { sort.end <- order(-y[,2]) -1L #indices start at 0 for C code sort.start<- order(-y[,1]) -1L newstrat <- n } else { sort.end <- order(strata, -y[,2]) -1L sort.start<- order(strata, -y[,1]) -1L newstrat <- cumsum(table(strata)) } if (missing(offset) || is.null(offset)) offset <- rep(0.0, n) if (missing(weights)|| is.null(weights))weights<- rep(1.0, n) else if (any(weights<=0)) stop("Invalid weights, must be >0") else weights <- as.vector(weights) if (is.null(nvar) || nvar==0) { # A special case: Null model. Just return obvious stuff # To keep the C code to a small set, we call the usual routines, but # with a dummy X matrix and 0 iterations nvar <- 1 x <- matrix(as.double(1:n), ncol=1) #keep the .C call happy maxiter <- 0 nullmodel <- TRUE if (length(init) !=0) stop("Wrong length for inital values") init <- 0.0 #dummy value to keep a .C call happy (doesn't like 0 length) } else { nullmodel <- FALSE maxiter <- control$iter.max if (is.null(init)) init <- rep(0., nvar) if (length(init) != nvar) stop("Wrong length for inital values") } # the returned value of agfit$coef starts as a copy of init, so make sure # is is a vector and not a matrix; as.double suffices. # Solidify the storage mode of other arguments storage.mode(y) <- storage.mode(x) <- "double" storage.mode(offset) <- storage.mode(weights) <- "double" storage.mode(newstrat) <- "integer" agfit <- .Call(Cagfit4, y, x, newstrat, weights, offset, as.double(init), sort.start, sort.end, as.integer(method=="efron"), as.integer(maxiter), as.double(control$eps), as.double(control$toler.chol), as.integer(1)) # internally rescale <> <> } @ Upon return we need to clean up three simple things. The first is the rare case that the agfit routine failed. These cases are rare, usually involve an overflow or underflow, and we encourage users to let us have a copy of the data when it occurs. (They end up in the \code{fail} directory of the library.) The second is that if any of the covariates were redudant then this will be marked by zeros on the diagonal of the variance matrix. Replace these coefficients and their variances with NA. The last is to post a warning message about possible infinite coefficients. The algorithm for determining this is unreliable, unfortunately. Sometimes coefficients are marked as infinite when the solution is not tending to infinity (usually associated with a very skewed covariate), and sometimes one that is tending to infinity is not marked. Que sera sera. Don't complain if the user asked for only one iteration; they will already know that it has not converged. <>= var <- matrix(agfit$imat,nvar,nvar) coef <- agfit$coef if (agfit$flag[1] < nvar) which.sing <- diag(var)==0 else which.sing <- rep(FALSE,nvar) if (maxiter >1) { infs <- abs(agfit$u %*% var) if (any(!is.finite(coef)) || any(!is.finite(var))) stop("routine failed due to numeric overflow.", "This should never happen. Please contact the author.") if (agfit$iter > maxiter) warning("Ran out of iterations and did not converge") else { infs <- ((infs > control$eps) & infs > control$toler.inf*abs(coef)) if (any(infs)) warning(paste("Loglik converged before variable ", paste((1:nvar)[infs],collapse=","), "; beta may be infinite. ")) } } @ The last of the code is very standard. Compute residuals and package up the results. <>= lp <- as.vector(x %*% coef + offset - sum(coef * colMeans(x))) score <- as.double(exp(lp)) resid <- .Call(Cagmart3, y, score, weights, newstrat, cbind(sort.end, sort.start), as.integer(method=='efron')) names(resid) <- rownames if (nullmodel) { list(loglik=agfit$loglik[2], linear.predictors = offset, residuals = resid, method= c("coxph.null", 'coxph') ) } else { names(coef) <- dimnames(x)[[2]] if (maxiter > 0) coef[which.sing] <- NA # always leave iter=0 alone flag <- agfit$flag names(flag) <- c("rank", "rescale", "step halving") concordance <- survConcordance.fit(y, lp, strata, weights) list(coefficients = coef, var = var, loglik = agfit$loglik, score = agfit$sctest, iter = agfit$iter, linear.predictors = as.vector(lp), residuals = resid, means = colMeans(x), concordance = concordance, first = agfit$u, info = flag, method= 'coxph') } @ The details of the C code contain the more challenging part of the computations. It starts with the usual dull stuff. My standard coding style for a variable zed to to use [[zed2]] as the variable name for the R object, and [[zed]] for the pointer to the contents of the object, i.e., what the C code will manipulate. For the matrix objects I make use of ragged arrays, this allows for reference to the i,j element as \code{cmat[i][j]} and makes for more readable code. <>= #include #include "survS.h" #include "survproto.h" SEXP agfit4(SEXP surv2, SEXP covar2, SEXP strata2, SEXP weights2, SEXP offset2, SEXP ibeta2, SEXP sort12, SEXP sort22, SEXP method2, SEXP maxiter2, SEXP eps2, SEXP tolerance2, SEXP doscale2) { int i,j,k, person; int indx1, istrat, p, p1; int nrisk; int nused, nvar; int rank, rank2, fail; double **covar, **cmat, **imat; /*ragged array versions*/ double *a, *oldbeta; double *scale; double *a2, **cmat2; double *eta; double denom, zbeta, risk; double dtime; double temp, temp2; double newlk =0; int halving; /*are we doing step halving at the moment? */ double tol_chol, eps; double meanwt; int deaths; double denom2, etasum; int *keep; /* marker for useless obs */ /* inputs */ double *start, *tstop, *event; double *weights, *offset; int *sort1, *sort2, maxiter; int *strata, nstrat; double method; /* saving this as double forces some double arithmetic */ int doscale; /* returned objects */ SEXP imat2, beta2, u2, loglik2; double *beta, *u, *loglik; SEXP sctest2, flag2, iter2; double *sctest; int *flag, *iter; SEXP rlist; static const char *outnames[]={"coef", "u", "imat", "loglik", "sctest", "flag", "iter", ""}; int nprotect; /* number of protect calls I have issued */ /* get sizes and constants */ nused = nrows(covar2); nvar = ncols(covar2); method= asInteger(method2); eps = asReal(eps2); tol_chol = asReal(tolerance2); maxiter = asInteger(maxiter2); doscale = asInteger(doscale2); nstrat = LENGTH(strata2); /* input arguments */ start = REAL(surv2); tstop = start + nused; event = tstop + nused; weights = REAL(weights2); offset = REAL(offset2); sort1 = INTEGER(sort12); sort2 = INTEGER(sort22); strata = INTEGER(strata2); /* ** scratch space ** nvar: a, a2, oldbeta, scale ** nvar*nvar: cmat, cmat2 ** nused: eta, keep */ eta = (double *) R_alloc(nused + 4*nvar + 2*nvar*nvar, sizeof(double)); a = eta + nused; a2= a + nvar; scale = a2 + nvar; oldbeta = scale + nvar; keep = (int *) R_alloc(nused, sizeof(int)); /* ** Set up the ragged arrays ** covar2 might not need to be duplicated, even though ** we are going to modify it, due to the way this routine was ** was called. In this case NAMED(covar2) will =0 */ PROTECT(imat2 = allocVector(REALSXP, nvar*nvar)); nprotect =1; if (NAMED(covar2)>0) { PROTECT(covar2 = duplicate(covar2)); nprotect++; } covar= dmatrix(REAL(covar2), nused, nvar); imat = dmatrix(REAL(imat2), nvar, nvar); cmat = dmatrix(oldbeta+ nvar, nvar, nvar); cmat2= dmatrix(oldbeta+ nvar + nvar*nvar, nvar, nvar); /* ** create the output structures */ PROTECT(rlist = mkNamed(VECSXP, outnames)); nprotect++; beta2 = SET_VECTOR_ELT(rlist, 0, duplicate(ibeta2)); beta = REAL(beta2); u2 = SET_VECTOR_ELT(rlist, 1, allocVector(REALSXP, nvar)); u = REAL(u2); SET_VECTOR_ELT(rlist, 2, imat2); loglik2 = SET_VECTOR_ELT(rlist, 3, allocVector(REALSXP, 2)); loglik = REAL(loglik2); sctest2 = SET_VECTOR_ELT(rlist, 4, allocVector(REALSXP, 1)); sctest = REAL(sctest2); flag2 = SET_VECTOR_ELT(rlist, 5, allocVector(INTSXP, 3)); flag = INTEGER(flag2); for (i=0; i<3; i++) flag[i]=0; iter2 = SET_VECTOR_ELT(rlist, 6, allocVector(INTSXP, 1)); iter = INTEGER(iter2); /* ** Subtract the mean from each covar, as this makes the variance ** computation much more stable. The mean is taken per stratum, ** the scaling is overall. */ if (nvar==1) doscale =0; /* scaling has no impact, so skip it */ for (i=0; i0) temp = temp2/temp; /* 1/scale */ else temp = 1.0; /* rare case of a constant covariate */ scale[i] = temp; for (person=0; person> <> <> } @ As we walk through the risk sets observations are both added and removed from a set of running totals. We have 6 running totals: \begin{itemize} \item sum of the weights, denom = $\sum w_i r_i$ \item totals for each covariate a[j] = $\sum w_ir_i x_{ij}$ \item totals for each covariate pair cmat[j,k]= $\sum w_ir_i x_{ij} x_{ik}$ \item the same three quantities, but only for times that are exactly tied with the current death time, named denom2, a2, cmat2. This allows for easy compuatation of the Efron approximation for ties. \end{itemize} We have to be careful to never subtract out an observation before it is added in, as the `number at risk' counter could become zero when it really should not be so; certain subtotals would then be inappropriately zeroed. The algorithm moves forward to the next unique ending time, removes old observations, and then adds new ones. Observations that are not part of any risk set add unnecessary noise since they will be added and then subtracted from all the totals, but the intermediate values are never used. If said observation had a large risk score this could be exceptionally bad. We do a first pass to mark them in the \code{keep} vector. For most sensible input all the elements of \code{keep} will be 1= true, but survSplit can create observations that are not used. <>= indx1 =0; person =0; for (k=0; k dtime. When survSplit was used to create a data set, this will often remove all. If so we can rezero temporaries and regain precision. \item Add new observations to the risk set and to the death counts. \end{enumerate} <>= for (person=0; person> /* ** add any new subjects who are at risk ** denom2, a2, cmat2, meanwt and deaths count only the deaths */ denom2= 0; meanwt =0; deaths=0; for (i=0; i0) { nrisk++; etasum += eta[p]; denom += risk; for (i=0; i> <> } } /* end of accumulation loop */ @ The last step in the above loop adds terms to the loglik, score and information matrices. Assume that there were 3 tied deaths. The difference between the Efron and Breslow approximations is that for the Efron the three tied subjects are given a weight of 1/3 for the first, 2/3 for the second, and 3/3 for the third death; for the Breslow they get 3/3 for all of them. Note that \code{imat} is symmetric, and that the cholesky routine will utilize the upper triangle of the matrix as input, using the lower part for its own purposes. The inverse from \code{chinv} is also in the upper triangle. <>= /* ** Add results into u and imat for all events at this time point */ if (method==0 || deaths ==1) { /*Breslow */ denom += denom2; newlk -= meanwt*log(denom); /* sum of death weights*/ for (i=0; i>= /* ** subtract out the subjects whose start time is to the right ** If everyone is removed reset the totals to zero. (This happens when ** the survSplit function is used, so it is worth checking). */ for (; indx1> } @ The next bit of code exists for the sake of rather rare data sets. Assume that there is a time dependent covariate that rapidly climbs in such a way that the eta gets large but the range of eta stays modest. An example would be something like ``payments made to date'' for a portfolio of loans. Then even though the data has been centered and the global mean is fine, the current values of eta are outrageous with respect to the exp function. Since replacing eta with (eta -c) for any c does not change the likelihood, do it. Unfortunately, we can't do this once and for all: this is a step that will occur at least twice per iteration for those rare cases, e.g., eta is too small at early times and too large at late ones. I've seen this issue in about 1 data set per decade, by the way. <>= /* ** We must avoid overflow in the exp function (~750 on Intel) ** and want to act well before that, but not take action very often. ** One of the case-cohort papers suggests an offset of -100 meaning ** that etas of 50-100 can occur in "ok" data, so make it larger ** than this. ** If the range of eta is more then log(1e16) = 37 then the data is ** hopeless: some observations will have effectively 0 weight. Keeping ** the mean sensible suffices to keep the max in check for all other * data sets. */ if (fabs(etasum/nrisk) > 200) { flag[1]++; /* a count, for debugging/profiling purposes */ temp = etasum/nrisk; for (i=0; i>= /* First iteration, which has different ending criteria */ <> loglik[0] = newlk; /* save the loglik for iteration zero */ loglik[1] = newlk; /* Calculate the score test */ for (i=0; i>= /* main loop */ halving =0 ; /* =1 when in the midst of "step halving" */ fail =0; /* iteration 1 is never marked as a failure */ for (*iter=1; *iter<= maxiter; (*iter)++) { R_CheckUserInterrupt(); /* be polite -- did the user hit cntrl-C? */ if (*iter >1) { /* on iteration 1 the cholesky has already been done */ rank2 = cholesky2(imat, nvar, tol_chol); /* Are we done? */ fail = isnan(newlk) + isinf(newlk) + abs(rank-rank2); if (fail ==0 && halving ==0 && fabs(1-(loglik[1]/newlk)) <= eps) break; } /* Update coefficients */ if (fail >0 || newlk < loglik[1]) { /*never true on iteration 1 */ /* ** The routine has not made progress past the last good value. */ halving =1; flag[2]++; for (i=0; i> } /*return for another iteration */ @ Save away the final bits, compute the inverse of imat and symmetrize it, release memory and return. If the routine did not converge (iter== maxiter), then the cholesky routine will not have been called. <>= (*iter)--; /* the loop index is always 1 beyond where it finished */ flag[0] = rank; loglik[1] = newlk; if (*iter == maxiter) cholesky2(imat, nvar, tol_chol); chinv2(imat, nvar); for (i=0; i>= #include "survS.h" #include "survproto.h" #include SEXP survfitci(SEXP ftime2, SEXP sort12, SEXP sort22, SEXP ntime2, SEXP status2, SEXP cstate2, SEXP wt2, SEXP id2, SEXP p2, SEXP i02, SEXP sefit2) { <> <> <> } @ Arguments to the routine are the following. For an R object ``zed'' I use the convention of [[zed2]] to refer to the object and [[zed]] to the contents of the object. \begin{description} \item[ftime] A two column matrix containing the entry and exit times for each subject. \item[sort1] Order vector for the entry times. The first element of sort1 points to the first entry time, etc. \item[sort2] Order vector for the event times. \item[ntime] Number of unique event time values. This fixes the size of the output arrays. \item[status] Status for each observation. 0= censored \item[cstate] The initial state for each subject, which will be updated during computation to always be the current state. \item[wt] Case weight for each observation. \item[id] The subject id for each observation. \item[p] The initial distribution of states. This will be updated during computation to be the current distribution. \item[i0] The initial influence matrix, number of subjects by number of states \item[sefit] If 1 then do the se compuatation, if 2 also return the full influence matrix upon which it is based, if 0 the se is not needed. \end{description} Declare all of the variables. <>= int i, j, k, kk; /* generic loop indices */ int ck, itime, eptr; /*specific indices */ double ctime; /*current time of interest, in the main loop */ int oldstate, newstate; /*when changing state */ double temp, *temp2; /* scratch double, and vector of length nstate */ double *dptr; /* reused in multiple contexts */ double *p; /* current prevalence vector */ double **hmat; /* hazard matrix at this time point */ double **umat; /* per subject leverage at this time point */ int *atrisk; /* 1 if the subject is currently at risk */ int *ns; /* number curently in each state */ int *nev; /* number of events at this time, by state */ double *ws; /* weighted count of number state */ double *wtp; /* case weights indexed by subject */ double wevent; /* weighted number of events at current time */ int nstate; /* number of states */ int n, nperson; /*number of obs, subjects*/ double **chaz; /* cumulative hazard matrix */ /* pointers to the R variables */ int *sort1, *sort2; /*sort index for entry time, event time */ double *entry,* etime; /*entry time, event time */ int ntime; /* number of unique event time values */ int *status; /*0=censored, 1,2,... new states */ int *cstate; /* current state for each subject */ int *dstate; /* the next state, =cstate if not an event time */ double *wt; /* weight for each observation */ double *i0; /* initial influence */ int *id; /* for each obs, which subject is it */ int sefit; /* returned objects */ SEXP rlist; /* the returned list and variable names of same */ const char *rnames[]= {"nrisk","nevent","ncensor", "p", "cumhaz", "std", "influence", ""}; SEXP setemp; double **pmat, **vmat, *cumhaz, *usave; int *ncensor, **nrisk, **nevent; @ Now set up pointers for all of the R objects sent to us. The two that will be updated need to be replaced by duplicates. <>= ntime= asInteger(ntime2); nperson = LENGTH(cstate2); /* number of unique subjects */ n = LENGTH(sort12); /* number of observations in the data */ PROTECT(cstate2 = duplicate(cstate2)); cstate = INTEGER(cstate2); entry= REAL(ftime2); etime= entry + n; sort1= INTEGER(sort12); sort2= INTEGER(sort22); status= INTEGER(status2); wt = REAL(wt2); id = INTEGER(id2); PROTECT(p2 = duplicate(p2)); /*copy of initial prevalence */ p = REAL(p2); nstate = LENGTH(p2); /* number of states */ i0 = REAL(i02); sefit = asInteger(sefit2); /* allocate space for the output objects ** Ones that are put into a list do not need to be protected */ PROTECT(rlist=mkNamed(VECSXP, rnames)); setemp = SET_VECTOR_ELT(rlist, 0, allocMatrix(INTSXP, ntime, nstate)); nrisk = imatrix(INTEGER(setemp), ntime, nstate); /* time by state */ setemp = SET_VECTOR_ELT(rlist, 1, allocMatrix(INTSXP, ntime, nstate)); nevent = imatrix(INTEGER(setemp), ntime, nstate); /* time by state */ setemp = SET_VECTOR_ELT(rlist, 2, allocVector(INTSXP, ntime)); ncensor = INTEGER(setemp); /* total at each time */ setemp = SET_VECTOR_ELT(rlist, 3, allocMatrix(REALSXP, ntime, nstate)); pmat = dmatrix(REAL(setemp), ntime, nstate); setemp = SET_VECTOR_ELT(rlist, 4, allocVector(REALSXP, nstate*nstate*ntime)); cumhaz = REAL(setemp); if (sefit >0) { setemp = SET_VECTOR_ELT(rlist, 5, allocMatrix(REALSXP, ntime, nstate)); vmat= dmatrix(REAL(setemp), ntime, nstate); } if (sefit >1) { setemp = SET_VECTOR_ELT(rlist, 6, allocVector(REALSXP, n*nstate*(ntime+1))); usave = REAL(setemp); } /* allocate space for scratch vectors */ ws = (double *) R_alloc(2*nstate, sizeof(double)); /*weighted number in state */ temp2 = ws + nstate; ns = (int *) R_alloc(2*nstate, sizeof(int)); nev = ns + nstate; atrisk = (int *) R_alloc(2*nperson, sizeof(int)); dstate = atrisk + nperson; wtp = (double *) R_alloc(nperson, sizeof(double)); hmat = (double**) dmatrix((double *)R_alloc(nstate*nstate, sizeof(double)), nstate, nstate); chaz = (double**) dmatrix((double *)R_alloc(nstate*nstate, sizeof(double)), nstate, nstate); if (sefit >0) umat = (double**) dmatrix((double *)R_alloc(nperson*nstate, sizeof(double)), nstate, nperson); /* R_alloc does not zero allocated memory */ for (i=0; i>= if (sefit ==1) { dptr = i0; for (j=0; j1) { /* copy influence, and save it */ dptr = i0; for (j=0; j>= itime =0; /*current time index, for output arrays */ eptr = 0; /*index to sort1, the entry times */ for (i=0; i> <> /* Take the current events and censors out of the risk set */ for (; i0) cstate[id[j]] = status[j]-1; /*new state */ atrisk[id[j]] =0; } else break; } itime++; } @ The key variables for the computation are the matrix $H$ and the current prevalence vector $P$. $H$ is created anew at each unique time point. Row $j$ of $H$ concerns everyone in state $j$ just before the time point, and contains the transitions at that time point. So the $jk$ element is the (weighted) fraction who change from state $j$ to state $k$, and the $jj$ element the fraction who stay put. Each row of $H$ by definition sums to 1. If no one is in the state then the $jj$ element is set to 1. A second version which we call H2 has 1 subtracted from each diagonal and so that the row sums are 0, we go back and forth depending on which is needed at the moment. If there are no events at this time point $P$ and $U$ do not update. <>= for (j=0; j0) { newstate = status[k] -1; /* 0 based subscripts */ oldstate = cstate[id[k]]; if (oldstate != newstate) { /* A "move" to the same state does not count */ dstate[id[k]] = newstate; nev[newstate]++; wevent += wt[k]; hmat[oldstate][newstate] += wt[k]; } } else ncensor[itime]++; } else break; } if (wevent > 0) { /* there was at least one move with weight > 0 */ /* finish computing H */ for (j=0; j0) { temp =0; for (k=0; k0) { <> } <> } @ The most complicated part of the code is the update of the per subject influence matrix $U$. The influence for a subject is the derivative of the current estimates wrt the case weight of that subject. Siince $p$ is a vector the influence $U$ is easily represented as a matrix with one row per subject and one column per state. Refer to equation \eqref{ci1} for the derivation. Let $m$ and $n$ be the old and new states for subject $i$, and $n_m$ the sum of weights for all subjects at risk in state $m$. Then \begin{equation*} U_{ij}(t) = \sum_k \left[ U_{ik}(t-)H_{kj}\right] + p_m(t-)(I_{n=j} - H_{mj})/ n_m \end{equation*} \begin{enumerate} \item The first term above is simple matrix multiplication. \item The second adds a vector with mean zero. \end{enumerate} If standard errors are not needed we can skip this calculation. <>= if (sefit >0) { /* Update U, part 1 U = U %*% H -- matrix multiplication */ for (j=0; j>= /* Finally, update chaz and p. */ for (j=0; j>= /* store into the matrices that will be passed back */ for (j=0; j0) { temp =0; for (k=0; k 1) for (k=0; k>= /* return a list */ UNPROTECT(3); return(rlist); @ survival/noweb/survfitCI.Rnw0000644000175100001440000005303013026514450015664 0ustar hornikusers\subsection{Competing risks} \newcommand{\Twid}{\mbox{\(\tt\sim\)}} The competing risks routine is very general, allowing subjects to enter or exit states multiple times. Early on I used the label \emph{current prevalence} estimate, since it estimates what fraction of the subjects are in any given state across time. However the word ``prevalence'' is likely to generate confusion whenever death is one of the states, due to its historic use as the fraction of living subjects who have a particular condition. We will use the phrase \emph{probability in state} or simply $P$ from this point forward. The easiest way to understand the estimate is to consider first the case of no censoring. In that setting the estimate of $F_k(t) = 1-S_k(t)$ for all states is obtained from a simple table of the current state at time $t$ of the subjects, divided by $n$, the original sample size. When there is censoring the conceptually simple way to extend this is via the redistribute-to-the-right algorithm, which allocates the case weight for a censored subject evenly to all the others in the same state at the time of censoring. The literature refers to these as ``cumulative incidence'' curves, which is confusing since P(state) is not the integral of incidence, but the routine name survfitCI endures. The cannonical call is \begin{verbatim} fit <- survfit(Surv(time, status, type='mstate') ~ sex, data=mine) \end{verbatim} Optionally, there can be an id statement or cluster term to indicate a data set with multiple transitions per subject. A multi-state survival fit has a status variable with multiple levels, the first of which by default is censoring, and others indicating the type of transition that occured. The result will be a matrix of survival curves, one for each event type. In no initial state is specified then subjects are assumed to start in a "null" state, which gets listed last and by default will not be printed or plotted. (But it is present, with a name of `'); The first part of the code is standard, parsing out options and checking the data. <>= <> survfitCI <- function(X, Y, weights, id, istate, type=c('kaplan-meier', 'fleming-harrington', 'fh2'), se.fit=TRUE, conf.int= .95, conf.type=c('log', 'log-log', 'plain', 'none'), conf.lower=c('usual', 'peto', 'modified'), influence = FALSE, start.time){ method <- match.arg(type) # error <- match.arg(error) # if (error != "inf") # warning("Only the infinetesimal jackknife error is supported for CI curves") conf.type <- match.arg(conf.type) conf.lower<- match.arg(conf.lower) if (is.logical(conf.int)) { # A common error is for users to use "conf.int = FALSE" # it's illegal per documentation, but be kind if (!conf.int) conf.type <- "none" conf.int <- .95 } type <- attr(Y, "type") # This line should be unreachable, unless they call "surfitCI" if (type !='mright' && type!='mcounting') stop(paste("multi-state computation doesn't support \"", type, "\" survival data", sep='')) # If there is a start.time directive, start by removing those observations if (!missing(start.time)) { if (!is.numeric(start.time) || length(start.time) !=1 || !is.finite(start.time)) stop("start.time must be a single numeric value") toss <- which(Y[,ncol(Y)] <= start.time) if (length(toss)) { n <- nrow(Y) Y <- Y[-toss,,drop=FALSE] X <- X[-toss] weights <- weights[-toss] if (length(id) ==n) id <- id[-toss] if (!missing(istate) && length(istate)==n) istate <- istate[-toss] } } n <- nrow(Y) status <- Y[,ncol(Y)] ncurve <- length(levels(X)) state.names <- attr(Y, "states") nstate <- length(state.names) has.istate <- !missing(istate) if (missing(istate) || is.null(istate)) { istate <- rep(nstate+ 1L, n) state.names <- c(state.names, "") } else { if (is.factor(istate) || is.character(istate)) { # Match levels with the survival variable temp <- as.factor(istate) # append any starting states not found in Y, but remember that # if istate was a factor then not all its levels might appear appear <- (levels(temp))[unique(as.numeric(temp))] state.names <- unique(c(attr(Y, "states"), appear)) istate <- as.numeric(factor(as.character(temp), levels=state.names)) } else { if (!is.numeric(istate) || any(istate != floor(istate)) || any(istate < 1)) stop("istate should be a vector of positive integers or a factor") if (max(istate) > nstate) state.names <- c(state.names, (1+nstate):max(istate)) } } if (length(id) ==0) id <- 1:n # these next two lines should be impossible, since istate came from # the data frame if (length(istate) ==1) istate <- rep(istate,n) if (length(istate) !=n) stop ("wrong length for istate") # The states of the status variable are the first columns in the output states <- unique(c(1:nstate, istate)) @ To make it easier to keep track of things in the computational kernel that does all the real work, we ensure that any ending states (ones you can reach) are 1, 2, 3 \ldots. The status vector will have values of 0 for censored. <>= curves <- vector("list", ncurve) names(curves) <- levels(X) if (ncol(Y)==2) { # 1 transition per subject indx <- which(status == istate & status!=0) if (length(indx)) { warning("an observation transitions to it's starting state, transition ignored") status[indx] <- 0 } if (length(id) && any(duplicated(id))) stop("Cannot have duplicate id values with (time, status) data") # make a table of transitions. Variable 'from' can range across # all of the states, 'to' can only have nstate categories nst <- length(state.names) transitions <- table(factor(istate, 1:nst), factor(Y[,2], 1:nstate)) dimnames(transitions) <-list(from=state.names, to=state.names[1:nstate]) # dummy entry time that is < any event time t0 <- min(0, Y[,1]) entry <- rep(t0-1, nrow(Y)) for (i in levels(X)) { indx <- which(X==i) curves[[i]] <- docurve2(entry[indx], Y[indx,1], status[indx], istate[indx], weights[indx], states, id[indx], se.fit) } } else { <> <> } <> } @ In the multi-state case we can calculate the current P(state) vector $p(t)$ using the product-limit form \begin{align*} p(t) &= p(0)\prod_{s<=t} [I + dA(s)] \\ &= p(0) \prod_{s<=t} H(s) \end{align*} Where $p$ is a row vector and $H$ is the multi-state hazard matrix. $H(t)$ is a simple transition matrix. Row $j$ of $H$ describes the outcome of everyone who was in state $j$ at time $t-0$; and is the fraction of them who are in states $1, 2, \ldots$ at time $t+0$. Let $Y_{ij}(t)$ be the indicator function which is 1 if subject $i$ is in state $j$ at time $t-0$, then \begin{equation} H_{jk}(t) = \frac{\sum_i w_i Y_{ij}(t) Y_{ik}(t+)} {\sum_i w_i Y_{ij}(t)} \label{H} \end{equation} Each row of $H$ sums to 1: everyone has to go somewhere. This formula collapses to the Kaplan-Meier in the simple case where $p(t)$ is a vector of length 2 with state 1 = alive and state 2 = dead. The variance is based on per-subject influence. Since $p(t)$ is a vector the influence can be written as a matrix with one row per subject and one column per state. $$ U_{ij}(t) \equiv \frac{partial p_j(t)}{\partial w_i}. $$ This can be calculate using a recursive formula. First, the derivative of a matrix product $AB$ is $d(A)B + Ad(B)$ where $d(A)$ is the elementwise derivative of $A$ and similarly for $B$. (Write out each element of the matrix product.) Since $p(t) = p(t-)H(t)$, the $i$th row of U satisfies \begin{align} U_i(t) &= \frac{partial p(t)}{\partial w_i} \nonumber \\ &= \frac{\partial p(t-)}{\partial w_i} H(t) + p(t-) \frac{\partial H(t}{\partial w_i} \nonumber \\ &= U_i(t-) H(t) + p(t-) \frac{\partial H(t}{\partial w_i} \label{ci} \end{align} The first term of \ref{ci} collapses to ordinary matrix multiplication. The second term does not: each at risk subject has a unique matrix derivative $\partial H$; $n$ vectors of length $p$ arrange into a matrix but $n$ $p$ by $p$ matrices are not so neat. However, note that \begin{enumerate} \item $\partial H$ is zero for anyone not in the risk set, since their weight does not appear in $H$. \item Each subject who is at risk will be in one (and only one) of the states at the event time, their weight only appears in that row of $H$. Thus for each at risk subject $\partial H$ has only one non-zero row. \end{enumerate} Say that the subject enters the given event time in state $j$ and ends it in state $k$. (For most $k=j$: if there are 100 at risk at time $t$ and 1 changes state, the other 99 stay put.) Let $n_j(t)= \sum_i Y_{ij}(t)w_i$ be the weighted number of subjects in state $j$, these are the contributers to row $j$ of $H$. Using equation \ref{H}, the derivative of row $j$ with respect to the subject is $(1_k - H_j)/n_j$ where $1_k$ is a vector with 1 in position $k$. The product of $p(t)$ with this matrix is the vector $p_j(t)(1_k - H_j)/n_j$. The second term thus turns out to be fairly simple to compute, but I have not seen a way to write it in a compact matrix form The weighted sum of each column of $U$ will be zero (if computed correctly) and the weighted sum of squares for each column will be the infinitesimal jackknife estimate of variance for the elements of $p$. The entire variance-covariance matrix for the states is $U'W^2U$ where $W$ is a diagonal matrix of weights, but we currently don't report that back. Note that this is for sampling weights. If one has real case weights, where an integer weight of 2 means 2 observations that were collapsed in to one row of data to save space, then the variance is $U'WU$. Case weights were somewhat common in my youth due to small computer memory, but I haven't seen such data in 20 years. Below is the function for a single curve. For the status variable a value if 0 is ``no event''. One nuisance in the function is that we need to ensure the tapply command gives totals for all states, not just the ones present in the data --- a call using the \code{subset} argument might not have all the states --- which leads to using factor commands. Another more confusing one is for multiple rows per subject data, where the cstate and U objects have only one row per subject; any given subject is only in one state at a time. This leads to indices of [[atrisk]] for the set of rows in the risk set but [[aindx]] for the subjects in the risk set, [[death]] for the rows that have an event as some given time and [[dindx]] for the corresponding subjects. The setup for (start, stop] data is a bit more work. We want to ensure that a given subject remains in the same group, that they have a continuous period of observation, and that they don't transfer from a state to itself. The last is not strictly an error, so only warn; it is usually not what was intended. <>= if (missing(id) || is.null(id)) stop("the id argument is required for start:stop data") indx <- order(id, Y[,2]) #ordered event times within subject indx1 <- indx[-length(indx)] #a pair of lagged indices indx2 <- indx[-1] #if indx1[5] == index2[5] that means that the 5th and 6th are the same id same <- (id[indx1] == id[indx2]) if (any(same & X[indx1] != X[indx2])) { who <- min(which(same & X[indx1] != X[indx2])) stop("subject is in two different groups, id ", id[indx1[who]]) } if (any(same & Y[indx1,2] != Y[indx2,1])) { who <- min(which(same & Y[indx1,2] != Y[indx2,1])) stop("gap in follow-up, id ", id[indx1[who]]) } if (any(Y[,1] == Y[,2])) stop("cannot have start time == stop time") if (any(same & (Y[indx1,3] == Y[indx2,3]) & (Y[indx1,3] !=0))) { who <- min(which(same & (Y[indx1,3] == Y[indx2,3]) & (Y[indx1,3] !=0))) warning("subject changes to the same state, id ", id[indx1[who]]) } # Make the table of transitions nst <- length(state.names) first <- indx[!duplicated(id[indx])] transitions <- table(factor(istate[first], 1:nst), factor(Y[first,3], 1:nstate)) if (any(same)) transitions <- transitions + table(factor(Y[indx1[same],3], 1:nst), factor(Y[indx2[same],3], 1:nstate)) dimnames(transitions) = list(from=state.names, to=state.names[1:nstate]) @ <>= # We only want to pay attention to the istate variable for the very first # observation of any given subject, but the program logic does better with # a full one. So construct one that will do this indx <- order(Y[,2]) uid <- unique(id) temp <- (istate[indx])[match(uid, id[indx])] #first istate for each subject istate <- temp[match(id, uid)] #replicate it to full length # Now to work for (i in levels(X)) { indx <- which(X==i) # temp <- docurve1(Y[indx,1], Y[indx,2], status[indx], # istate[indx], weights[indx], states, id[indx]) curves[[i]] <- docurve2(Y[indx,1], Y[indx,2], status[indx], istate[indx], weights[indx], states, id[indx], se.fit, influence) } @ <>= # Turn the result into a survfit type object grabit <- function(clist, element) { temp <-(clist[[1]][[element]]) if (is.matrix(temp)) { do.call("rbind", lapply(clist, function(x) x[[element]])) } else { xx <- as.vector(unlist(lapply(clist, function(x) x[element]))) if (class(temp)=="table") matrix(xx, byrow=T, ncol=length(temp)) else xx } } if (length(curves) ==1) { keep <- c("n", "time", "n.risk", "n.event", "n.censor", "pstate", "p0", "cumhaz", "influence") if (se.fit) keep <- c(keep, "std.err", "sp0") kfit <- (curves[[1]])[match(keep, names(curves[[1]]), nomatch=0)] names(kfit$p0) <- state.names } else { kfit <- list(n = as.vector(table(X)), #give it labels time = grabit(curves, "time"), n.risk= grabit(curves, "n.risk"), n.event= grabit(curves, "n.event"), n.censor=grabit(curves, "n.censor"), pstate = grabit(curves, "pstate"), p0 = grabit(curves, "p0"), transitions = transitions, strata= unlist(lapply(curves, function(x) length(x$time)))) kfit$p0 <- matrix(kfit$p0, ncol=nst, byrow=TRUE, dimnames=list(names(curves), state.names)) if (se.fit) { kfit$std.err <- grabit(curves, "std.err") kfit$sp0<- matrix(grabit(curves, "sp0"), ncol=nst, byrow=TRUE) } kfit$cumhaz <- array(unlist(lapply(curves, function(x) x$cumhaz)), dim=c(nst, nst, length(kfit$time))) if (influence) kfit$influence <- lapply(curves, function(x) x$influence) if (!missing(start.time)) kfit$start.time <- start.time } kfit$transitions <- transitions @ Add the confidence bands. The idea is modeled on survfitKM but with the important differences that we are dealing with $P$ instead of $S$, and the ``modified lower limit'' logic does not apply. We make the assumption that $\log(1-P)$ will have better CI behavior than $P$, with standard error of ${rm se}(P)/(1-P)$. <>= # # Last bit: add in the confidence bands: # modeled on survfit.km, though for P instead of S # # if (se.fit) { std.err <- kfit$std.err zval <- qnorm(1- (1-conf.int)/2, 0,1) if (conf.type=='plain') { temp <- zval* kfit$std.err kfit <- c(kfit, list(lower =pmax(kfit$pstate-temp, 0), upper=pmin(kfit$pstate+temp, 1), conf.type='plain', conf.int=conf.int)) } if (conf.type=='log') { #avoid some "log(0)" messages xx <- ifelse(kfit$pstate==1, 1, 1- kfit$pstate) temp1 <- ifelse(kfit$pstate==1, NA, exp(log(xx) + zval* kfit$std.err/xx)) temp2 <- ifelse(kfit$pstate==1, NA, exp(log(xx) - zval* kfit$std.err/xx)) kfit <- c(kfit, list(lower=pmax(1-temp1,0), upper= 1- temp2, conf.type='log', conf.int=conf.int)) } if (conf.type=='log-log') { who <- (kfit$pstate==0 | kfit$pstate==1) #special cases temp3 <- ifelse(kfit$pstate==1, NA, 1) xx <- ifelse(who, .1,kfit$pstate) #avoid some "log(0)" messages temp1 <- exp(-exp(log(-log(xx)) + zval*kfit$std.err/(xx*log(xx)))) temp1 <- ifelse(who, temp3, temp1) temp2 <- exp(-exp(log(-log(xx)) - zval*kfit$std.err/(xx*log(xx)))) temp2 <- ifelse(who, temp3, temp2) kfit <- c(kfit, list(lower=1-temp1, upper=1-temp2, conf.type='log-log', conf.int=conf.int)) } } kfit$states <- state.names kfit$type <- attr(Y, "type") kfit @ The updated docurve function is here. One issue that was not recognized originally is delayed entry. If most of the subjects start at time 0, say, but one of them starts at day 100 then that last subject is not a part of $p_0$. We will define $p_0$ as the distribution of states just before the first event. The code above has already ensured that each subject has a unique value for istate, so we don't have to search for the right one. The initial vector and leverage are \begin{align*} p_0 &= (\sum I{s_i=1}w_i, \sum I{s_i=2}w_i, \ldots)/ \sum w_i \\ \frac{\partial p_0}{\partial w_k} &= [(I{s_k=1}, I{s_k=2}, ...)- p_0]/\sum w_i \end{align*} The input data set is not necessarily sorted by time or subject. The data has been checked so that subjects don't have gaps, however. The cstate variable for each subject contains their first istate value. Only those intervals that overlap the first event time contribute to $p_0$. Now: what to report as the ``time'' for the initial row. The values for it come from (first event time -0), i.e. all who are at risk at the smallest \code{etime} with status $>0$. But for normal plotting the smallest start time seems to be a good default. In the usual (start, stop] data a large chunk of the subjects have a common start time. However, if the first event doesn't happen for a while and subjects are dribbling in, then the best point to start a plot is open to debate. Que sera sera. <>= docurve2 <- function(entry, etime, status, istate, wt, states, id, se.fit, influence=FALSE) { timeset <- sort(unique(etime)) nstate <- length(states) uid <- sort(unique(id)) index <- match(id, uid) first <- match(uid, id) # first row for each subject cstate <- istate[first] # The influence matrix can be huge, make sure we have enough memory if (influence) { needed <- nstate * (1.0 + length(timeset)) * length(first) if (needed > .Machine$integer.max) stop("length of the influence matrix is > the maximum integer") } storage.mode(wt) <- "double" # just in case someone had integer weights # Compute p0 if (all(status==0)) t0 <- max(etime) #failsafe else t0 <- min(etime[status!=0]) # first transition event at.zero <- (entry < t0 & etime >= t0) wtsum <- sum(wt[at.zero]) # weights for a subject may change p0 <- tapply(wt[at.zero], factor(istate[at.zero], levels=states), sum) / wtsum p0 <- ifelse(is.na(p0), 0, p0) #for a state not in at.zero, tapply gives NA # initial leverage matrix nid <- length(uid) i0 <- matrix(0., nid, nstate) if (all(p0 <1)) { #actually have to compute it who <- index[at.zero] # this will have no duplicates for (j in 1:nstate) i0[who,j] <- (ifelse(istate[at.zero]==j, 1, 0) - p0[j])/wtsum } storage.mode(cstate) <- "integer" storage.mode(status) <- "integer" # C code has 0 based subscripts if (influence) se.fit <- TRUE # se.fit is free in this case fit <- .Call(Csurvfitci, c(entry, etime), order(entry) - 1L, order(etime) - 1L, length(timeset), status, cstate - 1L, wt, index -1L, p0, i0, as.integer(se.fit) + 2L*as.integer(influence)) if (se.fit) out <- list(n=length(etime), time= timeset, p0 = p0, sp0= sqrt(colSums(i0^2)), pstate = fit$p, std.err=fit$std, n.risk = fit$nrisk, n.event= fit$nevent, n.censor=fit$ncensor, cumhaz=array(fit$cumhaz, dim=c(nstate, nstate, length(timeset)))) else out <- list(n=length(etime), time= timeset, p0=p0, pstate = fit$p, n.risk = fit$nrisk, n.event = fit$nevent, n.censor= fit$ncensor, cumhaz=array(fit$cumhaz, dim=c(nstate, nstate, length(timeset)))) if (influence) { temp <- array(fit$influence, dim=c(length(uid), nstate, 1+ length(timeset)), dimnames=list(uid, NULL, NULL)) out$influence <- aperm(temp, c(1,3,2)) } out } @ survival/noweb/plot.Rnw0000644000175100001440000004137513003734107014733 0ustar hornikusers\section{Plotting survival curves} I found a problem where plot.survfit, lines.survfit, and points.survfit sometimes did different things. This is due to copied code that later changed in one function but not another. Since they have so much code in common, this section of the noweb code consolodates them so as to restore order by using common code blocks. First define the top level routines. <>= plot.survfit<- function(x, conf.int, mark.time=FALSE, mark=3, col=1,lty=1, lwd=1, cex=1, log=FALSE, xscale=1, yscale=1, firstx=0, firsty=1, xmax, ymin=0, fun, xlab="", ylab="", xaxs='S', conf.times, conf.cap=.005, conf.offset=.012, ...) { dotnames <- names(list(...)) if (any(dotnames=='type')) stop("The graphical argument 'type' is not allowed") if (missing(mark.time) & !missing(mark)) mark.time <- TRUE <> if (missing(firsty) && !is.null(x$p0)) firsty <- 1-x$p0 <> <> <> <> <> plot.surv <- TRUE type <- 's' <> } lines.survfit <- function(x, type='s', mark=3, col=1, lty=1, lwd=1, cex=1, mark.time=FALSE, xscale=1, firstx=0, firsty=1, xmax, fun, conf.int=FALSE, conf.times, conf.cap=.005, conf.offset=.012, ...) { xlog <- par("xlog") if (missing(mark.time) & !missing(mark)) mark.time <- TRUE <> if (missing(firsty) && !is.null(x$p0)) firsty <- 1-x$p0 <> <> <> <> } points.survfit <- function(x, xscale, xmax, fun, censor=FALSE, col=1, pch, ...) { # this function is used rarely conf.int <- FALSE # never draw these with 'points' <> firstx <- firsty <- NA # part of the common args, but irrelevant for points <> if (ncurve==1 || (length(col)==1 && missing(pch))) { if (censor) points(stime, ssurv, ...) else points(stime[x$n.event>0], ssurv[x$n.event>0], ...) } else { c2 <- 1 #cycles through the colors and characters col <- rep(col, length=ncurve) if (!missing(pch)) { if (length(pch)==1) pch2 <- rep(strsplit(pch, '')[[1]], length=ncurve) else pch2 <- rep(pch, length=ncurve) } for (j in 1:ncol(ssurv)) { for (i in unique(stemp)) { if (censor) who <- which(stemp==i) else who <- which(stemp==i & x$n.event >0) if (missing(pch)) points(stime[who], ssurv[who,j], col=col[c2], ...) else points(stime[who], ssurv[who,j], col=col[c2], pch=pch2[c2], ...) c2 <- c2+1 } } } } @ Block of code to transform components of a [[survfitms]] object so that the standard plotting methods work. <>= if (inherits(x, "survfitms")) { x$surv <- 1- x$pstate if (is.matrix(x$surv)) { dimnames(x$surv) <- list(NULL, x$states) if (ncol(x$surv) > 1 && any(x$states == '')) { x$surv <- x$surv[, x$states != ''] if (is.matrix(x$p0)) x$p0 <- x$p0[, x$states != ''] else x$p0 <- x$p0[x$states != ''] } } if (!is.null(x$lower)) { x$lower <- 1- x$lower x$upper <- 1- x$upper } if (missing(fun)) fun <- "event" } @ <>= ssurv <- as.matrix(x$surv) stime <- x$time if( !is.null(x$upper)) { supper <- as.matrix(x$upper) slower <- as.matrix(x$lower) } else { conf.int <- FALSE supper <- NULL #marker for later code } # set up strata if (is.null(x$strata)) { nstrat <- 1 stemp <- rep(1, length(x$time)) # same length as stime } else { nstrat <- length(x$strata) stemp <- rep(1:nstrat, x$strata) # same length as stime } ncurve <- nstrat * ncol(ssurv) firsty <- matrix(firsty, nrow=nstrat, ncol=ncol(ssurv)) @ The xmax argument is used to prune back the survival curve to a small set of time points. This is a bit of bother since we have to do our own clipping of the data to prevent warning messages from the underlying plot routines. A further special case is when we are drawing lines and a curve got pruned so severely that only a horizontal segment from the curve start remains. In this case I need to reference the firsty arg. <>= if (!missing(xmax) && any(x$time>xmax)) { # prune back the survival curves # I need to replace x's over the limit with xmax, and y's over the # limit with either the prior y value or firsty keepx <- keepy <- NULL # lines to keep tempn <- table(stemp) offset <- cumsum(c(0, tempn)) for (i in 1:nstrat) { ttime <-stime[stemp==i] if (all(ttime <= xmax)) { keepx <- c(keepx, 1:tempn[i] + offset[i]) keepy <- c(keepy, 1:tempn[i] + offset[i]) } else { bad <- min((1:tempn[i])[ttime>xmax]) if (bad==1) { #lost them all if (!is.na(firstx)) { # and we are plotting lines keepy <- c(keepy, 1+offset[i]) ssurv[1+offset[i],] <- firsty[i,] } } else keepy<- c(keepy, c(1:(bad-1), bad-1) + offset[i]) keepx <- c(keepx, (1:bad)+offset[i]) stime[bad+offset[i]] <- xmax x$n.event[bad+offset[i]] <- 1 #don't plot a tick mark } } # ok, now actually prune it stime <- stime[keepx] stemp <- stemp[keepx] x$n.event <- x$n.event[keepx] if (!is.null(x$n.censor)) x$n.censor <- x$n.censor[keepx] ssurv <- ssurv[keepy,,drop=FALSE] if (!is.null(supper)) { supper <- supper[keepy,,drop=FALSE] slower <- slower[keepy,,drop=FALSE] } } #stime <- stime/xscale #scaling is deferred until xmax processing is done if (!missing(fun)) { if (is.character(fun)) { tfun <- switch(fun, 'log' = function(x) x, 'event'=function(x) 1-x, 'cumhaz'=function(x) -log(x), 'cloglog'=function(x) log(-log(x)), 'pct' = function(x) x*100, 'logpct'= function(x) 100*x, #special case further below 'identity'= function(x) x, stop("Unrecognized function argument") ) } else if (is.function(fun)) tfun <- fun else stop("Invalid 'fun' argument") ssurv <- tfun(ssurv ) if (!is.null(supper)) { supper <- tfun(supper) slower <- tfun(slower) } firsty <- tfun(firsty) } @ The data structure for a survival plot does not include the first plot point. Those routines start their computation at the first endpoint, and leave it to here to decide on a starting location. The points routine doesn't have to deal with this nuisance. \begin{itemize} \item The initial time value [[firstx]] is the first of \begin{enumerate} \item a value given to [[firstx]] by the user \item [[start.time]], if present in the surv object \item if a logarithmic axis is specified, the smallest time >0 in the object \item the smaller of the minimum time or 0 \end{enumerate} \end{itemize} <>= if (missing(firstx)) { if (!is.null(x$start.time)) firstx <- x$start.time else { if (xlog) firstx <- min(stime[stime>0]) else firstx <- min(0, stime) } } # The default for plot and lines is to add confidence limits # if there is only one curve if (missing(conf.int) && missing(conf.times)) conf.int <- (ncurve==1) if (missing(conf.times)) conf.times <- NULL else { if (!is.numeric(conf.times)) stop('conf.times must be numeric') if (missing(conf.int)) conf.int <- TRUE } if (is.logical(conf.int)) plot.surv <- TRUE else { temp <- match.arg(conf.int, c("both", "only", "none")) if (is.na(temp)) stop("invalid value for conf.int") if (temp=="none") conf.int <- FALSE else conf.int <- TRUE if (temp=="only") plot.surv <- FALSE else plot.surv <- TRUE } <> @ <>= # Marks are not placed on confidence bands mark <- rep(mark, length.out=ncurve) mcol <- rep(col, length.out=ncurve) if (is.numeric(mark.time)) mark.time <- sort(mark.time) # The actual number of curves is ncurve*3 if there are confidence bands, # unless conf.times has been given. Colors and line types in the latter # match the curves # If the number of line types is 1 and lty is an integer, then use lty # for the curve and lty+1 for the CI # If the length(lty) <= length(ncurve), use the same color for curve and CI # otherwise assume the user knows what they are about and has given a full # vector of line types. # Colors and line widths work like line types, excluding the +1 rule. if (conf.int & is.null(conf.times)) { if (length(lty)==1 && is.numeric(lty)) lty <- rep(c(lty, lty+1, lty+1), ncurve) else if (length(lty) <= ncurve) lty <- rep(rep(lty, each=3), length.out=(ncurve*3)) else lty <- rep(lty, length.out= ncurve*3) if (length(col) <= ncurve) col <- rep(rep(col, each=3), length.out=3*ncurve) else col <- rep(col, length.out=3*ncurve) if (length(lwd) <= ncurve) lwd <- rep(rep(lwd, each=3), length.out=3*ncurve) else lwd <- rep(lwd, length.out=3*ncurve) } else { col <- rep(col, length.out=ncurve) lty <- rep(lty, length.out=ncurve) lwd <- rep(lwd, length.out=ncurve) } @ Here is the rest of the setup for the plot routine, mostly having to do with setting up axes. The [[xlog]] and [[ylog]] variables are internal reminders of the choice, and [[logax]] is what will be passed to the plot function <>= if (is.logical(log)) { ylog <- log xlog <- FALSE if (ylog) logax <- 'y' else logax <- "" } else { ylog <- (log=='y' || log=='xy') xlog <- (log=='x' || log=='xy') logax <- log } if (!missing(fun)) { if (is.character(fun)) { if (fun=='log'|| fun=='logpct') ylog <- TRUE if (fun=='cloglog') { xlog <- TRUE if (ylog) logax <- 'xy' else logax <- 'x' } } } # The special x axis style only applies when firstx is not given if (missing(xaxs) && (firstx!=0 || !missing(fun) || (missing(fun) && inherits(x, "survfitms")))) xaxs <- par("xaxs") #use the default @ <>= #axis setting parmaters that depend on the fun argument if (!missing(fun)) { ymin <- tfun(ymin) #lines routine doesn't have it } # Do axis range computations if (xaxs=='S') { #special x- axis style for survival curves xaxs <- 'i' #what S thinks tempx <- max(stime) * 1.04 } else tempx <- max(stime) tempx <- c(firstx, tempx, firstx) if (ylog) { tempy <- range(ssurv[is.finite(ssurv)& ssurv>0]) if (tempy[2]==1) tempy[2] <- .99 if (any(ssurv==0)) { tempy[1] <- tempy[1]*.8 ssurv[ssurv==0] <- tempy[1] if (!is.null(supper)) { supper[supper==0] <- tempy[1] slower[slower==0] <- tempy[1] } } tempy <- c(tempy, firsty) } else tempy <- range(ssurv, firsty, finite=TRUE, na.rm=TRUE) if (missing(fun)) { tempx <- c(tempx, firstx) if (!ylog) tempy <- c(tempy, ymin) } # # Draw the basic box # plot(range(tempx, finite=TRUE, na.rm=TRUE)/xscale, range(tempy, finite=TRUE, na.rm=TRUE)*yscale, type='n', log=logax, xlab=xlab, ylab=ylab, xaxs=xaxs,...) if(yscale != 1) { if (ylog) par(usr =par("usr") -c(0, 0, log10(yscale), log10(yscale))) else par(usr =par("usr")/c(1, 1, yscale, yscale)) } if (xscale !=1) { if (xlog) par(usr =par("usr") -c(log10(xscale), log10(xscale), 0,0)) else par(usr =par("usr")*c(xscale, xscale, 1, 1)) } @ The use of [[par(usr)]] just above is a bit sneaky. I want the lines and points routines to be able to add to the plot, \emph{without} passing them a global parameter that determines the y-scale or forcing the user to repeat it. The xscale argument was added before yscale, and before I saw this trick. By then there were hundreds of lines of code that have an xscale argument to lines() so the other change was to ignore the argument there. The next functions do the actual drawing. <>= # Create a step function, removing redundancies that sometimes occur in # curves with lots of censoring. dostep <- function(x,y) { keep <- is.finite(x) & is.finite(y) if (!any(keep)) return() #all points were infinite or NA if (!all(keep)) { # these won't plot anyway, so simplify (CI values are often NA) x <- x[keep] y <- y[keep] } n <- length(x) if (n==1) list(x=x, y=y) else if (n==2) list(x=x[c(1,2,2)], y=y[c(1,1,2)]) else { # replace verbose horizonal sequences like # (1, .2), (1.4, .2), (1.8, .2), (2.3, .2), (2.9, .2), (3, .1) # with (1, .2), (.3, .2),(3, .1). # They are slow, and can smear the looks of the line type. temp <- rle(y)$lengths drops <- 1 + cumsum(temp[-length(temp)]) # points where the curve drops #create a step function if (n %in% drops) { #the last point is a drop xrep <- c(x[1], rep(x[drops], each=2)) yrep <- rep(y[c(1,drops)], c(rep(2, length(drops)), 1)) } else { xrep <- c(x[1], rep(x[drops], each=2), x[n]) yrep <- c(rep(y[c(1,drops)], each=2)) } list(x=xrep, y=yrep) } } drawmark <- function(x, y, mark.time, censor, cex, ...) { if (!is.numeric(mark.time)) { xx <- x[censor] yy <- y[censor] } else { #interpolate xx <- mark.time yy <- approx(x, y, xx, method="constant", f=0)$y } points(xx, yy, cex=cex, ...) } @ The code to actually draw curves for the plot. The code to draw the lines and confidence bands. <>= c1 <- 1 # keeps track of the curve number c2 <- 1 # keeps track of the lty, col, etc xend <- yend <- double(ncurve) if (length(conf.offset) ==1) temp.offset <- (1:ncurve - (ncurve-1)/2)* conf.offset* diff(par("usr")[1:2]) else temp.offset <- rep(conf.offset, length=ncurve) * diff(par("usr")[1:2]) temp.cap <- conf.cap * diff(par("usr")[1:2]) for (j in 1:ncol(ssurv)) { for (i in unique(stemp)) { #for each strata who <- which(stemp==i) censor <- if (is.null(x$n.censor)) (x$n.event[who] ==0) else (x$n.event[who] ==0 & x$n.censor[who] >0) #censoring ties xx <- c(firstx, stime[who]) censor <- c(FALSE, censor) #no mark at firstx yy <- c(firsty[i,j], ssurv[who,j]) if (plot.surv) { if (type=='s') lines(dostep(xx, yy), lty=lty[c2], col=col[c2], lwd=lwd[c2]) else lines(xx, yy, type=type, lty=lty[c2], col=col[c2], lwd=lwd[c2]) if (is.numeric(mark.time) || mark.time) drawmark(xx, yy, mark.time, censor, pch=mark[c1], col=mcol[c1], cex=cex) } xend[c1] <- max(xx) yend[c1] <- yy[length(yy)] if (conf.int && !is.null(conf.times)) { # add vertical bars at the specified times x2 <- conf.times + temp.offset[c1] templow <- approx(xx, c(firsty[i,j], slower[who,j]), x2, method='constant', f=1)$y temphigh<- approx(xx, c(firsty[i,j], supper[who,j]), x2, method='constant', f=1)$y segments(x2, templow, x2, temphigh, lty=lty[c2], col=col[c2], lwd=lwd[c2]) if (conf.cap>0) { segments(x2-temp.cap, templow, x2+temp.cap, templow, lty=lty[c2], col=col[c2], lwd=lwd[c2] ) segments(x2-temp.cap, temphigh, x2+temp.cap, temphigh, lty=lty[c2], col=col[c2], lwd=lwd[c2]) } } c1 <- c1 +1 c2 <- c2 +1 if (conf.int && is.null(conf.times)) { if (type == 's') { lines(dostep(xx, c(firsty[i,j], slower[who,j])), lty=lty[c2], col=col[c2],lwd=lwd[c2]) c2 <- c2 +1 lines(dostep(xx, c(firsty[i,j], supper[who,j])), lty=lty[c2], col=col[c2], lwd= lwd[c2]) c2 <- c2 + 1 } else { lines(xx, c(firsty[i,j], slower[who,j]), lty=lty[c2], col=col[c2],lwd=lwd[c2], type=type) c2 <- c2 +1 lines(xx, c(firsty[i,j], supper[who,j]), lty=lty[c2], col=col[c2], lwd= lwd[c2], type= type) c2 <- c2 + 1 } } } } invisible(list(x=xend, y=yend)) @ survival/noweb/finegray.Rnw0000644000175100001440000003065413046713075015567 0ustar hornikusers\section{The Fine-Gray model} For competing risks with ending states 1, 2, \ldots $k$, the Fine-Gray approach turns these into a set of simple 2-state Cox models: \begin{itemize} \item (not yet in state 1) $\longrightarrow$ state 1 \item (not yet in state 2) $\longrightarrow$ state 2 \item \ldots \end{itemize} Each of these is now a simple Cox model, assuming that we are willing to make a proportional hazards assumption. There is one added complication: when estimating the first model, one wants to use the data set that would have occured if the subjects being followed for state 1 had not had an artificial censoring, that is, had continued to be followed for event 1 even after event 2 occured. Sometimes this can be filled in directly, e.g., if we knew the enrollment dates for each subject along with the date that follow-up for the study was terminated, and there was no lost to follow-up (only administrative censoring.) Another example is the mgus2 data set, where follow-up for death continued after the occurence of plasma cell malignancy. In practice what is done is to estimate the overall censoring distribution and give subjects artificial follow-up. The function below creates a data set that can then be used with coxph. <>= finegray <- function(formula, data, subset, na.action= na.pass, etype, prefix="fg", count="", id, timefix=TRUE) { Call <- match.call() indx <- match(c("formula", "data", "subset", "id"), names(Call), nomatch=0) if (indx[1] ==0) stop("A formula argument is required") temp <- Call[c(1,indx)] # only keep the arguments we wanted temp$na.action <- na.action temp[[1L]] <- quote(stats::model.frame) # change the function called special <- c("strata", "cluster") temp$formula <- if(missing(data)) terms(formula, special) else terms(formula, special, data=data) mf <- eval(temp, parent.frame()) if (nrow(mf) ==0) stop("No (non-missing) observations") Terms <- terms(mf) Y <- model.extract(mf, "response") if (!inherits(Y, "Surv")) stop("Response must be a survival object") type <- attr(Y, "type") if (type!='mright' && type!='mcounting') stop("Fine-Gray model requires a multi-state survival") nY <- ncol(Y) states <- attr(Y, "states") if (timefix) Y <- aeqSurv(Y) strats <- attr(Terms, "specials")$strata if (length(strats)) { stemp <- untangle.specials(Terms, 'strata', 1) if (length(stemp$vars)==1) strata <- mf[[stemp$vars]] else strata <- survival::strata(mf[,stemp$vars], shortlabel=TRUE) istrat <- as.numeric(strata) mf[stemp$vars] <- NULL } else istrat <- rep(1, nrow(mf)) id <- model.extract(mf, "id") if (!is.null(id)) mf["(id)"] <- NULL # don't leave it in result cluster<- attr(Terms, "specials")$cluster if (length(cluster)) { if (!is.null(id)) stop("an id argument and a cluster() term are redundant") tempc <- untangle.specials(Terms, 'cluster', 1) id <- strata(mf[,tempc$vars], shortlabel=TRUE) #allow multiples mf[tempc$vars] <- NULL } # If there is start-stop data, then there needs to be a cluster() # argument or an id argument, and we check that this is indeed # a competing risks form of data. # Mark the first and last obs of each subject, as we need it later. # Observations may not be in time order within a subject delay <- FALSE # is there delayed entry? if (type=="mcounting") { if (is.null(id)) stop("(start, stop] data requires a subject id") else { index <- order(id, Y[,2]) # by time within id sorty <- Y[index,] first <- which(!duplicated(id[index])) last <- c(first[-1] -1, length(id)) if (any(sorty[-last, 3]) != 0) stop("a subject has a transition before their last time point") delta <- c(sorty[-1,1], 0) - sorty[,2] if (any(delta[-last] !=0)) stop("a subject has gaps in time") if (any(Y[first,1] > min(Y[,2]))) delay <- TRUE temp1 <- temp2 <- rep(FALSE, nrow(mf)) temp1[index[first]] <- TRUE temp2[index[last]] <- TRUE first <- temp1 #used later last <- temp2 } } else last <- rep(TRUE, nrow(mf)) if (missing(etype)) enum <- 1 #generate a data set for which endpoint? else { index <- match(etype, states) if (any(is.na(index))) stop ("etype argument has a state that is not in the data") enum <- index[1] if (length(index) > 1) warning("only the first endpoint was used") } # make sure count, if present is syntactically valid if (!missing(count)) count <- make.names(count) else count <- NULL oname <- paste0(prefix, c("start", "stop", "status", "wt")) <> <> } @ The censoring and truncation distributions are \begin{align*} G(t) &= \prod_{s \le t} \left(1 - \frac{c(s)}{r_c(s)} \right ) \\ H(t) &= \prod_{s > t} \left(1 - \frac{e(s)}{r_e(s)} \right ) \end{align*} where $c(t)$ is the number of subjects censored at time $t$, $e(t)$ is the number who enter at time $t$, and $r$ is the size of the relevant risk set. These are equations 5 and 6 of Geskus (Biometrics 2011). Note that both $G$ and $H$ are right continuous functions. For tied times the assumption is that event $<$ censor $<$ entry. For $G$ we use a modified Kapan-Meier where any events at censoring time $t$ are removed from the risk set just before time $t$. To avoid issues with times that are nearly identical (but not quite) we first convert to an integer time scale, and then move events backwards by .2. Since this is a competing risks data set any non-censored observation for a subject is their last, so this time shift does not goof up the alignment of start, stop data. For the truncation distribution it is the subjects with times at or before time $t$ that are in the risk set $r_e(t)$ for truncation at (or before) $t$. $H$ can be calculated using an ordinary KM on the reverse time scale. <>= find2 <- function(x, vec, left.open=FALSE, ...) { if (!left.open) findInterval(x, vec, ...) else { # the left.open arg is a recent addition to findInterval, and I want # this to work in 3.2.0 (my employer's default). In another cycle or # so we can drop this workaround and call findInterval directly # length(vec) - findInterval(-x, rev(-vec), ...) } } if (ncol(Y) ==2) { temp <- min(Y[,1], na.rm=TRUE) if (temp >0) zero <- 0 else zero <- 2*temp -1 # a value less than any observed y Y <- cbind(zero, Y) # add a start column } utime <- sort(unique(c(Y[,1:2]))) # all the unique times newtime <- matrix(findInterval(Y[,1:2], utime), ncol=2) status <- Y[,3] newtime[status !=0, 2] <- newtime[status !=0,2] - .2 Gsurv <- survfit(Surv(newtime[,1], newtime[,2], status==0) ~ istrat, se.fit=FALSE) @ The calculation for $H$ is also done on the integer scale. Otherwise we will someday be clobbered by times that differ only in round off error. The only nuisance is the status variable, which is 1 for the first row of each subject, since the data set may not be in sorted order. The offset of .2 used above is not needed, but due to the underlying integer scale it doesn't harm anything either. Reversal of the time scale leads to a left continuous function which we fix up later. <>= if (delay) Hsurv <- survfit(Surv(-newtime[,2], -newtime[,1], first) ~ istrat, se.fit =FALSE) @ Consider the following data set: \begin{itemize} \item Events of type 1 at times 1, 4, 5, 10 \item Events of type 2 at times 2, 5, 8 \item Censors at times 3, 4, 4, 6, 8, 9, 12 \end{itemize} The censoring distribution will have the following shape: \begin{center} \begin{tabular}{rcccccc} interval& (0,3]& (3,4] & (4,6] & (6,8] & (8,12] & 12+\\ C(t) & 1 &11/12 & (11/12)(8/10) & (11/15)(5/6)& (11/15)(5/6)(3/4)& 0 \\ & 1.0000 & .9167 & .7333 & .6111 & .4583 \end{tabular} \end{center} Notice that the event at time 4 is not counted in the risk set at time 4, so the jump is 8/10 rather than 8/11. Likewise at time 8 the risk set has 4 instead of 5: censors occur after deaths. When creating the data set for event type 1, subjects who have an event of type 2 get extended out using this censoring distribution. The event at time 2, for instance, appears as a censored observation with time dependent weights of $G(t)$. The type 2 event at time 5 has weight 1 up through time 5, then weights of $G(t)/C(5)$ for the remainder. This means a weight of 1 over (5,6], 5/6 over (6,8], (5/6)(3/4) over (9,12] and etc. Though there are 6 unique censoring intervals, in the created data set for event type 1 we only need to know case weights at times 1, 4, 5, and 10; the information from the (4,6] and (6,8] intervals will never be used. To create a minimal sized data set we can leave those intervals out. $G(t)$ only drops to zero if the largest time(s) are censored observations, so by definition no events lie in an interval with $G(t)=0$. If there is delayed entry, then the set of intervals is larger due to a merge with the jumps in Hsurv. The truncation distribution Hsurv ($H$) will become 0 at the first entry time; it is a left continuous function whereas Gsurv ($G$) is right continuous. We can slide $H$ one point to the left and merge them at the jump points. <>= status <- Y[, 3] # Do computations separately for each stratum stratfun <- function(i) { keep <- (istrat ==i) times <- sort(unique(Y[keep & status == enum, 2])) #unique event times if (length(times)==0) return(NULL) #no events in this stratum tdata <- mf[keep, -1, drop=FALSE] maxtime <- max(Y[keep, 2]) if (dim(Gsurv)==1) { # the phrase Gsurv[1] gives a warning when there is only one curve # keep only the event times, and convert back to the original time units if (delay) { dtime <- rev(-Hsurv$time[Hsurv$n.event > 0]) dprob <- c(rev(Hsurv$surv[Hsurv$n.event > 0])[-1], 1) ctime <- Gsurv$time[Gsurv$n.event > 0] cprob <- c(1, Gsurv$surv[Gsurv$n.event > 0]) temp <- sort(unique(c(dtime, ctime))) # these will all be integers index1 <- findInterval(temp, dtime) index2 <- findInterval(temp, ctime) ctime <- utime[temp] cprob <- dprob[index1] * cprob[index2+1] # G(t)H(t), eq 11 Geskus } else { ctime <- utime[Gsurv$time[Gsurv$n.event > 0]] cprob <- Gsurv$surv[Gsurv$n.event > 0] } } else { Gtemp <- Gsurv[i] if (delay) { Htemp <- Hsurv[i] dtime <- rev(-Htemp$time[Htemp$n.event > 0]) dprob <- c(rev(Htemp$surv[Htemp$n.event > 0])[-1], 1) ctime <- Gtemp$time[Gtemp$n.event > 0] cprob <- c(1, Gtemp$surv[Gtemp$n.event > 0]) temp <- sort(unique(c(dtime, ctime))) # these will all be integers index1 <- findInterval(temp, dtime) index2 <- findInterval(temp, ctime) ctime <- utime[temp] cprob <- dprob[index1] * cprob[index2+1] # G(t)H(t), eq 11 Geskus } else { ctime <- utime[Gtemp$time[Gtemp$n.event > 0]] cprob <- Gtemp$surv[Gtemp$n.event > 0] } } ct2 <- c(ctime, maxtime) cp2 <- c(1.0, cprob) index <- find2(times, ct2, left.open=TRUE) index <- sort(unique(index)) # the intervals that were actually seen # times before the first ctime get index 0, those between 1 and 2 get 1 ckeep <- rep(FALSE, length(ct2)) ckeep[index] <- TRUE expand <- (Y[keep, 3] !=0 & Y[keep,3] != enum & last[keep]) #which rows to expand split <- .Call(Cfinegray, Y[keep,1], Y[keep,2], ct2, cp2, expand, c(TRUE, ckeep)) tdata <- tdata[split$row,,drop=FALSE] tstat <- ifelse((status[keep])[split$row]== enum, 1, 0) tdata[[oname[1]]] <- split$start tdata[[oname[2]]] <- split$end tdata[[oname[3]]] <- tstat tdata[[oname[4]]] <- split$wt if (!is.null(count)) tdata[[count]] <- split$add tdata } if (max(istrat) ==1) result <- stratfun(1) else { tlist <- lapply(1:max(istrat), stratfun) result <- do.call("rbind", tlist) } rownames(result) <- NULL #remove all the odd labels that R adds attr(result, "event") <- states[enum] result @ survival/noweb/cch.Rnw0000644000175100001440000002327413060104346014507 0ustar hornikusers\section{Case-cohort function} This function was originally written by Norman Breslow, then adapted to the survival library by Thomas Lumley. Poor interaction with the \code{aeqSurv} function prompted a refactoring of the code. The method is an ordinary Cox model coupled with modification of the input data along with additional computation for the variance. A case-cohort study begins with a cohort of interest for which complete sampling is infeasable. A random subcohort is chosen for follow up, and then that subcohort is augmented by any subjects for whom an event occurs. Let $n$ be the number in the study and $m$ the number who were sampled. Consider an event at day 100 who was not part of the subcohort. Who is the risk set for this event? \begin{itemize} \item The Prentice estimate uses as a risk set all the subcohort members at risk on day 100 + this failure. To accomplish this we use (start,stop] data, and make the non-subcohort event a very short interval of ($100 - \epsilon$, 100]. The value of epsilon should be small enough that no other events fall in the interval, but large enough to preclude round off error. \item The Self-Prentice estimate was developed in a later paper on the asymptotic variance. For this the risk set does not include the non-subcohrt failure. This can be effectively accomplished by giving non-sucohort failures an offset of -100. They are still in the risk set, but with an effective weight of $\exp(-100) < 10^{-40}$ so have no effect. \item The Yin-Ling method leaves everyone in the sample, but reweights the non-events. Let $n$ be the number of non-events in the cohort and $m$ the non-events in the subcohort, and reweight all non-events by $n/m$. The events have weight 1, since they will always be included. This is a simple survey sampling correction. \item Borgan et. al. considered estimates for the case where stratified sampling has been done, with one or more of the strata oversampled. Their estimator I is the Self-Prentice, but with a case weight of $n_k/m_k$ for subcohort members in stratum $k$. Each event is compared to a population averge covariate rather than a sample average covariate. Estimator II is the same, but using the Prentice estimate; non-subcohort events have a weight of 1. \item Borgan et. al. consider several other estimators which are not included here. Method III uses subsampling, and there are variants of I and II that use time dependent stratum weights. \end{itemize} The historical input arguments are a bit of a mess: the three that could be part of a data frame were represented as one-sided formulas if they were part of the data frame, and simple expressions otherwise. This precludes the use of an na.action or subset argument. To rectify that make these part of the standard model.frame processing, We need to find out if the user handed a formula to us, but without evaluating them. If any of them are, then make sure it is a legal formula of the form \code{\textasciitilde x} for some single variable, and then replace the formula with the variable name. <>= cch <- function(formula, data, weights, subset, na.action, subcoh, id, stratum, cohort.size, method=c("Prentice", "SelfPrentice", "LinYing", "I.Borgan", "II.Borgan"), robust = FALSE, control, ...) { method <- match.arg(method) Call <- match.call() if (missing(control)) control <- coxph.control(...) for (i in c("subcoh", "id", "stratum")) { if (inherits(Call[[i]], 'formula')) { if (length(Call[[i]]) != 2 || !is.name(Call[[i]][[2]]) stop("a formula used for ", i, "must have a single variable and no response") Call[[i]] <- Call[[i]][[2]] } } # Grab the data. This is identical to coxph, but with 3 # more matching arguments indx <- match(c("formula", "data", "weights", "subset", "na.action", "subcoh", "id", "stratum"), names(Call), nomatch=0) if (indx[1] ==0) stop("a formula argument is required") temp <- Call[c(1,indx)] # only keep the arguments we wanted temp[[1L]] <- quote(stats::model.frame) # change the function called special <- c("strata", "cluster") temp$formula <- if(missing(data)) terms(formula, special) else terms(formula, special, data=data) mf <- eval(temp, parent.frame()) if (nrow(mf) ==0) stop("No (non-missing) observations") Terms <- terms(mf) Y <- model.extract(mf, "response") if (!inherits(Y, "Surv")) stop("Response must be a survival object") type <- attr(Y, "type") if (type!='right' && type!='counting') stop(paste("Cox model doesn't support \"", type, "\" survival data", sep='')) if (control$timefix) Y <- aeqSurv(Y) <> strats <- attr(Terms, "specials")$strata if (length(strats)) { stemp <- untangle.specials(Terms, 'strata', 1) if (length(stemp$vars)==1) strata.keep <- mf[[stemp$vars]] else strata.keep <- strata(mf[,stemp$vars], shortlabel=TRUE) strats <- as.numeric(strata.keep) } cluster<- attr(Terms, "specials")$cluster if (length(cluster)) { robust <- TRUE #flag to later compute a robust variance tempc <- untangle.specials(Terms, 'cluster', 1:10) ord <- attr(Terms, 'order')[tempc$terms] if (any(ord>1)) stop ("Cluster can not be used in an interaction") cluster <- strata(mf[,tempc$vars], shortlabel=TRUE) #allow multiples dropterms <- tempc$terms #we won't want this in the X matrix # Save away xlevels after removing cluster (we don't want to save upteen # levels of that variable, which we will never need). xlevels <- .getXlevels(Terms[-tempc$terms], mf) } else { dropterms <- NULL if (missing(robust)) robust <- FALSE xlevels <- .getXlevels(Terms, mf) } <> <> <> <> <> } @ Now we have the main ingredients. The first task is to see if any of the \code{id, subcoh, or stratum} arguments were present. The \code{stratum} argument is not the same as the strata term in the model. The asymptotic variance formula requires knowlege of $n$, which is found in the \code{cohort.size} argument, the robust variance does not require this. <>= n <- nrow(Y) id <- model.extract(mf, "") subcoh <- model.extract(mf, "") stratum <- model.extract(mf, "") weight <- model.weights(mf) if (length(weight)==0)) weight <- rep(1.0, n) offset <- model.offset(mf) if (length(offset) ==0) { has.offset <- FALSE offset <- rep(0., n) } else has.offset <- TRUE status <- Y[,ncol(Y)] if (is.null(subcoh)) stop("a subcoh argument is required") else { if (is.logical(subcoh)) subcoh <- as.numeric(subcoh) else if (!is.numeric(subcoh)) stop("subcoh must be numeric or logical") else if (any(subcoh!=0 & subcoh !=1)) stop("numeric subcoh values must be 0 or 1") if (any(status==0 & subcoh==0)) stop("all observations outside the subcohort must be events") } if (length(stratum) > 0) { if (missing(cohort.size)) stop("the estimates for stratified sampling require cohort.size") scount <- table(stratum) indx <- match(names(cohort.size), names(scount)) phat <- scount/cohort.size[indx] if (any(is.na(phat))) stop("no cohort.size element found for strata", (names(scount))[is.na(phat)]) if (any(phat <=0 | phat >1)) stop("strata sampling fraction that is <=0 or > 1") windex <- match(stratum, names(scount)) weight[status==0] <- (weight /phat[windex])[status==0] } @ The computation has 3 branches, Prentice, Self-Prentice, and Lin-Ying. <>= if (ncol(Y) ==2) { etime <- Y[,1] status <- Y[,2] } else { etime <- Y[,2] status <- Y[,3] } if (method=="Prentice" || method=="II.Borgan") { # construct fake entry times for the non-cohort delta <- min(diff(sort(unique(etime[status==1])))) # min time between times fake <- etime[subco==0] - delta/2 if (ncol(Y) ==2) { temp <- rep(0., n) temp[subco==0] <- fake Y <- cbind(temp, Y) } else Y[subco==0, 1] <- fake fit <- agreg.fit(X, Y, strata, offset, init, control, weights, method, rownames) } else if (method== "Self-Prentice" || method= "I.Borgan") { # Use an offset offset[subco==1] <- offset[subco==0] - 100 if (ncol(Y) ==2) fit <- coxph.fit(X, Y, strata, offset, init, control, weights, method, rownames) else fit <- coxph.fit(X, Y, strata, offset, init, control, weights, method, rownames) } else { # Lin-Ying method if (missing(cohort.size)) stop("Lin-Ying method requires the cohort size") else if (!numeric(cohort.size)) stop("cohort size must be numeric") else if (length(cohort.size) > 1) stop("cohort size must be numeric, with one value per stratum") nd <- sum(status) # number of events nc <- sum(subcoh) # number in subcohort ncd <- sum(status*subcoh) # number of events in subcohort lyweight <- (cohort.size - nd)/(nc - ncd) weight[status==0] <- weight[status==0]* lyweight if (ncol(Y) ==2) fit <- coxph.fit(X, Y, strata, offset, init, control, weights, method, rownames) else fit <- coxph.fit(X, Y, strata, offset, init, control, weights, method, rownames) } @ There are two possible variances for the estimate. The asymptotic variance survival/noweb/main.Rnw0000644000175100001440000000464712145504442014705 0ustar hornikusers\documentclass{article} \usepackage{noweb} \usepackage{amsmath} \usepackage{fancyvrb} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} \newcommand{\myfig}[1]{\resizebox{\textwidth}{!} {\includegraphics{figures/#1.pdf}}} \newcommand{\code}[1]{\texttt{#1}} \noweboptions{breakcode} \title{Survival Package Functions} \author{Terry Therneau} \begin{document} \maketitle \tableofcontents \section{Introduction} \begin{quotation} Let us change or traditional attitude to the construction of programs. Instead of imagining that our main task is to instruct a \emph{computer} what to do, let us concentrate rather on explaining to \emph{humans} what we want the computer to do. (Donald E. Knuth, 1984). \end{quotation} This is the definition of a coding style called \emph{literate programming}. I first made use of it in the \emph{coxme} library and have become a full convert. For the survival library only selected objects are documented in this way; as I make updates and changes I am slowly converting the source code. The first motivation for this is to make the code easier for me, both to create and to maintain. As to maintinance, I have found that whenver I need to update code I spend a lot of time in the ``what was I doing in these x lines?'' stage. The code never has enough documentation, even for the author. (The survival library is already better than the majority of packages in R, whose comment level is abysmal. In the pre-noweb source code about 1 line in 6 has a comment, for the noweb document the documentation/code ratio is 2:1.) I also find it helps in creating new code to have the real documentation of intent --- formulas with integrals and such --- closely integrated. The second motivation is to leave code that is well enough explained that someone else can take it over. The source code is structured using \emph{noweb}, one of the simpler literate programming environments. The source code files look remakably like Sweave, and the .Rnw mode of emacs works perfectly for them. This is not too surprising since Sweave was also based on noweb. Sweave is not sufficient to process the files, however, since it has a different intention. The noweb.R file contains functions that can tangle the code (extract a given R function), but the creation of the pdf still requires the noweb exectuable itself. I am working towards correcting that. survival/noweb/residuals.survreg.Rnw0000644000175100001440000003544412676276716017472 0ustar hornikusers\section{Accelerated Failure Time models} The [[surveg]] function fits parametric failure time models. This includes accerated failure time models, the Weibull, log-normal, and log-logistic models. It also fits as well as censored linear regression; with left censoring this is referred to in economics \emph{Tobit} regression. \subsection{Residuals} The residuals for a [[survreg]] model are one of several types \begin{description} \item[response] residual [[y]] value on the scale of the original data \item[deviance] an approximate deviance residual. A very bad idea statistically, retained for the sake of backwards compatability. \item[dfbeta] a matrix with one row per observation and one column per parameter showing the approximate influence of each observation on the final parameter value \item[dfbetas] the dfbeta residuals scaled by the standard error of each coefficient \item[working] residuals on the scale of the linear predictor \item[ldcase] likelihood displacement wrt case weights \item[ldresp] likelihood displacement wrt response changes \item[ldshape] likelihood displacement wrt changes in shape \item[matrix] matrix of derivatives of the log-likelihood wrt paramters \end{description} The other parameters are \begin{description} \item[rsigma] whether the scale parameters should be included in the result for dfbeta results. I can think of no reason why one would not want them --- unless of course the scale was fixed by the user, in which case there is no parameter. \item[collapse] optional vector of subject identifiers. This is for the case where a subject has multiple observations in a data set, and one wants to have residuals per subject rather than residuals per observation. \item[weighted] whether the residuals should be multiplied by the case weights. The sum of weighted residuals will be zero. \end{description} The routine starts with standard stuff, checking arguments for validity and etc. The two cases of response or working residuals require a lot less computation. and are the most common calls, so they are taken care of first. <>= # $Id$ # # Residuals for survreg objects residuals.survreg <- function(object, type=c('response', 'deviance', 'dfbeta', 'dfbetas', 'working', 'ldcase', 'ldresp', 'ldshape', 'matrix'), rsigma =TRUE, collapse=FALSE, weighted=FALSE, ...) { type <-match.arg(type) n <- length(object$linear.predictors) Terms <- object$terms if(!inherits(Terms, "terms")) stop("invalid terms component of object") # If the variance wasn't estimated then it has no error if (nrow(object$var) == length(object$coefficients)) rsigma <- FALSE # If there was a cluster directive in the model statment then remove # it. It does not correspond to a coefficient, and would just confuse # things later in the code. cluster <- untangle.specials(Terms,"cluster")$terms if (length(cluster) >0 ) Terms <- Terms[-cluster] strata <- attr(Terms, 'specials')$strata coef <- object$coefficients intercept <- attr(Terms, "intercept") response <- attr(Terms, "response") weights <- object$weights if (is.null(weights)) weighted <- FALSE <> <> <> <> } @ First retrieve the distribution, which is used multiple times. The common case is a character string pointing to some element of [[survreg.distributions]], but the other is a user supplied list of the form contained there. Some distributions are defined as the transform of another in which case we need to set [[itrans]] and [[dtrans]] and follow the link, otherwise the transformation and its inverse are the identity. <>= if (is.character(object$dist)) dd <- survreg.distributions[[object$dist]] else dd <- object$dist if (is.null(dd$itrans)) { itrans <- dtrans <-function(x)x } else { itrans <- dd$itrans dtrans <- dd$dtrans } if (!is.null(dd$dist)) dd <- survreg.distributions[[dd$dist]] deviance <- dd$deviance dens <- dd$density @ The next task is to decide what data we need. The response is always needed, but is normally saved as a part of the model. If it is a transformed distribution such as the Weibull (a transform of the extreme value) the saved object [[y]] is the transformed data, so we need to replicate that part of the survreg() code. (Why did I even allow for y=F in survreg? Because I was mimicing the lm function --- oh the long, long consequences of a design decision.) The covariate matrix [[x]] will be needed for all but response, deviance, and working residuals. If the model included a strata() term then there will be multiple scales, and the strata variable needs to be recovered. The variable [[sigma]] is set to a scalar if there are no strata, but otherwise to a vector with [[n]] elements containing the appropriate scale for each subject. The leverage type residuals all need the second derivative matrix. If there was a [[cluster]] statement in the model this will be found in [[naive.var]], otherwise in the [[var]] component. <>= if (is.null(object$naive.var)) vv <- object$var else vv <- object$naive.var need.x <- is.na(match(type, c('response', 'deviance', 'working'))) if (is.null(object$y) || !is.null(strata) || (need.x & is.null(object[['x']]))) mf <- stats::model.frame(object) y <- object$y if (is.null(y)) { y <- model.extract(mf, 'response') if (!is.null(dd$trans)) { tranfun <- dd$trans exactsurv <- y[,ncol(y)] ==1 if (any(exactsurv)) logcorrect <-sum(log(dd$dtrans(y[exactsurv,1]))) if (type=='interval') { if (any(y[,3]==3)) y <- cbind(tranfun(y[,1:2]), y[,3]) else y <- cbind(tranfun(y[,1]), y[,3]) } else if (type=='left') y <- cbind(tranfun(y[,1]), 2-y[,2]) else y <- cbind(tranfun(y[,1]), y[,2]) } else { if (type=='left') y[,2] <- 2- y[,2] else if (type=='interval' && all(y[,3]<3)) y <- y[,c(1,3)] } } if (!is.null(strata)) { temp <- untangle.specials(Terms, 'strata', 1) Terms2 <- Terms[-temp$terms] if (length(temp$vars)==1) strata.keep <- mf[[temp$vars]] else strata.keep <- strata(mf[,temp$vars], shortlabel=TRUE) strata <- as.numeric(strata.keep) nstrata <- max(strata) sigma <- object$scale[strata] } else { Terms2 <- Terms nstrata <- 1 sigma <- object$scale } if (need.x) { x <- object[['x']] #don't grab xlevels component if (is.null(x)) x <- model.matrix(Terms2, mf, contrasts.arg=object$contrasts) } @ The most common residual is type response, which requires almost no more work, for the others we need to create the matrix of derivatives before proceeding. We use the [[center]] component from the deviance function for the distribution, which returns the data point [[y]] itself for an exact, left, or right censored observation, and an appropriate midpoint for interval censored ones. <>= if (type=='response') { yhat0 <- deviance(y, sigma, object$parms) rr <- itrans(yhat0$center) - itrans(object$linear.predictor) } else { <> <> } @ The matrix of derviatives is used in all of the other cases. The starting point is the [[density]] function of the distribtion which return a matrix with columns of $F(x)$, $1-F(x)$, $f(x)$, $f'(x)/f(x)$ and $f''(x)/f(x)$. %' The matrix type residual contains columns for each of $$ L_i \quad \frac{\partial L_i}{\partial \eta_i} \quad \frac{\partial^2 L_i}{\partial \eta_i^2} \quad \frac{\partial L_i}{\partial \log(\sigma)} \quad \frac{\partial L_i}{\partial \log(\sigma)^2} \quad \frac{\partial^2 L_i}{\partial \eta \partial\log(\sigma)} $$ where $L_i$ is the contribution to the log-likelihood from each individual. Note that if there are multiple scales, i.e. a strata() term in the model, then terms 3--6 are the derivatives for that subject with respect to their \emph{particular} scale factor; derivatives with respect to all the other scales are zero for that subject. The log-likelihood can be written as \begin{align*} L &= \sum_{exact}\left[ \log(f(z_i)) -\log(\sigma_i) \right] + \sum_{censored} \log \left( \int_{z_i^l}^{z_i^u} f(u)du \right) \\ &\equiv \sum_{exact}\left[g_1(z_i) -\log(\sigma_i) \right] + \sum_{censored} \log(g_2(z_i^l, z_i^u)) \\ z_i &= (y_i - \eta_i)/ \sigma_i \end{align*} For the interval censored observations we have a $z$ defined at both the lower and upper endpoints. The linear predictor is $\eta = X\beta$. The derivatives are shown below. Note that $f(-\infty) = f(\infty) = F(-\infty)=0$, $F(\infty)=1$, $z^u = \infty$ for a right censored observation and $z^l = -\infty$ for a left censored one. \begin{align*} \frac{\partial g_1}{\partial \eta} &= - \frac{1}{\sigma} \left[\frac{f'(z)}{f(z)} \right] \\ %' \frac{\partial g_2}{\partial \eta} &= - \frac{1}{\sigma} \left[ \frac{f(z^u) - f(z^l)}{F(z^u) - F(z^l)} \right] \\ \frac{\partial^2 g_1}{\partial \eta^2} &= \frac{1}{\sigma^2} \left[ \frac{f''(z)}{f(z)} \right] - (\partial g_1 / \partial \eta)^2 \\ \frac{\partial^2 g_2}{\partial \eta^2} &= \frac{1}{\sigma^2} \left[ \frac{f'(z^u) - f'(z^l)}{F(z^u) - F(z^l)} \right] - (\partial g_2 / \partial \eta)^2 \\ \frac{\partial g_1}{\partial \log\sigma} && - \left[ \frac{zf'(z)}{f(z)} \right] \\ \frac{\partial g_2}{\partial \log\sigma} &= - \left[ \frac{z^uf(z^u) - z^lf(z^l)}{F(z^u) - F(z^l)} \right] \\ \frac{\partial^2 g_1}{\partial (\log\sigma)^2} &=& \left[ \frac{z^2 f''(z) + zf'(z)}{f(z)} \right] - (\partial g_1 / \partial \log\sigma)^2 \\ \frac{\partial^2 g_2}{\partial (\log\sigma)^2} &= \left[ \frac{(z^u)^2 f'(z^u) - (z^l)^2f'(z_l) } {F(z^u) - F(z^l)} \right] - \partial g_1 /\partial \log\sigma(1+\partial g_1 / \partial \log\sigma) \\ \frac{\partial^2 g_1}{\partial \eta \partial \log\sigma} &= \frac{zf''(z)}{\sigma f(z)} -\partial g_1/\partial \eta (1 + \partial g_1/\partial \log\sigma) \\ \frac{\partial^2 g_2}{\partial \eta \partial \log\sigma} &= \frac{z^uf'(z^u) - z^lf'(z^l)}{\sigma [F(z^u) - F(z^l)]} -\partial g_2/\partial \eta (1 + \partial g_2/\partial \log\sigma) \\ \end{align*} In the code [[z]] is the relevant point for exact, left, or right censored data, and [[z2]] the upper endpoint for an interval censored one. The variable [[tdenom]] contains the denominator for each subject (which is the same for all derivatives for that subject). For an interval censored observation we try to avoid numeric cancellation by using the appropriate tail of the distribution. For instance with $(z^l, z^u) = (12,15)$ the value of $F(x)$ will be very near 1 and it is better to subtract two upper tail values $(1-F)$ than two lower tail ones $F$. <>= status <- y[,ncol(y)] eta <- object$linear.predictors z <- (y[,1] - eta)/sigma dmat <- dens(z, object$parms) dtemp<- dmat[,3] * dmat[,4] #f' if (any(status==3)) { z2 <- (y[,2] - eta)/sigma dmat2 <- dens(z2, object$parms) } else { dmat2 <- dmat #dummy values z2 <- 0 } tdenom <- ((status==0) * dmat[,2]) + #right censored ((status==1) * 1 ) + #exact ((status==2) * dmat[,1]) + #left ((status==3) * ifelse(z>0, dmat[,2]-dmat2[,2], dmat2[,1] - dmat[,1])) #interval g <- log(ifelse(status==1, dmat[,3]/sigma, tdenom)) #loglik tdenom <- 1/tdenom dg <- -(tdenom/sigma) *(((status==0) * (0-dmat[,3])) + #dg/ eta ((status==1) * dmat[,4]) + ((status==2) * dmat[,3]) + ((status==3) * (dmat2[,3]- dmat[,3]))) ddg <- (tdenom/sigma^2) *(((status==0) * (0- dtemp)) + #ddg/eta^2 ((status==1) * dmat[,5]) + ((status==2) * dtemp) + ((status==3) * (dmat2[,3]*dmat2[,4] - dtemp))) ds <- ifelse(status<3, dg * sigma * z, tdenom*(z2*dmat2[,3] - z*dmat[,3])) dds <- ifelse(status<3, ddg* (sigma*z)^2, tdenom*(z2*z2*dmat2[,3]*dmat2[,4] - z * z*dmat[,3] * dmat[,4])) dsg <- ifelse(status<3, ddg* sigma*z, tdenom *(z2*dmat2[,3]*dmat2[,4] - z*dtemp)) deriv <- cbind(g, dg, ddg=ddg- dg^2, ds = ifelse(status==1, ds-1, ds), dds=dds - ds*(1+ds), dsg=dsg - dg*(1+ds)) @ Now, we can calcultate the actual residuals case by case. For the dfbetas there will be one column per coefficient, so if there are strata column 4 of the deriv matrix needs to be \emph{un}collapsed into a matrix with nstrata columns. The same manipulation is needed for the ld residuals. <>= if (type=='deviance') { yhat0 <- deviance(y, sigma, object$parms) rr <- (-1)*deriv[,2]/deriv[,3] #working residuals rr <- sign(rr)* sqrt(2*(yhat0$loglik - deriv[,1])) } else if (type=='working') rr <- (-1)*deriv[,2]/deriv[,3] else if (type=='dfbeta' || type== 'dfbetas' || type=='ldcase') { score <- deriv[,2] * x # score residuals if (rsigma) { if (nstrata > 1) { d4 <- matrix(0., nrow=n, ncol=nstrata) d4[cbind(1:n, strata)] <- deriv[,4] score <- cbind(score, d4) } else score <- cbind(score, deriv[,4]) } rr <- score %*% vv if (type=='dfbetas') rr <- rr %*% diag(1/sqrt(diag(vv))) if (type=='ldcase') rr<- rowSums(rr*score) } else if (type=='ldresp') { rscore <- deriv[,3] * (x * sigma) if (rsigma) { if (nstrata >1) { d6 <- matrix(0., nrow=n, ncol=nstrata) d6[cbind(1:n, strata)] <- deriv[,6]*sigma rscore <- cbind(rscore, d6) } else rscore <- cbind(rscore, deriv[,6] * sigma) } temp <- rscore %*% vv rr <- rowSums(rscore * temp) } else if (type=='ldshape') { sscore <- deriv[,6] *x if (rsigma) { if (nstrata >1) { d5 <- matrix(0., nrow=n, ncol=nstrata) d5[cbind(1:n, strata)] <- deriv[,5] sscore <- cbind(sscore, d5) } else sscore <- cbind(sscore, deriv[,5]) } temp <- sscore %*% vv rr <- rowSums(sscore * temp) } else { #type = matrix rr <- deriv } @ Finally the two optional steps of adding case weights and collapsing over subject id. <>= #case weights if (weighted) rr <- rr * weights #Expand out the missing values in the result if (!is.null(object$na.action)) { rr <- naresid(object$na.action, rr) if (is.matrix(rr)) n <- nrow(rr) else n <- length(rr) } # Collapse if desired if (!missing(collapse)) { if (length(collapse) !=n) stop("Wrong length for 'collapse'") rr <- drop(rowsum(rr, collapse)) } rr @ survival/noweb/concordance.Rnw0000644000175100001440000007213712676275125016252 0ustar hornikusers\subsection{Concordance} The concordance statistic is gaining popularity as a measure of goodness-of-fit in survival models. Consider all pairs of subjects with $(r_i, r_j)$ as the two risk scores for each pair and $(s_i, s_j)$ the corresponding survival times. The c-statistic is defined by dividing these sets into four groups. \begin{itemize} \item Concordant pairs: for a Cox model this will be pairs where a shorter survival is paired with a larger risk score, e.g. $r_i>r_j$ and $s_i < s_j$ \item Discordant pairs: the lower risk score has a shorter survival \item Tied pairs: there are three common choices \begin{itemize} \item Kendall's tau: any pair where $r_i=r_j$ or $s_i = s_j$ is considered tied. \item AUC: pairs with $r_i=r_j$ are tied; those with $s_i=s_j$ are considered incomparable. This is the definition of the AUC in logisitic regression, and has become the most common choice for Cox models as well. \item Somer's D: All ties are treated as incomparable. \end{itemize} \item Incomparable pairs: For survival this always includes pairs where the survival times cannot be ranked with certainty. For instance $s_i$ is censored at time 10 and $s_j$ is an event (or censor) at time 20. Subject $i$ may or may not survive longer than subject $j$. Note that if $s_i$ is censored at time 10 and $s_j$ is an event at time 10 then $s_i > s_j$. Add onto this those ties that are treated as incomparable.\\ Observations that are in different strata are also incomparable, since the Cox model only compares within strata. \end{itemize} Then the concordance statistic is defined as $(C + T/2)/(C + D + T)$. The denominator is the number of comparable pairs. The program creates 4 variables, which are the number of concordant pairs, discordant, tied on time, and tied on $x$ but not on time. The default concordance is based on the AUC definition, but all 4 values are reported back so that a user can recreate the others if desired. The primary compuational questions is how to do this efficiently, i.e., better that the naive $O(n^2)$ algorithm that loops across all $n(n-1)/2$ possible pairs. There are two key ideas. \begin{enumerate} \item Rearrange the counting so that we do it by death times. For each death we count the number of other subjects in the risk set whose score is higher, lower, or tied and add it into the totals. This also neatly solves the question of time-dependent covariates. \item To count the number higher and lower we need to rank the subjects in the risk set by their scores $r_i$. This can be done in $O(\log n)$ time if the data is kept in a binary tree. \end{enumerate} \begin{figure} \myfig{balance} \caption{A balanced tree of 13 nodes.} \label{treefig} \end{figure} Figure \ref{treefig} shows a balanced binary tree containing 13 risk scores. For each node the left child and all its descendants have a smaller value than the parent, the right child and all its descendents have a larger value. Each node in figure \ref{treefig} is also annotated with the total weight of observations in that node and the weight for all its children (not shown on graph). Assume that the tree shown represents all of the subjects still alive at the time a particular subject ``Smith'' expires, and that Smith has the risk score 2.1. The concordant pairs are all of those with a risk score greater than 2.1, which can be found by traversing the tree from the top down, adding the (parent - child) value each time we branch left (5-3 at the 2.6 node), with a last addition of the right hand child when we find the node with Smith's value (1). %' There are 3 concordant and 12-3=9 discordant pairs. This takes a little less than $\log_2(n)$ steps on average, as compared to an average of $n/2$ for the naive method. The difference can matter when $n$ is large since this traversal must be done for each event. (In the code below we start at Smith's node and walk up.) %' The classic way to store trees is as a linked list. There are several algorithms for adding and subtracting nodes from a tree while maintaining the balance (red-black trees, AA trees, etc) but we take a different approach. Since we need to deal with case weights in the model and we know all the risk score at the outset, the full set of risk scores is organised into a tree at the beginning and node counts are changed to zero as observations are removed. If we index the nodes of the tree as 1 for the top, 2--3 for the next horizontal row, 4--7 for the next, \ldots then the parent-child traversal becomes particularly easy. The parent of node $i$ is $i/2$ (integer arithmetic) and the children of node $i$ are $2i$ and $2i +1$. In C code the indices start at 0 and the children are $2i+1$ and $2i+2$ and the parent is $(i-1)/2$. The following bit of code returns the indices of a sorted list when placed into such a tree. The basic idea is that the rows of the tree start at indices 1, 2, 4, \ldots. For the above tree, the last row will contains the 1st, 3rd, \ldots, 11th smallest ranks. The next row above contains every other value of the ranks \emph{not yet assigned}, and etc to the top of the tree. There is some care to make sure the result is an integer. <>= btree <- function(n) { ranks <- rep(0L, n) #will be overwritten yet.to.do <- 1:n depth <- floor(logb(n,2)) start <- as.integer(2^depth) lastrow.length <- 1+n-start indx <- seq(1L, by=2L, length= lastrow.length) ranks[yet.to.do[indx]] <- start + 0:(length(indx)-1L) yet.to.do <- yet.to.do[-indx] while (start >1) { start <- as.integer(start/2) indx <- seq(1L, by=2L, length=start) ranks[yet.to.do[indx]] <- start + 0:(start-1L) yet.to.do <- yet.to.do[-indx] } ranks } @ Referring again to figure \ref{treefig}, [[btree(13)]] yields the vector [[8 4 9 2 10 5 11 1 12 6 13 3 7]] meaning that the smallest element will be in position 8 of the tree, the next smallest in position 4, etc. Here is a shorter recursive version. It knows the form of trees with 1, 2, or 3 nodes; and builds the others from them. The maximum depth of recursion is $\log_2(n) -1$. It is more clever but a bit slower. (Not that it matters as both take less than 5 seconds for a million elements.) <>= btree <- function(n) { tfun <- function(n, id, power) { if (n==1) id else if (n==2) c(2L *id, id) else if (n==3) c(2L*id, id, 2L*id +1L) else { nleft <- if (n== power*2) power else min(power-1, n-power/2) c(tfun(nleft, 2L *id, power/2), id, tfun(n-(nleft+1), 2L*id +1L, power/2)) } } tfun(n, 1L, 2^(floor(logb(n-1,2)))) } @ <<<<<<< local A second question is how to compute the variance of the result. ======= The next question is how to compute a variance for the result. One approach is to compute an infinitesimal jackknife (IJ) estimate, for which we need derivatives with respect to the weights. For each event the two numbers of interest are the numerator $C-D$ and the denominator $C+D + T$, which can be written directly in terms of the weights. \begin{align*} C -D &= \sum_i w_i \delta_i \sum_{t_j > t_i} w_j \rm{sign}(r_i - r_j) \\ C +D+T &= \sum_i w_i \delta_i \sum_{t_j > t_i} w_j \end{align*} The first derivatives of these quantities with respect to an arbitrary subject $k$ are \begin{align} \frac{\partial C-D}{\partial w_k} &= \sum_{t_j > t_k} w_j \delta_k \rm{sign}(r_k - r_j) - \sum_{t_j < t_k} w_j \delta_j \rm{sign}(r_k - r_j) \label{derivC} \\ \frac{\partial C+D+T}{\partial w_k} &= \sum_{t_j > t_k} w_j \delta_k + \sum_{t_j < t_k} w_j \delta_j \label{derivT}\\ \end{align} We need to keep two vectors of derivatives each of length $n$, the number of observations. The parent routine in R will worry about data sets with multiple rows per subject, for which the person has to be added back together. I had originally avoided this approach because it appears to be an $O(nd)$ computation, adding a bit to each at-risk subject each time there is an event. A key insight due to David Watson is that we can avoid this. Within the tree we keep the sum of weights for each node and its left and right children, along with a parallel triple that totals only the deaths. The tree is updated as each subject is added or deleted, containing the current cumulative totals. We only need to update derivative values for each subject when the subject enters and when they leave. (For ordinary Cox models everyone enters at 0, or rather leaves at zero since our code will go from longest to shortest time.) A second variance estimate is based on the Cox model. >>>>>>> other The insight used here is to consider a Cox model with time dependent covariates, where the covariate $x$ at each death time has been transformed into ${\rm rank}(x)$. <<<<<<< local It is easy to show that the Cox score statistic contribution at each death is $(D-C)/2$ where $C$ and $D$ are the number of concordant and discordant pairs contributed at that death time (for a Cox fit using the Breslow approximation). ======= One can show that the Cox score statistic contribution of $r_i - \overline{r}$ at each death time is equal to $(C-D)/2$ where $C$ and $D$ are the number of concordant and discordant pairs comparing that death to all those at risk, and using the Breslow approximation for ties. >>>>>>> other The contribution to the variance of the score statistic is $V(t) =\sum (r_i - \overline{r})^2 /n$, the $r_i$ being the ranks at that time point and $n$ the number at risk. How can we update this sum using an update formula? First remember the identity \begin{equation*} \sum w_i(x_i - \overline{x})^2 = \sum w_i(x_i-c)^2 - \sum w_i(c - \overline{x})^2 \end{equation*} true for any set of values $x$ and centering constant $c$. For weighted data define the rank of an observation with risk score $r_k$ as \begin{equation*} {\rm rank} = \sum_{r_i>>>>>> other Let $\mu_\ell$ be the mean rank for all observations currently in the tree of rank lower than $r_k$, the item we are about to add, $\mu_u$ be the mean for all those above in rank (after the addition), $\mu_g$ the grand mean, and $\mu_n$ the new grand mean after adding in subject $k$. We have \begin{align*} \mu_\ell &= \sum_{r_ik} w_i(r_i - \mu_n)^2 - \sum_{i>k} w_i(r_i - \mu_g)^2 &= (\sum_{i>k} w_i) [(\mu_u -\mu_n)^2 - ((\mu_u-w_k) - \mu_g)^2] \nonumber \\ &= (\sum_{i>k} w_i) (\mu_n + z - 2\mu_u)(\mu_n -z) \label{upper1} \\ &= (\sum_{i>k} w_i) (\mu_n+z - 2\mu_u) (-w_k/2) \label{upper}\\ z&\equiv \mu_g+ w_k \nonumber \end{align} For items of tied rank, their rank increases by the same amount as the overall mean, and so their contribution to the total SS is unchanged. The final part of the update step is to add in the SS contributed by the new observation. An observation is removed from the tree whenver the current time becomes less than the (start, stop] interval of the datum. The ranks for observations of lower risk are unchanged by the removal so equation \eqref{lower1} applies just as before, but with the new mean smaller than the old so the last term in equation \eqref{lower} changes sign. For the observations of higher risk both the mean and the ranks change by $w_k$ and equation \eqref{upper1} holds but with $z=\mu_0- w_k$. We can now define the C-routine that does the bulk of the work. First we give the outline shell of the code and then discuss the parts one by one. This routine is for ordinary survival data, and will be called once per stratum. Input variables are \begin{description} \item[n] the number of observations \item[y] matrix containing the time and status, data is sorted by ascending time, with deaths preceding censorings. \item[indx] the tree node at which this observation's risk score resides %' \item[wt] case weight for the observation \item[sum] scratch space, weights for each node of the tree: 3 values are for the node, all left children, and all right children \item[count] the returned counts of concordant, discordant, tied on x, tied on time, and the variance \end{description} <>= #include "survS.h" SEXP concordance1(SEXP y, SEXP wt2, SEXP indx2, SEXP ntree2) { int i, j, k, index; int child, parent; int n, ntree; double *time, *status; double *twt, *nwt, *count; double vss, myrank, wsum1, wsum2, wsum3; /*sum of wts below, tied, above*/ double lmean, umean, oldmean, newmean; double ndeath; /* weighted number of deaths at this point */ SEXP count2; double *wt; int *indx; n = nrows(y); ntree = asInteger(ntree2); wt = REAL(wt2); indx = INTEGER(indx2); time = REAL(y); status = time + n; PROTECT(count2 = allocVector(REALSXP, 5)); count = REAL(count2); /* count5 contains the information matrix */ twt = (double *) R_alloc(2*ntree, sizeof(double)); nwt = twt + ntree; for (i=0; i< 2*ntree; i++) twt[i] =0.0; for (i=0; i<5; i++) count[i]=0.0; vss=0; <> UNPROTECT(1); return(count2); } @ The key part of our computation is to update the vectors of weights. We don't actually pass the risk score values $r$ into the routine, %' it is enough for each observation to point to the appropriate tree node. The tree contains the for everyone whose survival is larger than the time currently under review, so starts with all weights equal to zero. For any pair of observations $i,j$ we need to add [[wt[i]*wt[j]]] to the appropriate count. Starting at the largest time (which is sorted last), walk through the tree. \begin{itemize} \item If it is a death time, we need to process all the deaths tied at this time. \begin{enumerate} \item Add [[wt[i] * wt[j]]] to the tied-on-time total, for all pairs $i,j$ of tied times. \item The addition to tied-on-r will be the weight of this observation times the sum of weights for all others with the same risk score and a a greater time, i.e., the weight found at [[indx[i]]] in the tree. \item Similarly for those with smaller or larger risk scores. First add in the children of this node. The left child will be smaller risk scores (and longer times) adding to the concordant pairs, the right child discordant. Then walk up the tree to the root. At each step up we add in data for the 'not me' branch. If we were the right branch (even number node) of a parent then when moving up we add in the left branch counts, and vice-versa. \end{enumerate} \item Now add this set of subject weights into the tree. The weight for a node is [[nwt]] and for the node and all its children is [[twt]]. \end{itemize} <>= for (i=n-1; i>=0; ) { ndeath =0; if (status[i]==1) { /* process all tied deaths at this point */ for (j=i; j>=0 && status[j]==1 && time[j]==time[i]; j--) { ndeath += wt[j]; index = indx[j]; for (k=i; k>j; k--) count[3] += wt[j]*wt[k]; /* tied on time */ count[2] += wt[j] * nwt[index]; /* tied on x */ child = (2*index) +1; /* left child */ if (child < ntree) count[0] += wt[j] * twt[child]; /*left children */ child++; if (child < ntree) count[1] += wt[j] * twt[child]; /*right children */ while (index >0) { /* walk up the tree */ parent = (index-1)/2; if (index & 1) /* I am the left child */ count[1] += wt[j] * (twt[parent] - twt[index]); else count[0] += wt[j] * (twt[parent] - twt[index]); index = parent; } } } else j = i-1; /* Add the weights for these obs into the tree and update variance*/ for (; i>j; i--) { wsum1=0; oldmean = twt[0]/2; index = indx[i]; nwt[index] += wt[i]; twt[index] += wt[i]; wsum2 = nwt[index]; child = 2*index +1; /* left child */ if (child < ntree) wsum1 += twt[child]; while (index >0) { parent = (index-1)/2; twt[parent] += wt[i]; if (!(index&1)) /* I am a right child */ wsum1 += (twt[parent] - twt[index]); index=parent; } wsum3 = twt[0] - (wsum1 + wsum2); /* sum of weights above */ lmean = wsum1/2; umean = wsum1 + wsum2 + wsum3/2; /* new upper mean */ newmean = twt[0]/2; myrank = wsum1 + wsum2/2; vss += wsum1*(newmean+ oldmean - 2*lmean) * (newmean - oldmean); vss += wsum3*(newmean+ oldmean+ wt[i]- 2*umean) *(oldmean-newmean); vss += wt[i]* (myrank -newmean)*(myrank -newmean); } count[4] += ndeath * vss/twt[0]; } @ The code for [start, stop) data is quite similar. As in the agreg routines there are two sort indices, the first indexes the data by stop time, longest to earliest, and the second by start time. The [[y]] variable now has three columns. <>= SEXP concordance2(SEXP y, SEXP wt2, SEXP indx2, SEXP ntree2, SEXP sortstop, SEXP sortstart) { int i, j, k, index; int child, parent; int n, ntree; int istart, iptr, jptr; double *time1, *time2, *status, dtime; double *twt, *nwt, *count; int *sort1, *sort2; double vss, myrank; double wsum1, wsum2, wsum3; /*sum of wts below, tied, above*/ double lmean, umean, oldmean, newmean; double ndeath; SEXP count2; double *wt; int *indx; n = nrows(y); ntree = asInteger(ntree2); wt = REAL(wt2); indx = INTEGER(indx2); sort2 = INTEGER(sortstop); sort1 = INTEGER(sortstart); time1 = REAL(y); time2 = time1 + n; status= time2 + n; PROTECT(count2 = allocVector(REALSXP, 5)); count = REAL(count2); twt = (double *) R_alloc(2*ntree, sizeof(double)); nwt = twt + ntree; for (i=0; i< 2*ntree; i++) twt[i] =0.0; for (i=0; i<5; i++) count[i]=0.0; vss =0; <> UNPROTECT(1); return(count2); } @ The processing changes in 2 ways \begin{itemize} \item The loops go from $0$ to $n-1$ instead of $n-1$ to 0. We need to use [[sort1[i]]] instead of [[i]] as the subscript for the time2 and wt vectors. (The sort vectors go backwards in time.) This happens enough that we use a temporary variables [[iptr]] and [[jptr]] to avoid the double subscript. \item As we move from the longest time to the shortest observations are added into the tree of weights whenever we encounter their stop time. This is just as before. Weights now also need to be removed from the tree whenever we encounter an observation's start time. %' It is convenient ``catch up'' on this second task whenever we encounter a death. \end{itemize} <>= istart = 0; /* where we are with start times */ for (i=0; i= dtime; istart++) { wsum1 =0; oldmean = twt[0]/2; jptr = sort1[istart]; index = indx[jptr]; nwt[index] -= wt[jptr]; twt[index] -= wt[jptr]; wsum2 = nwt[index]; child = 2*index +1; /* left child */ if (child < ntree) wsum1 += twt[child]; while (index >0) { parent = (index-1)/2; twt[parent] -= wt[jptr]; if (!(index&1)) /* I am a right child */ wsum1 += (twt[parent] - twt[index]); index=parent; } wsum3 = twt[0] - (wsum1 + wsum2); lmean = wsum1/2; umean = wsum1 + wsum2 + wsum3/2; /* new upper mean */ newmean = twt[0]/2; myrank = wsum1 + wsum2/2; vss += wsum1*(newmean+ oldmean - 2*lmean) * (newmean-oldmean); oldmean -= wt[jptr]; /* the z in equations above */ vss += wsum3*(newmean+ oldmean -2*umean) * (newmean-oldmean); vss -= wt[jptr]* (myrank -newmean)*(myrank -newmean); } /* Process deaths */ for (j=i; j 0) { /* walk up the tree */ parent = (index-1)/2; if (index &1) /* I am the left child */ count[1] += wt[jptr] * (twt[parent] - twt[index]); else count[0] += wt[jptr] * (twt[parent] - twt[index]); index = parent; } } } else j = i+1; /* Add the weights for these obs into the tree and compute variance */ for (; i0) { parent = (index-1)/2; twt[parent] += wt[iptr]; if (!(index&1)) /* I am a right child */ wsum1 += (twt[parent] - twt[index]); index=parent; } wsum3 = twt[0] - (wsum1 + wsum2); lmean = wsum1/2; umean = wsum1 + wsum2 + wsum3/2; /* new upper mean */ newmean = twt[0]/2; myrank = wsum1 + wsum2/2; vss += wsum1*(newmean+ oldmean - 2*lmean) * (newmean-oldmean); vss += wsum3*(newmean+ oldmean +wt[iptr] - 2*umean) * (oldmean-newmean); vss += wt[iptr]* (myrank -newmean)*(myrank -newmean); } count[4] += ndeath * vss/twt[0]; } @ One last wrinkle is tied risk scores: they are all set to point to the same node of the tree. Here is the main routine. <>= survConcordance <- function(formula, data, weights, subset, na.action) { Call <- match.call() # save a copy of of the call, as documentation m <- match.call(expand.dots=FALSE) m[[1L]] <- quote(stats::model.frame) m$formula <- if(missing(data)) terms(formula, "strata") else terms(formula, "strata", data=data) m <- eval(m, sys.parent()) Terms <- attr(m, 'terms') Y <- model.extract(m, "response") if (!inherits(Y, "Surv")) { if (is.numeric(Y) && is.vector(Y)) Y <- Surv(Y) else stop("left hand side of the formula must be a numeric vector or a surival") } n <- nrow(Y) wt <- model.extract(m, 'weights') offset<- attr(Terms, "offset") if (length(offset)>0) stop("Offset terms not allowed") stemp <- untangle.specials(Terms, 'strata') if (length(stemp$vars)) { if (length(stemp$vars)==1) strat <- m[[stemp$vars]] else strat <- strata(m[,stemp$vars], shortlabel=TRUE) Terms <- Terms[-stemp$terms] } else strat <- NULL x <- model.matrix(Terms, m)[,-1, drop=FALSE] #remove the intercept if (ncol(x) > 1) stop("Only one predictor variable allowed") count <- survConcordance.fit(Y, x, strat, wt) if (is.null(strat)) { concordance <- (count[1] + count[3]/2)/sum(count[1:3]) std.err <- count[5]/(2* sum(count[1:3])) } else { temp <- colSums(count) concordance <- (temp[1] + temp[3]/2)/ sum(temp[1:3]) std.err <- temp[5]/(2*sum(temp[1:3])) } fit <- list(concordance= concordance, stats=count, n=n, std.err=std.err, call=Call) na.action <- attr(m, "na.action") if (length(na.action)) fit$na.action <- na.action oldClass(fit) <- 'survConcordance' fit } print.survConcordance <- function(x, ...) { if(!is.null(cl <- x$call)) { cat("Call:\n") dput(cl) cat("\n") } omit <- x$na.action if(length(omit)) cat(" n=", x$n, " (", naprint(omit), ")\n", sep = "") else cat(" n=", x$n, "\n") cat("Concordance= ", format(x$concordance), " se= ", format(x$std.err), '\n', sep='') print(x$stats) invisible(x) } @ This part of the compuation is a separate function, since it is also called by the coxph routines. Although we are very careful to create integers and/or doubles for the arguments to .Call I still wrap them in the appropriate as.xxx construction: ``belt and suspenders''. Also, referring to the the mathematics many paragraphs ago, the C routine returns the variance of $(C-D)/2$ and we return the standard deviation of $(C-D)$. If this routine is called with all the x values identical, then $C$ and $D$ will both be zero, but the calculated variance of $C-D$ can be a nonzero tiny number due to round off error. Since this can cause a warning message from the sqrt function we check and correct this. <>= survConcordance.fit <- function(y, x, strata, weight) { # The coxph program may occassionally fail, and this will kill the C # routine below if (any(is.na(x)) || any(is.na(y))) return(NULL) <> docount <- function(stime, risk, wts) { if (attr(stime, 'type') == 'right') { ord <- order(stime[,1], -stime[,2]) ux <- sort(unique(risk)) n2 <- length(ux) index <- btree(n2)[match(risk[ord], ux)] - 1L .Call(Cconcordance1, stime[ord,], as.double(wts[ord]), as.integer(index), as.integer(length(ux))) } else if (attr(stime, 'type') == "counting") { sort.stop <- order(-stime[,2], stime[,3]) sort.start <- order(-stime[,1]) ux <- sort(unique(risk)) n2 <- length(ux) index <- btree(n2)[match(risk, ux)] - 1L .Call(Cconcordance2, stime, as.double(wts), as.integer(index), as.integer(length(ux)), as.integer(sort.stop-1L), as.integer(sort.start-1L)) } else stop("Invalid survival type for concordance") } if (missing(weight) || length(weight)==0) weight <- rep(1.0, length(x)) storage.mode(y) <- "double" if (missing(strata) || length(strata)==0) { count <- docount(y, x, weight) if (count[1]==0 && count[2]==0) count[5]<-0 else count[5] <- 2*sqrt(count[5]) names(count) <- c("concordant", "discordant", "tied.risk", "tied.time", "std(c-d)") } else { strata <- as.factor(strata) ustrat <- levels(strata)[table(strata) >0] #some strata may have 0 obs count <- matrix(0., nrow=length(ustrat), ncol=5) for (i in 1:length(ustrat)) { keep <- which(strata == ustrat[i]) count[i,] <- docount(y[keep,,drop=F], x[keep], weight[keep]) } count[,5] <- 2*sqrt(ifelse(count[,1]+count[,2]==0, 0, count[,5])) dimnames(count) <- list(ustrat, c("concordant", "discordant", "tied.risk", "tied.time", "std(c-d)")) } count } @ survival/noweb/refer.bib0000644000175100001440000016526511773346736015076 0ustar hornikusers@string{annals= {Annals of Stat.}} @string{applstat= {Applied Stat.}} @string{bioj = {Biometrical J.}} @string{biok = {Biometrika}} @string{commstata = {Comm. 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The object could have strata and will almost always have multiple columns. If there is only one subscript it is preferentially associated with the strata, if there is no strata argument \code{i} will associate with the columns. If there are two subscripts the first goes with the strata. The little \code{nmatch} function allow the user to use either names or integer indices. <>= dim.survfitms <- function(x) { if (is.null(x$strata)) { if (is.matrix(x$pstate)) c(1L, ncol(x$pstate)) else 1L } else { nr <- length(x$strata) if (is.matrix(x$pstate)) c(nr, ncol(x$pstate)) else nr } } @ <>= "[.survfitms" <- function(x, ..., drop=TRUE) { nmatch <- function(indx, target) { # This function lets R worry about character, negative, or logical subscripts # It always returns a set of positive integer indices temp <- 1:length(target) names(temp) <- target temp[indx] } if (missing(..1)) i<- NULL else i <- ..1 # rows if (missing(..2)) j<- NULL else j <- ..2 # cols n <- length(x$time) if (is.null(x$strata) && is.matrix(x$pstate)) { # No strata, but a matrix of P(state) values # In this case, allow them to use a single i subscript as well if (is.null(j) && !is.null(i)) { j <- i i <- NULL } } # 'i' is the subscript from the user's point of view, 'i2' is the # subscript from the program's view, i.e, the row indices to keep if (is.null(i)) { i2 <- 1:n if (is.null(x$strata)) i <- 1 else i <- seq(along=x$strata) } else { if (is.null(x$strata) && (length(i) > 1 || i != 1)) stop("subscript out of bounds") indx <- nmatch(i, names(x$strata)) #strata to keep if (any(is.na(indx))) stop(paste("strata", paste(i[is.na(indx)], collapse=' '), 'not matched')) # Now, i may not be in order: a user has curve[3:2] to reorder # a plot. Hence the "unlist(lapply(" construct which will reorder # the data in the curves temp <- rep(1:length(x$strata), x$strata) i2 <- unlist(lapply(i, function(x) which(temp==x))) if (length(i) <=1 && drop) x$strata <- NULL else x$strata <- x$strata[indx] } if (!is.null(j)) { indx <- nmatch(j, x$states) if (any(is.na(indx))) stop("subscript out of bounds", j[is.na(indx)]) else j <- as.vector(indx) } # if only one state is kept, still retain the data as a matrix if (length(i2) ==1 && !is.null(j) && missing(drop)) drop <- FALSE # all the elements that can have "nstate" elements or columns # The n.event variable can have fewer temp <- c("n.risk", "n.event", "n.censor", "pstate", "cumhaz", "std.err", "lower", "upper") sfun <- function(z) { if (is.null(j)) { if (is.array(z)) { if (length(dim(z)) > 2) z[,,i2, drop=drop] else z[i2,,drop=drop] } else z[i2] } else { if (is.array(z)) { if (length(dim(z)) > 2) z[j,j,i2, drop=drop] else z[i2,j, drop=drop] } else z[i2] } } for (k in temp) x[[k]] <- sfun(x[[k]]) if (!is.null(j)) x$states <- x$states[j] x$n <- x$n[i] x$time <- x$time[i2] x$transitions <- NULL # this is incorrect after subscripting if (is.matrix(x$p0)) { if (is.null(j)) x$p0<- x$p0[i,] else x$p0 <- x$p0[i,j] } else if (!is.null(j)) x$p0 <- x$p0[j] if (!is.null(x$influence)) { if (length(i) >1) x$influence <- x$influence[i] else if (is.list(x$influence)) x$influence <- x$influence[[i]] if (!is.null(j)) { if (is.list(x$influence)) x$influence <- lapply(x$influence, function(x) x[,j,]) else x$influence <- x$influence[,j,] } } x } @ The summary.survfit and summary.survfitms functions share a significant amount of code. One part of the code that once was subtle is dealing with intermediate time points; the findInterval function in base R has made that much easier. Since the result does not involve interpolation, one should be able to create a special index vector i and return \code{time[i]}, \code{surv[i,]}, etc, to subscript all the curves in a survfit object at once. But that approach, though efficient in theory, runs into two problems. First is the extrapolated value for the curves at time points before the first event, which is allowed to be different for different curves in survfitms objects. The second is that there is interpolation of a sort: the n.event and n.censor components are summed over intervals when the selected time points are sparse, and that process is very tricky for multiple curves at once. At one point the code took that approach, but it became too complex to maintain. The current approach is slower but more transparent: do the individual curves one by one, then paste together the results. <>= summary.survfit <- function(object, times, censored=FALSE, scale=1, extend=FALSE, rmean=getOption('survfit.rmean'), ...) { fit <- object #make a local copy if (!inherits(fit, 'survfit')) stop("summary.survfit can only be used for survfit objects") # The print.rmean option is depreciated, it is still listened # to in print.survfit, but ignored here if (is.null(rmean)) rmean <- "common" if (is.numeric(rmean)) { if (is.null(object$start.time)) { if (rmean < min(object$time)) stop("Truncation point for the mean is < smallest survival") } else if (rmean < object$start.time) stop("Truncation point for the mean is < smallest survival") } else { rmean <- match.arg(rmean, c('none', 'common', 'individual')) if (length(rmean)==0) stop("Invalid value for rmean option") } temp <- survmean(fit, scale=scale, rmean) table <- temp$matrix #for inclusion in the output list rmean.endtime <- temp$end.time fit$time <- fit$time/scale if (!is.null(fit$strata)) { nstrat <- length(fit$strata) } delta <- function(x, indx) { # sums between chosen times if (is.logical(indx)) indx <- which(indx) if (!is.null(x) && length(indx) >0) { fx <- function(x, indx) diff(c(0, c(0, cumsum(x))[indx+1])) if (is.matrix(x)) { temp <- apply(x, 2, fx, indx=indx) # don't return a vector when only 1 time point is given if (is.matrix(temp)) temp else matrix(temp, nrow=1) } else fx(x, indx) } else NULL } if (missing(times)) { <> } else { <> times <- sort(times) #in case the user forgot if (is.null(fit$strata)) fit <- findrow(fit, times, extend) else { ltemp <- vector("list", nstrat) for (i in 1:nstrat) ltemp[[i]] <- findrow(fit[i], times, extend) fit <- unpacksurv(fit, ltemp) } } # finish off the output structure fit$table <- table if (length(rmean.endtime)>0 && !is.na(rmean.endtime)) fit$rmean.endtime <- rmean.endtime # An ordinary survfit object contains std(cum hazard), change scales if (!is.null(fit$std.err)) fit$std.err <- fit$std.err * fit$surv # Expand the strata if (!is.null(fit$strata)) fit$strata <- factor(rep(1:nstrat, fit$strata), 1:nstrat, labels= names(fit$strata)) class(fit) <- "summary.survfit" fit } @ The simple case of no times argument. <>= if (!censored) { index <- (rowSums(as.matrix(fit$n.event)) >0) for (i in c("time","n.risk", "n.event", "surv", "pstate", "std.err", "upper", "lower", "cumhaz")) { if (!is.null(fit[[i]])) { # not all components in all objects temp <- fit[[i]] if (!is.array(temp)) temp <- temp[index] #simple vector else if (is.matrix(temp)) temp <- temp[index,,drop=FALSE] else temp <- temp[,,index, drop=FALSE] # 3 way fit[[i]] <- temp } } # The n.enter and n.censor values are accumualated # both of these are simple vectors if (is.null(fit$strata)) { for (i in c("n.enter", "n.censor")) if (!is.null(fit[[i]])) fit[[i]] <- delta(fit[[i]], index) } else { sindx <- rep(1:nstrat, fit$strata) for (i in c("n.enter", "n.censor")) { if (!is.null(fit[[i]])) fit[[i]] <- unlist(sapply(1:nstrat, function(j) delta(fit[[i]][sindx==j], index[sindx==j]))) } # the "factor" is needed for the case that a strata has no # events at all, and hence 0 lines of output fit$strata[] <- as.vector(table(factor(sindx[index], 1:nstrat))) } } #if missing(times) and censored=TRUE, the fit object is ok as it is @ To deal with selected times we first define a subscripting function. For indices of 0, which are requested times that are before the first event, it fills in an initial value. <>= ssub <- function(x, indx, init=0) { #select an object and index if (!is.null(x) && length(indx)>0) { # the as.vector() is a way to keep R from adding "init" as a row name if (is.matrix(x)) rbind(as.vector(init), x)[indx+1,,drop=FALSE] else c(init, x)[indx+1] } else NULL } # The left.open argument was added to findInterval in R 3.3, but # our local servers are version 3.2.x. Work around it. find2 <- function(x, vec, left.open=FALSE, ...) { if (!left.open) findInterval(x, vec, ...) else length(vec) - findInterval(-x, rev(-vec), ...) } @ This function does the real work, for any single curve. The default value for init is correct for survival curves. Say that the data has values at time 5, 10, 15, 20 \ldots, and a user asks for \code{times=c(7, 15, 20, 30)}. In the input object \code{n.risk} refers to the number at risk just before time 5, 10, \ldots; it is a left-continuous function. The survival is a right-continuous function. So at time 7 we want to take the survival from time 5 and number at risk from time 10; \code{indx1} will be the right-continuous index and \code{indx2} the left continuous one. The value of n.risk at time 30 has to be computed. For counts of events, censoring, and entry we want to know the total number that happened during the intervals of 0-7, 7-15, 15-20 and 20-30. Technically censorings at time 15 happen just after time 15 so would go into the third line of the report. However, this would lead to terrible confusion for the user since using \code{times=c(5, 10, 15, 20)} would lead to different counts than a call that did not contain the times argument, so all 3 of the intermediates are computed using indx1. A report at time 30 is made only if extend=TRUE, in which case we need to compute a tail value for n.risk. <>= findrow <- function(fit, times, extend, init=1) { # First, toss any printing times that are outside our range if (is.null(fit$start.time)) mintime <- min(fit$time, 0) else mintime <- fit$start.time ptimes <- times[times >= mintime] if (!extend) { maxtime <- max(fit$time) ptimes <- ptimes[ptimes <= maxtime] } ntime <- length(fit$time) index1 <- find2(ptimes, fit$time) index2 <- 1 + find2(ptimes, fit$time, left.open=TRUE) # The pmax() above encodes the assumption that n.risk for any # times before the first observation = n.risk at the first obs fit$time <- ptimes for (i in c("surv", "pstate", "upper", "lower")) { if (!is.null(fit[[i]])) fit[[i]] <- ssub(fit[[i]], index1, init) } for (i in c("std.err", "cumhaz")) { if (!is.null(fit[[i]])) fit[[i]] <- ssub(fit[[i]], index1, 0) } if (is.matrix(fit$n.risk)) { # Every observation in the data has to end with a censor or event. # So by definition the number at risk after the last observed time # value must be 0. fit$n.risk <- rbind(fit$n.risk,0)[index2,,drop=FALSE] } else fit$n.risk <- c(fit$n.risk, 0)[index2] for (i in c("n.event", "n.censor", "n.enter")) fit[[i]] <- delta(fit[[i]], index1) fit } # For a single component, turn it from a list into a single vector, matrix # or array unlistsurv <- function(x, name) { temp <- lapply(x, function(x) x[[name]]) if (is.vector(temp[[1]])) unlist(temp) else if (is.matrix(temp[[1]])) do.call("rbind", temp) else { # the cumulative hazard is the only component that is an array # it's third dimension is n xx <- unlist(temp) dd <- dim(temp[[1]]) dd[3] <- length(xx)/prod(dd[1:2]) array(xx, dim=dd) } } # unlist all the components built by a set of calls to findrow # and remake the strata unpacksurv <- function(fit, ltemp) { keep <- c("time", "surv", "pstate", "upper", "lower", "std.err", "cumhaz", "n.risk", "n.event", "n.censor", "n.enter") for (i in keep) if (!is.null(fit[[i]])) fit[[i]] <- unlistsurv(ltemp, i) fit$strata[] <- sapply(ltemp, function(x) length(x$time)) fit } @ Repeat the code for survfitms objects. The only real difference is the preservation of \code{pstate} and \code{cumhaz} instead of \code{surv}, use of survmean2, and use of p0 for initial states. <>= summary.survfitms <- function(object, times, censored=FALSE, scale=1, extend=FALSE, rmean= getOption("survfit.rmean"), ...) { fit <- object if (!inherits(fit, 'survfitms')) stop("summary.survfitms can only be used for survfitms objects") # The print.rmean option is depreciated, it is still listened # to in print.survfit, but ignored here if (is.null(rmean)) rmean <- "common" if (is.numeric(rmean)) { if (is.null(object$start.time)) { if (rmean < min(object$time)) stop("Truncation point for the mean is < smallest survival") } else if (rmean < object$start.time) stop("Truncation point for the mean is < smallest survival") } else { rmean <- match.arg(rmean, c('none', 'common', 'individual')) if (length(rmean)==0) stop("Invalid value for rmean option") } temp <- survmean2(fit, scale=scale, rmean) table <- temp$matrix #for inclusion in the output list rmean.endtime <- temp$end.time if (!missing(times)) { if (!is.numeric(times)) stop ("times must be numeric") times <- sort(times) } fit$time <- fit$time/scale if (!is.null(fit$strata)) { nstrat <- length(fit$strata) sindx <- rep(1:nstrat, fit$strata) } delta <- function(x, indx) { # sums between chosen times if (is.logical(indx)) indx <- which(indx) if (!is.null(x) && length(indx) >0) { fx <- function(x, indx) diff(c(0, c(0, cumsum(x))[indx+1])) if (is.matrix(x)) { temp <- apply(x, 2, fx, indx=indx) if (is.matrix(temp)) temp else matrix(temp, nrow=1) } else fx(x, indx) } else NULL } if (missing(times)) { <> } else { <> times <- sort(times) if (is.null(fit$strata)) fit <- findrow(fit, times, extend, fit$p0) else { ltemp <- vector("list", nstrat) for (i in 1:nstrat) ltemp[[i]] <- findrow(fit[i], times, extend, fit$p0[i,]) fit <- unpacksurv(fit, ltemp) } } # finish off the output structure fit$table <- table if (length(rmean.endtime)>0 && !is.na(rmean.endtime)) fit$rmean.endtime <- rmean.endtime if (!is.null(fit$strata)) fit$strata <- factor(rep(names(fit$strata), fit$strata)) class(fit) <- "summary.survfitms" fit } <> <> @ Printing for a survfitms object is different than for a survfit one. The big difference is that I don't have an estimate of the median, or any other quantile for that matter. Mean time in state makes sense, but I don't have a standard error for it at the moment. The other is that there is usually a mismatch between the n.event matrix and the n.risk matrix. The latter has all the states that were possible whereas the former only has states with an arrow pointing in. We need to manufacture the 0 events for the other states. <>= print.survfitms <- function(x, scale=1, rmean = getOption("survfit.rmean"), ...) { if (!is.null(cl<- x$call)) { cat("Call: ") dput(cl) cat("\n") } omit <- x$na.action if (length(omit)) cat(" ", naprint(omit), "\n") if (is.null(rmean)) rmean <- "common" if (is.numeric(rmean)) { if (is.null(x$start.time)) { if (rmean < min(x$time)) stop("Truncation point for the mean is < smallest survival") } else if (rmean < x$start.time) stop("Truncation point for the mean is < smallest survival") } else { rmean <- match.arg(rmean, c('none', 'common', 'individual')) if (length(rmean)==0) stop("Invalid value for rmean option") } temp <- survmean2(x, scale=scale, rmean) if (is.null(temp$end.time)) print(temp$matrix, ...) else { etime <- temp$end.time dd <- dimnames(temp$matrix) cname <- dd[[2]] cname[length(cname)] <- paste0(cname[length(cname)], '*') dd[[2]] <- cname dimnames(temp$matrix) <- dd print(temp$matrix, ...) if (length(etime) ==1) cat(" *mean time in state, restricted (max time =", format(etime, ...), ")\n") else cat(" *mean time in state, restricted (per curve cutoff)\n") } invisible(x) } @ This part of the computation is set out separately since it is called by both print and summary. <>= survmean2 <- function(x, scale, rmean) { nstate <- length(x$states) #there will always be at least 1 state ngrp <- max(1, length(x$strata)) if (ngrp >1) { igrp <- rep(1:ngrp, x$strata) rname <- names(x$strata) } else { igrp <- rep(1, length(x$time)) rname <- NULL } # The n.event matrix may not have nstate columms. Its # colnames are the first elements of states, however if (is.matrix(x$n.event)) { nc <- ncol(x$n.event) nevent <- tapply(x$n.event, list(rep(igrp, nc), col(x$n.event)), sum) dimnames(nevent) <- list(rname, x$states[1:nc]) } else { nevent <- tapply(x$n.event, igrp, sum) names(nevent) <- rname } outmat <- matrix(0., nrow=nstate*ngrp , ncol=2) outmat[,1] <- rep(x$n, nstate) outmat[1:length(nevent), 2] <- c(nevent) if (ngrp >1) rowname <- c(outer(rname, x$states, paste, sep=", ")) else rowname <- x$states # Caculate the mean time in each state if (rmean != "none") { if (is.numeric(rmean)) maxtime <- rep(rmean, ngrp) else if (rmean=="common") maxtime <- rep(max(x$time), ngrp) else maxtime <- tapply(x$time, igrp, max) meantime <- matrix(0., ngrp, nstate) p0 <- matrix(x$p0, nrow=ngrp) #in case there is only one row if (!is.null(x$influence)) stdtime <- meantime for (i in 1:ngrp) { if (is.matrix(x$pstate)) temp <- rbind(p0[i,], x$pstate[igrp==i,, drop=FALSE]) else temp <- matrix(c(p0[i], x$pstate[igrp==i]), ncol=1) if (is.null(x$start.time)) tt <- c(0, x$time[igrp==i]) else tt <- c(x$start.time, x$time[igrp==i]) # Now cut it off at maxtime delta <- diff(c(tt[tt nrow(temp)) delta <- delta[1:nrow(temp)] if (length(delta) < nrow(temp)) delta <- c(delta, rep(0, nrow(temp) - length(delta))) meantime[i,] <- colSums(delta*temp) if (!is.null(x$influence)) { # calculate the variance if (is.list(x$influence)) itemp <- apply(x$influence[[i]], 1, function(x) colSums(x*delta)) else itemp <- apply(x$influence, 1, function(x) colSums(x*delta)) stdtime[i,] <- sqrt(rowSums(itemp^2)) } } outmat <- cbind(outmat, c(meantime)/scale) cname <- c("n", "nevent", "rmean") if (!is.null(x$influence)) { outmat <- cbind(outmat, c(stdtime)/scale) cname <- c(cname, "std(rmean)") } # report back a single time, if there is only one if (all(maxtime == maxtime[1])) maxtime <- maxtime[1] } else cname <- c("n", "nevent") dimnames(outmat) <- list(rowname, cname) if (rmean=='none') list(matrix=outmat) else list(matrix=outmat, end.time=maxtime/scale) } @ The influence array has subject for the first element, the other two mimic the is of the same shape as the \code{pstate}, but with one copy per subject. For the variance we do exactly the same calculation as the mean, once per subject, and add up the squares of the result. As with \code{pstate} and \code{p0} a major nuisance for all this is the fact that the results at time 0 are in a separate object. This is a consequence of how survfit objects were set up 20+ years ago, namely that the starting point (time=0, surv=1) was not stored in the object. With (start, stop] data we want to save a starting time = min of the start values, and with multi-state the starting estimate is a vector. It would be so much easier if I had kept it the other way -- but with 400 dependent packages change is very hard. <>= @ survival/noweb/coxsurv2.Rnw0000644000175100001440000005764612630050675015566 0ustar hornikusers% % Second part of coxsurv.Rnw, broken in two to make it easier for me % to work with emacs. Now, we're ready to do the main compuation. %' Before this revision (the one documented here using noweb) there were three C routines used in calculating survival after a Cox model \begin{enumerate} \item agsurv1 creates a single curve, but for the most general case of a \emph{covariate path}. It is used for time dependent covariates. \item agsurv2 creates a set of curves. These curves are for a fixed covariate set, although (start, stop] data is supported. If there were 3 strata in the fit and 4 covariate sets are given, the result will be 12 curves. \item agsurv3 is used to create population survival curves. The result is average survival curve (for 3 different definitions of 'average'). If there were 3 strata and 100 subjects, the first curve returned would be the average for those 100 individual curves in strata 1, the second for strata 2, and the third for strata 3. \end{enumerate} In June 2010 the first two were re-written in (mostly) R, in the process of adding functionality and repairing some flaws in the computation of a weighted variance. In effect, the changes are similar to the rewrite of the survfitKM function a few years ago. Computations are separate for each strata, and each strata will have a different number of time points in the result. Thus we can't preallocate a matrix. Instead we generate an empty list, %' one per strata, and then populate it with the survival curves. At the end we unlist the individual components one by one. This is memory efficient, the number of curves is usually small enough that the "for" loop is no great cost, and it's easier to see what's going on than C code. First, compute the baseline survival curves for each strata. If the strata was a factor we want to leave it in the same order, otherwise sort it. This fitting routine was set out as a separate function for the sake of the rms package. They want to utilize the computation, but have a diffferent recreation process for the x and y data. <>= survfitcoxph.fit <- function(y, x, wt, x2, risk, newrisk, strata, se.fit, survtype, vartype, varmat, id, y2, strata2, unlist=TRUE) { if (is.factor(strata)) ustrata <- levels(strata) else ustrata <- sort(unique(strata)) nstrata <- length(ustrata) survlist <- vector('list', nstrata) names(survlist) <- ustrata for (i in 1:nstrata) { indx <- which(strata== ustrata[i]) survlist[[i]] <- agsurv(y[indx,,drop=F], x[indx,,drop=F], wt[indx], risk[indx], survtype, vartype) } <> if (unlist) { if (length(result)==1) { # the no strata case if (se.fit) result[[1]][c("n", "time", "n.risk", "n.event", "n.censor", "surv", "cumhaz", "std.err")] else result[[1]][c("n", "time", "n.risk", "n.event", "n.censor", "surv", "cumhaz")] } else { temp <-list(n = unlist(lapply(result, function(x) x$n), use.names=FALSE), time= unlist(lapply(result, function(x) x$time), use.names=FALSE), n.risk= unlist(lapply(result, function(x) x$n.risk), use.names=FALSE), n.event= unlist(lapply(result, function(x) x$n.event), use.names=FALSE), n.censor=unlist(lapply(result, function(x) x$n.censor), use.names=FALSE), strata = sapply(result, function(x) length(x$time))) names(temp$strata) <- names(result) if ((missing(id) || is.null(id)) && nrow(x2)>1) { temp$surv <- t(matrix(unlist(lapply(result, function(x) t(x$surv)), use.names=FALSE), nrow= nrow(x2))) dimnames(temp$surv) <- list(NULL, row.names(x2)) temp$cumhaz <- t(matrix(unlist(lapply(result, function(x) t(x$cumhaz)), use.names=FALSE), nrow= nrow(x2))) if (se.fit) temp$std.err <- t(matrix(unlist(lapply(result, function(x) t(x$std.err)), use.names=FALSE), nrow= nrow(x2))) } else { temp$surv <- unlist(lapply(result, function(x) x$surv), use.names=FALSE) temp$cumhaz <- unlist(lapply(result, function(x) x$cumhaz), use.names=FALSE) if (se.fit) temp$std.err <- unlist(lapply(result, function(x) x$std.err), use.names=FALSE) } temp } } else { names(result) <- ustrata result } } @ In an ordinary survival curve object with multiple strata, as produced by [[survfitKM]], the time, survival and etc components are each a single vector that contains the results for strata 1, followed by strata 2, \ldots. The strata compontent is a vector of integers, one per strata, that gives the number of elements belonging to each stratum. The reason is that each strata will have a different number of observations, so that a matrix form was not viable, and the underlying C routines were not capable of handling lists (the code predates the .Call function by a decade). The underlying computation of [[survfitcoxph.fit]] naturally creates the list form, we unlist it to [[survfit]] form as our last action unless the caller requests otherwise. For [[individual=FALSE]] we have a second dimension, namely each of the target covariate sets (if there are multiples). Each of these generates a unique set of survival and variance(survival) values, but all of the same size since each uses all the strata. The final output structure in this case has single vectors for the time, number of events, number censored, and number at risk values since they are common to all the curves, and a marix of survival and variance estimates, one column for each of the distinct target values. If $\Lambda_0$ is the baseline cumulative hazard from the above calculation, then $r_i \Lambda_0$ is the cumulative hazard for the $i$th new risk score $r_i$. The variance has two parts, the first of which is $r_i^2 H_1$ where $H_1$ is returned from the [[agsurv]] routine, and the second is \begin{align*} H_2(t) =& d'(t) V d(t) \\ %' d(t) = \int_0^t [z- \overline x(s)] d\Lambda(s) \end{align*} $V$ is the variance matrix for $\beta$ from the fitted Cox model, and $d(t)$ is the distance between the target covariate $z$ and the mean of the original data, summed up over the interval from 0 to $t$. Essentially the variance in $\hat \beta$ has a larger influence when prediction is far from the mean. The function below takes the basic curve from the list and multiplies it out to matrix form. <>= expand <- function(fit, x2, varmat, se.fit) { if (survtype==1) surv <- cumprod(fit$surv) else surv <- exp(-fit$cumhaz) if (is.matrix(x2) && nrow(x2) >1) { #more than 1 row in newdata fit$surv <- outer(surv, newrisk, '^') dimnames(fit$surv) <- list(NULL, row.names(x2)) if (se.fit) { varh <- matrix(0., nrow=length(fit$varhaz), ncol=nrow(x2)) for (i in 1:nrow(x2)) { dt <- outer(fit$cumhaz, x2[i,], '*') - fit$xbar varh[,i] <- (cumsum(fit$varhaz) + rowSums((dt %*% varmat)* dt))* newrisk[i]^2 } fit$std.err <- sqrt(varh) } fit$cumhaz <- outer(fit$cumhaz, newrisk, '*') } else { fit$surv <- surv^newrisk if (se.fit) { dt <- outer(fit$cumhaz, c(x2)) - fit$xbar varh <- (cumsum(fit$varhaz) + rowSums((dt %*% varmat)* dt)) * newrisk^2 fit$std.err <- sqrt(varh) } fit$cumhaz <- fit$cumhaz * newrisk } fit } @ In the lines just above: I have a matrix [[dt]] with one row per death time and one column per variable. For each row $d_i$ separately we want the quadratic form $d_i V d_i'$. The first matrix product can %' be done for all rows at once: found in the inner parenthesis. Ordinary (not matrix) multiplication followed by rowsums does the rest in one fell swoop. Now, if [[id]] is missing we can simply apply the [[expand]] function to each strata. For the case with [[id]] not missing, we create a single survival curve for each unique id (subject). A subject will spend blocks of time with different covariate sets, sometimes even jumping between strata. Retrieve each one and save it into a list, and then sew them together end to end. The [[n]] component is the number of observations in the strata --- but this subject might visit several. We report the first one they were in for printout. The [[time]] component will be cumulative on this subject's scale. %' Counting this is a bit trickier than I first thought. Say that the subject's first interval goes from 1 to 10, with observed time points in that interval at 2, 5, and 7, and a second interval from 12 to 20 with observed time points in the data of 15 and 18. On the subject's time scale things happen at days 1, 4, 6, 12 and 15. The deltas saved below are 2-1, 5-2, 7-5, 3+ 14-12, 17-14. Note the 3+ part, kept in the [[timeforward]] variable. Why all this ``adding up'' nuisance? If the subject spent time in two strata, the second one might be on an internal time scale of `time since entering the strata'. The two intervals in newdata could be 0--10 followed by 0--20. Time for the subject can't go backwards though: the change %` between internal/external time scales is a bit like following someone who was stepping back and forth over the international date line. In the code the [[indx]] variable points to the set of times that the subject was present, for this row of the new data. Note the $>$ on one end and $\le$ on the other. If someone's interval 1 was 0--10 and interval 2 was 10--20, and there happened to be a jump in the baseline survival curve at exactly time 10 (someone else died), that jump is counted only in the first interval. <>= if (missing(id) || is.null(id)) result <- lapply(survlist, expand, x2, varmat, se.fit) else { onecurve <- function(slist, x2, y2, strata2, newrisk, se.fit) { ntarget <- nrow(x2) #number of different time intervals surv <- vector('list', ntarget) n.event <- n.risk <- n.censor <- varh1 <- varh2 <- time <- surv hazard <- vector('list', ntarget) stemp <- as.integer(strata2) timeforward <- 0 for (i in 1:ntarget) { slist <- survlist[[stemp[i]]] indx <- which(slist$time > y2[i,1] & slist$time <= y2[i,2]) if (length(indx)==0) { timeforward <- timeforward + y2[i,2] - y2[i,1] # No deaths or censors in user interval. Possible # user error, but not uncommon at the tail of the curve. } else { time[[i]] <- diff(c(y2[i,1], slist$time[indx])) #time increments time[[i]][1] <- time[[i]][1] + timeforward timeforward <- y2[i,2] - max(slist$time[indx]) hazard[[i]] <- slist$hazard[indx]*newrisk[i] if (survtype==1) surv[[i]] <- slist$surv[indx]^newrisk[i] n.event[[i]] <- slist$n.event[indx] n.risk[[i]] <- slist$n.risk[indx] n.censor[[i]]<- slist$n.censor[indx] dt <- outer(slist$cumhaz[indx], x2[i,]) - slist$xbar[indx,,drop=F] varh1[[i]] <- slist$varhaz[indx] *newrisk[i]^2 varh2[[i]] <- rowSums((dt %*% varmat)* dt) * newrisk[i]^2 } } cumhaz <- cumsum(unlist(hazard)) if (survtype==1) surv <- cumprod(unlist(surv)) #increments (K-M) else surv <- exp(-cumhaz) if (se.fit) list(n=as.vector(table(strata)[stemp[1]]), time=cumsum(unlist(time)), n.risk = unlist(n.risk), n.event= unlist(n.event), n.censor= unlist(n.censor), surv = surv, cumhaz= cumhaz, std.err = sqrt(cumsum(unlist(varh1)) + unlist(varh2))) else list(n=as.vector(table(strata)[stemp[1]]), time=cumsum(unlist(time)), n.risk = unlist(n.risk), n.event= unlist(n.event), n.censor= unlist(n.censor), surv = surv, cumhaz= cumhaz) } if (all(id ==id[1])) { result <- list(onecurve(survlist, x2, y2, strata2, newrisk, se.fit)) } else { uid <- unique(id) result <- vector('list', length=length(uid)) for (i in 1:length(uid)) { indx <- which(id==uid[i]) result[[i]] <- onecurve(survlist, x2[indx,,drop=FALSE], y2[indx,,drop=FALSE], strata2[indx], newrisk[indx], se.fit) } names(result) <- uid } } @ Next is the code for the [[agsurv]] function, which actually does the work. The estimates of survival are the Kalbfleisch-Prentice (KP), Breslow, and Efron. Each has an increment at each unique death time. First a bit of notation: $Y_i(t)$ is 1 if bservation $i$ is ``at risk'' at time $t$ and 0 otherwise. For a simple surivival ([[ncol(y)==2]]) a subject is at risk until the time of censoring or death (first column of [[y]]). For (start, stop] data ([[ncol(y)==3]]) a subject becomes a part of the risk set at start+0 and stays through stop. $dN_i(t)$ will be 1 if subject $i$ had an event at time $t$. The risk score for each subject is $r_i = \exp(X_i \beta)$. The Breslow increment at time $t$ is $\sum w_i dN_i(t) / \sum w_i r_i Y_i(t)$, the number of events at time $t$ over the number at risk at time $t$. The final survival is [[exp(-cumsum(increment))]]. The Kalbfleish-Prentice increment is a multiplicative term $z$ which is the solution to the equation $$ \sum w_i r_i Y_i(t) = \sum dN_i(t) w_i \frac{r_i}{1- z(t)^{r_i}} $$ The left hand side is the weighted number at risk at time $t$, the right hand side is a sum over the tied events at that time. If there is only one event the equation has a closed form solution. If not, and knowing the solution must lie between 0 and 1, we do 35 steps of bisection to get a solution within 1e-8. An alternative is to use the -log of the Breslow estimate as a starting estimate, which is faster but requires a more sophisticated iteration logic. The final curve is $\prod_t z(t)^{r_c}$ where $r_c$ is the risk score for the target subject. The Efron estimate can be viewed as a modified Breslow estimate under the assumption that tied deaths are not really tied -- we just don't know the %' order. So if there are 3 subjects who die at some time $t$ we will have three psuedo-terms for $t$, $t+\epsilon$, and $t+ 2\epsilon$. All 3 subjects are present for the denominator of the first term, 2/3 of each for the second, and 1/3 for the third terms denominator. All contribute 1/3 of the weight to each numerator (1/3 chance they were the one to die there). The formulas will require $\sum w_i dN_i(t)$, $\sum w_ir_i dN_i(t)$, and $\sum w_i X_i dN_i(t)$, i.e., the sums only over the deaths. For simple survival data the risk sum $\sum w_i r_i Y_i(t)$ for all the unique death times $t$ is fast to compute as a cumulative sum, starting at the longest followup time and summing towards the shortest. There are two algorithms for (start, stop] data. \begin{itemize} \item Do a separate sum at each death time. The problem is for very large data sets. For each death time the selection [[who <- (start=t)]] is $O(n)$ and can take more time then all the remaining calculations together. \item Use the difference of two cumulative sums, one ordered by start time and one ordered by stop time. This is $O(2n)$ for the intial sums. The problem here is potential round off error if the sums get large, which can happen if the time scale were very, very finely divided. This issue is mostly precluded by subtracting means first. \end{itemize} We compute the extended number still at risk --- all whose stop time is $\ge$ each unique death time --- in the vector [[xin]]. From this we have to subtract all those who haven't actually entered yet %' found in [[xout]]. Remember that (3,20] enters at time 3+. The total at risk at any time is the difference between them. Output is only for the stop times; a call to approx is used to reconcile the two time sets. The [[irisk]] vector is for the printout, it is a sum of weighted counts rather than weighted risk scores. <>= agsurv <- function(y, x, wt, risk, survtype, vartype) { nvar <- ncol(as.matrix(x)) status <- y[,ncol(y)] dtime <- y[,ncol(y) -1] death <- (status==1) time <- sort(unique(dtime)) nevent <- as.vector(rowsum(wt*death, dtime)) ncens <- as.vector(rowsum(wt*(!death), dtime)) wrisk <- wt*risk rcumsum <- function(x) rev(cumsum(rev(x))) # sum from last to first nrisk <- rcumsum(rowsum(wrisk, dtime)) irisk <- rcumsum(rowsum(wt, dtime)) if (ncol(y) ==2) { temp2 <- rowsum(wrisk*x, dtime) xsum <- apply(temp2, 2, rcumsum) } else { delta <- min(diff(time))/2 etime <- c(sort(unique(y[,1])), max(y[,1])+delta) #unique entry times indx <- approx(etime, 1:length(etime), time, method='constant', rule=2, f=1)$y esum <- rcumsum(rowsum(wrisk, y[,1])) #not yet entered nrisk <- nrisk - c(esum,0)[indx] irisk <- irisk - c(rcumsum(rowsum(wt, y[,1])),0)[indx] xout <- apply(rowsum(wrisk*x, y[,1]), 2, rcumsum) #not yet entered xin <- apply(rowsum(wrisk*x, dtime), 2, rcumsum) # dtime or alive xsum <- xin - (rbind(xout,0))[indx,,drop=F] } ndeath <- rowsum(status, dtime) #unweighted death count @ The KP estimate requires a short C routine to do the iteration efficiently, and the Efron estimate needs a second C routine to efficiently compute the partial sums. <>= ntime <- length(time) if (survtype ==1) { #Kalbfleisch-Prentice indx <- (which(status==1))[order(dtime[status==1])] #deaths km <- .C(Cagsurv4, as.integer(ndeath), as.double(risk[indx]), as.double(wt[indx]), as.integer(ntime), as.double(nrisk), inc = double(ntime)) } if (survtype==3 || vartype==3) { # Efron approx xsum2 <- rowsum((wrisk*death) *x, dtime) erisk <- rowsum(wrisk*death, dtime) #risk score sums at each death tsum <- .C(Cagsurv5, as.integer(length(nevent)), as.integer(nvar), as.integer(ndeath), as.double(nrisk), as.double(erisk), as.double(xsum), as.double(xsum2), sum1 = double(length(nevent)), sum2 = double(length(nevent)), xbar = matrix(0., length(nevent), nvar)) } haz <- switch(survtype, nevent/nrisk, nevent/nrisk, nevent* tsum$sum1) varhaz <- switch(vartype, nevent/(nrisk * ifelse(nevent>=nrisk, nrisk, nrisk-nevent)), nevent/nrisk^2, nevent* tsum$sum2) xbar <- switch(vartype, (xsum/nrisk)*haz, (xsum/nrisk)*haz, nevent * tsum$xbar) result <- list(n= nrow(y), time=time, n.event=nevent, n.risk=irisk, n.censor=ncens, hazard=haz, cumhaz=cumsum(haz), varhaz=varhaz, ndeath=ndeath, xbar=apply(matrix(xbar, ncol=nvar),2, cumsum)) if (survtype==1) result$surv <- km$inc result } @ The arguments to this function are the number of unique times n, which is the length of the vectors ndeath (number at each time), denom, and the returned vector km. The risk and wt vectors contain individual values for the subjects with an event. Their length will be equal to sum(ndeath). <>= #include "survS.h" #include "survproto.h" void agsurv4(Sint *ndeath, double *risk, double *wt, Sint *sn, double *denom, double *km) { int i,j,k, l; int n; /* number of unique death times */ double sumt, guess, inc; n = *sn; j =0; for (i=0; i>= #include "survS.h" void agsurv5(Sint *n2, Sint *nvar2, Sint *dd, double *x1, double *x2, double *xsum, double *xsum2, double *sum1, double *sum2, double *xbar) { double temp; int i,j, k, kk; double d; int n, nvar; n = n2[0]; nvar = nvar2[0]; for (i=0; i< n; i++) { d = dd[i]; if (d==1){ temp = 1/x1[i]; sum1[i] = temp; sum2[i] = temp*temp; for (k=0; k< nvar; k++) xbar[i+ n*k] = xsum[i + n*k] * temp*temp; } else { temp = 1/x1[i]; for (j=0; j>= pyears <- function(formula, data, weights, subset, na.action, rmap, ratetable, scale=365.25, expect=c('event', 'pyears'), model=FALSE, x=FALSE, y=FALSE, data.frame=FALSE) { <> <> <> } @ Start out with the standard model processing, which involves making a copy of the input call, but keeping only the arguments we want. We then process the special argument [[rmap]]. This is discussed in the section on the [[survexp]] function so we need not repeat the explantation here. <>= expect <- match.arg(expect) Call <- match.call() # create a call to model.frame() that contains the formula (required) # and any other of the relevant optional arguments # then evaluate it in the proper frame indx <- match(c("formula", "data", "weights", "subset", "na.action"), names(Call), nomatch=0) if (indx[1] ==0) stop("A formula argument is required") m <- Call[c(1,indx)] # only keep the arguments we wanted m[[1L]] <- quote(stats::model.frame) # change the function called Terms <- if(missing(data)) terms(formula, 'ratetable') else terms(formula, 'ratetable',data=data) if (any(attr(Terms, 'order') >1)) stop("Pyears cannot have interaction terms") rate <- attr(Terms, "specials")$ratetable if (length(rate) >0 || !missing(rmap) || !missing(ratetable)) { has.ratetable <- TRUE if(length(rate) > 1) stop("Can have only 1 ratetable() call in a formula") if (missing(ratetable)) stop("No rate table specified") <> } else has.ratetable <- FALSE m <- eval(m, parent.frame()) Y <- model.extract(m, 'response') if (is.null(Y)) stop ("Follow-up time must appear in the formula") if (!is.Surv(Y)){ if (any(Y <0)) stop ("Negative follow up time") Y <- as.matrix(Y) if (ncol(Y) >2) stop("Y has too many columns") } else { stype <- attr(Y, 'type') if (stype == 'right') { if (any(Y[,1] <0)) stop("Negative survival time") nzero <- sum(Y[,1]==0 & Y[,2] ==1) if (nzero >0) warning(paste(nzero, "observations with an event and 0 follow-up time,", "any rate calculations are statistically questionable")) } else if (stype != 'counting') stop("Only right-censored and counting process survival types are supported") } n <- nrow(Y) if (is.null(n) || n==0) stop("Data set has 0 observations") weights <- model.extract(m, 'weights') if (is.null(weights)) weights <- rep(1.0, n) @ The next step is to check out the ratetable. For a population rate table a set of consistency checks is done by the [[match.ratetable]] function, giving a set of sanitized indices [[R]]. This function wants characters turned to factors. For a Cox model [[R]] will be a model matix whose covariates are coded in exactly the same way that variables were coded in the original Cox model. We call the model.matrix.coxph function so as not to have to repeat the steps found there (remove cluster statements, etc). <>= # rdata contains the variables matching the ratetable if (has.ratetable) { rdata <- data.frame(eval(rcall, m), stringsAsFactors=TRUE) if (is.ratetable(ratetable)) { israte <- TRUE rtemp <- match.ratetable(rdata, ratetable) R <- rtemp$R } else if (inherits(ratetable, 'coxph')) { israte <- FALSE Terms <- ratetable$terms if (!is.null(attr(Terms, 'offset'))) stop("Cannot deal with models that contain an offset") strats <- attr(Terms, "specials")$strata if (length(strats)) stop("pyears cannot handle stratified Cox models") if (any(names(m[,rate]) != attr(ratetable$terms, 'term.labels'))) stop("Unable to match new data to old formula") R <- model.matrix.coxph(ratetable, data=rdata) } else stop("Invalid ratetable") } @ Now we process the non-ratetable variables. Those of class [[tcut]] set up time-dependent classes. For these the cutpoints attribute sets the intervals, if there were 4 cutpoints of 1, 5,6, and 10 the 3 intervals will be 1-5, 5-6 and 6-10, and odims will be 3. All other variables are treated as factors. <>= ovars <- attr(Terms, 'term.labels') if (length(ovars)==0) { # no categories! X <- rep(1,n) ofac <- odim <- odims <- ocut <- 1 } else { odim <- length(ovars) ocut <- NULL odims <- ofac <- double(odim) X <- matrix(0, n, odim) outdname <- vector("list", odim) names(outdname) <- attr(Terms, 'term.labels') for (i in 1:odim) { temp <- m[[ovars[i]]] if (inherits(temp, 'tcut')) { X[,i] <- temp temp2 <- attr(temp, 'cutpoints') odims[i] <- length(temp2) -1 ocut <- c(ocut, temp2) ofac[i] <- 0 outdname[[i]] <- attr(temp, 'labels') } else { temp2 <- as.factor(temp) X[,i] <- temp2 temp3 <- levels(temp2) odims[i] <- length(temp3) ofac[i] <- 1 outdname[[i]] <- temp3 } } } @ Now do the computations. The code above has separated out the variables into 3 groups: \begin{itemize} \item The variables in the rate table. These determine where we \emph{start} in the rate table with respect to retrieving the relevant death rates. For the US table [[survexp.us]] this will be the date of study entry, age (in days) at study entry, and sex of each subject. \item The variables on the right hand side of the model. These are interpreted almost identically to a call to [[table]], with special treatment for those of class \emph{tcut}. \item The response variable, which tells the number of days of follow-up and optionally the status at the end of follow-up. \end{itemize} Start with the rate table variables. There is an oddity about US rate tables: the entry for age (year=1970, age=55) contains the daily rate for anyone who turns 55 in that year, from their birthday forward for 365 days. So if your birthday is on Oct 2, the 1970 table applies from 2Oct 1970 to 1Oct 1971. The underlying C code wants to make the 1970 rate table apply from 1Jan 1970 to 31Dec 1970. The easiest way to finess this is to fudge everyone's enter-the-study date. If you were born in March but entered in April, make it look like you entered in Febuary; that way you get the first 11 months at the entry year's rates, etc. The birth date is entry date - age in days (based on 1/1/1960). The other aspect of the rate tables is that ``older style'' tables, those that have the factor attribute, contained only decennial data which the C code would interpolate on the fly. The value of [[atts$factor]] was 10 indicating that there are 10 years in the interpolation interval. The newer tables do not do this and the C code is passed a 0/1 for continuous (age and year) versus discrete (sex, race). <>= ocut <-c(ocut,0) #just in case it were of length 0 osize <- prod(odims) if (has.ratetable) { #include expected atts <- attributes(ratetable) cuts <- atts$cutpoints if (is.null(atts$type)) { #old stlye table rfac <- atts$factor us.special <- (rfac >1) } else { rfac <- 1*(atts$type ==1) us.special <- (atts$type==4) } if (any(us.special)) { #special handling for US pop tables # Now, the 'entry' date on a US rate table is the number of days # since 1/1/1960, and the user data has been aligned to the # same system by match.ratetable and marked as "year". # The birth date is entry date - age in days (based on 1/1/1960). # I don't much care which date functions I use to do the arithmetic # below. Unfortunately R and Splus don't share one. My "date" # class is simple, but is also one of the earlier date class # attempts, has less features than others, and will one day fade # away; so I don't want to depend on it alone. # cols <- match(c("age", "year"), atts$dimid) if (any(is.na(cols))) stop("Ratetable does not have expected shape") if (exists("as.Date")) { # true for modern version of R bdate <- as.Date('1960/1/1') + (R[,cols[2]] - R[,cols[1]]) byear <- format(bdate, "%Y") offset <- bdate - as.Date(paste(byear, "01/01", sep='/'), origin="1960/01/01") } #else if (exists('month.day.year')) { # Splus, usually # bdate <- R[,cols[2]] - R[,cols[1]] # byear <- month.day.year(bdate)$year # offset <- bdate - julian(1,1,byear) # } #else if (exists('date.mdy')) { # Therneau's date class is available # bdate <- as.date(R[,cols[2]] - R[,cols[1]]) # byear <- date.mdy(bdate)$year # offset <- bdate - mdy.date(1,1,byear) # } else stop("Can't find an appropriate date class\n") R[,cols[2]] <- R[,cols[2]] - offset # Doctor up "cutpoints" - only needed for old style rate tables # for which the C code does interpolation on the fly if (any(rfac >1)) { temp <- which(us.special) nyear <- length(cuts[[temp]]) nint <- rfac[temp] #intervals to interpolate over cuts[[temp]] <- round(approx(nint*(1:nyear), cuts[[temp]], nint:(nint*nyear))$y - .0001) } } docount <- is.Surv(Y) temp <- .C(Cpyears1, as.integer(n), as.integer(ncol(Y)), as.integer(is.Surv(Y)), as.double(Y), as.double(weights), as.integer(length(atts$dim)), as.integer(rfac), as.integer(atts$dim), as.double(unlist(cuts)), as.double(ratetable), as.double(R), as.integer(odim), as.integer(ofac), as.integer(odims), as.double(ocut), as.integer(expect=='event'), as.double(X), pyears=double(osize), pn =double(osize), pcount=double(if(docount) osize else 1), pexpect=double(osize), offtable=double(1))[18:22] } else { #no expected docount <- as.integer(ncol(Y) >1) temp <- .C(Cpyears2, as.integer(n), as.integer(ncol(Y)), as.integer(docount), as.double(Y), as.double(weights), as.integer(odim), as.integer(ofac), as.integer(odims), as.double(ocut), as.double(X), pyears=double(osize), pn =double(osize), pcount=double(if (docount) osize else 1), offtable=double(1)) [11:14] } @ Create the output object. <>= has.tcut <- any(sapply(m, function(x) inherits(x, 'tcut'))) if (data.frame) { # Create a data frame as the output, rather than a set of # rate tables keep <- (temp$pyears >0) # what rows to keep in the output names(outdname) <- ovars if (length(outdname) ==1) { # if there is only one variable, the call to "do.call" loses # the variable name, since expand.grid returns a factor df <- data.frame((outdname[[1]])[keep], pyears= temp$pyears[keep]/scale, n = temp$pn[keep]) names(df) <- c(names(outdname), 'pyears', 'n') } else { df <- cbind(do.call("expand.grid", outdname)[keep,], pyears= temp$pyears[keep]/scale, n = temp$pn[keep]) } row.names(df) <- 1:nrow(df) if (has.ratetable) df$expected <- temp$pexpect[keep] if (expect=='pyears') df$expected <- df$expected/scale if (docount) df$event <- temp$pcount[keep] out <- list(call=Call, data= df, offtable=temp$offtable/scale, tcut=has.tcut) if (has.ratetable && !is.null(rtemp$summ)) out$summary <- rtemp$summ } else if (prod(odims) ==1) { #don't make it an array out <- list(call=Call, pyears=temp$pyears/scale, n=temp$pn, offtable=temp$offtable/scale, tcut = has.tcut) if (has.ratetable) { out$expected <- temp$pexpect if (expect=='pyears') out$expected <- out$expected/scale if (!is.null(rtemp$summ)) out$summary <- rtemp$summ } if (docount) out$event <- temp$pcount } else { out <- list(call = Call, pyears= array(temp$pyears/scale, dim=odims, dimnames=outdname), n = array(temp$pn, dim=odims, dimnames=outdname), offtable = temp$offtable/scale, tcut=has.tcut) if (has.ratetable) { out$expected <- array(temp$pexpect, dim=odims, dimnames=outdname) if (expect=='pyears') out$expected <- out$expected/scale if (!is.null(rtemp$summ)) out$summary <- rtemp$summ } if (docount) out$event <- array(temp$pcount, dim=odims, dimnames=outdname) } out$observations <- nrow(m) out$terms <- Terms na.action <- attr(m, "na.action") if (length(na.action)) out$na.action <- na.action if (model) out$model <- m else { if (x) out$x <- X if (y) out$y <- Y } class(out) <- 'pyears' out @ survival/noweb/coxph.Rnw0000644000175100001440000007074613026501446015105 0ustar hornikusers\section{Cox Models} \subsection{Coxph} The [[coxph]] routine is the underlying basis for all the models. The source was converted to noweb when adding time-transform terms. The call starts out with the basic building of a model frame and proceeds from there. The aeqSurv function is used to adjucate near ties in the time variable, numerical precision issues that occur when users base caculations on days/365.25 instead of days. <>= #tt <- function(x) x coxph <- function(formula, data, weights, subset, na.action, init, control, ties= c("efron", "breslow", "exact"), singular.ok =TRUE, robust=FALSE, model=FALSE, x=FALSE, y=TRUE, tt, method=ties, ...) { ties <- match.arg(ties) Call <- match.call() ## We want to pass any ... args to coxph.control, but not pass things ## like "dats=mydata" where someone just made a typo. The use of ... ## is simply to allow things like "eps=1e6" with easier typing extraArgs <- list(...) if (length(extraArgs)) { controlargs <- names(formals(coxph.control)) #legal arg names indx <- pmatch(names(extraArgs), controlargs, nomatch=0L) if (any(indx==0L)) stop(gettextf("Argument %s not matched", names(extraArgs)[indx==0L]), domain = NA) } if (missing(control)) control <- coxph.control(...) <> Y <- model.extract(mf, "response") if (!inherits(Y, "Surv")) stop("Response must be a survival object") type <- attr(Y, "type") if (type!='right' && type!='counting') stop(paste("Cox model doesn't support \"", type, "\" survival data", sep='')) data.n <- nrow(Y) #remember this before any time transforms if (control$timefix) Y <- aeqSurv(Y) <> # The time transform will expand the data frame mf. To do this # it needs Y and the strata. Everything else (cluster, offset, weights) # should be extracted after the transform # strats <- attr(Terms, "specials")$strata if (length(strats)) { stemp <- untangle.specials(Terms, 'strata', 1) if (length(stemp$vars)==1) strata.keep <- mf[[stemp$vars]] else strata.keep <- strata(mf[,stemp$vars], shortlabel=TRUE) strats <- as.numeric(strata.keep) } timetrans <- attr(Terms, "specials")$tt if (missing(tt)) tt <- NULL if (length(timetrans)) { <> } cluster<- attr(Terms, "specials")$cluster if (length(cluster)) { robust <- TRUE #flag to later compute a robust variance tempc <- untangle.specials(Terms, 'cluster', 1:10) ord <- attr(Terms, 'order')[tempc$terms] if (any(ord>1)) stop ("Cluster can not be used in an interaction") cluster <- strata(mf[,tempc$vars], shortlabel=TRUE) #allow multiples dropterms <- tempc$terms #we won't want this in the X matrix # Save away xlevels after removing cluster (we don't want to save upteen # levels of that variable, which we will never need). xlevels <- .getXlevels(Terms[-tempc$terms], mf) } else { dropterms <- NULL if (missing(robust)) robust <- FALSE xlevels <- .getXlevels(Terms, mf) } contrast.arg <- NULL #due to shared code with model.matrix.coxph <> <> <> <> <> } @ Standard code to grab the data. <>= # create a call to model.frame() that contains the formula (required) # and any other of the relevant optional arguments # then evaluate it in the proper frame indx <- match(c("formula", "data", "weights", "subset", "na.action"), names(Call), nomatch=0) if (indx[1] ==0) stop("A formula argument is required") temp <- Call[c(1,indx)] # only keep the arguments we wanted temp[[1L]] <- quote(stats::model.frame) # change the function called special <- c("strata", "cluster", "tt") temp$formula <- if(missing(data)) terms(formula, special) else terms(formula, special, data=data) # Make "tt" visible for coxph formulas, without making it visible elsewhere if (!is.null(attr(temp$formula, "specials")$tt)) { coxenv <- new.env(parent= environment(formula)) assign("tt", function(x) x, env=coxenv) environment(temp$formula) <- coxenv } mf <- eval(temp, parent.frame()) if (nrow(mf) ==0) stop("No (non-missing) observations") Terms <- terms(mf) @ An increasingly common error is for users to put the time variable on both sides of the formula, in the mistaken idea that this will deal with a failure of proportional hazards. Add a test for such models, and bail out. The \code{variables} attribute of the Terms object is the expression form of a list that contains the response variable followed by the predictors. Subscripting this, element 1 is the call to ``list'' itself so we always retain it. My \code{terms.inner} function works only with formula objects. <>= if (length(attr(Terms, 'variables')) > 2) { # a ~1 formula has length 2 ytemp <- terms.inner(formula[1:2]) xtemp <- terms.inner(formula[-2]) if (any(!is.na(match(xtemp, ytemp)))) warning("a variable appears on both the left and right sides of the formula") } @ At this point we deal with any time transforms. The model frame is expanded to a ``fake'' data set that has a separate stratum for each unique event-time/strata combination, and any tt() terms in the formula are processed. The first step is to create the index vector [[tindex]] and new strata [[.strata.]]. This last is included in a model.frame call (for others to use), internally the code simply replaces the [[strats]] variable. A (modestly) fast C-routine first counts up and indexes the observations. We start out with error checks; since the computation can be slow we want to complain early. <>= timetrans <- untangle.specials(Terms, 'tt') ntrans <- length(timetrans$terms) if (is.null(tt)) { tt <- function(x, time, riskset, weights){ #default to O'Brien's logit rank obrien <- function(x) { r <- rank(x) (r-.5)/(.5+length(r)-r) } unlist(tapply(x, riskset, obrien)) } } if (is.function(tt)) tt <- list(tt) #single function becomes a list if (is.list(tt)) { if (any(!sapply(tt, is.function))) stop("The tt argument must contain function or list of functions") if (length(tt) != ntrans) { if (length(tt) ==1) { temp <- vector("list", ntrans) for (i in 1:ntrans) temp[[i]] <- tt[[1]] tt <- temp } else stop("Wrong length for tt argument") } } else stop("The tt argument must contain a function or list of functions") if (ncol(Y)==2) { if (length(strats)==0) { sorted <- order(-Y[,1], Y[,2]) newstrat <- rep.int(0L, nrow(Y)) newstrat[1] <- 1L } else { sorted <- order(strats, -Y[,1], Y[,2]) #newstrat marks the first obs of each strata newstrat <- as.integer(c(1, 1*(diff(strats[sorted])!=0))) } if (storage.mode(Y) != "double") storage.mode(Y) <- "double" counts <- .Call(Ccoxcount1, Y[sorted,], as.integer(newstrat)) tindex <- sorted[counts$index] } else { if (length(strats)==0) { sort.end <- order(-Y[,2], Y[,3]) sort.start<- order(-Y[,1]) newstrat <- c(1L, rep(0, nrow(Y) -1)) } else { sort.end <- order(strats, -Y[,2], Y[,3]) sort.start<- order(strats, -Y[,1]) newstrat <- c(1L, as.integer(diff(strats[sort.end])!=0)) } if (storage.mode(Y) != "double") storage.mode(Y) <- "double" counts <- .Call(Ccoxcount2, Y, as.integer(sort.start -1L), as.integer(sort.end -1L), as.integer(newstrat)) tindex <- counts$index } @ The C routine has returned a list with 4 elements \begin{description} \item[nrisk] a vector containing the number at risk at each event time \item[time] the vector of event times \item[status] a vector of status values \item[index] a vector containing the set of subjects at risk for event time 1, followed by those at risk at event time 2, those at risk at event time 3, etc. \end{description} The new data frame is then a simple creation. The subtle part below is a desire to retain transformation information so that a downstream call to \code{termplot} will work. The tt function supplied by the user often finishes with a call to \code{pspline} or \code{ns}. If the returned value of the \code{tt} call has a class for which a \code{makepredictcall} method exists then we need to do 2 things: \begin{enumerate} \item Construct a fake call, e.g., ``pspline(age)'', then feed it and the result of tt as arguments to \code{makepredictcall} \item Replace that componenent in the predvars attribute of the terms. \end{enumerate} The \code{timetrans\$terms} value is a count of the right hand side of the formula. Some objects in the terms structure are unevaluated calls that include y, this adds 2 to the count (the call to ``list'' and the response). <>= Y <- Surv(rep(counts$time, counts$nrisk), counts$status) type <- 'right' # new Y is right censored, even if the old was (start, stop] mf <- mf[tindex,] strats <- rep(1:length(counts$nrisk), counts$nrisk) weights <- model.weights(mf) if (!is.null(weights) && any(!is.finite(weights))) stop("weights must be finite") tcall <- attr(Terms, 'variables')[timetrans$terms+2] pvars <- attr(Terms, 'predvars') pmethod <- sub("makepredictcall.", "", as.vector(methods("makepredictcall"))) for (i in 1:ntrans) { newtt <- (tt[[i]])(mf[[timetrans$var[i]]], Y[,1], strats, weights) mf[[timetrans$var[i]]] <- newtt nclass <- class(newtt) if (any(nclass %in% pmethod)) { # It has a makepredictcall method dummy <- as.call(list(as.name(class(newtt)[1]), tcall[[i]][[2]])) ptemp <- makepredictcall(newtt, dummy) pvars[[timetrans$terms[i]+2]] <- ptemp } } attr(Terms, "predvars") <- pvars @ This is the C code for time-transformation. For the first case it expects y to contain time and status sorted from longest time to shortest, and strata=1 for the first observation of each strata. <>= #include "survS.h" /* ** Count up risk sets and identify who is in each */ SEXP coxcount1(SEXP y2, SEXP strat2) { int ntime, nrow; int i, j, n; int stratastart=0; /* start row for this strata */ int nrisk=0; /* number at risk (=0 to stop -Wall complaint)*/ double *time, *status; int *strata; double dtime; SEXP rlist, rlistnames, rtime, rn, rindex, rstatus; int *rrindex, *rrstatus; n = nrows(y2); time = REAL(y2); status = time +n; strata = INTEGER(strat2); /* ** First pass: count the total number of death times (risk sets) ** and the total number of rows in the new data set. */ ntime=0; nrow=0; for (i=0; i> /* ** Pass 2, fill them in */ ntime=0; for (i=0; i> } @ The start-stop case is a bit more work. The set of subjects still at risk is an arbitrary set so we have to keep an index vector [[atrisk]]. At each new death time we write out the set of those at risk, with the deaths last. I toyed with the idea of a binary tree then realized it was not useful: at each death we need to list out all the subjects at risk into the index vector which is an $O(n)$ process, tree or not. <>= #include "survS.h" /* count up risk sets and identify who is in each, (start,stop] version */ SEXP coxcount2(SEXP y2, SEXP isort1, SEXP isort2, SEXP strat2) { int ntime, nrow; int i, j, istart, n; int nrisk=0, *atrisk; double *time1, *time2, *status; int *strata; double dtime; int iptr, jptr; SEXP rlist, rlistnames, rtime, rn, rindex, rstatus; int *rrindex, *rrstatus; int *sort1, *sort2; n = nrows(y2); time1 = REAL(y2); time2 = time1+n; status = time2 +n; strata = INTEGER(strat2); sort1 = INTEGER(isort1); sort2 = INTEGER(isort2); /* ** First pass: count the total number of death times (risk sets) ** and the total number of rows in the new data set */ ntime=0; nrow=0; istart =0; /* walks along the sort1 vector (start times) */ for (i=0; i= dtime; istart++) nrisk--; for(j= i+1; j> atrisk = (int *)R_alloc(n, sizeof(int)); /* marks who is at risk */ /* ** Pass 2, fill them in */ ntime=0; nrisk=0; j=0; /* pointer to time1 */; istart=0; for (i=0; i=dtime; istart++) { atrisk[sort1[istart]]=0; nrisk--; } for (j=1; j> } @ <>= /* ** Allocate memory */ PROTECT(rtime = allocVector(REALSXP, ntime)); PROTECT(rn = allocVector(INTSXP, ntime)); PROTECT(rindex=allocVector(INTSXP, nrow)); PROTECT(rstatus=allocVector(INTSXP,nrow)); rrindex = INTEGER(rindex); rrstatus= INTEGER(rstatus); @ <>= /* return the list */ PROTECT(rlist = allocVector(VECSXP, 4)); SET_VECTOR_ELT(rlist, 0, rn); SET_VECTOR_ELT(rlist, 1, rtime); SET_VECTOR_ELT(rlist, 2, rindex); SET_VECTOR_ELT(rlist, 3, rstatus); PROTECT(rlistnames = allocVector(STRSXP, 4)); SET_STRING_ELT(rlistnames, 0, mkChar("nrisk")); SET_STRING_ELT(rlistnames, 1, mkChar("time")); SET_STRING_ELT(rlistnames, 2, mkChar("index")); SET_STRING_ELT(rlistnames, 3, mkChar("status")); setAttrib(rlist, R_NamesSymbol, rlistnames); unprotect(6); return(rlist); @ We now return to the original thread of the program, though perhaps with new data, and build the $X$ matrix. Creation of the $X$ matrix for a Cox model requires just a bit of trickery. The baseline hazard for a Cox model plays the role of an intercept, but does not appear in the $X$ matrix. However, to create the columns of $X$ for factor variables correctly, we need to call the model.matrix routine in such a way that it \emph{thinks} there is an intercept. If there are strata the proper $X$ matrix is constructed as though there were one intercept per strata. One simple way to handle this is to call model.matrix on the original formula and then remove the terms we don't need. However, \begin{enumerate} \item The cluster() term, if any, could lead to thousands of extraneous ``intercept'' columns which are never needed. \item Likewise, nested case-control models can have thousands of strata, again leading many intercepts we never need. \item If there are strata by factor interactions in the model, the dummy intercepts-per-strata columns are necessary information for the model.matrix routine to correctly compute other columns of $X$. \end{enumerate} For reasons 1 and 2 above the usual plan is to remove cluster and strata terms from the ``Terms'' object \emph{before} calling model.matrix, unless there are strata by covariate interactions in which case we remove them after. For the first strategy the \code{assign} attribute of the resulting model matrix then needs to be fixed up, since we want it to index into the original formula. For example imagine the right hand side of \code{age + strata(sex) + trt} where trt is a factor with 3 levels. The assign attribute from the modified formula will be (0,1,2,2) corresponding to the intercept, age, and treatment columns. The final $X$ matrix has no intercept, and a proper assign attribute of (1,3,3) since trt is the third variable in the original formula. The dropterms variable contains terms to drop before creation of the X matrix. It was initialized far above in the code when we dealt with cluster terms. <>= attr(Terms, "intercept") <- 1 adrop <- 0 #levels of "assign" to be dropped; 0= intercept stemp <- untangle.specials(Terms, 'strata', 1) if (length(stemp$vars) > 0) { #if there is a strata statement hasinteractions <- FALSE for (i in stemp$vars) { #multiple strata terms are allowed # The factors attr has one row for each variable in the frame, one # col for each term in the model. Pick rows for each strata # var, and find if it participates in any interactions. if (any(attr(Terms, 'order')[attr(Terms, "factors")[i,] >0] >1)) hasinteractions <- TRUE } if (!hasinteractions) dropterms <- c(dropterms, stemp$terms) else adrop <- c(0, match(stemp$var, colnames(attr(Terms, 'factors')))) } if (length(dropterms)) { temppred <- attr(terms, "predvars") Terms2 <- Terms[ -dropterms] if (!is.null(temppred)) { # subscripting a Terms object currently drops predvars, in error attr(Terms2, "predvars") <- temppred[-(1+dropterms)] # "Call" object } X <- model.matrix(Terms2, mf, constrasts=contrast.arg) # we want to number the terms wrt the original model matrix # Do not forget the intercept, which will be a zero renumber <- match(colnames(attr(Terms2, "factors")), colnames(attr(Terms, "factors"))) attr(X, "assign") <- c(0, renumber)[1+attr(X, "assign")] } else X <- model.matrix(Terms, mf, contrasts=contrast.arg) # drop the intercept after the fact, and also drop strata if necessary Xatt <- attributes(X) xdrop <- Xatt$assign %in% adrop #columns to drop (always the intercept) X <- X[, !xdrop, drop=FALSE] attr(X, "assign") <- Xatt$assign[!xdrop] #if (any(adrop>0)) attr(X, "contrasts") <- Xatt$contrasts[-adrop] #else attr(X, "contrasts") <- Xatt$contrasts attr(X, "contrasts") <- Xatt$contrasts @ Finish the setup. If someone includes and init statement, make sure that it does not lead to instant code failure due to overflow/underflow. <>= offset <- model.offset(mf) if (is.null(offset) | all(offset==0)) offset <- rep(0., nrow(mf)) else if (any(!is.finite(offset))) stop("offsets must be finite") weights <- model.weights(mf) if (!is.null(weights) && any(!is.finite(weights))) stop("weights must be finite") assign <- attrassign(X, Terms) contr.save <- attr(X, "contrasts") if (missing(init)) init <- NULL else { if (length(init) != ncol(X)) stop("wrong length for init argument") temp <- X %*% init - sum(colMeans(X) * init) if (any(temp < .Machine$double.min.exp | temp > .Machine$double.max.exp)) stop("initial values lead to overflow or underflow of the exp function") } @ Check for penalized terms in the model, and set up infrastructure for the fitting routines to deal with them. <>= pterms <- sapply(mf, inherits, 'coxph.penalty') if (any(pterms)) { pattr <- lapply(mf[pterms], attributes) pname <- names(pterms)[pterms] # # Check the order of any penalty terms ord <- attr(Terms, "order")[match(pname, attr(Terms, 'term.labels'))] if (any(ord>1)) stop ('Penalty terms cannot be in an interaction') pcols <- assign[match(pname, names(assign))] fit <- coxpenal.fit(X, Y, strats, offset, init=init, control, weights=weights, method=method, row.names(mf), pcols, pattr, assign) } @ <>= else { if( method=="breslow" || method =="efron") { if (type== 'right') fitter <- get("coxph.fit") else fitter <- get("agreg.fit") } else if (method=='exact') { if (type== "right") fitter <- get("coxexact.fit") else fitter <- get("agexact.fit") } else stop(paste ("Unknown method", method)) fit <- fitter(X, Y, strats, offset, init, control, weights=weights, method=method, row.names(mf)) } @ <>= if (is.character(fit)) { fit <- list(fail=fit) class(fit) <- 'coxph' } else { if (!is.null(fit$coefficients) && any(is.na(fit$coefficients))) { vars <- (1:length(fit$coefficients))[is.na(fit$coefficients)] msg <-paste("X matrix deemed to be singular; variable", paste(vars, collapse=" ")) if (singular.ok) warning(msg) else stop(msg) } fit$n <- data.n fit$nevent <- sum(Y[,ncol(Y)]) fit$terms <- Terms fit$assign <- assign class(fit) <- fit$method if (robust) { fit$naive.var <- fit$var fit$method <- method # a little sneaky here: by calling resid before adding the # na.action method, I avoid having missings re-inserted # I also make sure that it doesn't have to reconstruct X and Y fit2 <- c(fit, list(x=X, y=Y, weights=weights)) if (length(strats)) fit2$strata <- strats if (length(cluster)) { temp <- residuals.coxph(fit2, type='dfbeta', collapse=cluster, weighted=TRUE) # get score for null model if (is.null(init)) fit2$linear.predictors <- 0*fit$linear.predictors else fit2$linear.predictors <- c(X %*% init) temp0 <- residuals.coxph(fit2, type='score', collapse=cluster, weighted=TRUE) } else { temp <- residuals.coxph(fit2, type='dfbeta', weighted=TRUE) fit2$linear.predictors <- 0*fit$linear.predictors temp0 <- residuals.coxph(fit2, type='score', weighted=TRUE) } fit$var <- t(temp) %*% temp u <- apply(as.matrix(temp0), 2, sum) fit$rscore <- coxph.wtest(t(temp0)%*%temp0, u, control$toler.chol)$test } #Wald test if (length(fit$coefficients) && is.null(fit$wald.test)) { #not for intercept only models, or if test is already done nabeta <- !is.na(fit$coefficients) # The init vector might be longer than the betas, for a sparse term if (is.null(init)) temp <- fit$coefficients[nabeta] else temp <- (fit$coefficients - init[1:length(fit$coefficients)])[nabeta] fit$wald.test <- coxph.wtest(fit$var[nabeta,nabeta], temp, control$toler.chol)$test } na.action <- attr(mf, "na.action") if (length(na.action)) fit$na.action <- na.action if (model) { if (length(timetrans)) { # Fix up the model frame -- still in the thinking stage mf[[".surv."]] <- Y mf[[".strata."]] <- strats stop("Time transform + model frame: code incomplete") } fit$model <- mf } if (x) { fit$x <- X if (length(strats)) { if (length(timetrans)) fit$strata <- strats else fit$strata <- strata.keep } } if (y) fit$y <- Y } @ If any of the weights were not 1, save the results. Add names to the means component, which are occassionally useful to survfit.coxph. Other objects below are used when we need to recreate a model frame. <>= if (!is.null(weights) && any(weights!=1)) fit$weights <- weights names(fit$means) <- names(fit$coefficients) fit$formula <- formula(Terms) if (length(xlevels) >0) fit$xlevels <- xlevels fit$contrasts <- contr.save if (any(offset !=0)) fit$offset <- offset fit$call <- Call fit$method <- method fit @ The model.matrix and model.frame routines are called after a Cox model to reconstruct those portions. Much of their code is shared with the coxph routine. <>= # In internal use "data" will often be an already derived model frame. # We detect this via it having a terms attribute. model.matrix.coxph <- function(object, data=NULL, contrast.arg=object$contrasts, ...) { # # If the object has an "x" component, return it, unless a new # data set is given if (is.null(data) && !is.null(object[['x']])) return(object[['x']]) #don't match "xlevels" Terms <- delete.response(object$terms) if (is.null(data)) mf <- stats::model.frame(object) else { if (is.null(attr(data, "terms"))) mf <- stats::model.frame(Terms, data, xlev=object$xlevels) else mf <- data #assume "data" is already a model frame } cluster <- attr(Terms, "specials")$cluster if (length(cluster)) { temp <- untangle.specials(Terms, "cluster") dropterms <- temp$terms } else dropterms <- NULL <> X } @ In parallel is the model.frame routine, which reconstructs the model frame. This routine currently doesn't do all that we want. To wit, the following code fails: \begin{verbatim} > tfun <- function(formula, ndata) { fit <- coxph(formula, data=ndata) model.frame(fit) } > tfun(Surv(time, status) ~ age, lung) Error: ndata not found \end{verbatim} The genesis of this problem is hard to unearth, but has to do with non standard evaluation rules used by model.frame.default. In essence it pays attention to the environment of the formula, but the enclos argument of eval appears to be ignored. I've not yet found a solution. <>= model.frame.coxph <- function(formula, ...) { dots <- list(...) nargs <- dots[match(c("data", "na.action", "subset", "weights"), names(dots), 0)] # If nothing has changed and the coxph object had a model component, # simply return it. if (length(nargs) ==0 && !is.null(formula$model)) return(formula$model) else { # Rebuild the original call to model.frame Terms <- terms(formula) fcall <- formula$call indx <- match(c("formula", "data", "weights", "subset", "na.action"), names(fcall), nomatch=0) if (indx[1] ==0) stop("The coxph call is missing a formula!") temp <- fcall[c(1,indx)] # only keep the arguments we wanted temp[[1]] <- quote(stats::model.frame) # change the function called temp$xlev <- formula$xlevels temp$formula <- Terms #keep the predvars attribute # Now, any arguments that were on this call overtake the ones that # were in the original call. if (length(nargs) >0) temp[names(nargs)] <- nargs # The documentation for model.frame implies that the environment arg # to eval will be ignored, but if we omit it there is a problem. if (is.null(environment(formula$terms))) mf <- eval(temp, parent.frame()) else mf <- eval(temp, environment(formula$terms), parent.frame()) if (!is.null(attr(formula$terms, "dataClasses"))) .checkMFClasses(attr(formula$terms, "dataClasses"), mf) if (!is.null(attr(Terms, "specials")$tt)) { # Do time transform tt <- eval(formula$call$tt) Y <- aeqSurv(model.response(mf)) strats <- attr(Terms, "specials")$strata if (length(strats)) { stemp <- untangle.specials(Terms, 'strata', 1) if (length(stemp$vars)==1) strata.keep <- mf[[stemp$vars]] else strata.keep <- strata(mf[,stemp$vars], shortlabel=TRUE) strats <- as.numeric(strata.keep) } <> mf[[".strata."]] <- strats } mf } } @ survival/noweb/statefig.Rnw0000644000175100001440000002410313004161624015550 0ustar hornikusers\section{State space figures} The statefig function was written to do ``good enough'' state space figures quickly and easily. There are certainly figures it can't draw and many figures that can be drawn better, but it accomplishes its purpose. The key argument \code{layout}, the first, is a vector of numbers. The value (1,3,4,2) for instance has a single state, then a column with 3 states, then a column with 4, then a column with 2. If \code{layout} is instead a 1 column matrix then do the same from top down. <>= statefig <- function(layout, connect, margin=.03, box=TRUE, cex=1, col=1, lwd=1, lty=1, bcol= col, acol=col, alwd = lwd, alty= lty) { # set up an empty canvas frame(); # new environment par(usr=c(0,1,0,1)) if (!is.numeric(layout)) stop("layout must be a numeric vector or matrix") if (!is.matrix(connect) || nrow(connect) != ncol(connect)) stop("connect must be a square matrix") nstate <- nrow(connect) dd <- dimnames(connect) if (!is.null(dd[[1]])) statenames <- dd[[1]] else if (is.null(dd[[2]])) stop("connect must have the state names as dimnames") else statenames <- dd[[2]] <> <> <> invisible(cbox) } <> @ The drawing region is always (0,1) by (0,1). A user can put enter their own matrix of coordinates. Otherwise the free space is divided with one portion on each end and 2 portions between boxes. If there were 3 columns for instance they will have x coordinates of 1/6, 1/6 + 1/3, 1/6 + 2/3. Ditto for dividing up the y coordinate. The primary nuisance is that we want to count down from the top instead of up from the bottom. A 1 by 1 matrix is treated as a column matrix. <>= if (is.matrix(layout) && ncol(layout)==2 && nrow(layout) > 1) { # the user provided their own if (any(layout <0) || any(layout >1)) stop("layout coordinates must be between 0 and 1") if (nrow(layout) != nstate) stop("layout matrix should have one row per state") cbox <- layout } else { if (any(layout <=0 | layout != floor(layout))) stop("non-integer number of states in layout argument") space <- function(n) (1:n -.5)/n # centers of the boxes if (sum(layout) != nstate) stop("number of boxes != number of states") cbox <- matrix(0, ncol=2, nrow=nstate) #coordinates will be here n <- length(layout) ix <- rep(seq(along=layout), layout) if (is.vector(layout) || ncol(layout)> 1) { #left to right cbox[,1] <- space(n)[ix] for (i in 1:n) cbox[ix==i,2] <- 1 -space(layout[i]) } else { # top to bottom cbox[,2] <- 1- space(n)[ix] for (i in 1:n) cbox[ix==i,1] <- space(layout[i]) } } @ Write the text out. Compute the width and height of each box. Then compute the margin. The only tricky thing here is that we want the area around the text to \emph{look} the same left-right and up-down, which depends on the geometry of the plotting region. <>= text(cbox[,1], cbox[,2], statenames, cex=cex, col=col) # write the labels textwd <- strwidth(statenames, cex=cex) textht <- strheight(statenames, cex=cex) temp <- par("pin") #plot region in inches dx <- margin * temp[2]/mean(temp) # extra to add in the x dimension dy <- margin * temp[1]/mean(temp) # extra to add in y if (box) { drawbox <- function(x, y, dx, dy, col) { lines(x+ c(-dx, dx, dx, -dx, -dx), y+ c(-dy, -dy, dy, dy, -dy), lwd=lwd, lty=lty, col=col) } bcol <- rep(bcol, length=nstate) for (i in 1:nstate) drawbox(cbox[i,1], cbox[i,2], textwd[i]/2 + dx, textht[i]/2 + dy, col=bcol[i]) dx <- 2*dx; dy <- 2*dy # move arrows out from the box } @ Now for the hard part, which is drawing the arrows. The entries in the connection matrix are 0= no connection or $1+d$ for $-1 < d < 1$. The connection is an arc that passes from the center of box 1 to the center of box 2, and through a point that is $dz$ units above the midpoint of the line from box 1 to box 2, where $2z$ is the length of that line. For $d=1$ we get a half circle to the right (with respect to traversing the line from A to B) and for $d= -1$ we get a half circle to the left. If $d=0$ it is a straight line. If A and B are the starting and ending points then AB is the chord of a circle. Draw radii from the center to A, B, and through the midpoint $c$ of AB. This last has length $dz$ above the chord and $r- dz$ below where $r$ is the radius. Then we have \begin{align*} r^2 & = z^2 + (r-dz)^2 \\ 2rdz &= z^2 + (dz)^2 \\ r &= \left[z (1+ d^2) \right ]/ 2d \end{align*} Be careful with negative $d$, which is used to denote left-hand arcs. The angle $\theta$ from A to B is the arctan of $B-A$, and the center of the circle is at $C = (A+B)/2 + (r - dz)(\sin \theta, -\cos \theta)$. We then need to draw the arc $C + r(\cos \phi, \sin \phi)$ for some range of angles $\phi$. The angles to the centers of the boxes are $\arctan(A-C)$ and $\arctan(B-C)$, but we want to start and end outside the box. It turned out that this is more subtle than I thought. The solution below uses two helper functions \code{statefigx} and \code{statefigy}. The first accepts $C$, $r$, the range of $\phi$ values, and a target $y$ value. It returns the angles, within the range, such that the endpoint of the arc has horizontal coordinate $x$, or an empty vector if none such exists. For an arc there are sometimes two solutions. The input angles $a_1$ and $a_2$ are prescaled so that $a_2 > a_1$. This is done to make sure we have an acute rather than obtuse angle, e.g., if $a_1=3$ and $a_2=-3$ (170 and -170 degrees) we don't want an angle of 0 pass the ``lies within the interval'' test, so $a_2$ is changed to $2\pi + a_2$ or 190 degrees. The angle $a_1$ is between $-\pi$ and $\pi$. <>= statefigx <- function(x, C, r, a1, a2) { amax <- max(a1, a2) amin <- min(a1, a2) temp <-(x - C[1])/r if (abs(temp) >1) return(NULL) # no intersection of the arc and x phi <- acos(temp) # this will be from 0 to pi # Add reflection about the X axis, in both forms phi <- c(phi, -phi, 2*pi - phi) phi[phi amin] } statefigy <- function(y, C, r, a1, a2) { amax <- max(a1, a2) amin <- min(a1, a2) temp <-(y - C[2])/r if (abs(temp) >1) return(NULL) # no intersection of the arc and y phi <- asin(temp) # will be from -pi/2 to pi/2 phi <- c(phi, sign(phi)*pi -phi) # reflect about the vertical phi <- c(phi, phi + 2*pi) phi[phi amin] } @ <>= phi <- function(x1, y1, x2, y2, d, delta1, delta2) { # d = height above the line theta <- atan2(y2-y1, x2-x1) # angle from center to center if (abs(d) < .001) d=.001 # a really small arc looks like a line z <- sqrt((x2-x1)^2 + (y2 - y1)^2) /2 # half length of chord ab <- c((x1 + x2)/2, (y1 + y2)/2) # center of chord r <- abs(z*(1 + d^2)/ (2*d)) if (d >0) C <- ab + (r - d*z)* c(-sin(theta), cos(theta)) # center of arc else C <- ab + (r + d*z)* c( sin(theta), -cos(theta)) a1 <- atan2(y1-C[2], x1-C[1]) a2 <- atan2(y2-C[2], x2-C[1]) if (abs(a2-a1) > pi) a2 <- a2 + 2*pi if (d > 0) { #counterclockwise phi1 <- min(statefigx(x1 + delta1[1], C, r, a1, a2), statefigx(x1 - delta1[1], C, r, a1, a2), statefigy(y1 + delta1[2], C, r, a1, a2), statefigy(y1 - delta1[2], C, r, a1, a2), na.rm=TRUE) phi2 <- max(statefigx(x2 + delta2[1], C, r, a1, a2), statefigx(x2 - delta2[1], C, r, a1, a2), statefigy(y2 + delta2[2], C, r, a1, a2), statefigy(y2 - delta2[2], C, r, a1, a2), na.rm=TRUE) } else { # clockwise phi1 <- max(statefigx(x1 + delta1[1], C, r, a1, a2), statefigx(x1 - delta1[1], C, r, a1, a2), statefigy(y1 + delta1[2], C, r, a1, a2), statefigy(y1 - delta1[2], C, r, a1, a2), na.rm=TRUE) phi2 <- min(statefigx(x2 + delta2[1], C, r, a1, a2), statefigx(x2 - delta2[1], C, r, a1, a2), statefigy(y2 + delta2[2], C, r, a1, a2), statefigy(y2 - delta2[2], C, r, a1, a2), na.rm=TRUE) } list(center=C, angle=c(phi1, phi2), r=r) } @ Now draw the arrows, one at a time. I arbitrarily declare that 20 segments is enough for a smooth curve. <>= arrow2 <- function(...) arrows(..., angle=20, length=.1) doline <- function(x1, x2, d, delta1, delta2, lwd, lty, col) { if (d==0 && x1[1] ==x2[1]) { # vertical line if (x1[2] > x2[2]) # downhill arrow2(x1[1], x1[2]- delta1[2], x2[1], x2[2] + delta2[2], lwd=lwd, lty=lty, col=col) else arrow2(x1[1], x1[2]+ delta1[2], x2[1], x2[2] - delta2[2], lwd=lwd, lty=lty, col=col) } else if (d==0 && x1[2] == x2[2]) { # horizontal line if (x1[1] > x2[1]) # right to left arrow2(x1[1]-delta1[1], x1[2], x2[1] + delta2[1], x2[2], lwd=lwd, lty=lty, col=col) else arrow2(x1[1]+delta1[1], x1[2], x2[1] - delta2[1], x2[2], lwd=lwd, lty=lty, col=col) } else { temp <- phi(x1[1], x1[2], x2[1], x2[2], d, delta1, delta2) phi <- seq(temp$angle[1], temp$angle[2], length=21) lines(temp$center[1] + temp$r*cos(phi), temp$center[2] + temp$r*sin(phi), lwd=lwd, lty=lty, col=col) arrow2(temp$center[1] + temp$r*cos(phi[20]), temp$center[2] + temp$r*sin(phi[20]), temp$center[1] + temp$r*cos(phi[21]), temp$center[2] + temp$r*sin(phi[21]), lwd=lwd, lty=lty, col=col) } } for (i in 1:nstate) { for (j in 1:nstate) { if (i != j && connect[i,j] !=0) { doline(cbox[i,], cbox[j,], connect[i,j]-1, delta1 = c(textwd[i]/2 + dx, textht[i]/2 + dy), delta2 = c(textwd[j]/2 + dx, textht[j]/2 + dy), lty=alty[1], lwd=alwd[1], col=acol[1]) } } } @ survival/noweb/tmerge.Rnw0000644000175100001440000005464613054077374015261 0ustar hornikusers\section{tmerge} The tmerge function was designed around a set of specific problems. The idea is to build up a time dependent data set one endpoint at at time. The primary arguments are \begin{itemize} \item data1: the base data set that will be added onto \item data2: the source for new information \item id: the subject identifier in the new data \item \ldots: additional arguments that add variables to the data set \item tstart, tstop: used to set the time range for each subject \item options \end{itemize} The created data set has three new variables (at least), which are \code{id}, \code{tstart} and \code{tstop}. The key part of the call are the ``\ldots'' arguments which each can be one of four types: tdc() and cumtdc() add a time dependent variable, event() and cumevent() add a new endpoint. In the survival routines time intervals are open on the left and closed on the right, i.e., (tstart, tstop]. Time dependent covariates apply from the start of an interval and events occur at the end of an interval. If a data set already had intervals of (0,10] and (10, 14] a new time dependent covariate or event at time 8 would lead to three intervals of (0,8], (8,10], and (10,14]; the new time-dependent covariate value would be added to the second interval, a new event would be added to the first one. A typical call would be <>= newdata <- tmerge(newdata, old, id=clinic, diabetes=tdc(diab.time)) @ which would add a new time dependent covariate \code{diabetes} to the data set. <>= tmerge <- function(data1, data2, id, ..., tstart, tstop, options) { Call <- match.call() # The function wants to recognize special keywords in the # arguments, so define a set of functions which will be used to # mark objects new <- new.env(parent=parent.frame()) assign("tdc", function(time, value=NULL) { x <- list(time=time, value=value); class(x) <- "tdc"; x}, envir=new) assign("cumtdc", function(time, value=NULL) { x <- list(time=time, value=value); class(x) <-"cumtdc"; x}, envir=new) assign("event", function(time, value=NULL, censor=NULL) { x <- list(time=time, value=value, censor=censor); class(x) <-"event"; x}, envir=new) assign("cumevent", function(time, value=NULL, censor=NULL) { x <- list(time=time, value=value, censor=censor); class(x) <-"cumevent"; x}, envir=new) if (missing(data1) || missing(data2) || missing(id)) stop("the data1, data2, and id arguments are required") if (!inherits(data1, "data.frame")) stop("data1 must be a data frame") <> <> <> } @ The program can't use formulas because the \ldots arguments need to be named. This results in a bit of evaluation magic to correctly assess arguments. The routine below could have been set out as a separate top-level routine, the argument is where we want to document it: within the tmerge page or not. I decided on the former. <>= tmerge.control <- function(idname="id", tstartname="tstart", tstopname="tstop", delay =0, na.rm=TRUE, tdcstart=NA, ...) { extras <- list(...) if (length(extras) > 0) stop("unrecognized option(s):", paste(names(extras), collapse=', ')) if (length(idname) != 1 || make.names(idname) != idname) stop("idname option must be a valid variable name") if (!is.null(tstartname) && (length(tstartname) !=1 || make.names(tstartname) != tstartname)) stop("tstart option must be NULL or a valid variable name") if (length(tstopname) != 1 || make.names(tstopname) != tstopname) stop("tstop option must be a valid variable name") if (length(delay) !=1 || !is.numeric(delay) || delay < 0) stop("delay option must be a number >= 0") if (length(na.rm) !=1 || ! is.logical(na.rm)) stop("na.rm option must be TRUE or FALSE") if (length(tdcstart) !=1) stop("tdcstart must be a single value") list(idname=idname, tstartname=tstartname, tstopname=tstopname, delay=delay, na.rm=na.rm, tdcstart=tdcstart) } tname <- attr(data1, "tname") firstcall <- is.null(tname) #first call to the function if (!firstcall && any(is.null(match(unlist(tname), names(data1))))) stop("data1 does not match its own tname attribute") if (!missing(options)) { if (!is.list(options)) stop("options must be a list") if (!is.null(tname)) { # If an option name matches one already in tname, don't confuse # the tmerge.control routine with duplicate arguments temp <- match(names(options), names(tname), nomatch=0) topt <- do.call(tmerge.control, c(options, tname[temp==0])) if (any(temp >0)) { # A variable name is changing midstream, update the # variable names in data1 varname <- tname[c("idname", "tstartname", "tstopname")] temp2 <- match(varname, names(data1)) names(data1)[temp2] <- varname } } else topt <- do.call(tmerge.control, options) } else if (length(tname)) topt <- do.call(tmerge.control, tname) else topt <- tmerge.control() # id, tstart, tstop are found in data2 if (missing(id)) stop("the id argument is required") if (missing(data1) || missing(data2)) stop("two data sets are required") id <- eval(Call[["id"]], data2, enclos=emptyenv()) #don't find it elsewhere if (is.null(id)) stop("id variable not found in data2") if (firstcall) { if (!missing(tstop)) { tstop <- eval(Call[["tstop"]], data2) if (length(tstop) != length(id)) stop("tstop and id must be the same length") # The neardate routine will check for legal tstop data type } if (!missing(tstart)) { tstart <- eval(Call[["tstart"]], data2) if (length(tstart)==1) tstart <- rep(tstart, length(id)) if (length(tstart) != length(id)) stop("tstart and id must be the same length") if (any(tstart >= tstop)) stop("tstart must be < tstop") } } else { if (!missing(tstart) || !missing(tstop)) stop("tstart and tstop arguments only apply to the first call") } @ Get the \ldots arguments. They are evaluated in a special frame, set up earlier, so that the definitions of the functions tdc, cumtdc, event, and cumevent are local to tmerge. Check that they are all legal: each argument is named, and is one of the four allowed types. <>= # grab the... arguments notdot <- c("data1", "data2", "id", "tstart", "tstop", "options") dotarg <- Call[is.na(match(names(Call), notdot))] dotarg[[1]] <- as.name("list") # The as-yet dotarg arguments if (missing(data2)) args <- eval(dotarg, envir=new) else args <- eval(dotarg, data2, enclos=new) argclass <- sapply(args, function(x) (class(x))[1]) argname <- names(args) if (any(argname== "")) stop("all additional argments must have a name") check <- match(argclass, c("tdc", "cumtdc", "event", "cumevent")) if (any(is.na(check))) stop(paste("argument(s)", argname[is.na(check)], "not a recognized type")) @ The tcount matrix keeps track of what we have done, and is added to the final object at the end. This is useful to the user for debugging what may have gone right or wrong in their usage. <>= # The tcount matrix is useful for debugging tcount <- matrix(0L, length(argname), 8) dimnames(tcount) <- list(argname, c("early","late", "gap", "within", "boundary", "leading", "trailing", "tied")) tevent <- attr(data1, "tevent") # event type variables tcens <- attr(data1, "tcensor")# censor code for variables if (is.null(tcens)) tcens <- vector('list', 0) @ The very first call to the routine is special, since this is when the range of legal times is set. We also apply an initial sort to the data if necessary so that times are in order. There are 2 cases: \begin{enumerate} \item Adding a time range: tstop comes from data2, optional tstart, and the id can be simply matched, by which we mean no duplicates in data1. \item The more common case: there is no tstop, one observation per subject, and the first optional argument is an event or cumevent. We then use its time as the range. \end{enumerate} One thing we could add, but didn't, was to warn if any of the three new variables will stomp on ones already in data1. <>= newdata <- data1 #make a copy if (firstcall) { # We don't look for topt$id. What if the user had id=clinic, but their # starting data set also had a variable named "id". We want clinic for # this first call. idname <- Call[["id"]] if (!is.name(idname)) stop("on the first call 'id' must be a single variable name") # The line below finds tstop and tstart variables in data1 indx <- match(c(topt$idname, topt$tstartname, topt$tstopname), names(data1), nomatch=0) if (any(indx[1:2]>0) && FALSE) { # warning currently turned off. Be chatty? overwrite <- c(topt$tstartname, topt$tstopname)[indx[2:3]] warning("overwriting data1 variables", paste(overwrite, collapse=' ')) } temp <- as.character(idname) if (!is.na(match(temp, names(data1)))) { data1[[topt$idname]] <- data1[[temp]] baseid <- data1[[temp]] } else stop("id variable not found in data1") if (any(duplicated(baseid))) stop("for the first call (that establishes the time range) data1 must have no duplicate identifiers") if (length(baseid)== length(id) && all(baseid == id)) newdata <- data1 else { # Note: 'id' is the idlist for data 2 indx2 <- match(id, baseid) if (any(is.na(indx2))) stop("'id' has values not in data1") newdata <- data1[indx2,] } if (missing(tstop)) { # case 2 if (length(argclass)==0 || argclass[1] != "event") stop("neither a tstop argument nor an initial event argument was found") tstop <- args[[1]][[1]] } # at this point newdata and data2 are in the same order, same # rows if (any(is.na(tstop))) stop("missing time value, when that variable defines the span") if (missing(tstart)) tstart <- rep(0, length(id)) if (any(tstart >= tstop)) stop("tstart must be > tstop") newdata[[topt$tstartname]] <- tstart newdata[[topt$tstopname]] <- tstop if (any(duplicated(id))) { # sort by time within id indx1 <- match(id, unique(id)) newdata <- newdata[order(indx1, tstop),] } n <- nrow(newdata) temp <- newdata[[topt$idname]] if (any(tstart >= tstop)) stop("tstart must be < tstop") if (any(newdata$tstart[-n] > newdata$tstop[-1] & temp[-n] == temp[-1])) stop("there are overlapping time intervals") } else { #not a first call if (any(is.na(match(id, data1[[topt$idname]])))) stop("id values were found in data2 which are not in data1") } @ Now for the real work. For each additional argument we first match the id/time pairs of the new data to the current data set, and categorize each into a type. If the time value in data2 is NA, then that addition is skipped. Ditto if the value is NA and options narm=TRUE. This is a convenience for the user, who will often be merging in a variable like ``day of first diabetes diagnosis'' which is missing for those who never had that outcome occur. <>= saveid <- id for (ii in seq(along.with=args)) { argi <- args[[ii]] baseid <- newdata[[topt$idname]] dstart <- newdata[[topt$tstartname]] dstop <- newdata[[topt$tstopname]] argcen <- argi$censor # if an event time is missing then skip that obs etime <- argi$time if (length(etime) != length(saveid)) stop("argument ", argname[ii], " is not the same length as id") if (!is.null(argi$value)) { if (length(argi$value) != length(saveid)) stop("argument", argname[ii], "is not the same length as id") if (topt$na.rm) keep <- !(is.na(etime) | is.na(argi$value)) else keep <- !is.na(etime) if (!all(keep)) { etime <- etime[keep] argi$value <- argi$value[keep] } } else { keep <- !is.na(etime) etime <- etime[keep] } id <- saveid[keep] # Later steps become easier if we sort the new data by id and time # The match() is critical when baseid is not in sorted order. The # etime part of the sort will change from one ii value to the next. indx <- order(match(id, baseid), etime) id <- id[indx] etime <- etime[indx] if (!is.null(argi$value)) yinc <- argi$value[indx] else yinc <- NULL # indx1 points to the closest start time in the baseline data (data1) # that is <= etime. indx2 to the closest end time that is >=etime. # If etime falls into a (tstart, tstop) interval, indx1 and indx2 # will match # If the "delay" argument is set and this event is of type tdc, then # move any etime that is after the entry time for a subject. if (topt$delay >0 && argclass[ii] %in% c("tdc", "cumtdc")) { mintime <- tapply(dstart, baseid, min) index <- match(id, names(mintime)) etime <- ifelse(etime <= mintime[index], etime, etime+ topt$delay) } indx1 <- neardate(id, baseid, etime, dstart, best="prior") indx2 <- neardate(id, baseid, etime, dstop, best="after") # The event times fall into one of 5 categories # 1. Before the first interval # 2. After the last interval # 3. Outside any interval but with time span, i.e, it falls into # a gap in follow-up # 4. Strictly inside an interval (does't touch either end) # 5. Inside an interval, but touching. itype <- ifelse(is.na(indx1), 1, ifelse(is.na(indx2), 2, ifelse(indx2 > indx1, 3, ifelse(etime== dstart[indx1] | etime== dstop[indx2], 5, 4)))) # Subdivide the events that touch on a boundary # 1: intervals of (a,b] (b,d], new count at b "tied edge" # 2: intervals of (a,b] (c,d] with c>b, new count at c, "front edge" # 3: intervals of (a,b] (c,d] with c>b, new count at b, "back edge" # subtype <- ifelse(itype!=5, 0, ifelse(indx1 == indx2+1, 1, ifelse(etime==dstart[indx1], 2, 3))) tcount[ii,1:7] <- table(factor(itype+subtype, levels=c(1:4, 6:8))) # count ties. id and etime are not necessarily sorted tcount[ii,8] <- sum(tapply(etime, id, function(x) sum(duplicated(x)))) <> } @ An argument of \code{tdc(etime)} causes a time-dependent covariate value of 1, one of \code{tdc(etime, x)} causes the created time dependent variable to have a value of x. <>= if (is.null(yinc)) yinc <- rep(1.0, length(etime)) @ A \code{tdc} or \code{cumtdc} operator defines a new time-dependent variable which applies to all future times. Say that we had the following scenario for one subject \begin{center} \begin{tabular}{rr|rr} \multicolumn{2}{c}{current} & \multicolumn{2}{c}{addition} \\ tstart & tstop & time & x \\ 2 & 5 & 1 & 20.2 \\ 6 & 7 & 7 & 11 \\ 7 & 15 & 8 & 17.3 \\ 15 & 30 \\ \end{tabular} \end{center} The resulting data set will have intervals of (2,5), (6,7), (7,8) and (8,15) with covariate values of 20.2, 20.2, 11, and 17.3. Only a covariate change that occurs within an interval causes a new data row. Covariate changes that happen after the last interval are ignored, i.e. at change at time $\ge 30$ in the above example. If instead this had been events at times 1, 7, and 8, the first event would be ignored since it happens outside of any interval, so would an event at exactly time 2. The event at time 7 would be recorded in the (6,7) interval and the one at time 8 in the (7,8) interval: events happen at the ends of intervals. In both cases new rows are only generated for new time values that fall strictly within one of the old intervals. When a subject has two increments on the same day the later one wins. This is correct behavior for cumtdc, a bit odd for cumevent, and the user's problem for tdc and event. We report back the number of ties so that the user can deal with it. Where are we now with the variables? \begin{center} \begin{tabular}{cccc} itype& class & indx1 & indx2 \\ \hline 1 & before & NA & next interval \\ 2 & after & prior interval & NA \\ 3 & in a gap & prior interval & next interval \\ 4 & within interval & containing interval & containing interval \\ 5-1 & on a join & next interval & prior interval \\ 5-2 & front edge & containing & containing \\ 5-3 & back edge & containing & containing \\ \end{tabular} \end{center} If there are any itype 4, start by expanding the data set to add new cut points, which will turn all the 4's into 5-1 types. When expanding, all the event type variables turn into ``censor'' at the newly added times and other variables stay the same. A subject could have more than one new cutpoint added within an interval so we have to count each. In newdata all the rows for a given subject are contiguous and in time order, though the data set may not be in subject order. <>= indx4 <- which(itype==4) n4 <- length(indx4) if (n4 > 0) { icount <- tapply(etime[indx4], indx1[indx4], function(x) sort(unique(x))) n.add <- sapply(icount, length) #number of rows to add # expand the data irep <- rep.int(1L, nrow(newdata)) erow <- unique(indx1[indx4]) # which rows in newdata to be expanded irep[erow] <- 1+ n.add # number of rows in new data jrep <- rep(1:nrow(newdata), irep) #stutter the duplicated rows newdata <- newdata[jrep,] #expand it out dstart <- dstart[jrep] dstop <- dstop[jrep] #fix up times nfix <- length(erow) temp <- vector("list", nfix) iend <- (cumsum(irep))[irep >1] #end row of each duplication set for (j in 1:nfix) temp[[j]] <- -(seq(n.add[j] -1, 0)) + iend[j] newrows <- unlist(temp) # icount is a list, each element of which is a vector # the natural way to turn that into a vector is unlist(), but that # leads to problems if etime is a date: we lose the time origin if (is.numeric(icount[[1]])) icount <- unlist(icount) else icount <- do.call('c', icount) dstart[newrows] <- dstop[newrows-1] <- icount newdata[[topt$tstartname]] <- dstart newdata[[topt$tstopname]] <- dstop for (ename in tevent) newdata[newrows-1, ename] <- tcens[[ename]] # refresh indices baseid <- newdata[[topt$idname]] indx1 <- neardate(id, baseid, etime, dstart, best="prior") indx2 <- neardate(id, baseid, etime, dstop, best="after") subtype[itype==4] <- 1 #all the "insides" are now on a tied edge itype[itype==4] <- 5 } @ Now we can add the new variable. Events and cumevents are easy because each affects only one interval. Counts are more work and for this we use a C routine. <>= # add it in if (argclass[ii] %in% c("cumtdc", "cumevent")) { if (!is.numeric(yinc)) stop("invalid increment for cumtdc or cumevent") yinc <- unlist(tapply(yinc, match(id, baseid), cumsum)) } newvar <- newdata[[argname[ii]]] #does the variable exist? if (argclass[ii] %in% c("event", "cumevent")) { if (is.null(newvar)) { if (is.factor(yinc)) newvar <- factor(rep(levels(yinc)[1], nrow(newdata)), levels(yinc)) else if (is.numeric(yinc)) newvar <- rep(0L, nrow(newdata)) else stop("invalid value for a status variable") } keep <- (subtype==1 | subtype==3) # all other events are thrown away newvar[indx2[keep]] <- yinc[keep] if (!(argname[ii] %in% tevent)) { tevent <- c(tevent, argname[[ii]]) if (is.factor(yinc)) tcens <- c(tcens, levels(yinc)[1]) else tcens <- c(tcens, 0) names(tcens) <- tevent } } else { keep <- itype != 2 # changes after the last interval are ignored indx <- ifelse(subtype==1, indx1, ifelse(subtype==3, indx2+1L, indx2)) # we want to pass the right kind of NA to the C code if (is.na(topt$tdcstart)) topt$tdcstart <- as.numeric(topt$tdcstart) if (is.null(newvar)) { # not overwriting a prior value if (is.null(argi$value)) newvar <- rep(0.0, nrow(newdata)) else newvar <- rep(topt$tdcstart, nrow(newdata)) } if (is.numeric(yinc)) { # this is the usual case if (!is.numeric(newvar)) stop("data and options$tdcstart do not agree on data type") # id can be any data type; feed integers to the C routine storage.mode(yinc) <- storage.mode(dstop) <- "double" storage.mode(newvar) <- storage.mode(etime) <- "double" newvar <- .Call(Ctmerge, match(baseid, baseid), dstop, newvar, match(id, baseid)[keep], etime[keep], yinc[keep], indx[keep]) } else { # deal with a factor or character if (!(is.factor(yinc) || is.factor(yinc))) stop("the second argument of tdc must be numeric, character, or factor") newlev <- unique(c(levels(as.factor(yinc)), levels(as.factor(newvar)))) y2 <- factor(yinc, levels=newlev) newvar <- factor(newvar, levels=newlev) storage.mode(dstop) <- storage.mode(etime) <- "double" new <- .Call(Ctmerge, match(baseid, baseid), dstop, as.numeric(newvar), match(id, baseid)[keep], etime[keep], as.numeric(yinc[keep]), indx[keep]) if (is.factor(yinc)) newvar <- factor(new, labels=newlev) else newvar <- newlev[new] } } newdata[[argname[ii]]] <- newvar @ Finish up by adding the attributes and the class <>= attr(newdata, "tname") <- topt[c("idname", "tstartname", "tstopname")] attr(newdata, "tcount") <- rbind(attr(data1, "tcount"), tcount) if (length(tevent)) { attr(newdata, "tevent") <- tevent attr(newdata, "tcensor" ) <- tcens } row.names(newdata) <- NULL #These are a mess; kill them off. # Not that it works: R just assigns new row names. class(newdata) <- c("data.frame") newdata @ The print routine is for checking: it simply prints out the attributes. <>= print.tmerge <- function(x, ...) { print(attr(x, "tcount")) } "[.tmerge" <- function(x, ..., drop=TRUE){ class(x) <- "data.frame" NextMethod(,x) } @ survival/noweb/rates/0000755000175100001440000000000012730271054014374 5ustar hornikuserssurvival/noweb/rates/minn2004.dat0000755000175100001440000000313212730271054016337 0ustar hornikusers"age" "tm" "tf" "0-1" 546 437 "1-2" 42 26 "2-3" 23 17 "3-4" 19 15 "4-5" 19 12 "5-6" 17 15 "6-7" 11 13 "7-8" 11 14 "8-9" 11 7 "9-10" 8 10 "10-11" 12 13 "11-12" 19 7 "12-13" 21 12 "13-14" 21 19 "14-15" 37 18 "15-16" 47 30 "16-17" 46 36 "17-18" 69 35 "18-19" 96 30 "19-20" 99 34 "20-21" 98 27 "21-22" 127 26 "22-23" 97 30 "23-24" 103 32 "24-25" 102 25 "25-26" 88 33 "26-27" 89 45 "27-28" 104 36 "28-29" 98 46 "29-30" 73 34 "30-31" 98 46 "31-32" 99 56 "32-33" 105 43 "33-34" 101 50 "34-35" 100 49 "35-36" 126 60 "36-37" 121 67 "37-38" 136 79 "38-39" 132 88 "39-40" 138 93 "40-41" 172 94 "41-42" 195 117 "42-43" 183 118 "43-44" 208 135 "44-45" 188 130 "45-46" 253 140 "46-47" 275 171 "47-48" 307 186 "48-49" 366 209 "49-50" 343 189 "50-51" 394 246 "51-52" 410 227 "52-53" 439 273 "53-54" 470 293 "54-55" 546 320 "55-56" 586 410 "56-57" 610 373 "57-58" 626 367 "58-59" 851 520 "59-60" 833 540 "60-61" 940 615 "61-62" 901 587 "62-63" 1110 748 "63-64" 1189 796 "64-65" 1295 855 "65-66" 1435 912 "66-67" 1508 1017 "67-68" 1708 1090 "68-69" 1997 1306 "69-70" 1946 1187 "70-71" 2226 1577 "71-72" 2393 1779 "72-73" 2836 1965 "73-74" 3169 1982 "74-75" 3327 2273 "75-76" 3844 2401 "76-77" 4155 2497 "77-78" 4721 2877 "78-79" 5001 3178 "79-80" 5780 3734 "80-81" 6211 4082 "81-82" 7445 4989 "82-83" 7704 5471 "83-84" 9480 5894 "84-85" 9460 6776 "85-86" 9942 6639 "86-87" 11693 7916 "87-88" 12960 8911 "88-89" 14720 10343 "89-90" 15762 11477 "90-91" 17490 12966 "91-92" 18946 14849 "92-93" 21889 16948 "93-94" 23140 19640 "94-95" 24436 18973 "95-96" 26418 23152 "96-97" 32863 22606 "97-98" 33507 27263 "98-99" 30091 31076 "99-100" 29382 33769 survival/noweb/rates/minndecennial.dat0000755000175100001440000016134012730271054017702 0ustar hornikusers1950 0 m white 0.02712 1950 1 m white 0.00177 1950 2 m white 0.00141 1950 3 m white 0.00096 1950 4 m white 0.00078 1950 5 m white 0.00076 1950 6 m white 0.00072 1950 7 m white 0.00069 1950 8 m white 0.00066 1950 9 m white 0.00065 1950 10 m white 0.00065 1950 11 m white 0.00067 1950 12 m white 0.00073 1950 13 m white 0.00084 1950 14 m white 0.00099 1950 15 m white 0.00116 1950 16 m white 0.00132 1950 17 m white 0.00143 1950 18 m white 0.00150 1950 19 m white 0.00154 1950 20 m white 0.00156 1950 21 m white 0.00157 1950 22 m white 0.00157 1950 23 m white 0.00155 1950 24 m white 0.00152 1950 25 m white 0.00148 1950 26 m white 0.00144 1950 27 m white 0.00143 1950 28 m white 0.00143 1950 29 m white 0.00145 1950 30 m white 0.00147 1950 31 m white 0.00152 1950 32 m white 0.00161 1950 33 m white 0.00173 1950 34 m white 0.00188 1950 35 m white 0.00206 1950 36 m white 0.00226 1950 37 m white 0.00249 1950 38 m white 0.00273 1950 39 m white 0.00300 1950 40 m white 0.00329 1950 41 m white 0.00361 1950 42 m white 0.00397 1950 43 m white 0.00436 1950 44 m white 0.00478 1950 45 m white 0.00523 1950 46 m white 0.00572 1950 47 m white 0.00625 1950 48 m white 0.00681 1950 49 m white 0.00738 1950 50 m white 0.00801 1950 51 m white 0.00871 1950 52 m white 0.00952 1950 53 m white 0.01043 1950 54 m white 0.01142 1950 55 m white 0.01250 1950 56 m white 0.01368 1950 57 m white 0.01496 1950 58 m white 0.01631 1950 59 m white 0.01773 1950 60 m white 0.01926 1950 61 m white 0.02095 1950 62 m white 0.02285 1950 63 m white 0.02493 1950 64 m white 0.02716 1950 65 m white 0.02957 1950 66 m white 0.03220 1950 67 m white 0.03509 1950 68 m white 0.03811 1950 69 m white 0.04125 1950 70 m white 0.04468 1950 71 m white 0.04857 1950 72 m white 0.05309 1950 73 m white 0.05832 1950 74 m white 0.06413 1950 75 m white 0.07042 1950 76 m white 0.07712 1950 77 m white 0.08410 1950 78 m white 0.09116 1950 79 m white 0.09835 1950 80 m white 0.10601 1950 81 m white 0.11448 1950 82 m white 0.12409 1950 83 m white 0.13494 1950 84 m white 0.14680 1950 85 m white 0.15953 1950 86 m white 0.17299 1950 87 m white 0.18704 1950 88 m white 0.20198 1950 89 m white 0.21789 1950 90 m white 0.23434 1950 91 m white 0.25088 1950 92 m white 0.26707 1950 93 m white 0.28286 1950 94 m white 0.29854 1950 95 m white 0.31419 1950 96 m white 0.32989 1950 97 m white 0.34570 1950 98 m white 0.36158 1950 99 m white 0.37747 1950 100 m white 0.39346 1950 101 m white 0.40961 1950 102 m white 0.42600 1950 103 m white 0.44270 1950 104 m white 0.45966 1950 105 m white 0.47677 1950 106 m white 0.49392 1950 107 m white 0.51100 1950 108 m white 0.52810 1950 109 m white 0.54529 1950 0 f white 0.02165 1950 1 f white 0.00140 1950 2 f white 0.00109 1950 3 f white 0.00072 1950 4 f white 0.00062 1950 5 f white 0.00057 1950 6 f white 0.00052 1950 7 f white 0.00048 1950 8 f white 0.00045 1950 9 f white 0.00042 1950 10 f white 0.00040 1950 11 f white 0.00039 1950 12 f white 0.00039 1950 13 f white 0.00040 1950 14 f white 0.00043 1950 15 f white 0.00046 1950 16 f white 0.00049 1950 17 f white 0.00052 1950 18 f white 0.00055 1950 19 f white 0.00058 1950 20 f white 0.00060 1950 21 f white 0.00063 1950 22 f white 0.00065 1950 23 f white 0.00066 1950 24 f white 0.00067 1950 25 f white 0.00068 1950 26 f white 0.00069 1950 27 f white 0.00071 1950 28 f white 0.00074 1950 29 f white 0.00077 1950 30 f white 0.00081 1950 31 f white 0.00086 1950 32 f white 0.00093 1950 33 f white 0.00102 1950 34 f white 0.00113 1950 35 f white 0.00126 1950 36 f white 0.00139 1950 37 f white 0.00153 1950 38 f white 0.00167 1950 39 f white 0.00180 1950 40 f white 0.00195 1950 41 f white 0.00213 1950 42 f white 0.00234 1950 43 f white 0.00260 1950 44 f white 0.00290 1950 45 f white 0.00322 1950 46 f white 0.00355 1950 47 f white 0.00388 1950 48 f white 0.00418 1950 49 f white 0.00447 1950 50 f white 0.00477 1950 51 f white 0.00512 1950 52 f white 0.00556 1950 53 f white 0.00608 1950 54 f white 0.00666 1950 55 f white 0.00730 1950 56 f white 0.00802 1950 57 f white 0.00882 1950 58 f white 0.00967 1950 59 f white 0.01057 1950 60 f white 0.01157 1950 61 f white 0.01271 1950 62 f white 0.01405 1950 63 f white 0.01555 1950 64 f white 0.01718 1950 65 f white 0.01899 1950 66 f white 0.02103 1950 67 f white 0.02336 1950 68 f white 0.02591 1950 69 f white 0.02864 1950 70 f white 0.03165 1950 71 f white 0.03503 1950 72 f white 0.03889 1950 73 f white 0.04315 1950 74 f white 0.04775 1950 75 f white 0.05279 1950 76 f white 0.05837 1950 77 f white 0.06458 1950 78 f white 0.07138 1950 79 f white 0.07871 1950 80 f white 0.08663 1950 81 f white 0.09521 1950 82 f white 0.10453 1950 83 f white 0.11450 1950 84 f white 0.12509 1950 85 f white 0.13641 1950 86 f white 0.14855 1950 87 f white 0.16165 1950 88 f white 0.17584 1950 89 f white 0.19105 1950 90 f white 0.20705 1950 91 f white 0.22365 1950 92 f white 0.24060 1950 93 f white 0.25809 1950 94 f white 0.27626 1950 95 f white 0.29486 1950 96 f white 0.31362 1950 97 f white 0.33229 1950 98 f white 0.35104 1950 99 f white 0.37005 1950 100 f white 0.38905 1950 101 f white 0.40778 1950 102 f white 0.42600 1950 103 f white 0.44356 1950 104 f white 0.46063 1950 105 f white 0.47742 1950 106 f white 0.49414 1950 107 f white 0.51100 1950 108 f white 0.52810 1950 109 f white 0.54529 1960 0 m white 0.02470 1960 1 m white 0.00147 1960 2 m white 0.00097 1960 3 m white 0.00078 1960 4 m white 0.00066 1960 5 m white 0.00063 1960 6 m white 0.00060 1960 7 m white 0.00058 1960 8 m white 0.00054 1960 9 m white 0.00049 1960 10 m white 0.00045 1960 11 m white 0.00044 1960 12 m white 0.00049 1960 13 m white 0.00060 1960 14 m white 0.00078 1960 15 m white 0.00096 1960 16 m white 0.00114 1960 17 m white 0.00131 1960 18 m white 0.00146 1960 19 m white 0.00160 1960 20 m white 0.00175 1960 21 m white 0.00188 1960 22 m white 0.00193 1960 23 m white 0.00186 1960 24 m white 0.00172 1960 25 m white 0.00154 1960 26 m white 0.00138 1960 27 m white 0.00129 1960 28 m white 0.00128 1960 29 m white 0.00135 1960 30 m white 0.00144 1960 31 m white 0.00154 1960 32 m white 0.00161 1960 33 m white 0.00167 1960 34 m white 0.00171 1960 35 m white 0.00177 1960 36 m white 0.00186 1960 37 m white 0.00202 1960 38 m white 0.00226 1960 39 m white 0.00257 1960 40 m white 0.00293 1960 41 m white 0.00330 1960 42 m white 0.00369 1960 43 m white 0.00407 1960 44 m white 0.00447 1960 45 m white 0.00489 1960 46 m white 0.00536 1960 47 m white 0.00593 1960 48 m white 0.00662 1960 49 m white 0.00742 1960 50 m white 0.00830 1960 51 m white 0.00920 1960 52 m white 0.01008 1960 53 m white 0.01088 1960 54 m white 0.01165 1960 55 m white 0.01244 1960 56 m white 0.01334 1960 57 m white 0.01441 1960 58 m white 0.01572 1960 59 m white 0.01723 1960 60 m white 0.01888 1960 61 m white 0.02061 1960 62 m white 0.02245 1960 63 m white 0.02439 1960 64 m white 0.02644 1960 65 m white 0.02861 1960 66 m white 0.03098 1960 67 m white 0.03363 1960 68 m white 0.03667 1960 69 m white 0.04007 1960 70 m white 0.04379 1960 71 m white 0.04777 1960 72 m white 0.05199 1960 73 m white 0.05644 1960 74 m white 0.06117 1960 75 m white 0.06619 1960 76 m white 0.07170 1960 77 m white 0.07798 1960 78 m white 0.08530 1960 79 m white 0.09373 1960 80 m white 0.10380 1960 81 m white 0.11515 1960 82 m white 0.12660 1960 83 m white 0.13690 1960 84 m white 0.14584 1960 85 m white 0.15696 1960 86 m white 0.16895 1960 87 m white 0.18228 1960 88 m white 0.19809 1960 89 m white 0.21622 1960 90 m white 0.23552 1960 91 m white 0.25471 1960 92 m white 0.27336 1960 93 m white 0.29018 1960 94 m white 0.30408 1960 95 m white 0.31416 1960 96 m white 0.32915 1960 97 m white 0.34450 1960 98 m white 0.36018 1960 99 m white 0.37616 1960 100 m white 0.39242 1960 101 m white 0.40891 1960 102 m white 0.42562 1960 103 m white 0.44250 1960 104 m white 0.45951 1960 105 m white 0.47662 1960 106 m white 0.49378 1960 107 m white 0.51095 1960 108 m white 0.52810 1960 109 m white 0.54519 1960 0 f white 0.01808 1960 1 f white 0.00133 1960 2 f white 0.00086 1960 3 f white 0.00066 1960 4 f white 0.00058 1960 5 f white 0.00047 1960 6 f white 0.00039 1960 7 f white 0.00033 1960 8 f white 0.00030 1960 9 f white 0.00028 1960 10 f white 0.00027 1960 11 f white 0.00028 1960 12 f white 0.00030 1960 13 f white 0.00033 1960 14 f white 0.00036 1960 15 f white 0.00041 1960 16 f white 0.00045 1960 17 f white 0.00049 1960 18 f white 0.00051 1960 19 f white 0.00052 1960 20 f white 0.00052 1960 21 f white 0.00053 1960 22 f white 0.00054 1960 23 f white 0.00055 1960 24 f white 0.00057 1960 25 f white 0.00058 1960 26 f white 0.00060 1960 27 f white 0.00062 1960 28 f white 0.00064 1960 29 f white 0.00066 1960 30 f white 0.00069 1960 31 f white 0.00073 1960 32 f white 0.00078 1960 33 f white 0.00084 1960 34 f white 0.00090 1960 35 f white 0.00098 1960 36 f white 0.00107 1960 37 f white 0.00117 1960 38 f white 0.00127 1960 39 f white 0.00137 1960 40 f white 0.00148 1960 41 f white 0.00162 1960 42 f white 0.00180 1960 43 f white 0.00204 1960 44 f white 0.00232 1960 45 f white 0.00264 1960 46 f white 0.00296 1960 47 f white 0.00327 1960 48 f white 0.00357 1960 49 f white 0.00386 1960 50 f white 0.00419 1960 51 f white 0.00454 1960 52 f white 0.00491 1960 53 f white 0.00527 1960 54 f white 0.00566 1960 55 f white 0.00607 1960 56 f white 0.00654 1960 57 f white 0.00715 1960 58 f white 0.00792 1960 59 f white 0.00884 1960 60 f white 0.00989 1960 61 f white 0.01100 1960 62 f white 0.01210 1960 63 f white 0.01313 1960 64 f white 0.01417 1960 65 f white 0.01526 1960 66 f white 0.01654 1960 67 f white 0.01822 1960 68 f white 0.02041 1960 69 f white 0.02306 1960 70 f white 0.02602 1960 71 f white 0.02916 1960 72 f white 0.03250 1960 73 f white 0.03600 1960 74 f white 0.03974 1960 75 f white 0.04364 1960 76 f white 0.04796 1960 77 f white 0.05315 1960 78 f white 0.05956 1960 79 f white 0.06715 1960 80 f white 0.07600 1960 81 f white 0.08569 1960 82 f white 0.09565 1960 83 f white 0.10526 1960 84 f white 0.11466 1960 85 f white 0.13063 1960 86 f white 0.14807 1960 87 f white 0.16620 1960 88 f white 0.18485 1960 89 f white 0.20398 1960 90 f white 0.22376 1960 91 f white 0.24393 1960 92 f white 0.26376 1960 93 f white 0.28252 1960 94 f white 0.29952 1960 95 f white 0.31416 1960 96 f white 0.32915 1960 97 f white 0.34450 1960 98 f white 0.36018 1960 99 f white 0.37616 1960 100 f white 0.39242 1960 101 f white 0.40891 1960 102 f white 0.42562 1960 103 f white 0.44250 1960 104 f white 0.45951 1960 105 f white 0.47662 1960 106 f white 0.49378 1960 107 f white 0.51095 1960 108 f white 0.52810 1960 109 f white 0.54519 1970 0 m total 0.01975 1970 1 m total 0.00123 1970 2 m total 0.00085 1970 3 m total 0.00073 1970 4 m total 0.00058 1970 5 m total 0.00053 1970 6 m total 0.00050 1970 7 m total 0.00048 1970 8 m total 0.00044 1970 9 m total 0.00038 1970 10 m total 0.00033 1970 11 m total 0.00032 1970 12 m total 0.00038 1970 13 m total 0.00055 1970 14 m total 0.00079 1970 15 m total 0.00107 1970 16 m total 0.00134 1970 17 m total 0.00158 1970 18 m total 0.00176 1970 19 m total 0.00189 1970 20 m total 0.00203 1970 21 m total 0.00220 1970 22 m total 0.00226 1970 23 m total 0.00217 1970 24 m total 0.00195 1970 25 m total 0.00168 1970 26 m total 0.00144 1970 27 m total 0.00127 1970 28 m total 0.00123 1970 29 m total 0.00127 1970 30 m total 0.00135 1970 31 m total 0.00143 1970 32 m total 0.00150 1970 33 m total 0.00155 1970 34 m total 0.00159 1970 35 m total 0.00165 1970 36 m total 0.00176 1970 37 m total 0.00192 1970 38 m total 0.00214 1970 39 m total 0.00240 1970 40 m total 0.00269 1970 41 m total 0.00300 1970 42 m total 0.00335 1970 43 m total 0.00375 1970 44 m total 0.00421 1970 45 m total 0.00471 1970 46 m total 0.00525 1970 47 m total 0.00581 1970 48 m total 0.00638 1970 49 m total 0.00699 1970 50 m total 0.00761 1970 51 m total 0.00833 1970 52 m total 0.00920 1970 53 m total 0.01028 1970 54 m total 0.01152 1970 55 m total 0.01289 1970 56 m total 0.01430 1970 57 m total 0.01566 1970 58 m total 0.01693 1970 59 m total 0.01817 1970 60 m total 0.01943 1970 61 m total 0.02085 1970 62 m total 0.02252 1970 63 m total 0.02454 1970 64 m total 0.02691 1970 65 m total 0.02960 1970 66 m total 0.03248 1970 67 m total 0.03538 1970 68 m total 0.03812 1970 69 m total 0.04073 1970 70 m total 0.04324 1970 71 m total 0.04602 1970 72 m total 0.04950 1970 73 m total 0.05407 1970 74 m total 0.05960 1970 75 m total 0.06574 1970 76 m total 0.07196 1970 77 m total 0.07822 1970 78 m total 0.08439 1970 79 m total 0.09068 1970 80 m total 0.09785 1970 81 m total 0.10609 1970 82 m total 0.11476 1970 83 m total 0.12340 1970 84 m total 0.13203 1970 85 m total 0.14266 1970 86 m total 0.15539 1970 87 m total 0.16875 1970 88 m total 0.18181 1970 89 m total 0.19442 1970 90 m total 0.20736 1970 91 m total 0.22169 1970 92 m total 0.23684 1970 93 m total 0.25237 1970 94 m total 0.26697 1970 95 m total 0.27962 1970 96 m total 0.29090 1970 97 m total 0.30135 1970 98 m total 0.31111 1970 99 m total 0.32017 1970 100 m total 0.32857 1970 101 m total 0.33633 1970 102 m total 0.34347 1970 103 m total 0.35004 1970 104 m total 0.35606 1970 105 m total 0.36157 1970 106 m total 0.36661 1970 107 m total 0.37121 1970 108 m total 0.37540 1970 109 m total 0.37922 1970 0 f total 0.01436 1970 1 f total 0.00084 1970 2 f total 0.00071 1970 3 f total 0.00052 1970 4 f total 0.00039 1970 5 f total 0.00038 1970 6 f total 0.00034 1970 7 f total 0.00031 1970 8 f total 0.00028 1970 9 f total 0.00026 1970 10 f total 0.00023 1970 11 f total 0.00022 1970 12 f total 0.00024 1970 13 f total 0.00030 1970 14 f total 0.00038 1970 15 f total 0.00048 1970 16 f total 0.00058 1970 17 f total 0.00064 1970 18 f total 0.00066 1970 19 f total 0.00065 1970 20 f total 0.00062 1970 21 f total 0.00061 1970 22 f total 0.00059 1970 23 f total 0.00059 1970 24 f total 0.00060 1970 25 f total 0.00062 1970 26 f total 0.00062 1970 27 f total 0.00064 1970 28 f total 0.00067 1970 29 f total 0.00072 1970 30 f total 0.00077 1970 31 f total 0.00084 1970 32 f total 0.00090 1970 33 f total 0.00094 1970 34 f total 0.00099 1970 35 f total 0.00103 1970 36 f total 0.00110 1970 37 f total 0.00118 1970 38 f total 0.00130 1970 39 f total 0.00143 1970 40 f total 0.00157 1970 41 f total 0.00172 1970 42 f total 0.00189 1970 43 f total 0.00208 1970 44 f total 0.00229 1970 45 f total 0.00252 1970 46 f total 0.00277 1970 47 f total 0.00303 1970 48 f total 0.00329 1970 49 f total 0.00357 1970 50 f total 0.00386 1970 51 f total 0.00419 1970 52 f total 0.00454 1970 53 f total 0.00494 1970 54 f total 0.00539 1970 55 f total 0.00588 1970 56 f total 0.00642 1970 57 f total 0.00699 1970 58 f total 0.00758 1970 59 f total 0.00821 1970 60 f total 0.00892 1970 61 f total 0.00972 1970 62 f total 0.01058 1970 63 f total 0.01148 1970 64 f total 0.01248 1970 65 f total 0.01356 1970 66 f total 0.01481 1970 67 f total 0.01636 1970 68 f total 0.01825 1970 69 f total 0.02043 1970 70 f total 0.02276 1970 71 f total 0.02522 1970 72 f total 0.02797 1970 73 f total 0.03111 1970 74 f total 0.03467 1970 75 f total 0.03855 1970 76 f total 0.04271 1970 77 f total 0.04734 1970 78 f total 0.05253 1970 79 f total 0.05832 1970 80 f total 0.06486 1970 81 f total 0.07206 1970 82 f total 0.07972 1970 83 f total 0.08773 1970 84 f total 0.09633 1970 85 f total 0.10722 1970 86 f total 0.11992 1970 87 f total 0.13284 1970 88 f total 0.14490 1970 89 f total 0.15639 1970 90 f total 0.16899 1970 91 f total 0.18378 1970 92 f total 0.19958 1970 93 f total 0.21560 1970 94 f total 0.23109 1970 95 f total 0.24584 1970 96 f total 0.25854 1970 97 f total 0.26980 1970 98 f total 0.27996 1970 99 f total 0.28949 1970 100 f total 0.29836 1970 101 f total 0.30659 1970 102 f total 0.31420 1970 103 f total 0.32122 1970 104 f total 0.32768 1970 105 f total 0.33361 1970 106 f total 0.33904 1970 107 f total 0.34401 1970 108 f total 0.34855 1970 109 f total 0.35269 1970 0 m white 0.01963 1970 1 m white 0.00123 1970 2 m white 0.00084 1970 3 m white 0.00071 1970 4 m white 0.00056 1970 5 m white 0.00053 1970 6 m white 0.00051 1970 7 m white 0.00048 1970 8 m white 0.00044 1970 9 m white 0.00039 1970 10 m white 0.00033 1970 11 m white 0.00032 1970 12 m white 0.00038 1970 13 m white 0.00054 1970 14 m white 0.00078 1970 15 m white 0.00106 1970 16 m white 0.00132 1970 17 m white 0.00155 1970 18 m white 0.00172 1970 19 m white 0.00185 1970 20 m white 0.00199 1970 21 m white 0.00215 1970 22 m white 0.00221 1970 23 m white 0.00211 1970 24 m white 0.00190 1970 25 m white 0.00163 1970 26 m white 0.00139 1970 27 m white 0.00123 1970 28 m white 0.00119 1970 29 m white 0.00123 1970 30 m white 0.00132 1970 31 m white 0.00139 1970 32 m white 0.00147 1970 33 m white 0.00151 1970 34 m white 0.00155 1970 35 m white 0.00161 1970 36 m white 0.00171 1970 37 m white 0.00187 1970 38 m white 0.00207 1970 39 m white 0.00232 1970 40 m white 0.00260 1970 41 m white 0.00290 1970 42 m white 0.00324 1970 43 m white 0.00364 1970 44 m white 0.00411 1970 45 m white 0.00462 1970 46 m white 0.00517 1970 47 m white 0.00573 1970 48 m white 0.00631 1970 49 m white 0.00692 1970 50 m white 0.00755 1970 51 m white 0.00827 1970 52 m white 0.00914 1970 53 m white 0.01022 1970 54 m white 0.01146 1970 55 m white 0.01283 1970 56 m white 0.01423 1970 57 m white 0.01560 1970 58 m white 0.01688 1970 59 m white 0.01813 1970 60 m white 0.01941 1970 61 m white 0.02085 1970 62 m white 0.02253 1970 63 m white 0.02456 1970 64 m white 0.02693 1970 65 m white 0.02961 1970 66 m white 0.03248 1970 67 m white 0.03539 1970 68 m white 0.03814 1970 69 m white 0.04078 1970 70 m white 0.04332 1970 71 m white 0.04612 1970 72 m white 0.04962 1970 73 m white 0.05419 1970 74 m white 0.05971 1970 75 m white 0.06581 1970 76 m white 0.07201 1970 77 m white 0.07826 1970 78 m white 0.08445 1970 79 m white 0.09082 1970 80 m white 0.09811 1970 81 m white 0.10650 1970 82 m white 0.11531 1970 83 m white 0.12404 1970 84 m white 0.13271 1970 85 m white 0.14340 1970 86 m white 0.15624 1970 87 m white 0.16981 1970 88 m white 0.18320 1970 89 m white 0.19632 1970 90 m white 0.20995 1970 91 m white 0.22519 1970 92 m white 0.24150 1970 93 m white 0.25847 1970 94 m white 0.27493 1970 95 m white 0.29014 1970 96 m white 0.30431 1970 97 m white 0.31784 1970 98 m white 0.33085 1970 99 m white 0.34324 1970 100 m white 0.35479 1970 101 m white 0.36553 1970 102 m white 0.37550 1970 103 m white 0.38471 1970 104 m white 0.39320 1970 105 m white 0.40101 1970 106 m white 0.40818 1970 107 m white 0.41475 1970 108 m white 0.42075 1970 109 m white 0.42624 1970 0 f white 0.01403 1970 1 f white 0.00085 1970 2 f white 0.00069 1970 3 f white 0.00052 1970 4 f white 0.00040 1970 5 f white 0.00039 1970 6 f white 0.00035 1970 7 f white 0.00032 1970 8 f white 0.00029 1970 9 f white 0.00026 1970 10 f white 0.00023 1970 11 f white 0.00022 1970 12 f white 0.00024 1970 13 f white 0.00029 1970 14 f white 0.00037 1970 15 f white 0.00047 1970 16 f white 0.00056 1970 17 f white 0.00062 1970 18 f white 0.00064 1970 19 f white 0.00062 1970 20 f white 0.00060 1970 21 f white 0.00058 1970 22 f white 0.00057 1970 23 f white 0.00057 1970 24 f white 0.00058 1970 25 f white 0.00059 1970 26 f white 0.00060 1970 27 f white 0.00062 1970 28 f white 0.00065 1970 29 f white 0.00070 1970 30 f white 0.00075 1970 31 f white 0.00082 1970 32 f white 0.00087 1970 33 f white 0.00092 1970 34 f white 0.00095 1970 35 f white 0.00099 1970 36 f white 0.00105 1970 37 f white 0.00113 1970 38 f white 0.00124 1970 39 f white 0.00137 1970 40 f white 0.00151 1970 41 f white 0.00166 1970 42 f white 0.00183 1970 43 f white 0.00202 1970 44 f white 0.00224 1970 45 f white 0.00248 1970 46 f white 0.00273 1970 47 f white 0.00299 1970 48 f white 0.00326 1970 49 f white 0.00353 1970 50 f white 0.00383 1970 51 f white 0.00415 1970 52 f white 0.00450 1970 53 f white 0.00490 1970 54 f white 0.00534 1970 55 f white 0.00584 1970 56 f white 0.00637 1970 57 f white 0.00694 1970 58 f white 0.00754 1970 59 f white 0.00818 1970 60 f white 0.00889 1970 61 f white 0.00969 1970 62 f white 0.01055 1970 63 f white 0.01146 1970 64 f white 0.01247 1970 65 f white 0.01356 1970 66 f white 0.01481 1970 67 f white 0.01636 1970 68 f white 0.01826 1970 69 f white 0.02044 1970 70 f white 0.02276 1970 71 f white 0.02522 1970 72 f white 0.02796 1970 73 f white 0.03110 1970 74 f white 0.03466 1970 75 f white 0.03853 1970 76 f white 0.04269 1970 77 f white 0.04732 1970 78 f white 0.05252 1970 79 f white 0.05834 1970 80 f white 0.06491 1970 81 f white 0.07214 1970 82 f white 0.07983 1970 83 f white 0.08787 1970 84 f white 0.09649 1970 85 f white 0.10744 1970 86 f white 0.12025 1970 87 f white 0.13332 1970 88 f white 0.14556 1970 89 f white 0.15727 1970 90 f white 0.17016 1970 91 f white 0.18539 1970 92 f white 0.20189 1970 93 f white 0.21905 1970 94 f white 0.23615 1970 95 f white 0.25298 1970 96 f white 0.26762 1970 97 f white 0.28133 1970 98 f white 0.29413 1970 99 f white 0.30615 1970 100 f white 0.31742 1970 101 f white 0.32794 1970 102 f white 0.33772 1970 103 f white 0.34679 1970 104 f white 0.35517 1970 105 f white 0.36289 1970 106 f white 0.36999 1970 107 f white 0.37651 1970 108 f white 0.38248 1970 109 f white 0.38793 1980 0 m total 0.01171 1980 1 m total 0.00082 1980 2 m total 0.00066 1980 3 m total 0.00057 1980 4 m total 0.00045 1980 5 m total 0.00038 1980 6 m total 0.00035 1980 7 m total 0.00032 1980 8 m total 0.00028 1980 9 m total 0.00023 1980 10 m total 0.00019 1980 11 m total 0.00019 1980 12 m total 0.00028 1980 13 m total 0.00044 1980 14 m total 0.00066 1980 15 m total 0.00088 1980 16 m total 0.00106 1980 17 m total 0.00122 1980 18 m total 0.00135 1980 19 m total 0.00146 1980 20 m total 0.00158 1980 21 m total 0.00169 1980 22 m total 0.00174 1980 23 m total 0.00172 1980 24 m total 0.00164 1980 25 m total 0.00153 1980 26 m total 0.00144 1980 27 m total 0.00136 1980 28 m total 0.00131 1980 29 m total 0.00128 1980 30 m total 0.00126 1980 31 m total 0.00124 1980 32 m total 0.00123 1980 33 m total 0.00126 1980 34 m total 0.00131 1980 35 m total 0.00139 1980 36 m total 0.00148 1980 37 m total 0.00158 1980 38 m total 0.00169 1980 39 m total 0.00180 1980 40 m total 0.00194 1980 41 m total 0.00213 1980 42 m total 0.00234 1980 43 m total 0.00259 1980 44 m total 0.00287 1980 45 m total 0.00317 1980 46 m total 0.00353 1980 47 m total 0.00400 1980 48 m total 0.00457 1980 49 m total 0.00523 1980 50 m total 0.00593 1980 51 m total 0.00663 1980 52 m total 0.00733 1980 53 m total 0.00801 1980 54 m total 0.00870 1980 55 m total 0.00943 1980 56 m total 0.01023 1980 57 m total 0.01116 1980 58 m total 0.01228 1980 59 m total 0.01358 1980 60 m total 0.01500 1980 61 m total 0.01653 1980 62 m total 0.01828 1980 63 m total 0.02025 1980 64 m total 0.02240 1980 65 m total 0.02473 1980 66 m total 0.02716 1980 67 m total 0.02962 1980 68 m total 0.03204 1980 69 m total 0.03450 1980 70 m total 0.03711 1980 71 m total 0.03997 1980 72 m total 0.04316 1980 73 m total 0.04674 1980 74 m total 0.05074 1980 75 m total 0.05510 1980 76 m total 0.05982 1980 77 m total 0.06503 1980 78 m total 0.07075 1980 79 m total 0.07696 1980 80 m total 0.08374 1980 81 m total 0.09104 1980 82 m total 0.09872 1980 83 m total 0.10673 1980 84 m total 0.11521 1980 85 m total 0.12563 1980 86 m total 0.13713 1980 87 m total 0.14881 1980 88 m total 0.16025 1980 89 m total 0.17187 1980 90 m total 0.18480 1980 91 m total 0.19966 1980 92 m total 0.21563 1980 93 m total 0.23177 1980 94 m total 0.24710 1980 95 m total 0.26149 1980 96 m total 0.27438 1980 97 m total 0.28654 1980 98 m total 0.29797 1980 99 m total 0.30867 1980 100 m total 0.31865 1980 101 m total 0.32792 1980 102 m total 0.33650 1980 103 m total 0.34443 1980 104 m total 0.35174 1980 105 m total 0.35845 1980 106 m total 0.36461 1980 107 m total 0.37024 1980 108 m total 0.37539 1980 109 m total 0.38009 1980 0 f total 0.00903 1980 1 f total 0.00056 1980 2 f total 0.00045 1980 3 f total 0.00036 1980 4 f total 0.00031 1980 5 f total 0.00030 1980 6 f total 0.00028 1980 7 f total 0.00025 1980 8 f total 0.00023 1980 9 f total 0.00020 1980 10 f total 0.00017 1980 11 f total 0.00016 1980 12 f total 0.00018 1980 13 f total 0.00022 1980 14 f total 0.00028 1980 15 f total 0.00035 1980 16 f total 0.00040 1980 17 f total 0.00044 1980 18 f total 0.00047 1980 19 f total 0.00049 1980 20 f total 0.00051 1980 21 f total 0.00053 1980 22 f total 0.00053 1980 23 f total 0.00053 1980 24 f total 0.00050 1980 25 f total 0.00048 1980 26 f total 0.00046 1980 27 f total 0.00045 1980 28 f total 0.00045 1980 29 f total 0.00047 1980 30 f total 0.00049 1980 31 f total 0.00052 1980 32 f total 0.00055 1980 33 f total 0.00060 1980 34 f total 0.00065 1980 35 f total 0.00072 1980 36 f total 0.00080 1980 37 f total 0.00089 1980 38 f total 0.00099 1980 39 f total 0.00110 1980 40 f total 0.00122 1980 41 f total 0.00135 1980 42 f total 0.00150 1980 43 f total 0.00165 1980 44 f total 0.00181 1980 45 f total 0.00198 1980 46 f total 0.00217 1980 47 f total 0.00238 1980 48 f total 0.00260 1980 49 f total 0.00282 1980 50 f total 0.00305 1980 51 f total 0.00330 1980 52 f total 0.00359 1980 53 f total 0.00395 1980 54 f total 0.00436 1980 55 f total 0.00482 1980 56 f total 0.00529 1980 57 f total 0.00578 1980 58 f total 0.00627 1980 59 f total 0.00678 1980 60 f total 0.00733 1980 61 f total 0.00795 1980 62 f total 0.00868 1980 63 f total 0.00954 1980 64 f total 0.01051 1980 65 f total 0.01159 1980 66 f total 0.01274 1980 67 f total 0.01393 1980 68 f total 0.01514 1980 69 f total 0.01643 1980 70 f total 0.01783 1980 71 f total 0.01942 1980 72 f total 0.02129 1980 73 f total 0.02351 1980 74 f total 0.02604 1980 75 f total 0.02874 1980 76 f total 0.03167 1980 77 f total 0.03508 1980 78 f total 0.03914 1980 79 f total 0.04384 1980 80 f total 0.04903 1980 81 f total 0.05459 1980 82 f total 0.06067 1980 83 f total 0.06733 1980 84 f total 0.07467 1980 85 f total 0.08396 1980 86 f total 0.09429 1980 87 f total 0.10503 1980 88 f total 0.11595 1980 89 f total 0.12752 1980 90 f total 0.14085 1980 91 f total 0.15604 1980 92 f total 0.17184 1980 93 f total 0.18743 1980 94 f total 0.20278 1980 95 f total 0.21823 1980 96 f total 0.23221 1980 97 f total 0.24560 1980 98 f total 0.25834 1980 99 f total 0.27040 1980 100 f total 0.28176 1980 101 f total 0.29242 1980 102 f total 0.30237 1980 103 f total 0.31163 1980 104 f total 0.32023 1980 105 f total 0.32817 1980 106 f total 0.33550 1980 107 f total 0.34224 1980 108 f total 0.34843 1980 109 f total 0.35411 1980 0 m white 0.01125 1980 1 m white 0.00078 1980 2 m white 0.00063 1980 3 m white 0.00051 1980 4 m white 0.00044 1980 5 m white 0.00038 1980 6 m white 0.00035 1980 7 m white 0.00032 1980 8 m white 0.00028 1980 9 m white 0.00023 1980 10 m white 0.00018 1980 11 m white 0.00018 1980 12 m white 0.00026 1980 13 m white 0.00044 1980 14 m white 0.00066 1980 15 m white 0.00088 1980 16 m white 0.00107 1980 17 m white 0.00123 1980 18 m white 0.00135 1980 19 m white 0.00146 1980 20 m white 0.00157 1980 21 m white 0.00168 1980 22 m white 0.00173 1980 23 m white 0.00170 1980 24 m white 0.00162 1980 25 m white 0.00151 1980 26 m white 0.00141 1980 27 m white 0.00133 1980 28 m white 0.00127 1980 29 m white 0.00125 1980 30 m white 0.00122 1980 31 m white 0.00119 1980 32 m white 0.00118 1980 33 m white 0.00120 1980 34 m white 0.00125 1980 35 m white 0.00132 1980 36 m white 0.00141 1980 37 m white 0.00151 1980 38 m white 0.00161 1980 39 m white 0.00172 1980 40 m white 0.00186 1980 41 m white 0.00205 1980 42 m white 0.00227 1980 43 m white 0.00251 1980 44 m white 0.00279 1980 45 m white 0.00309 1980 46 m white 0.00345 1980 47 m white 0.00391 1980 48 m white 0.00449 1980 49 m white 0.00516 1980 50 m white 0.00587 1980 51 m white 0.00658 1980 52 m white 0.00728 1980 53 m white 0.00796 1980 54 m white 0.00865 1980 55 m white 0.00938 1980 56 m white 0.01018 1980 57 m white 0.01110 1980 58 m white 0.01221 1980 59 m white 0.01349 1980 60 m white 0.01490 1980 61 m white 0.01642 1980 62 m white 0.01816 1980 63 m white 0.02013 1980 64 m white 0.02229 1980 65 m white 0.02464 1980 66 m white 0.02710 1980 67 m white 0.02958 1980 68 m white 0.03203 1980 69 m white 0.03451 1980 70 m white 0.03715 1980 71 m white 0.04006 1980 72 m white 0.04326 1980 73 m white 0.04683 1980 74 m white 0.05080 1980 75 m white 0.05510 1980 76 m white 0.05978 1980 77 m white 0.06497 1980 78 m white 0.07072 1980 79 m white 0.07702 1980 80 m white 0.08392 1980 81 m white 0.09135 1980 82 m white 0.09913 1980 83 m white 0.10718 1980 84 m white 0.11563 1980 85 m white 0.12594 1980 86 m white 0.13737 1980 87 m white 0.14904 1980 88 m white 0.16056 1980 89 m white 0.17238 1980 90 m white 0.18563 1980 91 m white 0.20094 1980 92 m white 0.21748 1980 93 m white 0.23433 1980 94 m white 0.25058 1980 95 m white 0.26617 1980 96 m white 0.28001 1980 97 m white 0.29311 1980 98 m white 0.30545 1980 99 m white 0.31703 1980 100 m white 0.32784 1980 101 m white 0.33791 1980 102 m white 0.34724 1980 103 m white 0.35588 1980 104 m white 0.36384 1980 105 m white 0.37117 1980 106 m white 0.37790 1980 107 m white 0.38407 1980 108 m white 0.38971 1980 109 m white 0.39486 1980 0 f white 0.00874 1980 1 f white 0.00050 1980 2 f white 0.00041 1980 3 f white 0.00035 1980 4 f white 0.00031 1980 5 f white 0.00029 1980 6 f white 0.00027 1980 7 f white 0.00025 1980 8 f white 0.00023 1980 9 f white 0.00019 1980 10 f white 0.00016 1980 11 f white 0.00015 1980 12 f white 0.00017 1980 13 f white 0.00021 1980 14 f white 0.00028 1980 15 f white 0.00035 1980 16 f white 0.00041 1980 17 f white 0.00045 1980 18 f white 0.00048 1980 19 f white 0.00049 1980 20 f white 0.00050 1980 21 f white 0.00052 1980 22 f white 0.00052 1980 23 f white 0.00051 1980 24 f white 0.00049 1980 25 f white 0.00047 1980 26 f white 0.00045 1980 27 f white 0.00043 1980 28 f white 0.00044 1980 29 f white 0.00045 1980 30 f white 0.00048 1980 31 f white 0.00050 1980 32 f white 0.00054 1980 33 f white 0.00058 1980 34 f white 0.00063 1980 35 f white 0.00070 1980 36 f white 0.00078 1980 37 f white 0.00087 1980 38 f white 0.00096 1980 39 f white 0.00105 1980 40 f white 0.00116 1980 41 f white 0.00129 1980 42 f white 0.00143 1980 43 f white 0.00158 1980 44 f white 0.00174 1980 45 f white 0.00192 1980 46 f white 0.00211 1980 47 f white 0.00233 1980 48 f white 0.00255 1980 49 f white 0.00278 1980 50 f white 0.00301 1980 51 f white 0.00326 1980 52 f white 0.00355 1980 53 f white 0.00390 1980 54 f white 0.00430 1980 55 f white 0.00475 1980 56 f white 0.00521 1980 57 f white 0.00569 1980 58 f white 0.00618 1980 59 f white 0.00671 1980 60 f white 0.00728 1980 61 f white 0.00792 1980 62 f white 0.00866 1980 63 f white 0.00951 1980 64 f white 0.01048 1980 65 f white 0.01155 1980 66 f white 0.01269 1980 67 f white 0.01388 1980 68 f white 0.01510 1980 69 f white 0.01640 1980 70 f white 0.01781 1980 71 f white 0.01942 1980 72 f white 0.02130 1980 73 f white 0.02351 1980 74 f white 0.02603 1980 75 f white 0.02872 1980 76 f white 0.03164 1980 77 f white 0.03504 1980 78 f white 0.03911 1980 79 f white 0.04382 1980 80 f white 0.04903 1980 81 f white 0.05460 1980 82 f white 0.06069 1980 83 f white 0.06736 1980 84 f white 0.07471 1980 85 f white 0.08399 1980 86 f white 0.09432 1980 87 f white 0.10511 1980 88 f white 0.11613 1980 89 f white 0.12785 1980 90 f white 0.14143 1980 91 f white 0.15697 1980 92 f white 0.17324 1980 93 f white 0.18947 1980 94 f white 0.20568 1980 95 f white 0.22228 1980 96 f white 0.23729 1980 97 f white 0.25173 1980 98 f white 0.26551 1980 99 f white 0.27859 1980 100 f white 0.29094 1980 101 f white 0.30255 1980 102 f white 0.31342 1980 103 f white 0.32355 1980 104 f white 0.33297 1980 105 f white 0.34168 1980 106 f white 0.34973 1980 107 f white 0.35715 1980 108 f white 0.36397 1980 109 f white 0.37022 1990 0 m total 0.00823 1990 1 m total 0.00056 1990 2 m total 0.00038 1990 3 m total 0.00031 1990 4 m total 0.00026 1990 5 m total 0.00023 1990 6 m total 0.00022 1990 7 m total 0.00021 1990 8 m total 0.00019 1990 9 m total 0.00016 1990 10 m total 0.00013 1990 11 m total 0.00013 1990 12 m total 0.00018 1990 13 m total 0.00030 1990 14 m total 0.00046 1990 15 m total 0.00065 1990 16 m total 0.00083 1990 17 m total 0.00098 1990 18 m total 0.00108 1990 19 m total 0.00115 1990 20 m total 0.00121 1990 21 m total 0.00127 1990 22 m total 0.00129 1990 23 m total 0.00128 1990 24 m total 0.00123 1990 25 m total 0.00119 1990 26 m total 0.00115 1990 27 m total 0.00113 1990 28 m total 0.00113 1990 29 m total 0.00115 1990 30 m total 0.00118 1990 31 m total 0.00120 1990 32 m total 0.00124 1990 33 m total 0.00130 1990 34 m total 0.00137 1990 35 m total 0.00146 1990 36 m total 0.00155 1990 37 m total 0.00164 1990 38 m total 0.00173 1990 39 m total 0.00181 1990 40 m total 0.00190 1990 41 m total 0.00201 1990 42 m total 0.00214 1990 43 m total 0.00230 1990 44 m total 0.00250 1990 45 m total 0.00274 1990 46 m total 0.00302 1990 47 m total 0.00332 1990 48 m total 0.00363 1990 49 m total 0.00396 1990 50 m total 0.00433 1990 51 m total 0.00478 1990 52 m total 0.00530 1990 53 m total 0.00591 1990 54 m total 0.00660 1990 55 m total 0.00736 1990 56 m total 0.00820 1990 57 m total 0.00913 1990 58 m total 0.01016 1990 59 m total 0.01127 1990 60 m total 0.01241 1990 61 m total 0.01361 1990 62 m total 0.01493 1990 63 m total 0.01645 1990 64 m total 0.01817 1990 65 m total 0.01999 1990 66 m total 0.02191 1990 67 m total 0.02404 1990 68 m total 0.02645 1990 69 m total 0.02916 1990 70 m total 0.03220 1990 71 m total 0.03551 1990 72 m total 0.03904 1990 73 m total 0.04269 1990 74 m total 0.04645 1990 75 m total 0.05037 1990 76 m total 0.05463 1990 77 m total 0.05940 1990 78 m total 0.06497 1990 79 m total 0.07142 1990 80 m total 0.07890 1990 81 m total 0.08715 1990 82 m total 0.09575 1990 83 m total 0.10415 1990 84 m total 0.11240 1990 85 m total 0.12196 1990 86 m total 0.13298 1990 87 m total 0.14466 1990 88 m total 0.15686 1990 89 m total 0.16970 1990 90 m total 0.18384 1990 91 m total 0.19931 1990 92 m total 0.21509 1990 93 m total 0.23043 1990 94 m total 0.24525 1990 95 m total 0.26004 1990 96 m total 0.27536 1990 97 m total 0.28943 1990 98 m total 0.30390 1990 99 m total 0.31910 1990 100 m total 0.33505 1990 101 m total 0.35181 1990 102 m total 0.36940 1990 103 m total 0.38787 1990 104 m total 0.40726 1990 105 m total 0.42762 1990 106 m total 0.44900 1990 107 m total 0.47145 1990 108 m total 0.49503 1990 109 m total 0.51978 1990 0 f total 0.00631 1990 1 f total 0.00052 1990 2 f total 0.00033 1990 3 f total 0.00025 1990 4 f total 0.00020 1990 5 f total 0.00018 1990 6 f total 0.00016 1990 7 f total 0.00015 1990 8 f total 0.00013 1990 9 f total 0.00012 1990 10 f total 0.00011 1990 11 f total 0.00011 1990 12 f total 0.00013 1990 13 f total 0.00017 1990 14 f total 0.00022 1990 15 f total 0.00028 1990 16 f total 0.00034 1990 17 f total 0.00039 1990 18 f total 0.00042 1990 19 f total 0.00043 1990 20 f total 0.00044 1990 21 f total 0.00045 1990 22 f total 0.00045 1990 23 f total 0.00044 1990 24 f total 0.00043 1990 25 f total 0.00042 1990 26 f total 0.00041 1990 27 f total 0.00040 1990 28 f total 0.00040 1990 29 f total 0.00040 1990 30 f total 0.00041 1990 31 f total 0.00042 1990 32 f total 0.00044 1990 33 f total 0.00049 1990 34 f total 0.00056 1990 35 f total 0.00064 1990 36 f total 0.00072 1990 37 f total 0.00081 1990 38 f total 0.00090 1990 39 f total 0.00098 1990 40 f total 0.00108 1990 41 f total 0.00119 1990 42 f total 0.00130 1990 43 f total 0.00141 1990 44 f total 0.00153 1990 45 f total 0.00167 1990 46 f total 0.00183 1990 47 f total 0.00201 1990 48 f total 0.00220 1990 49 f total 0.00242 1990 50 f total 0.00267 1990 51 f total 0.00295 1990 52 f total 0.00327 1990 53 f total 0.00360 1990 54 f total 0.00396 1990 55 f total 0.00434 1990 56 f total 0.00477 1990 57 f total 0.00530 1990 58 f total 0.00592 1990 59 f total 0.00662 1990 60 f total 0.00736 1990 61 f total 0.00810 1990 62 f total 0.00881 1990 63 f total 0.00950 1990 64 f total 0.01019 1990 65 f total 0.01091 1990 66 f total 0.01173 1990 67 f total 0.01275 1990 68 f total 0.01404 1990 69 f total 0.01557 1990 70 f total 0.01730 1990 71 f total 0.01914 1990 72 f total 0.02105 1990 73 f total 0.02298 1990 74 f total 0.02498 1990 75 f total 0.02706 1990 76 f total 0.02941 1990 77 f total 0.03227 1990 78 f total 0.03586 1990 79 f total 0.04016 1990 80 f total 0.04492 1990 81 f total 0.05004 1990 82 f total 0.05573 1990 83 f total 0.06205 1990 84 f total 0.06904 1990 85 f total 0.07761 1990 86 f total 0.08705 1990 87 f total 0.09716 1990 88 f total 0.10797 1990 89 f total 0.11983 1990 90 f total 0.13353 1990 91 f total 0.14890 1990 92 f total 0.16491 1990 93 f total 0.18102 1990 94 f total 0.19753 1990 95 f total 0.21475 1990 96 f total 0.23143 1990 97 f total 0.24775 1990 98 f total 0.26375 1990 99 f total 0.27957 1990 100 f total 0.29635 1990 101 f total 0.31413 1990 102 f total 0.33298 1990 103 f total 0.35296 1990 104 f total 0.37413 1990 105 f total 0.39658 1990 106 f total 0.42038 1990 107 f total 0.44560 1990 108 f total 0.47233 1990 109 f total 0.50068 1990 0 m white 0.00749 1990 1 m white 0.00049 1990 2 m white 0.00034 1990 3 m white 0.00028 1990 4 m white 0.00024 1990 5 m white 0.00022 1990 6 m white 0.00021 1990 7 m white 0.00020 1990 8 m white 0.00018 1990 9 m white 0.00015 1990 10 m white 0.00013 1990 11 m white 0.00013 1990 12 m white 0.00017 1990 13 m white 0.00029 1990 14 m white 0.00045 1990 15 m white 0.00064 1990 16 m white 0.00081 1990 17 m white 0.00095 1990 18 m white 0.00104 1990 19 m white 0.00109 1990 20 m white 0.00114 1990 21 m white 0.00118 1990 22 m white 0.00120 1990 23 m white 0.00118 1990 24 m white 0.00115 1990 25 m white 0.00111 1990 26 m white 0.00108 1990 27 m white 0.00106 1990 28 m white 0.00107 1990 29 m white 0.00109 1990 30 m white 0.00112 1990 31 m white 0.00114 1990 32 m white 0.00118 1990 33 m white 0.00123 1990 34 m white 0.00130 1990 35 m white 0.00138 1990 36 m white 0.00147 1990 37 m white 0.00155 1990 38 m white 0.00163 1990 39 m white 0.00171 1990 40 m white 0.00180 1990 41 m white 0.00191 1990 42 m white 0.00203 1990 43 m white 0.00219 1990 44 m white 0.00237 1990 45 m white 0.00260 1990 46 m white 0.00287 1990 47 m white 0.00317 1990 48 m white 0.00347 1990 49 m white 0.00379 1990 50 m white 0.00415 1990 51 m white 0.00460 1990 52 m white 0.00512 1990 53 m white 0.00573 1990 54 m white 0.00643 1990 55 m white 0.00719 1990 56 m white 0.00804 1990 57 m white 0.00897 1990 58 m white 0.01000 1990 59 m white 0.01110 1990 60 m white 0.01223 1990 61 m white 0.01341 1990 62 m white 0.01474 1990 63 m white 0.01626 1990 64 m white 0.01799 1990 65 m white 0.01982 1990 66 m white 0.02175 1990 67 m white 0.02389 1990 68 m white 0.02631 1990 69 m white 0.02905 1990 70 m white 0.03210 1990 71 m white 0.03542 1990 72 m white 0.03897 1990 73 m white 0.04263 1990 74 m white 0.04640 1990 75 m white 0.05033 1990 76 m white 0.05460 1990 77 m white 0.05939 1990 78 m white 0.06496 1990 79 m white 0.07143 1990 80 m white 0.07893 1990 81 m white 0.08719 1990 82 m white 0.09579 1990 83 m white 0.10417 1990 84 m white 0.11238 1990 85 m white 0.12192 1990 86 m white 0.13295 1990 87 m white 0.14471 1990 88 m white 0.15706 1990 89 m white 0.17012 1990 90 m white 0.18458 1990 91 m white 0.20048 1990 92 m white 0.21675 1990 93 m white 0.23260 1990 94 m white 0.24792 1990 95 m white 0.26329 1990 96 m white 0.27914 1990 97 m white 0.29399 1990 98 m white 0.30869 1990 99 m white 0.32413 1990 100 m white 0.34033 1990 101 m white 0.35735 1990 102 m white 0.37522 1990 103 m white 0.39398 1990 104 m white 0.41368 1990 105 m white 0.43436 1990 106 m white 0.45608 1990 107 m white 0.47888 1990 108 m white 0.50282 1990 109 m white 0.52797 1990 0 f white 0.00545 1990 1 f white 0.00046 1990 2 f white 0.00030 1990 3 f white 0.00023 1990 4 f white 0.00018 1990 5 f white 0.00017 1990 6 f white 0.00015 1990 7 f white 0.00014 1990 8 f white 0.00013 1990 9 f white 0.00012 1990 10 f white 0.00011 1990 11 f white 0.00011 1990 12 f white 0.00013 1990 13 f white 0.00016 1990 14 f white 0.00022 1990 15 f white 0.00028 1990 16 f white 0.00034 1990 17 f white 0.00039 1990 18 f white 0.00041 1990 19 f white 0.00042 1990 20 f white 0.00043 1990 21 f white 0.00044 1990 22 f white 0.00044 1990 23 f white 0.00042 1990 24 f white 0.00041 1990 25 f white 0.00039 1990 26 f white 0.00038 1990 27 f white 0.00037 1990 28 f white 0.00037 1990 29 f white 0.00037 1990 30 f white 0.00038 1990 31 f white 0.00039 1990 32 f white 0.00041 1990 33 f white 0.00046 1990 34 f white 0.00052 1990 35 f white 0.00060 1990 36 f white 0.00067 1990 37 f white 0.00076 1990 38 f white 0.00085 1990 39 f white 0.00094 1990 40 f white 0.00104 1990 41 f white 0.00115 1990 42 f white 0.00126 1990 43 f white 0.00138 1990 44 f white 0.00149 1990 45 f white 0.00163 1990 46 f white 0.00179 1990 47 f white 0.00197 1990 48 f white 0.00216 1990 49 f white 0.00238 1990 50 f white 0.00262 1990 51 f white 0.00290 1990 52 f white 0.00321 1990 53 f white 0.00354 1990 54 f white 0.00390 1990 55 f white 0.00428 1990 56 f white 0.00472 1990 57 f white 0.00524 1990 58 f white 0.00585 1990 59 f white 0.00652 1990 60 f white 0.00724 1990 61 f white 0.00797 1990 62 f white 0.00867 1990 63 f white 0.00935 1990 64 f white 0.01005 1990 65 f white 0.01077 1990 66 f white 0.01160 1990 67 f white 0.01262 1990 68 f white 0.01391 1990 69 f white 0.01545 1990 70 f white 0.01718 1990 71 f white 0.01902 1990 72 f white 0.02093 1990 73 f white 0.02286 1990 74 f white 0.02486 1990 75 f white 0.02694 1990 76 f white 0.02929 1990 77 f white 0.03216 1990 78 f white 0.03575 1990 79 f white 0.04004 1990 80 f white 0.04479 1990 81 f white 0.04989 1990 82 f white 0.05558 1990 83 f white 0.06191 1990 84 f white 0.06895 1990 85 f white 0.07754 1990 86 f white 0.08705 1990 87 f white 0.09725 1990 88 f white 0.10818 1990 89 f white 0.12018 1990 90 f white 0.13408 1990 91 f white 0.14976 1990 92 f white 0.16617 1990 93 f white 0.18271 1990 94 f white 0.19967 1990 95 f white 0.21737 1990 96 f white 0.23434 1990 97 f white 0.25091 1990 98 f white 0.26715 1990 99 f white 0.28318 1990 100 f white 0.30017 1990 101 f white 0.31818 1990 102 f white 0.33727 1990 103 f white 0.35750 1990 104 f white 0.37895 1990 105 f white 0.40169 1990 106 f white 0.42579 1990 107 f white 0.45134 1990 108 f white 0.47842 1990 109 f white 0.50712 survival/noweb/rates/us2004.dat0000755000175100001440000000650612730271054016035 0ustar hornikusers"age" "tm" "wm" "bm" "tf" "wf" "bf" "0-1" 748 609 622 507 1525 1237 "1-2" 51 46 46 42 76 66 "2-3" 33 27 30 23 47 41 "3-4" 25 20 22 18 40 30 "4-5" 21 17 20 15 31 25 "5-6" 19 15 17 13 28 24 "6-7" 18 14 17 12 26 21 "7-8" 17 13 16 12 24 19 "8-9" 15 12 14 11 21 18 "9-10" 12 11 12 10 17 18 "10-11" 10 11 10 9 15 18 "11-12" 11 11 10 10 16 19 "12-13" 16 14 15 12 22 21 "13-14" 27 18 26 17 35 24 "14-15" 43 24 41 23 55 27 "15-16" 61 31 58 31 77 31 "16-17" 78 37 75 38 100 36 "17-18" 94 42 90 43 123 41 "18-19" 106 45 102 45 144 46 "19-20" 117 45 111 45 163 51 "20-21" 127 46 120 44 182 56 "21-22" 136 46 128 44 200 62 "22-23" 142 47 133 44 215 68 "23-24" 144 48 134 44 225 72 "24-25" 142 49 131 45 231 77 "25-26" 139 51 128 46 236 83 "26-27" 136 52 124 47 242 89 "27-28" 134 54 122 48 246 95 "28-29" 134 56 121 50 249 101 "29-30" 134 59 121 53 250 107 "30-31" 135 63 122 56 251 113 "31-32" 137 67 125 59 253 121 "32-33" 141 71 128 64 257 129 "33-34" 147 76 135 68 264 137 "34-35" 155 82 143 74 274 147 "35-36" 165 89 153 81 286 158 "36-37" 177 97 164 88 301 170 "37-38" 191 107 178 97 320 187 "38-39" 208 119 194 108 341 210 "39-40" 225 132 212 119 366 235 "40-41" 244 145 230 130 391 262 "41-42" 263 159 249 142 419 288 "42-43" 285 173 269 155 456 314 "43-44" 311 188 293 169 504 342 "44-45" 341 206 320 185 563 371 "45-46" 374 224 348 203 627 402 "46-47" 407 244 378 221 693 434 "47-48" 443 263 411 239 764 469 "48-49" 481 282 445 256 839 506 "49-50" 521 300 481 272 919 545 "50-51" 565 320 522 289 1006 587 "51-52" 612 343 566 309 1100 633 "52-53" 659 370 609 334 1193 678 "53-54" 704 400 652 364 1281 724 "54-55" 749 435 694 399 1365 770 "55-56" 795 472 737 437 1454 820 "56-57" 846 514 786 479 1553 877 "57-58" 906 559 844 524 1661 940 "58-59" 981 611 917 576 1778 1011 "59-60" 1071 670 1006 634 1907 1089 "60-61" 1176 739 1111 703 2050 1176 "61-62" 1293 817 1228 780 2206 1274 "62-63" 1416 898 1350 860 2368 1376 "63-64" 1536 978 1469 939 2528 1479 "64-65" 1656 1058 1586 1017 2684 1583 "65-66" 1785 1147 1714 1104 2838 1691 "66-67" 1933 1250 1863 1206 3002 1809 "67-68" 2099 1366 2031 1323 3183 1940 "68-69" 2286 1497 2219 1454 3396 2089 "69-70" 2492 1641 2427 1599 3641 2258 "70-71" 2706 1794 2643 1753 3900 2437 "71-72" 2936 1962 2874 1922 4170 2627 "72-73" 3203 2150 3143 2112 4479 2845 "73-74" 3518 2364 3460 2326 4838 3096 "74-75" 3873 2599 3817 2562 5243 3376 "75-76" 4241 2836 4184 2798 5686 3669 "76-77" 4617 3085 4558 3046 6146 3972 "77-78" 5032 3382 4976 3345 6608 4298 "78-79" 5508 3748 5462 3716 7052 4655 "79-80" 6050 4179 6020 4156 7485 5047 "80-81" 6656 4646 6648 4630 7937 5476 "81-82" 7299 5131 7313 5119 8419 5934 "82-83" 7968 5661 8005 5656 8913 6420 "83-84" 8659 6261 8716 6267 9433 6941 "84-85" 9401 6953 9477 6975 10002 7517 "85-86" 10250 7665 10355 7706 10686 8113 "86-87" 11164 8441 11304 8506 11409 8752 "87-88" 12147 9288 12325 9380 12174 9435 "88-89" 13202 10208 13424 10332 12982 10164 "89-90" 14332 11208 14601 11367 13832 10944 "90-91" 15538 12291 15859 12489 14728 11774 "91-92" 16823 13460 17202 13704 15670 12658 "92-93" 18188 14720 18628 15014 16658 13597 "93-94" 19633 16073 20140 16422 17692 14594 "94-95" 21159 17522 21737 17931 18775 15649 "95-96" 22764 19069 23417 19543 19904 16764 "96-97" 24448 20713 25179 21257 21081 17940 "97-98" 26206 22455 27018 23072 22304 19179 "98-99" 28035 24292 28931 24987 23573 20480 "99-100" 29931 26222 30911 26997 24887 21843 survival/noweb/rates/minn2000.dat0000755000175100001440000000314112730271054016333 0ustar hornikusers"age" "tm" "tf" "0-1" 690 527 "1-2" 48 19 "2-3" 22 23 "3-4" 24 21 "4-5" 10 12 "5-6" 31 6 "6-7" 19 10 "7-8" 15 21 "8-9" 25 17 "9-10" 12 17 "10-11" 15 9 "11-12" 16 11 "12-13" 26 13 "13-14" 21 11 "14-15" 27 13 "15-16" 48 22 "16-17" 56 52 "17-18" 68 38 "18-19" 96 38 "19-20" 104 37 "20-21" 94 49 "21-22" 112 52 "22-23" 121 43 "23-24" 129 44 "24-25" 85 38 "25-26" 86 31 "26-27" 92 41 "27-28" 90 38 "28-29" 107 60 "29-30" 95 47 "30-31" 76 24 "31-32" 102 47 "32-33" 114 73 "33-34" 120 52 "34-35" 120 51 "35-36" 114 78 "36-37" 138 55 "37-38" 167 73 "38-39" 146 113 "39-40" 146 95 "40-41" 172 109 "41-42" 184 94 "42-43" 210 85 "43-44" 217 136 "44-45" 196 158 "45-46" 242 156 "46-47" 222 179 "47-48" 313 185 "48-49" 344 202 "49-50" 422 196 "50-51" 340 164 "51-52" 419 237 "52-53" 473 278 "53-54" 483 346 "54-55" 496 410 "55-56" 600 398 "56-57" 675 390 "57-58" 753 519 "58-59" 844 547 "59-60" 936 639 "60-61" 893 652 "61-62" 1000 720 "62-63" 1178 791 "63-64" 1417 813 "64-65" 1471 922 "65-66" 1662 1018 "66-67" 1715 1157 "67-68" 2011 1247 "68-69" 2134 1287 "69-70" 2464 1501 "70-71" 2381 1612 "71-72" 2887 1757 "72-73" 3289 2021 "73-74" 3426 2092 "74-75" 3877 2345 "75-76" 4052 2688 "76-77" 4909 2986 "77-78" 4932 3120 "78-79" 5622 3188 "79-80" 5976 3962 "80-81" 6904 4011 "81-82" 7746 4747 "82-83" 8306 5726 "83-84" 8708 5953 "84-85" 10239 6401 "85-86" 11700 7760 "86-87" 13367 8453 "87-88" 13765 9334 "88-89" 14163 10811 "89-90" 16641 11691 "90-91" 16276 13313 "91-92" 19386 15347 "92-93" 20879 16963 "93-94" 22306 19140 "94-95" 26532 19216 "95-96" 26930 22643 "96-97" 30038 21151 "97-98" 38402 25261 "98-99" 30986 27854 "99-100" 30367 25704 survival/noweb/rates/us2003.dat0000755000175100001440000000651112730271054016030 0ustar hornikusers"age" "tm" "wm" "bm" "tf" "wf" "bf" "0-1" 761 608 637 505 1556 1245 "1-2" 52 41 46 37 86 61 "2-3" 37 30 33 27 54 46 "3-4" 29 22 26 20 44 32 "4-5" 22 17 20 17 29 18 "5-6" 20 16 18 15 28 22 "6-7" 18 14 17 13 24 19 "7-8" 16 13 16 12 21 17 "8-9" 15 12 14 11 19 16 "9-10" 13 11 12 10 17 16 "10-11" 11 10 10 9 17 16 "11-12" 12 11 11 10 19 18 "12-13" 18 13 16 12 26 19 "13-14" 29 17 27 16 39 22 "14-15" 44 23 42 23 56 24 "15-16" 62 29 60 30 76 28 "16-17" 79 36 76 37 98 32 "17-18" 95 41 91 42 121 37 "18-19" 108 44 103 44 145 43 "19-20" 119 46 112 45 168 51 "20-21" 129 47 121 46 192 58 "21-22" 139 49 129 46 215 66 "22-23" 145 50 133 47 232 72 "23-24" 146 51 133 47 241 77 "24-25" 142 52 130 47 245 80 "25-26" 138 52 124 48 246 83 "26-27" 133 53 120 48 249 88 "27-28" 131 55 117 49 250 93 "28-29" 131 57 118 51 251 99 "29-30" 134 60 121 54 251 105 "30-31" 138 63 125 56 251 112 "31-32" 142 67 130 60 253 120 "32-33" 147 72 136 64 258 130 "33-34" 154 78 142 69 268 142 "34-35" 163 85 150 76 282 158 "35-36" 173 94 159 83 299 174 "36-37" 185 103 170 91 318 192 "37-38" 199 114 184 100 341 211 "38-39" 217 126 201 111 367 232 "39-40" 236 138 220 123 396 253 "40-41" 257 151 240 135 426 275 "41-42" 278 164 260 147 459 297 "42-43" 301 178 281 160 499 322 "43-44" 327 193 305 173 546 350 "44-45" 357 208 332 187 603 381 "45-46" 389 226 361 202 663 415 "46-47" 422 244 392 218 726 450 "47-48" 458 263 423 236 796 486 "48-49" 493 282 455 253 872 524 "49-50" 530 303 488 272 955 564 "50-51" 571 325 523 292 1048 608 "51-52" 615 350 562 314 1146 654 "52-53" 661 379 605 341 1239 700 "53-54" 707 410 650 373 1320 745 "54-55" 756 446 699 409 1396 790 "55-56" 808 485 752 449 1474 839 "56-57" 866 528 810 493 1565 897 "57-58" 933 576 876 541 1672 965 "58-59" 1013 631 953 594 1800 1044 "59-60" 1106 694 1043 655 1945 1134 "60-61" 1216 767 1149 726 2107 1234 "61-62" 1338 849 1269 807 2280 1342 "62-63" 1466 934 1394 890 2452 1451 "63-64" 1592 1016 1519 970 2614 1557 "64-65" 1719 1097 1645 1050 2766 1661 "65-66" 1854 1186 1781 1138 2912 1767 "66-67" 2009 1290 1938 1242 3070 1883 "67-68" 2185 1409 2116 1362 3258 2015 "68-69" 2384 1543 2317 1496 3493 2171 "69-70" 2605 1692 2538 1645 3776 2350 "70-71" 2832 1847 2762 1800 4085 2541 "71-72" 3069 2014 2998 1968 4405 2741 "72-73" 3344 2207 3272 2161 4750 2966 "73-74" 3669 2432 3600 2387 5117 3220 "74-75" 4040 2684 3976 2642 5504 3496 "75-76" 4429 2945 4370 2904 5911 3788 "76-77" 4827 3216 4771 3175 6337 4090 "77-78" 5260 3526 5208 3488 6786 4407 "78-79" 5745 3895 5700 3864 7262 4747 "79-80" 6291 4325 6256 4305 7772 5119 "80-81" 6907 4795 6883 4785 8336 5523 "81-82" 7576 5297 7565 5296 8936 5963 "82-83" 8284 5863 8290 5871 9530 6460 "83-84" 9022 6515 9049 6535 10090 7035 "84-85" 9814 7271 9866 7305 10635 7704 "85-86" 10699 8014 10781 8070 11362 8315 "86-87" 11654 8826 11768 8908 12131 8969 "87-88" 12680 9711 12832 9823 12945 9669 "88-89" 13782 10674 13975 10820 13803 10417 "89-90" 14961 11719 15201 11904 14708 11216 "90-91" 16220 12851 16511 13080 15660 12066 "91-92" 17561 14074 17908 14351 16661 12972 "92-93" 18986 15392 19394 15723 17712 13935 "93-94" 20495 16807 20968 17198 18812 14956 "94-95" 22087 18322 22630 18778 19963 16037 "95-96" 23763 19939 24380 20466 21164 17180 "96-97" 25520 21658 26214 22261 22415 18386 "97-98" 27355 23479 28128 24162 23715 19655 "98-99" 29265 25400 30120 26168 25064 20988 "99-100" 31244 27418 32182 28273 26461 22386 survival/noweb/rates/usinfant.dat0000755000175100001440000000331012730271054016715 0ustar hornikusersyear,period,total.m, total.f, white.m, white.f, black.m, black.f 1999,0-24 hrs,6116 ,5045 ,3820 ,3158 ,2100 ,1691 1999,1-6 d,2140 ,1588 ,1507 ,1116 ,574 ,411 1999,7-27 d,2099 ,1740 ,1407 ,1156 ,623 ,521 1999,28-365 d,5291 ,3918 ,3463 ,2440 ,1600 ,1302 2000,0-24 hrs,6118 ,4985 ,3811 ,3147 ,2076 ,1655 2000,1-6 d,2243 ,1567 ,1549 ,1100 ,589 ,410 2000,7-27 d,2150 ,1713 ,1453 ,1141 ,620 ,493 2000,28-365 d,5207 ,4052 ,3364 ,2579 ,1616 ,1312 2001,0-24 hrs,6122 ,4776 ,3859 ,3052 ,2047 ,1559 2001,1-6 d,2139 ,1574 ,1513 ,1092 ,558 ,420 2001,7-27 d,1976 ,1678 ,1378 ,1119 ,520 ,481 2001,28-365 d,5240 ,4063 ,3349 ,2593 ,1639 ,1274 2002,0-24 hrs,6303 ,5063 ,4008 ,3198 ,2042 ,1661 2002,1-6 d,2050 ,1588 ,1497 ,1092 ,476 ,433 2002,7-27 d,2055 ,1688 ,1436 ,1123 ,536 ,498 2002,28-365 d,5309 ,3978 ,3492 ,2523 ,1598 ,1280 2003,0-24 hrs,6387 ,5082 ,4110 ,3295 ,2034 ,1581 2003,1-6 d,2123 ,1541 ,1503 ,1101 ,533 ,372 2003,7-27 d,2126 ,1634 ,1432 ,1054 ,607 ,513 2003,28-365 d,5266 ,3866 ,3455 ,2490 ,1566 ,1196 2004,0-24 hrs,6472 ,4974 ,4054 ,3169 ,2003 ,1575 2004,1-6 d,1826 ,1582 ,1421 ,1087 ,488 ,432 2004,7-27 d,2092 ,1647 ,1365 ,1102 ,633 ,491 2004,28-365 d,5328 ,4015 ,3425 ,2608 ,1645 ,1227 2005,"0-24 hrs",6212,5145,3884,3283,2059,1669 2005,"1-6 d",2129,1526,1497,1074,540,381 2005,"7-28 d",2103,1655,1415,1086,602,489 2005,"28-365 d",5574,4096,3675,2600,1666,1289 2006,"0-24 hrs",6331,5063,3996,3170,2061,1685 2006,"1-6 d",2041,1668,1440,1148,504,448 2006,"7-28 d",2192,1694,1427,1121,659,519 2006,"28-365 d",5416,4122,3482,2619,1662,1320 2007,"0-24 hrs",6346,5124,3971,3232,2089,1654 2007,"1-6 d",2061,1562,1423,1096,530,390 2007,"7-28 d",2180,1785,1451,1160,637,542 2007,"28-365 d",5706,4374,3695,2779,1719,1383 survival/noweb/rates/us2002.dat0000755000175100001440000000651612730271054016034 0ustar hornikusers"age" "tm" "wm" "bm" "tf" "wf" "bf" "0-1" 764 627 642 512 1540 1322 "1-2" 52 42 47 38 82 61 "2-3" 37 28 33 26 54 41 "3-4" 28 20 25 18 43 27 "4-5" 23 17 21 15 37 27 "5-6" 19 16 17 15 26 21 "6-7" 16 13 16 12 20 18 "7-8" 16 12 15 11 19 18 "8-9" 17 13 15 13 27 17 "9-10" 16 13 14 12 28 19 "10-11" 18 13 16 11 25 20 "11-12" 18 13 16 12 27 19 "12-13" 22 14 20 13 35 22 "13-14" 26 19 24 18 35 21 "14-15" 32 21 30 20 46 25 "15-16" 44 25 43 25 52 28 "16-17" 75 39 73 40 91 33 "17-18" 91 44 88 45 113 42 "18-19" 121 47 115 46 165 51 "19-20" 140 46 132 46 191 51 "20-21" 139 45 129 44 206 60 "21-22" 144 50 134 49 226 66 "22-23" 139 47 125 42 231 71 "23-24" 142 45 130 42 234 72 "24-25" 139 49 126 46 244 70 "25-26" 134 50 120 46 248 81 "26-27" 138 51 123 46 258 89 "27-28" 130 51 114 44 259 93 "28-29" 130 56 117 53 244 92 "29-30" 138 60 123 52 267 123 "30-31" 141 63 129 56 256 115 "31-32" 145 67 132 59 272 120 "32-33" 139 72 125 63 255 137 "33-34" 158 79 146 70 270 149 "34-35" 164 85 148 76 312 158 "35-36" 178 96 158 86 346 175 "36-37" 187 103 168 93 352 185 "37-38" 201 112 187 100 336 199 "38-39" 222 122 202 108 393 228 "39-40" 240 143 223 129 402 262 "40-41" 266 149 251 136 425 262 "41-42" 283 165 265 147 468 313 "42-43" 297 175 277 157 492 311 "43-44" 328 199 307 177 541 382 "44-45" 358 209 335 185 587 403 "45-46" 384 230 356 207 664 425 "46-47" 425 238 396 213 721 440 "47-48" 446 258 414 231 774 478 "48-49" 495 286 453 254 907 542 "49-50" 528 303 487 272 961 569 "50-51" 570 319 523 284 1043 619 "51-52" 618 352 566 318 1147 663 "52-53" 643 363 591 329 1174 659 "53-54" 702 414 647 383 1288 714 "54-55" 732 443 676 408 1382 791 "55-56" 842 510 787 474 1555 902 "56-57" 832 501 777 465 1506 861 "57-58" 947 589 887 554 1668 968 "58-59" 1038 644 972 604 1848 1077 "59-60" 1176 727 1112 686 2025 1183 "60-61" 1210 758 1138 722 2116 1182 "61-62" 1351 848 1284 802 2242 1352 "62-63" 1488 920 1414 879 2484 1402 "63-64" 1611 1010 1541 967 2603 1543 "64-65" 1738 1115 1662 1071 2817 1637 "65-66" 1891 1211 1818 1165 2934 1778 "66-67" 2037 1306 1967 1254 3078 1945 "67-68" 2241 1457 2178 1411 3244 2055 "68-69" 2434 1559 2364 1510 3528 2185 "69-70" 2674 1740 2605 1685 3824 2444 "70-71" 2922 1899 2863 1856 4082 2578 "71-72" 3197 2045 3127 1988 4555 2877 "72-73" 3406 2252 3334 2202 4843 3044 "73-74" 3802 2463 3741 2416 5207 3252 "74-75" 4121 2714 4066 2664 5507 3540 "75-76" 4519 3010 4465 2954 5916 3944 "76-77" 4957 3263 4895 3209 6471 4236 "77-78" 5357 3609 5304 3561 6779 4626 "78-79" 5842 3947 5806 3918 7300 4793 "79-80" 6498 4411 6446 4381 8182 5400 "80-81" 7028 4930 6981 4914 8734 5693 "81-82" 7636 5330 7634 5329 8850 6028 "82-83" 8673 6218 8698 6206 9949 7102 "83-84" 8848 6455 8892 6453 9466 7125 "84-85" 10216 7506 10247 7530 11265 8036 "85-86" 11175 8322 11228 8358 12035 8728 "86-87" 12191 9200 12272 9254 12836 9465 "87-88" 13263 10139 13382 10221 13669 10249 "88-89" 14391 11140 14558 11262 14533 11081 "89-90" 15572 12204 15798 12379 15426 11962 "90-91" 16805 13328 17104 13574 16349 12894 "91-92" 18086 14512 18474 14848 17300 13878 "92-93" 19412 15753 19905 16202 18276 14915 "93-94" 20779 17049 21396 17636 19277 16004 "94-95" 22182 18395 22944 19151 20301 17147 "95-96" 23615 19788 24546 20746 21345 18345 "96-97" 25074 21222 26196 22418 22407 19596 "97-98" 26550 22690 27890 24167 23484 20901 "98-99" 28037 24188 29624 25990 24574 22259 "99-100" 29527 25705 31389 27881 25674 23670 survival/noweb/rates/us1996.dat0000755000175100001440000000654412730271054016062 0ustar hornikusers"age" "tm" "wm" "bm" "tf" "wf" "bf" "0-1" 802 659 666 544 1602 1325 "1-2" 60 54 52 43 110 108 "2-3" 45 33 40 28 73 63 "3-4" 36 28 32 24 59 47 "4-5" 28 23 25 19 49 41 "5-6" 26 20 23 17 42 33 "6-7" 24 18 22 16 39 28 "7-8" 23 16 20 15 36 24 "8-9" 20 15 19 14 31 22 "9-10" 17 14 16 13 25 21 "10-11" 15 14 14 13 19 21 "11-12" 15 14 14 13 19 22 "12-13" 22 17 20 16 29 24 "13-14" 36 22 33 20 54 29 "14-15" 56 28 51 27 89 35 "15-16" 79 35 70 34 126 41 "16-17" 99 42 89 41 161 48 "17-18" 116 47 103 46 191 54 "18-19" 128 48 113 47 215 59 "19-20" 135 48 118 45 235 64 "20-21" 142 47 124 43 257 68 "21-22" 150 47 130 42 280 74 "22-23" 155 47 133 41 298 81 "23-24" 156 49 134 42 304 88 "24-25" 154 52 132 45 304 96 "25-26" 151 55 130 48 300 103 "26-27" 149 58 128 50 298 112 "27-28" 151 62 130 53 304 121 "28-29" 158 66 136 56 318 132 "29-30" 168 70 145 59 340 143 "30-31" 178 74 154 62 363 155 "31-32" 189 79 164 66 384 166 "32-33" 199 85 173 70 406 180 "33-34" 209 91 182 75 427 195 "34-35" 219 98 191 81 449 212 "35-36" 230 105 201 86 471 230 "36-37" 241 113 211 93 494 248 "37-38" 254 121 222 99 523 266 "38-39" 268 129 234 106 558 285 "39-40" 285 138 248 114 600 305 "40-41" 303 147 263 123 645 326 "41-42" 322 158 280 132 694 349 "42-43" 343 171 298 144 744 373 "43-44" 366 184 318 157 796 397 "44-45" 390 200 340 171 850 423 "45-46" 415 216 363 186 910 451 "46-47" 443 234 388 203 974 481 "47-48" 473 254 416 222 1038 514 "48-49" 507 277 449 245 1100 549 "49-50" 546 305 487 272 1163 588 "50-51" 593 338 534 304 1236 636 "51-52" 649 376 589 342 1321 691 "52-53" 709 416 647 380 1415 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0.00513 1940 41 m white 0.00554 1940 42 m white 0.006 1940 43 m white 0.0065 1940 44 m white 0.00706 1940 45 m white 0.00766 1940 46 m white 0.00833 1940 47 m white 0.00904 1940 48 m white 0.00981 1940 49 m white 0.01064 1940 50 m white 0.01155 1940 51 m white 0.01253 1940 52 m white 0.0136 1940 53 m white 0.01476 1940 54 m white 0.01602 1940 55 m white 0.01737 1940 56 m white 0.01881 1940 57 m white 0.02034 1940 58 m white 0.02195 1940 59 m white 0.02366 1940 60 m white 0.02548 1940 61 m white 0.02743 1940 62 m white 0.02952 1940 63 m white 0.03177 1940 64 m white 0.0342 1940 65 m white 0.03685 1940 66 m white 0.03975 1940 67 m white 0.04293 1940 68 m white 0.04643 1940 69 m white 0.05028 1940 70 m white 0.05454 1940 71 m white 0.05924 1940 72 m white 0.06443 1940 73 m white 0.07014 1940 74 m white 0.07637 1940 75 m white 0.08313 1940 76 m white 0.0904 1940 77 m white 0.09818 1940 78 m white 0.10647 1940 79 m white 0.1153 1940 80 m white 0.12471 1940 81 m white 0.13472 1940 82 m white 0.14537 1940 83 m white 0.15668 1940 84 m white 0.16859 1940 85 m white 0.18104 1940 86 m white 0.19395 1940 87 m white 0.20727 1940 88 m white 0.22091 1940 89 m white 0.23482 1940 90 m white 0.24894 1940 91 m white 0.26322 1940 92 m white 0.2776 1940 93 m white 0.29202 1940 94 m white 0.30642 1940 95 m white 0.32076 1940 96 m white 0.33496 1940 97 m white 0.34898 1940 98 m white 0.36275 1940 99 m white 0.37623 1940 100 m white 0.38935 1940 101 m white 0.40205 1940 102 m white 0.41429 1940 103 m white 0.42599 1940 104 m white 0.43712 1940 105 m white 0.4476 1940 106 m white 0.45738 1940 107 m white 0.4664 1940 108 m white 0.47462 1940 109 m white 0.48476 1940 0-1d f white 0.01187 1940 1-7d f white 0.00757 1940 7-28d f white 0.00447 1940 0 f white 0.03789 1940 1 f white 0.00432 1940 2 f white 0.0022 1940 3 f white 0.00161 1940 4 f white 0.00128 1940 5 f white 0.0011 1940 6 f white 0.00096 1940 7 f white 0.00085 1940 8 f white 0.00077 1940 9 f white 0.00072 1940 10 f white 7e-04 1940 11 f white 7e-04 1940 12 f white 0.00072 1940 13 f white 0.00077 1940 14 f white 0.00086 1940 15 f white 0.00096 1940 16 f white 0.00107 1940 17 f white 0.00117 1940 18 f white 0.00126 1940 19 f white 0.00136 1940 20 f white 0.00145 1940 21 f white 0.00154 1940 22 f white 0.00162 1940 23 f white 0.0017 1940 24 f white 0.00176 1940 25 f white 0.00182 1940 26 f white 0.00188 1940 27 f white 0.00195 1940 28 f white 0.00203 1940 29 f white 0.00211 1940 30 f white 0.0022 1940 31 f white 0.0023 1940 32 f white 0.0024 1940 33 f white 0.00252 1940 34 f white 0.00264 1940 35 f white 0.00278 1940 36 f white 0.00292 1940 37 f white 0.00309 1940 38 f white 0.00326 1940 39 f white 0.00346 1940 40 f white 0.00368 1940 41 f white 0.00393 1940 42 f white 0.0042 1940 43 f white 0.00451 1940 44 f white 0.00485 1940 45 f white 0.00523 1940 46 f white 0.00564 1940 47 f white 0.00608 1940 48 f white 0.00655 1940 49 f white 0.00706 1940 50 f white 0.00762 1940 51 f white 0.00822 1940 52 f white 0.00888 1940 53 f white 0.00961 1940 54 f white 0.0104 1940 55 f white 0.01128 1940 56 f white 0.01224 1940 57 f white 0.0133 1940 58 f white 0.01446 1940 59 f white 0.01574 1940 60 f white 0.01714 1940 61 f white 0.01867 1940 62 f white 0.02035 1940 63 f white 0.02217 1940 64 f white 0.02419 1940 65 f white 0.02643 1940 66 f white 0.02893 1940 67 f white 0.03174 1940 68 f white 0.03489 1940 69 f white 0.03841 1940 70 f white 0.04233 1940 71 f white 0.04669 1940 72 f white 0.0515 1940 73 f white 0.0568 1940 74 f white 0.06259 1940 75 f white 0.06889 1940 76 f white 0.07569 1940 77 f white 0.083 1940 78 f white 0.09083 1940 79 f white 0.09921 1940 80 f white 0.10819 1940 81 f white 0.1178 1940 82 f white 0.12809 1940 83 f white 0.13906 1940 84 f white 0.1507 1940 85 f white 0.16294 1940 86 f white 0.17573 1940 87 f white 0.18902 1940 88 f white 0.20276 1940 89 f white 0.2169 1940 90 f white 0.23141 1940 91 f white 0.24624 1940 92 f white 0.26136 1940 93 f white 0.27671 1940 94 f white 0.29226 1940 95 f white 0.30796 1940 96 f white 0.32379 1940 97 f white 0.33968 1940 98 f white 0.35561 1940 99 f white 0.37152 1940 100 f white 0.38739 1940 101 f white 0.40316 1940 102 f white 0.4188 1940 103 f white 0.43427 1940 104 f white 0.44951 1940 105 f white 0.4645 1940 106 f white 0.47919 1940 107 f white 0.49353 1940 108 f white 0.5075 1940 109 f white 0.52104 1940 0-1d m nonwhite 0.01541 1940 1-7d m nonwhite 0.01479 1940 7-28d m nonwhite 0.01365 1940 0 m nonwhite 0.09863 1940 1 m nonwhite 0.02036 1940 2 m nonwhite 0.00959 1940 3 m nonwhite 0.00516 1940 4 m nonwhite 0.00389 1940 5 m nonwhite 0.0033 1940 6 m nonwhite 0.00284 1940 7 m nonwhite 0.00249 1940 8 m nonwhite 0.00225 1940 9 m nonwhite 0.00212 1940 10 m nonwhite 0.00207 1940 11 m nonwhite 0.00212 1940 12 m nonwhite 0.00224 1940 13 m nonwhite 0.00248 1940 14 m nonwhite 0.00285 1940 15 m nonwhite 0.00329 1940 16 m nonwhite 0.00372 1940 17 m nonwhite 0.00411 1940 18 m nonwhite 0.00445 1940 19 m nonwhite 0.00479 1940 20 m nonwhite 0.00511 1940 21 m nonwhite 0.00537 1940 22 m nonwhite 0.00555 1940 23 m nonwhite 0.0056 1940 24 m nonwhite 0.00554 1940 25 m nonwhite 0.00543 1940 26 m nonwhite 0.00535 1940 27 m nonwhite 0.00537 1940 28 m nonwhite 0.00548 1940 29 m nonwhite 0.00566 1940 30 m nonwhite 0.00588 1940 31 m nonwhite 0.00613 1940 32 m nonwhite 0.00637 1940 33 m nonwhite 0.0066 1940 34 m nonwhite 0.00683 1940 35 m nonwhite 0.00708 1940 36 m nonwhite 0.00734 1940 37 m nonwhite 0.00763 1940 38 m nonwhite 0.00796 1940 39 m nonwhite 0.00832 1940 40 m nonwhite 0.00872 1940 41 m nonwhite 0.00916 1940 42 m nonwhite 0.00963 1940 43 m nonwhite 0.01015 1940 44 m nonwhite 0.01072 1940 45 m nonwhite 0.01135 1940 46 m nonwhite 0.01203 1940 47 m nonwhite 0.01278 1940 48 m nonwhite 0.01361 1940 49 m nonwhite 0.0145 1940 50 m nonwhite 0.01544 1940 51 m nonwhite 0.01643 1940 52 m nonwhite 0.01745 1940 53 m nonwhite 0.01849 1940 54 m nonwhite 0.0196 1940 55 m nonwhite 0.02079 1940 56 m nonwhite 0.02212 1940 57 m nonwhite 0.02361 1940 58 m nonwhite 0.02529 1940 59 m nonwhite 0.02715 1940 60 m nonwhite 0.02914 1940 61 m nonwhite 0.03123 1940 62 m nonwhite 0.0334 1940 63 m nonwhite 0.03562 1940 64 m nonwhite 0.03794 1940 65 m nonwhite 0.04043 1940 66 m nonwhite 0.04314 1940 67 m nonwhite 0.04614 1940 68 m nonwhite 0.04949 1940 69 m nonwhite 0.05322 1940 70 m nonwhite 0.05736 1940 71 m nonwhite 0.06196 1940 72 m nonwhite 0.06704 1940 73 m nonwhite 0.0726 1940 74 m nonwhite 0.07854 1940 75 m nonwhite 0.0847 1940 76 m nonwhite 0.09093 1940 77 m nonwhite 0.09709 1940 78 m nonwhite 0.10309 1940 79 m nonwhite 0.10904 1940 80 m nonwhite 0.11511 1940 81 m nonwhite 0.12147 1940 82 m nonwhite 0.12828 1940 83 m nonwhite 0.13572 1940 84 m nonwhite 0.14392 1940 85 m nonwhite 0.15301 1940 86 m nonwhite 0.16312 1940 87 m nonwhite 0.17438 1940 88 m nonwhite 0.18694 1940 89 m nonwhite 0.20091 1940 90 m nonwhite 0.21643 1940 91 m nonwhite 0.23363 1940 92 m nonwhite 0.25264 1940 93 m nonwhite 0.2736 1940 94 m nonwhite 0.29664 1940 95 m nonwhite 0.32189 1940 96 m nonwhite 0.34948 1940 97 m nonwhite 0.37954 1940 98 m nonwhite 0.41221 1940 99 m nonwhite 0.44761 1940 100 m nonwhite 0.48588 1940 101 m nonwhite 0.52715 1940 102 m nonwhite 0.57155 1940 103 m nonwhite 0.61921 1940 104 m nonwhite 0.67028 1940 105 m nonwhite 0.72486 1940 106 m nonwhite 0.72486 1940 107 m nonwhite 0.72486 1940 108 m nonwhite 0.72486 1940 109 m nonwhite 0.72486 1940 0-1d f nonwhite 0.0127 1940 1-7d f nonwhite 0.01148 1940 7-28d f nonwhite 0.01016 1940 0 f nonwhite 0.08717 1940 1 f nonwhite 0.02038 1940 2 f nonwhite 0.00986 1940 3 f nonwhite 0.00546 1940 4 f nonwhite 0.00393 1940 5 f nonwhite 0.0031 1940 6 f nonwhite 0.00251 1940 7 f nonwhite 0.00212 1940 8 f nonwhite 0.0019 1940 9 f nonwhite 0.00183 1940 10 f nonwhite 0.00189 1940 11 f nonwhite 0.00203 1940 12 f nonwhite 0.00225 1940 13 f nonwhite 0.00256 1940 14 f nonwhite 0.00299 1940 15 f nonwhite 0.00349 1940 16 f nonwhite 0.004 1940 17 f nonwhite 0.00448 1940 18 f nonwhite 0.00495 1940 19 f nonwhite 0.00545 1940 20 f nonwhite 0.00593 1940 21 f nonwhite 0.00636 1940 22 f nonwhite 0.0067 1940 23 f nonwhite 0.00693 1940 24 f nonwhite 0.00709 1940 25 f nonwhite 0.0072 1940 26 f nonwhite 0.00726 1940 27 f nonwhite 0.00731 1940 28 f nonwhite 0.00733 1940 29 f nonwhite 0.0073 1940 30 f nonwhite 0.00725 1940 31 f nonwhite 0.00719 1940 32 f nonwhite 0.00712 1940 33 f nonwhite 0.00706 1940 34 f nonwhite 0.00701 1940 35 f nonwhite 0.00697 1940 36 f nonwhite 0.00696 1940 37 f nonwhite 0.00699 1940 38 f nonwhite 0.00706 1940 39 f nonwhite 0.00717 1940 40 f nonwhite 0.00732 1940 41 f nonwhite 0.00751 1940 42 f nonwhite 0.00773 1940 43 f nonwhite 0.00799 1940 44 f nonwhite 0.00828 1940 45 f nonwhite 0.00864 1940 46 f nonwhite 0.00907 1940 47 f nonwhite 0.00959 1940 48 f nonwhite 0.0102 1940 49 f nonwhite 0.01091 1940 50 f nonwhite 0.01171 1940 51 f nonwhite 0.0126 1940 52 f nonwhite 0.01358 1940 53 f nonwhite 0.01464 1940 54 f nonwhite 0.01577 1940 55 f nonwhite 0.01696 1940 56 f nonwhite 0.01819 1940 57 f nonwhite 0.01947 1940 58 f nonwhite 0.02078 1940 59 f nonwhite 0.02213 1940 60 f nonwhite 0.02353 1940 61 f nonwhite 0.02499 1940 62 f nonwhite 0.02652 1940 63 f nonwhite 0.02814 1940 64 f nonwhite 0.02987 1940 65 f nonwhite 0.03171 1940 66 f nonwhite 0.0337 1940 67 f nonwhite 0.03585 1940 68 f nonwhite 0.0382 1940 69 f nonwhite 0.0408 1940 70 f nonwhite 0.04373 1940 71 f nonwhite 0.04708 1940 72 f nonwhite 0.05092 1940 73 f nonwhite 0.05527 1940 74 f nonwhite 0.05998 1940 75 f nonwhite 0.06485 1940 76 f nonwhite 0.06966 1940 77 f nonwhite 0.07421 1940 78 f nonwhite 0.07837 1940 79 f nonwhite 0.08232 1940 80 f nonwhite 0.08633 1940 81 f nonwhite 0.09066 1940 82 f nonwhite 0.09556 1940 83 f nonwhite 0.10131 1940 84 f nonwhite 0.1081 1940 85 f nonwhite 0.11615 1940 86 f nonwhite 0.12567 1940 87 f nonwhite 0.13686 1940 88 f nonwhite 0.14993 1940 89 f nonwhite 0.16508 1940 90 f nonwhite 0.18253 1940 91 f nonwhite 0.20249 1940 92 f nonwhite 0.22515 1940 93 f nonwhite 0.25073 1940 94 f nonwhite 0.27943 1940 95 f nonwhite 0.31146 1940 96 f nonwhite 0.34703 1940 97 f nonwhite 0.38635 1940 98 f nonwhite 0.42962 1940 99 f nonwhite 0.47705 1940 100 f nonwhite 0.52884 1940 101 f nonwhite 0.58521 1940 102 f nonwhite 0.64637 1940 103 f nonwhite 0.71251 1940 104 f nonwhite 0.78385 1940 105 f nonwhite 0.86059 1940 106 f nonwhite 0.86059 1940 107 f nonwhite 0.86059 1940 108 f nonwhite 0.86059 1940 109 f nonwhite 0.86059 1940 0-1d m black 0.01921 1940 1-7d m black 0.01688 1940 7-28d m black 0.0115 1940 0 m black 0.08228 1940 1 m black 0.00937 1940 2 m black 0.00432 1940 3 m black 0.00269 1940 4 m black 0.00216 1940 5 m black 0.00186 1940 6 m black 0.00163 1940 7 m black 0.00147 1940 8 m black 0.00137 1940 9 m black 0.00134 1940 10 m black 0.00138 1940 11 m black 0.00149 1940 12 m black 0.00167 1940 13 m black 0.00194 1940 14 m black 0.00231 1940 15 m black 0.00274 1940 16 m black 0.0032 1940 17 m black 0.00369 1940 18 m black 0.00422 1940 19 m black 0.00483 1940 20 m black 0.00544 1940 21 m black 0.00602 1940 22 m black 0.0065 1940 23 m black 0.00685 1940 24 m black 0.00711 1940 25 m black 0.00733 1940 26 m black 0.00754 1940 27 m black 0.0078 1940 28 m black 0.0081 1940 29 m black 0.0084 1940 30 m black 0.00872 1940 31 m black 0.00906 1940 32 m black 0.00943 1940 33 m black 0.00983 1940 34 m black 0.01025 1940 35 m black 0.01071 1940 36 m black 0.01121 1940 37 m black 0.01174 1940 38 m black 0.0123 1940 39 m black 0.01293 1940 40 m black 0.01362 1940 41 m black 0.0144 1940 42 m black 0.01528 1940 43 m black 0.01629 1940 44 m black 0.0174 1940 45 m black 0.01859 1940 46 m black 0.01986 1940 47 m black 0.02118 1940 48 m black 0.02255 1940 49 m black 0.02394 1940 50 m black 0.02536 1940 51 m black 0.02679 1940 52 m black 0.02823 1940 53 m black 0.02966 1940 54 m black 0.03108 1940 55 m black 0.03248 1940 56 m black 0.03386 1940 57 m black 0.0352 1940 58 m black 0.0365 1940 59 m black 0.03779 1940 60 m black 0.0391 1940 61 m black 0.04045 1940 62 m black 0.04189 1940 63 m black 0.04343 1940 64 m black 0.04508 1940 65 m black 0.04685 1940 66 m black 0.04875 1940 67 m black 0.05077 1940 68 m black 0.05294 1940 69 m black 0.05532 1940 70 m black 0.05799 1940 71 m black 0.06104 1940 72 m black 0.06455 1940 73 m black 0.06857 1940 74 m black 0.07309 1940 75 m black 0.07803 1940 76 m black 0.08336 1940 77 m black 0.08902 1940 78 m black 0.09495 1940 79 m black 0.10107 1940 80 m black 0.1073 1940 81 m black 0.11353 1940 82 m black 0.11969 1940 83 m black 0.12573 1940 84 m black 0.13173 1940 85 m black 0.13783 1940 86 m black 0.14415 1940 87 m black 0.15083 1940 88 m black 0.15799 1940 89 m black 0.16574 1940 90 m black 0.17417 1940 91 m black 0.1834 1940 92 m black 0.19352 1940 93 m black 0.20463 1940 94 m black 0.21685 1940 95 m black 0.23027 1940 96 m black 0.245 1940 97 m black 0.26113 1940 98 m black 0.27877 1940 99 m black 0.29802 1940 100 m black 0.319 1940 101 m black 0.34178 1940 102 m black 0.36649 1940 103 m black 0.39322 1940 104 m black 0.42208 1940 105 m black 0.45317 1940 106 m black 0.48658 1940 107 m black 0.52244 1940 108 m black 0.56082 1940 109 m black 0.60185 1940 0-1d f black 0.01486 1940 1-7d f black 0.0123 1940 7-28d f black 0.00974 1940 0 f black 0.06584 1940 1 f black 0.00796 1940 2 f black 0.00372 1940 3 f black 0.00248 1940 4 f black 0.00209 1940 5 f black 0.00175 1940 6 f black 0.00146 1940 7 f black 0.00123 1940 8 f black 0.00108 1940 9 f black 0.00101 1940 10 f black 0.00104 1940 11 f black 0.00116 1940 12 f black 0.0014 1940 13 f black 0.00182 1940 14 f black 0.00241 1940 15 f black 0.00307 1940 16 f black 0.00371 1940 17 f black 0.00424 1940 18 f black 0.00465 1940 19 f black 0.00501 1940 20 f black 0.00532 1940 21 f black 0.00559 1940 22 f black 0.00583 1940 23 f black 0.00603 1940 24 f black 0.00616 1940 25 f black 0.00627 1940 26 f black 0.0064 1940 27 f black 0.00657 1940 28 f black 0.0068 1940 29 f black 0.00705 1940 30 f black 0.00733 1940 31 f black 0.00764 1940 32 f black 0.00799 1940 33 f black 0.00837 1940 34 f black 0.0088 1940 35 f black 0.00924 1940 36 f black 0.00971 1940 37 f black 0.0102 1940 38 f black 0.0107 1940 39 f black 0.01123 1940 40 f black 0.01181 1940 41 f black 0.01246 1940 42 f black 0.0132 1940 43 f black 0.01405 1940 44 f black 0.01499 1940 45 f black 0.01602 1940 46 f black 0.01711 1940 47 f black 0.01824 1940 48 f black 0.01942 1940 49 f black 0.02062 1940 50 f black 0.02187 1940 51 f black 0.02315 1940 52 f black 0.02447 1940 53 f black 0.02583 1940 54 f black 0.02721 1940 55 f black 0.02858 1940 56 f black 0.02992 1940 57 f black 0.03121 1940 58 f black 0.03242 1940 59 f black 0.03358 1940 60 f black 0.03472 1940 61 f black 0.03586 1940 62 f black 0.03703 1940 63 f black 0.03825 1940 64 f black 0.03954 1940 65 f black 0.0409 1940 66 f black 0.04233 1940 67 f black 0.04384 1940 68 f black 0.04544 1940 69 f black 0.04718 1940 70 f black 0.04912 1940 71 f black 0.05129 1940 72 f black 0.05376 1940 73 f black 0.05655 1940 74 f black 0.05963 1940 75 f black 0.06294 1940 76 f black 0.06641 1940 77 f black 0.06998 1940 78 f black 0.07362 1940 79 f black 0.07737 1940 80 f black 0.08127 1940 81 f black 0.0854 1940 82 f black 0.08981 1940 83 f black 0.09457 1940 84 f black 0.09971 1940 85 f black 0.10529 1940 86 f black 0.11135 1940 87 f black 0.11793 1940 88 f black 0.12509 1940 89 f black 0.13287 1940 90 f black 0.14132 1940 91 f black 0.15048 1940 92 f black 0.1604 1940 93 f black 0.17112 1940 94 f black 0.1827 1940 95 f black 0.19517 1940 96 f black 0.20858 1940 97 f black 0.22299 1940 98 f black 0.23843 1940 99 f black 0.25496 1940 100 f black 0.27261 1940 101 f black 0.29143 1940 102 f black 0.31148 1940 103 f black 0.3328 1940 104 f black 0.35543 1940 105 f black 0.37941 1940 106 f black 0.40481 1940 107 f black 0.43165 1940 108 f black 0.46 1940 109 f black 0.48988 1950 0-1d m total 0.01148 1950 1-7d m total 0.00912 1950 7-28d m total 0.00315 1950 0 m total 0.03339 1950 1 m total 0.00244 1950 2 m total 0.00152 1950 3 m total 0.00114 1950 4 m total 0.00096 1950 5 m total 0.00087 1950 6 m total 0.00078 1950 7 m total 0.00071 1950 8 m total 0.00066 1950 9 m total 0.00063 1950 10 m total 0.00063 1950 11 m total 0.00066 1950 12 m total 0.00071 1950 13 m total 0.00081 1950 14 m total 0.00095 1950 15 m total 0.00112 1950 16 m total 0.00129 1950 17 m total 0.00143 1950 18 m total 0.00155 1950 19 m total 0.00168 1950 20 m total 0.00179 1950 21 m total 0.00188 1950 22 m total 0.00195 1950 23 m total 0.00198 1950 24 m total 0.00198 1950 25 m total 0.00196 1950 26 m total 0.00195 1950 27 m total 0.00197 1950 28 m total 0.00201 1950 29 m total 0.00207 1950 30 m total 0.00214 1950 31 m total 0.00224 1950 32 m total 0.00236 1950 33 m total 0.00251 1950 34 m total 0.00267 1950 35 m total 0.00287 1950 36 m total 0.0031 1950 37 m total 0.00337 1950 38 m total 0.00368 1950 39 m total 0.00402 1950 40 m total 0.0044 1950 41 m total 0.00482 1950 42 m total 0.0053 1950 43 m total 0.00583 1950 44 m total 0.0064 1950 45 m total 0.00702 1950 46 m total 0.00769 1950 47 m total 0.00843 1950 48 m total 0.00922 1950 49 m total 0.01005 1950 50 m total 0.01095 1950 51 m total 0.01193 1950 52 m total 0.01301 1950 53 m total 0.0142 1950 54 m total 0.01549 1950 55 m total 0.01686 1950 56 m total 0.01831 1950 57 m total 0.01984 1950 58 m total 0.02143 1950 59 m total 0.02308 1950 60 m total 0.02482 1950 61 m total 0.02668 1950 62 m total 0.02868 1950 63 m total 0.03078 1950 64 m total 0.03295 1950 65 m total 0.03528 1950 66 m total 0.03784 1950 67 m total 0.0407 1950 68 m total 0.0433 1950 69 m total 0.04711 1950 70 m total 0.05069 1950 71 m total 0.05464 1950 72 m total 0.05905 1950 73 m total 0.06389 1950 74 m total 0.0691 1950 75 m total 0.07472 1950 76 m total 0.08077 1950 77 m total 0.08726 1950 78 m total 0.09406 1950 79 m total 0.10113 1950 80 m total 0.10872 1950 81 m total 0.11704 1950 82 m total 0.12632 1950 83 m total 0.13672 1950 84 m total 0.14809 1950 85 m total 0.16018 1950 86 m total 0.17277 1950 87 m total 0.18562 1950 88 m total 0.19867 1950 89 m total 0.21209 1950 90 m total 0.22595 1950 91 m total 0.24032 1950 92 m total 0.25525 1950 93 m total 0.27089 1950 94 m total 0.28718 1950 95 m total 0.30394 1950 96 m total 0.32097 1950 97 m total 0.33807 1950 98 m total 0.35537 1950 99 m total 0.37301 1950 100 m total 0.39079 1950 101 m total 0.40852 1950 102 m total 0.426 1950 103 m total 0.44319 1950 104 m total 0.46021 1950 105 m total 0.47714 1950 106 m total 0.49405 1950 107 m total 0.511 1950 108 m total 0.5281 1950 109 m total 0.5452 1950 0-1d f total 0.00873 1950 1-7d f total 0.00647 1950 7-28d f total 0.00253 1950 0 f total 0.02594 1950 1 f total 0.00215 1950 2 f total 0.00125 1950 3 f total 0.00096 1950 4 f total 0.00076 1950 5 f total 0.00066 1950 6 f total 0.00058 1950 7 f total 0.00051 1950 8 f total 0.00046 1950 9 f total 0.00043 1950 10 f total 0.00042 1950 11 f total 0.00042 1950 12 f total 0.00044 1950 13 f total 0.00048 1950 14 f total 0.00054 1950 15 f total 0.00062 1950 16 f total 7e-04 1950 17 f total 0.00077 1950 18 f total 0.00082 1950 19 f total 0.00087 1950 20 f total 0.00092 1950 21 f total 0.00097 1950 22 f total 0.00101 1950 23 f total 0.00105 1950 24 f total 0.00109 1950 25 f total 0.00113 1950 26 f total 0.00117 1950 27 f total 0.00123 1950 28 f total 0.0013 1950 29 f total 0.00137 1950 30 f total 0.00145 1950 31 f total 0.00155 1950 32 f total 0.00165 1950 33 f total 0.00177 1950 34 f total 0.00188 1950 35 f total 0.00202 1950 36 f total 0.00216 1950 37 f total 0.00234 1950 38 f total 0.00253 1950 39 f total 0.00274 1950 40 f total 0.00297 1950 41 f total 0.00323 1950 42 f total 0.00351 1950 43 f total 0.00381 1950 44 f total 0.00414 1950 45 f total 0.00449 1950 46 f total 0.00487 1950 47 f total 0.00527 1950 48 f total 0.00569 1950 49 f total 0.00612 1950 50 f total 0.00658 1950 51 f total 0.00708 1950 52 f total 0.00766 1950 53 f total 0.00828 1950 54 f total 0.00895 1950 55 f total 0.00967 1950 56 f total 0.01048 1950 57 f total 0.01138 1950 58 f total 0.01238 1950 59 f total 0.01345 1950 60 f total 0.01462 1950 61 f total 0.01589 1950 62 f total 0.01728 1950 63 f total 0.01871 1950 64 f total 0.02016 1950 65 f total 0.02176 1950 66 f total 0.02364 1950 67 f total 0.02592 1950 68 f total 0.02858 1950 69 f total 0.03155 1950 70 f total 0.03484 1950 71 f total 0.03848 1950 72 f total 0.04251 1950 73 f total 0.04687 1950 74 f total 0.05153 1950 75 f total 0.05659 1950 76 f total 0.06213 1950 77 f total 0.06824 1950 78 f total 0.07488 1950 79 f total 0.082 1950 80 f total 0.08964 1950 81 f total 0.09788 1950 82 f total 0.10678 1950 83 f total 0.11624 1950 84 f total 0.12621 1950 85 f total 0.13685 1950 86 f total 0.1483 1950 87 f total 0.16069 1950 88 f total 0.17409 1950 89 f total 0.18839 1950 90 f total 0.20352 1950 91 f total 0.2194 1950 92 f total 0.23595 1950 93 f total 0.25342 1950 94 f total 0.27185 1950 95 f total 0.29089 1950 96 f total 0.31017 1950 97 f total 0.32935 1950 98 f total 0.34866 1950 99 f total 0.36834 1950 100 f total 0.38802 1950 101 f total 0.40736 1950 102 f total 0.426 1950 103 f total 0.44375 1950 104 f total 0.46084 1950 105 f total 0.47756 1950 106 f total 0.49419 1950 107 f total 0.511 1950 108 f total 0.5281 1950 109 f total 0.54529 1950 0-1d m white 0.01101 1950 1-7d m white 0.00875 1950 7-28d m white 0.00274 1950 0 m white 0.03069 1950 1 m white 0.00211 1950 2 m white 0.00139 1950 3 m white 0.00106 1950 4 m white 9e-04 1950 5 m white 0.00081 1950 6 m white 0.00075 1950 7 m white 0.00068 1950 8 m white 0.00063 1950 9 m white 6e-04 1950 10 m white 6e-04 1950 11 m white 0.00062 1950 12 m white 0.00067 1950 13 m white 0.00076 1950 14 m white 9e-04 1950 15 m white 0.00104 1950 16 m white 0.0012 1950 17 m white 0.00132 1950 18 m white 0.00144 1950 19 m white 0.00153 1950 20 m white 0.00162 1950 21 m white 0.0017 1950 22 m white 0.00174 1950 23 m white 0.00175 1950 24 m white 0.00174 1950 25 m white 0.00171 1950 26 m white 0.00168 1950 27 m white 0.00169 1950 28 m white 0.00173 1950 29 m white 0.00176 1950 30 m white 0.00182 1950 31 m white 0.0019 1950 32 m white 0.00201 1950 33 m white 0.00215 1950 34 m white 0.00229 1950 35 m white 0.00249 1950 36 m white 0.00269 1950 37 m white 0.00294 1950 38 m white 0.00322 1950 39 m white 0.00355 1950 40 m white 0.00392 1950 41 m white 0.00432 1950 42 m white 0.00477 1950 43 m white 0.00526 1950 44 m white 0.00579 1950 45 m white 0.00638 1950 46 m white 0.007 1950 47 m white 0.00771 1950 48 m white 0.00847 1950 49 m white 0.00925 1950 50 m white 0.01012 1950 51 m white 0.01107 1950 52 m white 0.01211 1950 53 m white 0.01328 1950 54 m white 0.01453 1950 55 m white 0.01588 1950 56 m white 0.01731 1950 57 m white 0.01882 1950 58 m white 0.02041 1950 59 m white 0.02207 1950 60 m white 0.02381 1950 61 m white 0.02569 1950 62 m white 0.02772 1950 63 m white 0.02985 1950 64 m white 0.03207 1950 65 m white 0.03445 1950 66 m white 0.03706 1950 67 m white 0.04 1950 68 m white 0.0432 1950 69 m white 0.04662 1950 70 m white 0.05028 1950 71 m white 0.05434 1950 72 m white 0.05886 1950 73 m white 0.06385 1950 74 m white 0.0692 1950 75 m white 0.07501 1950 76 m white 0.0812 1950 77 m white 0.08788 1950 78 m white 0.09489 1950 79 m white 0.10211 1950 80 m white 0.10994 1950 81 m white 0.11851 1950 82 m white 0.12801 1950 83 m white 0.13877 1950 84 m white 0.15052 1950 85 m white 0.16305 1950 86 m white 0.17591 1950 87 m white 0.18897 1950 88 m white 0.20205 1950 89 m white 0.21518 1950 90 m white 0.22903 1950 91 m white 0.24284 1950 92 m white 0.25763 1950 93 m white 0.27303 1950 94 m white 0.28959 1950 95 m white 0.30553 1950 96 m white 0.32227 1950 97 m white 0.33911 1950 98 m white 0.35617 1950 99 m white 0.37357 1950 100 m white 0.39112 1950 101 m white 0.40866 1950 102 m white 0.426 1950 103 m white 0.44312 1950 104 m white 0.46014 1950 105 m white 0.47709 1950 106 m white 0.49403 1950 107 m white 0.511 1950 108 m white 0.5281 1950 109 m white 0.5452 1950 0-1d f white 0.00832 1950 1-7d f white 0.00613 1950 7-28d f white 0.00219 1950 0 f white 0.02355 1950 1 f white 0.00189 1950 2 f white 0.00112 1950 3 f white 0.00087 1950 4 f white 0.00069 1950 5 f white 0.00061 1950 6 f white 0.00054 1950 7 f white 0.00047 1950 8 f white 0.00044 1950 9 f white 4e-04 1950 10 f white 4e-04 1950 11 f white 0.00039 1950 12 f white 4e-04 1950 13 f white 0.00043 1950 14 f white 0.00048 1950 15 f white 0.00054 1950 16 f white 0.00059 1950 17 f white 0.00063 1950 18 f white 0.00067 1950 19 f white 0.00069 1950 20 f white 0.00074 1950 21 f white 0.00076 1950 22 f white 8e-04 1950 23 f white 0.00082 1950 24 f white 0.00085 1950 25 f white 0.00088 1950 26 f white 0.00092 1950 27 f white 0.00097 1950 28 f white 0.00101 1950 29 f white 0.00109 1950 30 f white 0.00114 1950 31 f white 0.00123 1950 32 f white 0.00131 1950 33 f white 0.00141 1950 34 f white 0.0015 1950 35 f white 0.00161 1950 36 f white 0.00173 1950 37 f white 0.00188 1950 38 f white 0.00204 1950 39 f white 0.00222 1950 40 f white 0.00241 1950 41 f white 0.00264 1950 42 f white 0.00287 1950 43 f white 0.00313 1950 44 f white 0.00343 1950 45 f white 0.00372 1950 46 f white 0.00407 1950 47 f white 0.00441 1950 48 f white 0.0048 1950 49 f white 0.00519 1950 50 f white 0.00561 1950 51 f white 0.00608 1950 52 f white 0.00663 1950 53 f white 0.00721 1950 54 f white 0.00784 1950 55 f white 0.00854 1950 56 f white 0.0093 1950 57 f white 0.01019 1950 58 f white 0.01117 1950 59 f white 0.01224 1950 60 f white 0.0134 1950 61 f white 0.01468 1950 62 f white 0.01608 1950 63 f white 0.01751 1950 64 f white 0.019 1950 65 f white 0.02063 1950 66 f white 0.02254 1950 67 f white 0.0249 1950 68 f white 0.02764 1950 69 f white 0.03068 1950 70 f white 0.0341 1950 71 f white 0.03786 1950 72 f white 0.04203 1950 73 f white 0.0465 1950 74 f white 0.05129 1950 75 f white 0.05651 1950 76 f white 0.06221 1950 77 f white 0.0685 1950 78 f white 0.07537 1950 79 f white 0.08269 1950 80 f white 0.09062 1950 81 f white 0.0991 1950 82 f white 0.1083 1950 83 f white 0.11815 1950 84 f white 0.12855 1950 85 f white 0.13969 1950 86 f white 0.15142 1950 87 f white 0.16407 1950 88 f white 0.17746 1950 89 f white 0.19168 1950 90 f white 0.20653 1950 91 f white 0.22232 1950 92 f white 0.23835 1950 93 f white 0.25571 1950 94 f white 0.27393 1950 95 f white 0.29261 1950 96 f white 0.31159 1950 97 f white 0.3305 1950 98 f white 0.34954 1950 99 f white 0.36895 1950 100 f white 0.38839 1950 101 f white 0.40752 1950 102 f white 0.426 1950 103 f white 0.44367 1950 104 f white 0.46076 1950 105 f white 0.4775 1950 106 f white 0.49417 1950 107 f white 0.511 1950 108 f white 0.5281 1950 109 f white 0.54529 1950 0-1d m nonwhite 0.01449 1950 1-7d m nonwhite 0.01154 1950 7-28d m nonwhite 0.0057 1950 0 m nonwhite 0.05089 1950 1 m nonwhite 0.00466 1950 2 m nonwhite 0.0026 1950 3 m nonwhite 0.00176 1950 4 m nonwhite 0.00144 1950 5 m nonwhite 0.00124 1950 6 m nonwhite 0.00106 1950 7 m nonwhite 0.00096 1950 8 m nonwhite 0.00087 1950 9 m nonwhite 0.00083 1950 10 m nonwhite 0.00084 1950 11 m nonwhite 0.00089 1950 12 m nonwhite 0.00099 1950 13 m nonwhite 0.00115 1950 14 m nonwhite 0.00137 1950 15 m nonwhite 0.00164 1950 16 m nonwhite 0.00192 1950 17 m nonwhite 0.0022 1950 18 m nonwhite 0.00249 1950 19 m nonwhite 0.00282 1950 20 m nonwhite 0.00314 1950 21 m nonwhite 0.00344 1950 22 m nonwhite 0.00369 1950 23 m nonwhite 0.00387 1950 24 m nonwhite 0.00399 1950 25 m nonwhite 0.00409 1950 26 m nonwhite 0.0042 1950 27 m nonwhite 0.00435 1950 28 m nonwhite 0.00452 1950 29 m nonwhite 0.00471 1950 30 m nonwhite 0.00492 1950 31 m nonwhite 0.00515 1950 32 m nonwhite 0.00543 1950 33 m nonwhite 0.00574 1950 34 m nonwhite 0.00608 1950 35 m nonwhite 0.00646 1950 36 m nonwhite 0.00687 1950 37 m nonwhite 0.00732 1950 38 m nonwhite 0.00778 1950 39 m nonwhite 0.00826 1950 40 m nonwhite 0.00879 1950 41 m nonwhite 0.0094 1950 42 m nonwhite 0.01011 1950 43 m nonwhite 0.01093 1950 44 m nonwhite 0.01185 1950 45 m nonwhite 0.01285 1950 46 m nonwhite 0.01394 1950 47 m nonwhite 0.0151 1950 48 m nonwhite 0.01635 1950 49 m nonwhite 0.01768 1950 50 m nonwhite 0.01909 1950 51 m nonwhite 0.02058 1950 52 m nonwhite 0.02217 1950 53 m nonwhite 0.02388 1950 54 m nonwhite 0.02571 1950 55 m nonwhite 0.02762 1950 56 m nonwhite 0.02953 1950 57 m nonwhite 0.03139 1950 58 m nonwhite 0.0332 1950 59 m nonwhite 0.03498 1950 60 m nonwhite 0.03676 1950 61 m nonwhite 0.03855 1950 62 m nonwhite 0.04036 1950 63 m nonwhite 0.04216 1950 64 m nonwhite 0.04394 1950 65 m nonwhite 0.04576 1950 66 m nonwhite 0.04765 1950 67 m nonwhite 0.04967 1950 68 m nonwhite 0.05178 1950 69 m nonwhite 0.05393 1950 70 m nonwhite 0.0562 1950 71 m nonwhite 0.05867 1950 72 m nonwhite 0.0614 1950 73 m nonwhite 0.06441 1950 74 m nonwhite 0.06764 1950 75 m nonwhite 0.07108 1950 76 m nonwhite 0.07474 1950 77 m nonwhite 0.07862 1950 78 m nonwhite 0.08256 1950 79 m nonwhite 0.08657 1950 80 m nonwhite 0.09086 1950 81 m nonwhite 0.09566 1950 82 m nonwhite 0.10117 1950 83 m nonwhite 0.10692 1950 84 m nonwhite 0.11278 1950 85 m nonwhite 0.11944 1950 86 m nonwhite 0.12761 1950 87 m nonwhite 0.138 1950 88 m nonwhite 0.15093 1950 89 m nonwhite 0.16595 1950 90 m nonwhite 0.18255 1950 91 m nonwhite 0.20022 1950 92 m nonwhite 0.21845 1950 93 m nonwhite 0.23758 1950 94 m nonwhite 0.25796 1950 95 m nonwhite 0.27907 1950 96 m nonwhite 0.3004 1950 97 m nonwhite 0.32147 1950 98 m nonwhite 0.34259 1950 99 m nonwhite 0.36411 1950 100 m nonwhite 0.38552 1950 101 m nonwhite 0.40632 1950 102 m nonwhite 0.426 1950 103 m nonwhite 0.44425 1950 104 m nonwhite 0.46141 1950 105 m nonwhite 0.47794 1950 106 m nonwhite 0.49431 1950 107 m nonwhite 0.511 1950 108 m nonwhite 0.5281 1950 109 m nonwhite 0.54529 1950 0-1d f nonwhite 0.01123 1950 1-7d f nonwhite 0.00863 1950 7-28d f nonwhite 0.00465 1950 0 f nonwhite 0.04087 1950 1 f nonwhite 0.00388 1950 2 f nonwhite 0.00215 1950 3 f nonwhite 0.00166 1950 4 f nonwhite 0.00127 1950 5 f nonwhite 0.00107 1950 6 f nonwhite 9e-04 1950 7 f nonwhite 0.00076 1950 8 f nonwhite 0.00065 1950 9 f nonwhite 0.00058 1950 10 f nonwhite 0.00055 1950 11 f nonwhite 0.00057 1950 12 f nonwhite 0.00064 1950 13 f nonwhite 0.00079 1950 14 f nonwhite 0.001 1950 15 f nonwhite 0.00125 1950 16 f nonwhite 0.0015 1950 17 f nonwhite 0.00173 1950 18 f nonwhite 0.00192 1950 19 f nonwhite 0.0021 1950 20 f nonwhite 0.00227 1950 21 f nonwhite 0.00244 1950 22 f nonwhite 0.00261 1950 23 f nonwhite 0.00276 1950 24 f nonwhite 0.0029 1950 25 f nonwhite 0.00303 1950 26 f nonwhite 0.00318 1950 27 f nonwhite 0.00334 1950 28 f nonwhite 0.00352 1950 29 f nonwhite 0.0037 1950 30 f nonwhite 0.0039 1950 31 f nonwhite 0.00413 1950 32 f nonwhite 0.00439 1950 33 f nonwhite 0.0047 1950 34 f nonwhite 0.00504 1950 35 f nonwhite 0.00542 1950 36 f nonwhite 0.00582 1950 37 f nonwhite 0.00626 1950 38 f nonwhite 0.00671 1950 39 f nonwhite 0.00719 1950 40 f nonwhite 0.0077 1950 41 f nonwhite 0.00826 1950 42 f nonwhite 0.0089 1950 43 f nonwhite 0.00962 1950 44 f nonwhite 0.01042 1950 45 f nonwhite 0.01127 1950 46 f nonwhite 0.01216 1950 47 f nonwhite 0.01308 1950 48 f nonwhite 0.01402 1950 49 f nonwhite 0.01498 1950 50 f nonwhite 0.01599 1950 51 f nonwhite 0.01707 1950 52 f nonwhite 0.01824 1950 53 f nonwhite 0.01953 1950 54 f nonwhite 0.02093 1950 55 f nonwhite 0.02239 1950 56 f nonwhite 0.02387 1950 57 f nonwhite 0.02532 1950 58 f nonwhite 0.02673 1950 59 f nonwhite 0.02813 1950 60 f nonwhite 0.02954 1950 61 f nonwhite 0.03098 1950 62 f nonwhite 0.03245 1950 63 f nonwhite 0.03396 1950 64 f nonwhite 0.03548 1950 65 f nonwhite 0.03704 1950 66 f nonwhite 0.03865 1950 67 f nonwhite 0.04033 1950 68 f nonwhite 0.04203 1950 69 f nonwhite 0.04373 1950 70 f nonwhite 0.04553 1950 71 f nonwhite 0.04748 1950 72 f nonwhite 0.04969 1950 73 f nonwhite 0.05216 1950 74 f nonwhite 0.05486 1950 75 f nonwhite 0.05773 1950 76 f nonwhite 0.06074 1950 77 f nonwhite 0.06385 1950 78 f nonwhite 0.06692 1950 79 f nonwhite 0.07001 1950 80 f nonwhite 0.07327 1950 81 f nonwhite 0.07689 1950 82 f nonwhite 0.08102 1950 83 f nonwhite 0.0849 1950 84 f nonwhite 0.0884 1950 85 f nonwhite 0.0927 1950 86 f nonwhite 0.09898 1950 87 f nonwhite 0.1084 1950 88 f nonwhite 0.12145 1950 89 f nonwhite 0.13734 1950 90 f nonwhite 0.15535 1950 91 f nonwhite 0.17477 1950 92 f nonwhite 0.19489 1950 93 f nonwhite 0.21619 1950 94 f nonwhite 0.23913 1950 95 f nonwhite 0.263 1950 96 f nonwhite 0.2871 1950 97 f nonwhite 0.3107 1950 98 f nonwhite 0.33427 1950 99 f nonwhite 0.35831 1950 100 f nonwhite 0.38208 1950 101 f nonwhite 0.40489 1950 102 f nonwhite 0.426 1950 103 f nonwhite 0.44494 1950 104 f nonwhite 0.46218 1950 105 f nonwhite 0.47845 1950 106 f nonwhite 0.49448 1950 107 f nonwhite 0.511 1950 108 f nonwhite 0.5281 1950 109 f nonwhite 0.54529 1960 0-1d m total 0.01157 1960 1-7d m total 0.00752 1960 7-28d m total 0.00229 1960 0 m total 0.02913 1960 1 m total 0.00181 1960 2 m total 0.00115 1960 3 m total 0.00088 1960 4 m total 0.00074 1960 5 m total 0.00066 1960 6 m total 6e-04 1960 7 m total 0.00055 1960 8 m total 0.00051 1960 9 m total 0.00047 1960 10 m total 0.00044 1960 11 m total 0.00044 1960 12 m total 5e-04 1960 13 m total 0.00062 1960 14 m total 0.00078 1960 15 m total 0.00097 1960 16 m total 0.00114 1960 17 m total 0.00131 1960 18 m total 0.00145 1960 19 m total 0.00156 1960 20 m total 0.00169 1960 21 m total 0.0018 1960 22 m total 0.00187 1960 23 m total 0.00187 1960 24 m total 0.00181 1960 25 m total 0.00175 1960 26 m total 0.00169 1960 27 m total 0.00167 1960 28 m total 0.00169 1960 29 m total 0.00174 1960 30 m total 0.00181 1960 31 m total 0.00189 1960 32 m total 0.00199 1960 33 m total 0.0021 1960 34 m total 0.00224 1960 35 m total 0.0024 1960 36 m total 0.00259 1960 37 m total 0.00281 1960 38 m total 0.00308 1960 39 m total 0.00338 1960 40 m total 0.00373 1960 41 m total 0.00412 1960 42 m total 0.00455 1960 43 m total 0.00501 1960 44 m total 0.00551 1960 45 m total 0.00605 1960 46 m total 0.00665 1960 47 m total 0.00735 1960 48 m total 0.00818 1960 49 m total 0.00911 1960 50 m total 0.01014 1960 51 m total 0.0112 1960 52 m total 0.01228 1960 53 m total 0.01333 1960 54 m total 0.0144 1960 55 m total 0.01549 1960 56 m total 0.0167 1960 57 m total 0.01809 1960 58 m total 0.01971 1960 59 m total 0.02154 1960 60 m total 0.0235 1960 61 m total 0.02554 1960 62 m total 0.02769 1960 63 m total 0.02992 1960 64 m total 0.03226 1960 65 m total 0.03474 1960 66 m total 0.03739 1960 67 m total 0.04017 1960 68 m total 0.04307 1960 69 m total 0.04612 1960 70 m total 0.04936 1960 71 m total 0.05285 1960 72 m total 0.05665 1960 73 m total 0.06083 1960 74 m total 0.06541 1960 75 m total 0.07035 1960 76 m total 0.07571 1960 77 m total 0.08176 1960 78 m total 0.0887 1960 79 m total 0.09661 1960 80 m total 0.10598 1960 81 m total 0.11654 1960 82 m total 0.12732 1960 83 m total 0.13728 1960 84 m total 0.14623 1960 85 m total 0.15768 1960 86 m total 0.17002 1960 87 m total 0.18343 1960 88 m total 0.19868 1960 89 m total 0.21564 1960 90 m total 0.2332 1960 91 m total 0.25056 1960 92 m total 0.26792 1960 93 m total 0.28481 1960 94 m total 0.3005 1960 95 m total 0.31416 1960 96 m total 0.32915 1960 97 m total 0.3445 1960 98 m total 0.36018 1960 99 m total 0.37616 1960 100 m total 0.39242 1960 101 m total 0.40891 1960 102 m total 0.42562 1960 103 m total 0.4425 1960 104 m total 0.45951 1960 105 m total 0.47662 1960 106 m total 0.49378 1960 107 m total 0.51095 1960 108 m total 0.5281 1960 109 m total 0.54519 1960 0-1d f total 0.00898 1960 1-7d f total 0.00538 1960 7-28d f total 0.00183 1960 0 f total 0.02256 1960 1 f total 0.00158 1960 2 f total 0.00093 1960 3 f total 0.00071 1960 4 f total 6e-04 1960 5 f total 0.00052 1960 6 f total 0.00045 1960 7 f total 0.00039 1960 8 f total 0.00035 1960 9 f total 0.00032 1960 10 f total 3e-04 1960 11 f total 0.00029 1960 12 f total 3e-04 1960 13 f total 0.00034 1960 14 f total 0.00038 1960 15 f total 0.00044 1960 16 f total 5e-04 1960 17 f total 0.00055 1960 18 f total 0.00059 1960 19 f total 0.00061 1960 20 f total 0.00064 1960 21 f total 0.00067 1960 22 f total 7e-04 1960 23 f total 0.00073 1960 24 f total 0.00076 1960 25 f total 0.00079 1960 26 f total 0.00082 1960 27 f total 0.00087 1960 28 f total 0.00092 1960 29 f total 0.00098 1960 30 f total 0.00106 1960 31 f total 0.00114 1960 32 f total 0.00122 1960 33 f total 0.00131 1960 34 f total 0.0014 1960 35 f total 0.00151 1960 36 f total 0.00163 1960 37 f total 0.00177 1960 38 f total 0.00192 1960 39 f total 0.0021 1960 40 f total 0.0023 1960 41 f total 0.00251 1960 42 f total 0.00274 1960 43 f total 0.00298 1960 44 f total 0.00324 1960 45 f total 0.00351 1960 46 f total 0.00381 1960 47 f total 0.00415 1960 48 f total 0.00453 1960 49 f total 0.00495 1960 50 f total 0.00541 1960 51 f total 0.0059 1960 52 f total 0.00639 1960 53 f total 0.00686 1960 54 f total 0.00733 1960 55 f total 0.00783 1960 56 f total 0.00841 1960 57 f total 0.00911 1960 58 f total 0.00997 1960 59 f total 0.01097 1960 60 f total 0.01209 1960 61 f total 0.01327 1960 62 f total 0.01451 1960 63 f total 0.01578 1960 64 f total 0.01711 1960 65 f total 0.01854 1960 66 f total 0.02014 1960 67 f total 0.02199 1960 68 f total 0.02415 1960 69 f total 0.02661 1960 70 f total 0.02929 1960 71 f total 0.03219 1960 72 f total 0.03546 1960 73 f total 0.03914 1960 74 f total 0.04327 1960 75 f total 0.04767 1960 76 f total 0.05246 1960 77 f total 0.05804 1960 78 f total 0.06469 1960 79 f total 0.0724 1960 80 f total 0.08144 1960 81 f total 0.09143 1960 82 f total 0.10154 1960 83 f total 0.11096 1960 84 f total 0.11975 1960 85 f total 0.13423 1960 86 f total 0.15009 1960 87 f total 0.16689 1960 88 f total 0.18478 1960 89 f total 0.20364 1960 90 f total 0.22329 1960 91 f total 0.24327 1960 92 f total 0.26302 1960 93 f total 0.28181 1960 94 f total 0.29903 1960 95 f total 0.31416 1960 96 f total 0.32915 1960 97 f total 0.3445 1960 98 f total 0.36018 1960 99 f total 0.37616 1960 100 f total 0.39242 1960 101 f total 0.40891 1960 102 f total 0.42562 1960 103 f total 0.4425 1960 104 f total 0.45951 1960 105 f total 0.47662 1960 106 f total 0.49378 1960 107 f total 0.51095 1960 108 f total 0.5281 1960 109 f total 0.54519 1960 0-1d m white 0.01079 1960 1-7d m white 0.00709 1960 7-28d m white 0.00191 1960 0 m white 0.02592 1960 1 m white 0.00153 1960 2 m white 0.00101 1960 3 m white 0.00081 1960 4 m white 0.00069 1960 5 m white 0.00062 1960 6 m white 0.00057 1960 7 m white 0.00053 1960 8 m white 0.00049 1960 9 m white 0.00045 1960 10 m white 0.00042 1960 11 m white 0.00042 1960 12 m white 0.00047 1960 13 m white 0.00059 1960 14 m white 0.00075 1960 15 m white 0.00093 1960 16 m white 0.00111 1960 17 m white 0.00126 1960 18 m white 0.00139 1960 19 m white 0.00149 1960 20 m white 0.00159 1960 21 m white 0.00169 1960 22 m white 0.00174 1960 23 m white 0.00172 1960 24 m white 0.00165 1960 25 m white 0.00156 1960 26 m white 0.00149 1960 27 m white 0.00145 1960 28 m white 0.00145 1960 29 m white 0.00149 1960 30 m white 0.00156 1960 31 m white 0.00163 1960 32 m white 0.00171 1960 33 m white 0.00181 1960 34 m white 0.00193 1960 35 m white 0.00207 1960 36 m white 0.00225 1960 37 m white 0.00246 1960 38 m white 0.0027 1960 39 m white 0.00299 1960 40 m white 0.00332 1960 41 m white 0.00368 1960 42 m white 0.00409 1960 43 m white 0.00454 1960 44 m white 0.00504 1960 45 m white 0.00558 1960 46 m white 0.00617 1960 47 m white 0.00686 1960 48 m white 0.00766 1960 49 m white 0.00856 1960 50 m white 0.00955 1960 51 m white 0.01058 1960 52 m white 0.01162 1960 53 m white 0.01264 1960 54 m white 0.01368 1960 55 m white 0.01475 1960 56 m white 0.01593 1960 57 m white 0.0173 1960 58 m white 0.01891 1960 59 m white 0.02074 1960 60 m white 0.02271 1960 61 m white 0.02476 1960 62 m white 0.0269 1960 63 m white 0.02912 1960 64 m white 0.03143 1960 65 m white 0.03389 1960 66 m white 0.03652 1960 67 m white 0.0393 1960 68 m white 0.04225 1960 69 m white 0.04538 1960 70 m white 0.04871 1960 71 m white 0.0523 1960 72 m white 0.05623 1960 73 m white 0.0606 1960 74 m white 0.06542 1960 75 m white 0.07066 1960 76 m white 0.07636 1960 77 m white 0.08271 1960 78 m white 0.08986 1960 79 m white 0.09788 1960 80 m white 0.10732 1960 81 m white 0.11799 1960 82 m white 0.12895 1960 83 m white 0.1392 1960 84 m white 0.14861 1960 85 m white 0.16039 1960 86 m white 0.17303 1960 87 m white 0.18665 1960 88 m white 0.20194 1960 89 m white 0.21877 1960 90 m white 0.23601 1960 91 m white 0.25289 1960 92 m white 0.26973 1960 93 m white 0.28612 1960 94 m white 0.30128 1960 95 m white 0.31416 1960 96 m white 0.32915 1960 97 m white 0.3445 1960 98 m white 0.36018 1960 99 m white 0.37616 1960 100 m white 0.39242 1960 101 m white 0.40891 1960 102 m white 0.42562 1960 103 m white 0.4425 1960 104 m white 0.45951 1960 105 m white 0.47662 1960 106 m white 0.49378 1960 107 m white 0.51095 1960 108 m white 0.5281 1960 109 m white 0.54519 1960 0-1d f white 0.00828 1960 1-7d f white 0.00499 1960 7-28d f white 0.00146 1960 0 f 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0.00229 1960 43 f white 0.00252 1960 44 f white 0.00276 1960 45 f white 0.00303 1960 46 f white 0.00331 1960 47 f white 0.00362 1960 48 f white 0.00396 1960 49 f white 0.00432 1960 50 f white 0.00473 1960 51 f white 0.00517 1960 52 f white 0.0056 1960 53 f white 0.00601 1960 54 f white 0.00642 1960 55 f white 0.00687 1960 56 f white 0.0074 1960 57 f white 0.00805 1960 58 f white 0.00886 1960 59 f white 0.00981 1960 60 f white 0.01088 1960 61 f white 0.01203 1960 62 f white 0.01325 1960 63 f white 0.01454 1960 64 f white 0.01592 1960 65 f white 0.01742 1960 66 f white 0.01909 1960 67 f white 0.021 1960 68 f white 0.02319 1960 69 f white 0.02567 1960 70 f white 0.02836 1960 71 f white 0.03129 1960 72 f white 0.03462 1960 73 f white 0.03845 1960 74 f white 0.04278 1960 75 f white 0.04742 1960 76 f white 0.05245 1960 77 f white 0.05827 1960 78 f white 0.06509 1960 79 f white 0.07294 1960 80 f white 0.08213 1960 81 f white 0.09231 1960 82 f white 0.10264 1960 83 f white 0.11235 1960 84 f white 0.12151 1960 85 f white 0.13625 1960 86 f white 0.15237 1960 87 f white 0.16936 1960 88 f white 0.18731 1960 89 f white 0.20611 1960 90 f white 0.2256 1960 91 f white 0.24536 1960 92 f white 0.26481 1960 93 f white 0.28322 1960 94 f white 0.29988 1960 95 f white 0.31416 1960 96 f white 0.32915 1960 97 f white 0.3445 1960 98 f white 0.36018 1960 99 f white 0.37616 1960 100 f white 0.39242 1960 101 f white 0.40891 1960 102 f white 0.42562 1960 103 f white 0.4425 1960 104 f white 0.45951 1960 105 f white 0.47662 1960 106 f white 0.49378 1960 107 f white 0.51095 1960 108 f white 0.5281 1960 109 f white 0.54519 1960 0-1d m nonwhite 0.01594 1960 1-7d m nonwhite 0.00988 1960 7-28d m nonwhite 0.00443 1960 0 m nonwhite 0.04699 1960 1 m nonwhite 0.00337 1960 2 m nonwhite 0.00197 1960 3 m nonwhite 0.00134 1960 4 m nonwhite 0.00102 1960 5 m nonwhite 0.00087 1960 6 m nonwhite 0.00076 1960 7 m nonwhite 0.00068 1960 8 m nonwhite 0.00063 1960 9 m nonwhite 6e-04 1960 10 m nonwhite 6e-04 1960 11 m nonwhite 0.00064 1960 12 m nonwhite 0.00072 1960 13 m nonwhite 0.00085 1960 14 m nonwhite 0.00102 1960 15 m nonwhite 0.0012 1960 16 m nonwhite 0.0014 1960 17 m nonwhite 0.00162 1960 18 m nonwhite 0.00186 1960 19 m nonwhite 0.0021 1960 20 m nonwhite 0.00236 1960 21 m nonwhite 0.00262 1960 22 m nonwhite 0.00283 1960 23 m nonwhite 0.00298 1960 24 m nonwhite 0.00307 1960 25 m nonwhite 0.00316 1960 26 m nonwhite 0.00327 1960 27 m nonwhite 0.00339 1960 28 m nonwhite 0.00353 1960 29 m nonwhite 0.0037 1960 30 m nonwhite 0.00389 1960 31 m nonwhite 0.00409 1960 32 m nonwhite 0.00431 1960 33 m nonwhite 0.00455 1960 34 m nonwhite 0.00483 1960 35 m nonwhite 0.00513 1960 36 m nonwhite 0.00546 1960 37 m nonwhite 0.00585 1960 38 m nonwhite 0.00633 1960 39 m nonwhite 0.00688 1960 40 m nonwhite 0.00749 1960 41 m nonwhite 0.00814 1960 42 m nonwhite 0.00875 1960 43 m nonwhite 0.00931 1960 44 m nonwhite 0.00984 1960 45 m nonwhite 0.01038 1960 46 m nonwhite 0.01101 1960 47 m nonwhite 0.01183 1960 48 m nonwhite 0.01292 1960 49 m nonwhite 0.01422 1960 50 m nonwhite 0.01565 1960 51 m nonwhite 0.0171 1960 52 m nonwhite 0.01854 1960 53 m nonwhite 0.01994 1960 54 m nonwhite 0.02131 1960 55 m nonwhite 0.02273 1960 56 m nonwhite 0.02427 1960 57 m nonwhite 0.02589 1960 58 m nonwhite 0.02762 1960 59 m nonwhite 0.02947 1960 60 m nonwhite 0.03137 1960 61 m nonwhite 0.03335 1960 62 m nonwhite 0.03554 1960 63 m nonwhite 0.03801 1960 64 m nonwhite 0.04072 1960 65 m nonwhite 0.04365 1960 66 m nonwhite 0.04665 1960 67 m nonwhite 0.04953 1960 68 m nonwhite 0.05213 1960 69 m nonwhite 0.05448 1960 70 m nonwhite 0.0569 1960 71 m nonwhite 0.05944 1960 72 m nonwhite 0.06177 1960 73 m nonwhite 0.06375 1960 74 m nonwhite 0.06548 1960 75 m nonwhite 0.06673 1960 76 m nonwhite 0.06803 1960 77 m nonwhite 0.07037 1960 78 m nonwhite 0.0746 1960 79 m nonwhite 0.08065 1960 80 m nonwhite 0.08836 1960 81 m nonwhite 0.09668 1960 82 m nonwhite 0.10452 1960 83 m nonwhite 0.11038 1960 84 m nonwhite 0.1141 1960 85 m nonwhite 0.1228 1960 86 m nonwhite 0.13313 1960 87 m nonwhite 0.14588 1960 88 m nonwhite 0.16219 1960 89 m nonwhite 0.18166 1960 90 m nonwhite 0.20304 1960 91 m nonwhite 0.22519 1960 92 m nonwhite 0.24791 1960 93 m nonwhite 0.2705 1960 94 m nonwhite 0.2927 1960 95 m nonwhite 0.31416 1960 96 m nonwhite 0.32915 1960 97 m nonwhite 0.3445 1960 98 m nonwhite 0.36018 1960 99 m nonwhite 0.37616 1960 100 m nonwhite 0.39242 1960 101 m nonwhite 0.40891 1960 102 m nonwhite 0.42562 1960 103 m nonwhite 0.4425 1960 104 m nonwhite 0.45951 1960 105 m nonwhite 0.47662 1960 106 m nonwhite 0.49378 1960 107 m nonwhite 0.51095 1960 108 m nonwhite 0.5281 1960 109 m nonwhite 0.54519 1960 0-1d f nonwhite 0.01272 1960 1-7d f nonwhite 0.00742 1960 7-28d f nonwhite 0.00385 1960 0 f nonwhite 0.03828 1960 1 f nonwhite 0.00289 1960 2 f nonwhite 0.0016 1960 3 f nonwhite 0.00115 1960 4 f nonwhite 0.00092 1960 5 f nonwhite 0.00077 1960 6 f nonwhite 0.00066 1960 7 f nonwhite 0.00056 1960 8 f nonwhite 0.00049 1960 9 f nonwhite 0.00043 1960 10 f nonwhite 4e-04 1960 11 f nonwhite 0.00039 1960 12 f nonwhite 0.00041 1960 13 f nonwhite 0.00046 1960 14 f nonwhite 0.00053 1960 15 f nonwhite 0.00063 1960 16 f nonwhite 0.00073 1960 17 f nonwhite 0.00084 1960 18 f nonwhite 0.00094 1960 19 f nonwhite 0.00104 1960 20 f nonwhite 0.00116 1960 21 f nonwhite 0.00128 1960 22 f nonwhite 0.0014 1960 23 f nonwhite 0.0015 1960 24 f nonwhite 0.0016 1960 25 f nonwhite 0.00171 1960 26 f nonwhite 0.00182 1960 27 f nonwhite 0.00197 1960 28 f nonwhite 0.00214 1960 29 f nonwhite 0.00234 1960 30 f nonwhite 0.00256 1960 31 f nonwhite 0.00279 1960 32 f nonwhite 0.00303 1960 33 f nonwhite 0.00326 1960 34 f nonwhite 0.0035 1960 35 f nonwhite 0.00374 1960 36 f nonwhite 0.00402 1960 37 f nonwhite 0.00434 1960 38 f nonwhite 0.00471 1960 39 f nonwhite 0.00514 1960 40 f nonwhite 0.00561 1960 41 f nonwhite 0.00611 1960 42 f nonwhite 0.00656 1960 43 f nonwhite 0.00696 1960 44 f nonwhite 0.00733 1960 45 f nonwhite 0.00769 1960 46 f nonwhite 0.00814 1960 47 f nonwhite 0.00875 1960 48 f nonwhite 0.00957 1960 49 f nonwhite 0.01058 1960 50 f nonwhite 0.01167 1960 51 f nonwhite 0.01279 1960 52 f nonwhite 0.01392 1960 53 f nonwhite 0.01504 1960 54 f nonwhite 0.01617 1960 55 f nonwhite 0.01731 1960 56 f nonwhite 0.01852 1960 57 f nonwhite 0.01983 1960 58 f nonwhite 0.0213 1960 59 f nonwhite 0.02287 1960 60 f nonwhite 0.02459 1960 61 f nonwhite 0.02632 1960 62 f nonwhite 0.02784 1960 63 f nonwhite 0.02901 1960 64 f nonwhite 0.02995 1960 65 f nonwhite 0.03072 1960 66 f nonwhite 0.03162 1960 67 f nonwhite 0.03296 1960 68 f nonwhite 0.035 1960 69 f nonwhite 0.03762 1960 70 f nonwhite 0.04066 1960 71 f nonwhite 0.04372 1960 72 f nonwhite 0.04646 1960 73 f nonwhite 0.04853 1960 74 f nonwhite 0.05007 1960 75 f nonwhite 0.05127 1960 76 f nonwhite 0.05274 1960 77 f nonwhite 0.0551 1960 78 f nonwhite 0.05897 1960 79 f nonwhite 0.0642 1960 80 f nonwhite 0.0706 1960 81 f nonwhite 0.07731 1960 82 f nonwhite 0.08349 1960 83 f nonwhite 0.08813 1960 84 f nonwhite 0.09127 1960 85 f nonwhite 0.10205 1960 86 f nonwhite 0.11467 1960 87 f nonwhite 0.12972 1960 88 f nonwhite 0.1479 1960 89 f nonwhite 0.16879 1960 90 f nonwhite 0.19137 1960 91 f nonwhite 0.21496 1960 92 f nonwhite 0.23959 1960 93 f nonwhite 0.26478 1960 94 f nonwhite 0.28995 1960 95 f nonwhite 0.31416 1960 96 f nonwhite 0.32915 1960 97 f nonwhite 0.3445 1960 98 f nonwhite 0.36018 1960 99 f nonwhite 0.37616 1960 100 f nonwhite 0.39242 1960 101 f nonwhite 0.40891 1960 102 f nonwhite 0.42562 1960 103 f nonwhite 0.4425 1960 104 f nonwhite 0.45951 1960 105 f nonwhite 0.47662 1960 106 f nonwhite 0.49378 1960 107 f nonwhite 0.51095 1960 108 f nonwhite 0.5281 1960 109 f nonwhite 0.54519 1970 0-1d m total 0.00984 1970 1-7d m total 0.00555 1970 7-28d m total 0.00159 1970 0 m total 0.02245 1970 1 m total 0.00133 1970 2 m total 0.00094 1970 3 m total 0.00078 1970 4 m total 0.00064 1970 5 m total 0.00058 1970 6 m total 0.00054 1970 7 m total 0.00051 1970 8 m total 0.00046 1970 9 m total 0.00041 1970 10 m total 0.00036 1970 11 m total 0.00035 1970 12 m total 0.00042 1970 13 m total 0.00059 1970 14 m total 0.00084 1970 15 m total 0.00114 1970 16 m total 0.00142 1970 17 m total 0.00167 1970 18 m total 0.00185 1970 19 m total 0.00198 1970 20 m total 0.00212 1970 21 m total 0.00226 1970 22 m total 0.00235 1970 23 m total 0.00235 1970 24 m total 0.00228 1970 25 m total 0.00217 1970 26 m total 0.00206 1970 27 m total 0.00199 1970 28 m total 0.00198 1970 29 m total 0.00203 1970 30 m total 0.0021 1970 31 m total 0.00218 1970 32 m total 0.00228 1970 33 m total 0.00239 1970 34 m total 0.00252 1970 35 m total 0.00268 1970 36 m total 0.00288 1970 37 m total 0.00312 1970 38 m total 0.00339 1970 39 m total 0.00369 1970 40 m total 0.00401 1970 41 m total 0.00435 1970 42 m total 0.00473 1970 43 m total 0.00518 1970 44 m total 0.00568 1970 45 m total 0.00623 1970 46 m total 0.00681 1970 47 m total 0.00744 1970 48 m total 0.00812 1970 49 m total 0.00887 1970 50 m total 0.00969 1970 51 m total 0.01059 1970 52 m total 0.01161 1970 53 m total 0.01275 1970 54 m total 0.014 1970 55 m total 0.01534 1970 56 m total 0.01676 1970 57 m total 0.01827 1970 58 m total 0.01987 1970 59 m total 0.02158 1970 60 m total 0.02339 1970 61 m total 0.02532 1970 62 m total 0.02738 1970 63 m total 0.0296 1970 64 m total 0.032 1970 65 m total 0.03463 1970 66 m total 0.03746 1970 67 m total 0.04044 1970 68 m total 0.0435 1970 69 m total 0.04665 1970 70 m total 0.04991 1970 71 m total 0.05344 1970 72 m total 0.0574 1970 73 m total 0.06193 1970 74 m total 0.06703 1970 75 m total 0.07264 1970 76 m total 0.07856 1970 77 m total 0.08462 1970 78 m total 0.0907 1970 79 m total 0.09688 1970 80 m total 0.10367 1970 81 m total 0.11125 1970 82 m total 0.11929 1970 83 m total 0.1277 1970 84 m total 0.13663 1970 85 m total 0.1473 1970 86 m total 0.15979 1970 87 m total 0.17281 1970 88 m total 0.18521 1970 89 m total 0.19681 1970 90 m total 0.20839 1970 91 m total 0.22122 1970 92 m total 0.23512 1970 93 m total 0.25023 1970 94 m total 0.26546 1970 95 m total 0.27962 1970 96 m total 0.2909 1970 97 m total 0.30135 1970 98 m total 0.31111 1970 99 m total 0.32017 1970 100 m total 0.32857 1970 101 m total 0.33633 1970 102 m total 0.34347 1970 103 m total 0.35004 1970 104 m total 0.35606 1970 105 m total 0.36157 1970 106 m total 0.36661 1970 107 m total 0.37121 1970 108 m total 0.3754 1970 109 m total 0.37922 1970 0-1d f total 0.00758 1970 1-7d f total 0.00405 1970 7-28d f total 0.00134 1970 0 f total 0.01746 1970 1 f total 0.00116 1970 2 f total 0.00077 1970 3 f total 6e-04 1970 4 f total 0.00051 1970 5 f total 0.00043 1970 6 f total 0.00038 1970 7 f total 0.00034 1970 8 f total 0.00031 1970 9 f total 0.00028 1970 10 f total 0.00026 1970 11 f total 0.00025 1970 12 f total 0.00027 1970 13 f total 0.00033 1970 14 f total 4e-04 1970 15 f total 0.00049 1970 16 f total 0.00058 1970 17 f total 0.00066 1970 18 f total 0.00069 1970 19 f total 0.00071 1970 20 f total 0.00072 1970 21 f total 0.00073 1970 22 f total 0.00075 1970 23 f total 0.00077 1970 24 f total 0.00079 1970 25 f total 0.00081 1970 26 f total 0.00083 1970 27 f total 0.00086 1970 28 f total 9e-04 1970 29 f total 0.00096 1970 30 f total 0.00102 1970 31 f total 0.0011 1970 32 f total 0.00119 1970 33 f total 0.00129 1970 34 f total 0.0014 1970 35 f total 0.00152 1970 36 f total 0.00165 1970 37 f total 0.0018 1970 38 f total 0.00197 1970 39 f total 0.00215 1970 40 f total 0.00233 1970 41 f total 0.00251 1970 42 f total 0.00273 1970 43 f total 0.00297 1970 44 f total 0.00325 1970 45 f total 0.00354 1970 46 f total 0.00384 1970 47 f total 0.00416 1970 48 f total 0.00449 1970 49 f total 0.00484 1970 50 f total 0.00523 1970 51 f total 0.00565 1970 52 f total 0.00611 1970 53 f total 0.0066 1970 54 f total 0.00712 1970 55 f total 0.00768 1970 56 f total 0.00829 1970 57 f total 0.00894 1970 58 f total 0.00962 1970 59 f total 0.01035 1970 60 f total 0.01113 1970 61 f total 0.012 1970 62 f total 0.01298 1970 63 f total 0.01411 1970 64 f total 0.01538 1970 65 f total 0.01678 1970 66 f total 0.01832 1970 67 f total 0.02004 1970 68 f total 0.02195 1970 69 f total 0.02407 1970 70 f total 0.02632 1970 71 f total 0.02879 1970 72 f total 0.03165 1970 73 f total 0.03503 1970 74 f total 0.03893 1970 75 f total 0.04325 1970 76 f total 0.0479 1970 77 f total 0.05295 1970 78 f total 0.0584 1970 79 f total 0.06432 1970 80 f total 0.07097 1970 81 f total 0.07834 1970 82 f total 0.08612 1970 83 f total 0.09419 1970 84 f total 0.10275 1970 85 f total 0.11282 1970 86 f total 0.12462 1970 87 f total 0.13685 1970 88 f total 0.14859 1970 89 f total 0.16006 1970 90 f total 0.17264 1970 91 f total 0.18718 1970 92 f total 0.20243 1970 93 f total 0.2175 1970 94 f total 0.23186 1970 95 f total 0.24584 1970 96 f total 0.25854 1970 97 f total 0.2698 1970 98 f total 0.27996 1970 99 f total 0.28949 1970 100 f total 0.29836 1970 101 f total 0.30659 1970 102 f total 0.3142 1970 103 f total 0.32122 1970 104 f total 0.32768 1970 105 f total 0.33361 1970 106 f total 0.33904 1970 107 f total 0.34401 1970 108 f total 0.34855 1970 109 f total 0.35269 1970 0-1d m white 0.00892 1970 1-7d m white 0.00527 1970 7-28d m white 0.00139 1970 0 m white 0.02006 1970 1 m white 0.00116 1970 2 m white 0.00083 1970 3 m white 0.00072 1970 4 m white 0.00059 1970 5 m white 0.00054 1970 6 m white 0.00051 1970 7 m white 0.00048 1970 8 m white 0.00044 1970 9 m white 0.00039 1970 10 m white 0.00034 1970 11 m white 0.00032 1970 12 m white 0.00039 1970 13 m white 0.00055 1970 14 m white 8e-04 1970 15 m white 0.00107 1970 16 m white 0.00134 1970 17 m white 0.00156 1970 18 m white 0.00172 1970 19 m white 0.00181 1970 20 m white 0.0019 1970 21 m white 0.00201 1970 22 m white 0.00205 1970 23 m white 0.00203 1970 24 m white 0.00195 1970 25 m white 0.00184 1970 26 m white 0.00173 1970 27 m white 0.00165 1970 28 m white 0.00162 1970 29 m white 0.00165 1970 30 m white 0.0017 1970 31 m white 0.00176 1970 32 m white 0.00183 1970 33 m white 0.00192 1970 34 m white 0.00203 1970 35 m white 0.00217 1970 36 m white 0.00235 1970 37 m white 0.00256 1970 38 m white 0.00281 1970 39 m white 0.0031 1970 40 m white 0.0034 1970 41 m white 0.00372 1970 42 m white 0.00409 1970 43 m white 0.00452 1970 44 m white 0.00501 1970 45 m white 0.00555 1970 46 m white 0.00612 1970 47 m white 0.00673 1970 48 m white 0.00739 1970 49 m white 0.00812 1970 50 m white 0.00892 1970 51 m white 0.0098 1970 52 m white 0.01081 1970 53 m white 0.01194 1970 54 m white 0.01318 1970 55 m white 0.01452 1970 56 m white 0.01594 1970 57 m white 0.01745 1970 58 m white 0.01906 1970 59 m white 0.02077 1970 60 m white 0.02258 1970 61 m white 0.02451 1970 62 m white 0.02657 1970 63 m white 0.02879 1970 64 m white 0.0312 1970 65 m white 0.03386 1970 66 m white 0.03674 1970 67 m white 0.03977 1970 68 m white 0.04284 1970 69 m white 0.04597 1970 70 m white 0.04916 1970 71 m white 0.05262 1970 72 m white 0.05655 1970 73 m white 0.06118 1970 74 m white 0.06647 1970 75 m white 0.07231 1970 76 m white 0.07843 1970 77 m white 0.08472 1970 78 m white 0.09103 1970 79 m white 0.09749 1970 80 m white 0.10466 1970 81 m white 0.11273 1970 82 m white 0.12127 1970 83 m white 0.13012 1970 84 m white 0.13942 1970 85 m white 0.15033 1970 86 m white 0.16321 1970 87 m white 0.17666 1970 88 m white 0.18947 1970 89 m white 0.20145 1970 90 m white 0.21344 1970 91 m white 0.22684 1970 92 m white 0.24152 1970 93 m white 0.25767 1970 94 m white 0.27426 1970 95 m white 0.29014 1970 96 m white 0.30431 1970 97 m white 0.31784 1970 98 m white 0.33085 1970 99 m white 0.34324 1970 100 m white 0.35479 1970 101 m white 0.36553 1970 102 m white 0.3755 1970 103 m white 0.38471 1970 104 m white 0.3932 1970 105 m white 0.40101 1970 106 m white 0.40818 1970 107 m white 0.41475 1970 108 m white 0.42075 1970 109 m white 0.42624 1970 0-1d f white 0.00686 1970 1-7d f white 0.00373 1970 7-28d f white 0.00115 1970 0 f white 0.01532 1970 1 f white 0.00101 1970 2 f white 0.00067 1970 3 f white 0.00054 1970 4 f white 0.00047 1970 5 f white 4e-04 1970 6 f white 0.00036 1970 7 f white 0.00032 1970 8 f white 0.00029 1970 9 f white 0.00027 1970 10 f white 0.00025 1970 11 f white 0.00024 1970 12 f white 0.00026 1970 13 f white 0.00031 1970 14 f white 0.00038 1970 15 f white 0.00046 1970 16 f white 0.00055 1970 17 f white 0.00061 1970 18 f white 0.00064 1970 19 f white 0.00064 1970 20 f white 0.00064 1970 21 f white 0.00065 1970 22 f white 0.00065 1970 23 f white 0.00066 1970 24 f white 0.00067 1970 25 f white 0.00068 1970 26 f white 7e-04 1970 27 f white 0.00072 1970 28 f white 0.00075 1970 29 f white 0.00079 1970 30 f white 0.00084 1970 31 f white 9e-04 1970 32 f white 0.00097 1970 33 f white 0.00104 1970 34 f white 0.00113 1970 35 f white 0.00122 1970 36 f white 0.00133 1970 37 f white 0.00146 1970 38 f white 0.00161 1970 39 f white 0.00177 1970 40 f white 0.00193 1970 41 f white 0.00211 1970 42 f white 0.0023 1970 43 f white 0.00254 1970 44 f white 0.0028 1970 45 f white 0.00308 1970 46 f white 0.00336 1970 47 f white 0.00366 1970 48 f white 0.00397 1970 49 f white 0.0043 1970 50 f white 0.00466 1970 51 f white 0.00507 1970 52 f white 0.0055 1970 53 f white 0.00596 1970 54 f white 0.00646 1970 55 f white 0.00699 1970 56 f white 0.00758 1970 57 f white 0.00819 1970 58 f white 0.00884 1970 59 f white 0.00953 1970 60 f white 0.01027 1970 61 f white 0.0111 1970 62 f white 0.01203 1970 63 f white 0.01309 1970 64 f white 0.01429 1970 65 f white 0.01563 1970 66 f white 0.01713 1970 67 f white 0.01883 1970 68 f white 0.02075 1970 69 f white 0.02288 1970 70 f white 0.02513 1970 71 f white 0.02759 1970 72 f white 0.03048 1970 73 f white 0.03396 1970 74 f white 0.03803 1970 75 f white 0.04255 1970 76 f white 0.0474 1970 77 f white 0.05264 1970 78 f white 0.05829 1970 79 f white 0.0644 1970 80 f white 0.07128 1970 81 f white 0.07893 1970 82 f white 0.08702 1970 83 f white 0.09539 1970 84 f white 0.10427 1970 85 f white 0.11465 1970 86 f white 0.12685 1970 87 f white 0.13944 1970 88 f white 0.15144 1970 89 f white 0.16303 1970 90 f white 0.1757 1970 91 f white 0.19046 1970 92 f white 0.20617 1970 93 f white 0.22206 1970 94 f white 0.23758 1970 95 f white 0.25298 1970 96 f white 0.26762 1970 97 f white 0.28133 1970 98 f white 0.29413 1970 99 f white 0.30615 1970 100 f white 0.31742 1970 101 f white 0.32794 1970 102 f white 0.33772 1970 103 f white 0.34679 1970 104 f white 0.35517 1970 105 f white 0.36289 1970 106 f white 0.36999 1970 107 f white 0.37651 1970 108 f white 0.38248 1970 109 f white 0.38793 1970 0-1d m nonwhite 0.01522 1970 1-7d m nonwhite 0.00742 1970 7-28d m nonwhite 0.00272 1970 0 m nonwhite 0.03408 1970 1 m nonwhite 0.00217 1970 2 m nonwhite 0.00155 1970 3 m nonwhite 0.00109 1970 4 m nonwhite 0.00094 1970 5 m nonwhite 0.00082 1970 6 m nonwhite 0.00074 1970 7 m nonwhite 0.00067 1970 8 m nonwhite 6e-04 1970 9 m nonwhite 0.00053 1970 10 m nonwhite 0.00048 1970 11 m nonwhite 0.00048 1970 12 m nonwhite 0.00058 1970 13 m nonwhite 8e-04 1970 14 m nonwhite 0.00113 1970 15 m nonwhite 0.00151 1970 16 m nonwhite 0.0019 1970 17 m nonwhite 0.0023 1970 18 m nonwhite 0.0027 1970 19 m nonwhite 0.00309 1970 20 m nonwhite 0.00357 1970 21 m nonwhite 0.0041 1970 22 m nonwhite 0.00452 1970 23 m nonwhite 0.00473 1970 24 m nonwhite 0.00475 1970 25 m nonwhite 0.00468 1970 26 m nonwhite 0.00464 1970 27 m nonwhite 0.00464 1970 28 m nonwhite 0.00474 1970 29 m nonwhite 0.00494 1970 30 m nonwhite 0.00515 1970 31 m nonwhite 0.00535 1970 32 m nonwhite 0.00558 1970 33 m nonwhite 0.00587 1970 34 m nonwhite 0.00621 1970 35 m nonwhite 0.00657 1970 36 m nonwhite 0.00697 1970 37 m nonwhite 0.00742 1970 38 m nonwhite 0.00791 1970 39 m nonwhite 0.00843 1970 40 m nonwhite 0.00898 1970 41 m nonwhite 0.00955 1970 42 m nonwhite 0.01016 1970 43 m nonwhite 0.0108 1970 44 m nonwhite 0.01149 1970 45 m nonwhite 0.01222 1970 46 m nonwhite 0.01298 1970 47 m nonwhite 0.01381 1970 48 m nonwhite 0.01472 1970 49 m nonwhite 0.01573 1970 50 m nonwhite 0.01683 1970 51 m nonwhite 0.01802 1970 52 m nonwhite 0.01927 1970 53 m nonwhite 0.02054 1970 54 m nonwhite 0.02182 1970 55 m nonwhite 0.02314 1970 56 m nonwhite 0.02453 1970 57 m nonwhite 0.02602 1970 58 m nonwhite 0.02763 1970 59 m nonwhite 0.02939 1970 60 m nonwhite 0.03127 1970 61 m nonwhite 0.03324 1970 62 m nonwhite 0.03532 1970 63 m nonwhite 0.03744 1970 64 m nonwhite 0.03959 1970 65 m nonwhite 0.04171 1970 66 m nonwhite 0.04389 1970 67 m nonwhite 0.04636 1970 68 m nonwhite 0.04935 1970 69 m nonwhite 0.05292 1970 70 m nonwhite 0.05714 1970 71 m nonwhite 0.06169 1970 72 m nonwhite 0.06617 1970 73 m nonwhite 0.07001 1970 74 m nonwhite 0.07318 1970 75 m nonwhite 0.07636 1970 76 m nonwhite 0.08001 1970 77 m nonwhite 0.0835 1970 78 m nonwhite 0.08666 1970 79 m nonwhite 0.08942 1970 80 m nonwhite 0.0916 1970 81 m nonwhite 0.09353 1970 82 m nonwhite 0.09587 1970 83 m nonwhite 0.09937 1970 84 m nonwhite 0.10418 1970 85 m nonwhite 0.11257 1970 86 m nonwhite 0.12156 1970 87 m nonwhite 0.13089 1970 88 m nonwhite 0.1398 1970 89 m nonwhite 0.14832 1970 90 m nonwhite 0.15687 1970 91 m nonwhite 0.1662 1970 92 m nonwhite 0.17656 1970 93 m nonwhite 0.18827 1970 94 m nonwhite 0.20064 1970 95 m nonwhite 0.2127 1970 96 m nonwhite 0.21795 1970 97 m nonwhite 0.22278 1970 98 m nonwhite 0.22723 1970 99 m nonwhite 0.23132 1970 100 m nonwhite 0.23506 1970 101 m nonwhite 0.23848 1970 102 m nonwhite 0.2416 1970 103 m nonwhite 0.24445 1970 104 m nonwhite 0.24705 1970 105 m nonwhite 0.24941 1970 106 m nonwhite 0.25155 1970 107 m nonwhite 0.2535 1970 108 m nonwhite 0.25526 1970 109 m nonwhite 0.25686 1970 0-1d f nonwhite 0.0117 1970 1-7d f nonwhite 0.00592 1970 7-28d f nonwhite 0.00236 1970 0 f nonwhite 0.02765 1970 1 f nonwhite 0.00189 1970 2 f nonwhite 0.0013 1970 3 f nonwhite 9e-04 1970 4 f nonwhite 0.00068 1970 5 f nonwhite 0.00062 1970 6 f nonwhite 0.00052 1970 7 f nonwhite 0.00045 1970 8 f nonwhite 0.00039 1970 9 f nonwhite 0.00035 1970 10 f nonwhite 0.00033 1970 11 f nonwhite 0.00033 1970 12 f nonwhite 0.00036 1970 13 f nonwhite 0.00044 1970 14 f nonwhite 0.00054 1970 15 f nonwhite 0.00067 1970 16 f nonwhite 8e-04 1970 17 f nonwhite 0.00093 1970 18 f nonwhite 0.00103 1970 19 f nonwhite 0.00111 1970 20 f nonwhite 0.00121 1970 21 f nonwhite 0.00132 1970 22 f nonwhite 0.00141 1970 23 f nonwhite 0.0015 1970 24 f nonwhite 0.00157 1970 25 f nonwhite 0.00164 1970 26 f nonwhite 0.00173 1970 27 f nonwhite 0.00183 1970 28 f nonwhite 0.00195 1970 29 f nonwhite 0.0021 1970 30 f nonwhite 0.00225 1970 31 f nonwhite 0.00242 1970 32 f nonwhite 0.00262 1970 33 f nonwhite 0.00286 1970 34 f nonwhite 0.00313 1970 35 f nonwhite 0.00343 1970 36 f nonwhite 0.00373 1970 37 f nonwhite 0.00405 1970 38 f nonwhite 0.00438 1970 39 f nonwhite 0.00472 1970 40 f nonwhite 0.00507 1970 41 f nonwhite 0.00542 1970 42 f nonwhite 0.00581 1970 43 f nonwhite 0.00624 1970 44 f nonwhite 0.00672 1970 45 f nonwhite 0.00725 1970 46 f nonwhite 0.00779 1970 47 f nonwhite 0.00836 1970 48 f nonwhite 0.00892 1970 49 f nonwhite 0.0095 1970 50 f nonwhite 0.01013 1970 51 f nonwhite 0.01081 1970 52 f nonwhite 0.01153 1970 53 f nonwhite 0.01229 1970 54 f nonwhite 0.01308 1970 55 f nonwhite 0.01392 1970 56 f nonwhite 0.01483 1970 57 f nonwhite 0.01581 1970 58 f nonwhite 0.01689 1970 59 f nonwhite 0.01809 1970 60 f nonwhite 0.01937 1970 61 f nonwhite 0.02073 1970 62 f nonwhite 0.02226 1970 63 f nonwhite 0.02392 1970 64 f nonwhite 0.02566 1970 65 f nonwhite 0.02738 1970 66 f nonwhite 0.02909 1970 67 f nonwhite 0.03093 1970 68 f nonwhite 0.03308 1970 69 f nonwhite 0.03561 1970 70 f nonwhite 0.03863 1970 71 f nonwhite 0.04194 1970 72 f nonwhite 0.04519 1970 73 f nonwhite 0.0479 1970 74 f nonwhite 0.05004 1970 75 f nonwhite 0.05208 1970 76 f nonwhite 0.05446 1970 77 f nonwhite 0.05704 1970 78 f nonwhite 0.05997 1970 79 f nonwhite 0.06321 1970 80 f nonwhite 0.06656 1970 81 f nonwhite 0.06991 1970 82 f nonwhite 0.07342 1970 83 f nonwhite 0.07716 1970 84 f nonwhite 0.08122 1970 85 f nonwhite 0.08747 1970 86 f nonwhite 0.09465 1970 87 f nonwhite 0.10282 1970 88 f nonwhite 0.11201 1970 89 f nonwhite 0.12222 1970 90 f nonwhite 0.13355 1970 91 f nonwhite 0.14548 1970 92 f nonwhite 0.15672 1970 93 f nonwhite 0.16605 1970 94 f nonwhite 0.17401 1970 95 f nonwhite 0.1822 1970 96 f nonwhite 0.18719 1970 97 f nonwhite 0.1918 1970 98 f nonwhite 0.19605 1970 99 f nonwhite 0.19996 1970 100 f nonwhite 0.20355 1970 101 f nonwhite 0.20684 1970 102 f nonwhite 0.20985 1970 103 f nonwhite 0.21259 1970 104 f nonwhite 0.2151 1970 105 f nonwhite 0.21738 1970 106 f nonwhite 0.21945 1970 107 f nonwhite 0.22134 1970 108 f nonwhite 0.22305 1970 109 f nonwhite 0.2246 1970 0-1d m black 0.01522 1970 1-7d m black 0.00742 1970 7-28d m black 0.00272 1970 0 m black 0.03606 1970 1 m black 0.00224 1970 2 m black 0.00159 1970 3 m black 0.00111 1970 4 m black 0.00097 1970 5 m black 0.00084 1970 6 m black 0.00076 1970 7 m black 0.00068 1970 8 m black 0.00061 1970 9 m black 0.00054 1970 10 m black 0.00049 1970 11 m black 0.00049 1970 12 m black 0.00059 1970 13 m black 0.00081 1970 14 m black 0.00114 1970 15 m black 0.00152 1970 16 m black 0.00192 1970 17 m black 0.00233 1970 18 m black 0.00275 1970 19 m black 0.00319 1970 20 m black 0.00372 1970 21 m black 0.00433 1970 22 m black 0.00482 1970 23 m black 0.00508 1970 24 m black 0.00511 1970 25 m black 0.00503 1970 26 m black 0.00500 1970 27 m black 0.00500 1970 28 m black 0.00512 1970 29 m black 0.00534 1970 30 m black 0.00558 1970 31 m black 0.00579 1970 32 m black 0.00605 1970 33 m black 0.00636 1970 34 m black 0.00672 1970 35 m black 0.00712 1970 36 m black 0.00754 1970 37 m black 0.00801 1970 38 m black 0.00853 1970 39 m black 0.00908 1970 40 m black 0.00966 1970 41 m black 0.01025 1970 42 m black 0.01089 1970 43 m black 0.01157 1970 44 m black 0.01231 1970 45 m black 0.01309 1970 46 m black 0.01391 1970 47 m black 0.01478 1970 48 m black 0.01573 1970 49 m black 0.01676 1970 50 m black 0.01788 1970 51 m black 0.01909 1970 52 m black 0.02037 1970 53 m black 0.02169 1970 54 m black 0.02305 1970 55 m black 0.02445 1970 56 m black 0.02593 1970 57 m black 0.02751 1970 58 m black 0.02922 1970 59 m black 0.03108 1970 60 m black 0.03308 1970 61 m black 0.03520 1970 62 m black 0.03739 1970 63 m black 0.03858 1970 64 m black 0.04175 1970 65 m black 0.04386 1970 66 m black 0.04603 1970 67 m black 0.04852 1970 68 m black 0.05108 1970 69 m black 0.05528 1970 70 m black 0.05965 1970 71 m black 0.06434 1970 72 m black 0.06892 1970 73 m black 0.07276 1970 74 m black 0.07585 1970 75 m black 0.07887 1970 76 m black 0.08233 1970 77 m black 0.08575 1970 78 m black 0.08513 1970 79 m black 0.09244 1970 80 m black 0.09554 1970 81 m black 0.09852 1970 82 m black 0.10180 1970 83 m black 0.10573 1970 84 m black 0.11035 1970 85 m black 0.11744 1970 86 m black 0.12512 1970 87 m black 0.13349 1970 88 m black 0.14237 1970 89 m black 0.15170 1970 90 m black 0.16139 1970 91 m black 0.17144 1970 92 m black 0.18173 1970 93 m black 0.19211 1970 94 m black 0.20240 1970 95 m black 0.21270 1970 96 m black 0.21795 1970 97 m black 0.22278 1970 98 m black 0.22723 1970 99 m black 0.23132 1970 100 m black 0.23506 1970 101 m black 0.23848 1970 102 m black 0.24160 1970 103 m black 0.24445 1970 104 m black 0.24705 1970 105 m black 0.24941 1970 106 m black 0.25155 1970 107 m black 0.25350 1970 108 m black 0.25526 1970 109 m black 0.25686 1970 0-1d f black 0.01097 1970 1-7d f black 0.00555 1970 7-28d f black 0.00223 1970 0 f black 0.02765 1970 1 f black 0.00189 1970 2 f black 0.0013 1970 3 f black 9e-04 1970 4 f black 0.00068 1970 5 f black 0.00062 1970 6 f black 0.00052 1970 7 f black 0.00045 1970 8 f black 0.00039 1970 9 f black 0.00035 1970 10 f black 0.00033 1970 11 f black 0.00033 1970 12 f black 0.00036 1970 13 f black 0.00044 1970 14 f black 0.00054 1970 15 f black 0.00067 1970 16 f black 8e-04 1970 17 f black 0.00093 1970 18 f black 0.00103 1970 19 f black 0.00111 1970 20 f black 0.00121 1970 21 f black 0.00132 1970 22 f black 0.00141 1970 23 f black 0.0015 1970 24 f black 0.00157 1970 25 f black 0.00164 1970 26 f black 0.00173 1970 27 f black 0.00183 1970 28 f black 0.00195 1970 29 f black 0.0021 1970 30 f black 0.00225 1970 31 f black 0.00242 1970 32 f black 0.00262 1970 33 f black 0.00286 1970 34 f black 0.00313 1970 35 f black 0.00343 1970 36 f black 0.00373 1970 37 f black 0.00405 1970 38 f black 0.00438 1970 39 f black 0.00472 1970 40 f black 0.00507 1970 41 f black 0.00542 1970 42 f black 0.00581 1970 43 f black 0.00624 1970 44 f black 0.00672 1970 45 f black 0.00725 1970 46 f black 0.00779 1970 47 f black 0.00836 1970 48 f black 0.00892 1970 49 f black 0.0095 1970 50 f black 0.01013 1970 51 f black 0.01081 1970 52 f black 0.01153 1970 53 f black 0.01229 1970 54 f black 0.01308 1970 55 f black 0.01392 1970 56 f black 0.01483 1970 57 f black 0.01581 1970 58 f black 0.01689 1970 59 f black 0.01809 1970 60 f black 0.01937 1970 61 f black 0.02073 1970 62 f black 0.02226 1970 63 f black 0.02392 1970 64 f black 0.02566 1970 65 f black 0.02738 1970 66 f black 0.02909 1970 67 f black 0.03093 1970 68 f black 0.03308 1970 69 f black 0.03561 1970 70 f black 0.03863 1970 71 f black 0.04194 1970 72 f black 0.04519 1970 73 f black 0.0479 1970 74 f black 0.05004 1970 75 f black 0.05208 1970 76 f black 0.05446 1970 77 f black 0.05704 1970 78 f black 0.05997 1970 79 f black 0.06321 1970 80 f black 0.06656 1970 81 f black 0.06991 1970 82 f black 0.07342 1970 83 f black 0.07716 1970 84 f black 0.08122 1970 85 f black 0.08747 1970 86 f black 0.09465 1970 87 f black 0.10282 1970 88 f black 0.11201 1970 89 f black 0.12222 1970 90 f black 0.13355 1970 91 f black 0.14548 1970 92 f black 0.15672 1970 93 f black 0.16605 1970 94 f black 0.17401 1970 95 f black 0.1822 1970 96 f black 0.18719 1970 97 f black 0.1918 1970 98 f black 0.19605 1970 99 f black 0.19996 1970 100 f black 0.20355 1970 101 f black 0.20684 1970 102 f black 0.20985 1970 103 f black 0.21259 1970 104 f black 0.2151 1970 105 f black 0.21738 1970 106 f black 0.21945 1970 107 f black 0.22134 1970 108 f black 0.22305 1970 109 f black 0.2246 1980 0-1d m total 0.00503 1980 1-7d m total 0.00278 1980 7-28d m total 0.00152 1980 0 m total 0.01393 1980 1 m total 0.00101 1980 2 m total 0.00073 1980 3 m total 0.00058 1980 4 m total 0.00047 1980 5 m total 0.00042 1980 6 m total 0.00039 1980 7 m total 0.00036 1980 8 m total 0.00032 1980 9 m total 0.00026 1980 10 m total 0.00021 1980 11 m total 0.00021 1980 12 m total 3e-04 1980 13 m total 0.00048 1980 14 m total 0.00072 1980 15 m total 0.00096 1980 16 m total 0.00118 1980 17 m total 0.00137 1980 18 m total 0.00153 1980 19 m total 0.00167 1980 20 m total 0.00181 1980 21 m total 0.00194 1980 22 m total 0.00203 1980 23 m total 0.00205 1980 24 m total 0.00203 1980 25 m total 0.00199 1980 26 m total 0.00196 1980 27 m total 0.00193 1980 28 m total 0.00191 1980 29 m total 0.00191 1980 30 m total 0.00191 1980 31 m total 0.00191 1980 32 m total 0.00193 1980 33 m total 0.00198 1980 34 m total 0.00205 1980 35 m total 0.00216 1980 36 m total 0.00229 1980 37 m total 0.00244 1980 38 m total 0.00261 1980 39 m total 0.0028 1980 40 m total 0.00303 1980 41 m total 0.00332 1980 42 m total 0.00363 1980 43 m total 0.00398 1980 44 m total 0.00435 1980 45 m total 0.00476 1980 46 m total 0.00522 1980 47 m total 0.00576 1980 48 m total 0.00638 1980 49 m total 0.00705 1980 50 m total 0.00775 1980 51 m total 0.00846 1980 52 m total 0.00924 1980 53 m total 0.0101 1980 54 m total 0.01105 1980 55 m total 0.01206 1980 56 m total 0.0131 1980 57 m total 0.01423 1980 58 m total 0.01549 1980 59 m total 0.0169 1980 60 m total 0.01846 1980 61 m total 0.02016 1980 62 m total 0.02201 1980 63 m total 0.02398 1980 64 m total 0.02604 1980 65 m total 0.02817 1980 66 m total 0.03044 1980 67 m total 0.03289 1980 68 m total 0.03563 1980 69 m total 0.03868 1980 70 m total 0.04207 1980 71 m total 0.04571 1980 72 m total 0.04951 1980 73 m total 0.05338 1980 74 m total 0.05736 1980 75 m total 0.06167 1980 76 m total 0.06647 1980 77 m total 0.0717 1980 78 m total 0.0774 1980 79 m total 0.08365 1980 80 m total 0.09069 1980 81 m total 0.09859 1980 82 m total 0.10708 1980 83 m total 0.11579 1980 84 m total 0.12463 1980 85 m total 0.13419 1980 86 m total 0.14479 1980 87 m total 0.15554 1980 88 m total 0.16618 1980 89 m total 0.177 1980 90 m total 0.18848 1980 91 m total 0.20125 1980 92 m total 0.21542 1980 93 m total 0.2308 1980 94 m total 0.24641 1980 95 m total 0.26149 1980 96 m total 0.27438 1980 97 m total 0.28654 1980 98 m total 0.29797 1980 99 m total 0.30867 1980 100 m total 0.31865 1980 101 m total 0.32792 1980 102 m total 0.3365 1980 103 m total 0.34443 1980 104 m total 0.35174 1980 105 m total 0.35845 1980 106 m total 0.36461 1980 107 m total 0.37024 1980 108 m total 0.37539 1980 109 m total 0.38009 1980 0-1d f total 0.00421 1980 1-7d f total 0.00212 1980 7-28d f total 0.00126 1980 0 f total 0.0112 1980 1 f total 0.00086 1980 2 f total 0.00056 1980 3 f total 0.00042 1980 4 f total 0.00033 1980 5 f total 0.00031 1980 6 f total 0.00027 1980 7 f total 0.00024 1980 8 f total 0.00022 1980 9 f total 0.00019 1980 10 f total 0.00018 1980 11 f total 0.00018 1980 12 f total 2e-04 1980 13 f total 0.00026 1980 14 f total 0.00033 1980 15 f total 4e-04 1980 16 f total 0.00047 1980 17 f total 0.00052 1980 18 f total 0.00055 1980 19 f total 0.00057 1980 20 f total 0.00058 1980 21 f total 6e-04 1980 22 f total 0.00062 1980 23 f total 0.00063 1980 24 f total 0.00064 1980 25 f total 0.00065 1980 26 f total 0.00066 1980 27 f total 0.00067 1980 28 f total 7e-04 1980 29 f total 0.00072 1980 30 f total 0.00075 1980 31 f total 0.00079 1980 32 f total 0.00083 1980 33 f total 0.00089 1980 34 f total 0.00096 1980 35 f total 0.00104 1980 36 f total 0.00114 1980 37 f total 0.00125 1980 38 f total 0.00137 1980 39 f total 0.00149 1980 40 f total 0.00163 1980 41 f total 0.0018 1980 42 f total 0.00199 1980 43 f total 0.00218 1980 44 f total 0.00239 1980 45 f total 0.00262 1980 46 f total 0.00286 1980 47 f total 0.00315 1980 48 f total 0.00347 1980 49 f total 0.00381 1980 50 f total 0.00416 1980 51 f total 0.00452 1980 52 f total 0.0049 1980 53 f total 0.00532 1980 54 f total 0.00578 1980 55 f total 0.00627 1980 56 f total 0.00678 1980 57 f total 0.00733 1980 58 f total 0.00796 1980 59 f total 0.00867 1980 60 f total 0.00947 1980 61 f total 0.01035 1980 62 f total 0.01129 1980 63 f total 0.01226 1980 64 f total 0.01325 1980 65 f total 0.01427 1980 66 f total 0.01538 1980 67 f total 0.01664 1980 68 f total 0.01811 1980 69 f total 0.0198 1980 70 f total 0.02169 1980 71 f total 0.02375 1980 72 f total 0.026 1980 73 f total 0.02842 1980 74 f total 0.03106 1980 75 f total 0.03388 1980 76 f total 0.03704 1980 77 f total 0.04073 1980 78 f total 0.04515 1980 79 f total 0.05033 1980 80 f total 0.05622 1980 81 f total 0.06269 1980 82 f total 0.06973 1980 83 f total 0.07722 1980 84 f total 0.08519 1980 85 f total 0.09409 1980 86 f total 0.10405 1980 87 f total 0.1142 1980 88 f total 0.12427 1980 89 f total 0.13471 1980 90 f total 0.14661 1980 91 f total 0.16024 1980 92 f total 0.1746 1980 93 f total 0.18904 1980 94 f total 0.20348 1980 95 f total 0.21823 1980 96 f total 0.23221 1980 97 f total 0.2456 1980 98 f total 0.25834 1980 99 f total 0.2704 1980 100 f total 0.28176 1980 101 f total 0.29242 1980 102 f total 0.30237 1980 103 f total 0.31163 1980 104 f total 0.32023 1980 105 f total 0.32817 1980 106 f total 0.3355 1980 107 f total 0.34224 1980 108 f total 0.34843 1980 109 f total 0.35411 1980 0-1d m white 0.00438 1980 1-7d m white 0.00256 1980 7-28d m white 0.00139 1980 0 m white 0.01231 1980 1 m white 0.00092 1980 2 m white 0.00066 1980 3 m white 0.00053 1980 4 m white 0.00043 1980 5 m white 0.00039 1980 6 m white 0.00037 1980 7 m white 0.00034 1980 8 m white 3e-04 1980 9 m white 0.00024 1980 10 m white 0.00019 1980 11 m white 0.00019 1980 12 m white 0.00028 1980 13 m white 0.00046 1980 14 m white 0.00071 1980 15 m white 0.00096 1980 16 m white 0.00118 1980 17 m white 0.00137 1980 18 m white 0.00151 1980 19 m white 0.00163 1980 20 m white 0.00175 1980 21 m white 0.00186 1980 22 m white 0.00193 1980 23 m white 0.00193 1980 24 m white 0.00189 1980 25 m white 0.00183 1980 26 m white 0.00177 1980 27 m white 0.00172 1980 28 m white 0.00168 1980 29 m white 0.00167 1980 30 m white 0.00166 1980 31 m white 0.00165 1980 32 m white 0.00166 1980 33 m white 0.00169 1980 34 m white 0.00175 1980 35 m white 0.00184 1980 36 m white 0.00196 1980 37 m white 0.00209 1980 38 m white 0.00224 1980 39 m white 0.0024 1980 40 m white 0.00261 1980 41 m white 0.00287 1980 42 m white 0.00316 1980 43 m white 0.00348 1980 44 m white 0.00382 1980 45 m white 0.0042 1980 46 m white 0.00463 1980 47 m white 0.00514 1980 48 m white 0.00573 1980 49 m white 0.00639 1980 50 m white 0.00706 1980 51 m white 0.00775 1980 52 m white 0.0085 1980 53 m white 0.00934 1980 54 m white 0.01027 1980 55 m white 0.01125 1980 56 m white 0.01227 1980 57 m white 0.01338 1980 58 m white 0.01464 1980 59 m white 0.01605 1980 60 m white 0.01762 1980 61 m white 0.01933 1980 62 m white 0.02119 1980 63 m white 0.02316 1980 64 m white 0.02523 1980 65 m white 0.02738 1980 66 m white 0.02968 1980 67 m white 0.03218 1980 68 m white 0.03495 1980 69 m white 0.03805 1980 70 m white 0.04148 1980 71 m white 0.04516 1980 72 m white 0.04901 1980 73 m white 0.05295 1980 74 m white 0.05703 1980 75 m white 0.06146 1980 76 m white 0.06642 1980 77 m white 0.0718 1980 78 m white 0.07762 1980 79 m white 0.08394 1980 80 m white 0.09099 1980 81 m white 0.09886 1980 82 m white 0.10733 1980 83 m white 0.11613 1980 84 m white 0.12523 1980 85 m white 0.13507 1980 86 m white 0.14592 1980 87 m white 0.15691 1980 88 m white 0.16774 1980 89 m white 0.17875 1980 90 m white 0.19058 1980 91 m white 0.20389 1980 92 m white 0.21864 1980 93 m white 0.23453 1980 94 m white 0.25061 1980 95 m white 0.26617 1980 96 m white 0.28001 1980 97 m white 0.29311 1980 98 m white 0.30545 1980 99 m white 0.31703 1980 100 m white 0.32784 1980 101 m white 0.33791 1980 102 m white 0.34724 1980 103 m white 0.35588 1980 104 m white 0.36384 1980 105 m white 0.37117 1980 106 m white 0.3779 1980 107 m white 0.38407 1980 108 m white 0.38971 1980 109 m white 0.39486 1980 0-1d f white 0.00361 1980 1-7d f white 0.0019 1980 7-28d f white 0.00111 1980 0 f white 0.00965 1980 1 f white 0.00077 1980 2 f white 0.00051 1980 3 f white 0.00037 1980 4 f white 3e-04 1980 5 f white 0.00028 1980 6 f white 0.00026 1980 7 f white 0.00023 1980 8 f white 0.00021 1980 9 f white 0.00018 1980 10 f white 0.00017 1980 11 f white 0.00016 1980 12 f white 0.00019 1980 13 f white 0.00025 1980 14 f white 0.00032 1980 15 f white 4e-04 1980 16 f white 0.00047 1980 17 f white 0.00052 1980 18 f white 0.00054 1980 19 f white 0.00055 1980 20 f white 0.00056 1980 21 f white 0.00057 1980 22 f white 0.00057 1980 23 f white 0.00058 1980 24 f white 0.00058 1980 25 f white 0.00058 1980 26 f white 0.00058 1980 27 f white 0.00059 1980 28 f white 6e-04 1980 29 f white 0.00063 1980 30 f white 0.00065 1980 31 f white 0.00068 1980 32 f white 0.00072 1980 33 f white 0.00077 1980 34 f white 0.00083 1980 35 f white 9e-04 1980 36 f white 0.00099 1980 37 f white 0.00109 1980 38 f white 0.00119 1980 39 f white 0.0013 1980 40 f white 0.00143 1980 41 f white 0.00158 1980 42 f white 0.00174 1980 43 f white 0.00192 1980 44 f white 0.00211 1980 45 f white 0.00231 1980 46 f white 0.00254 1980 47 f white 0.0028 1980 48 f white 0.0031 1980 49 f white 0.00343 1980 50 f white 0.00376 1980 51 f white 0.0041 1980 52 f white 0.00447 1980 53 f white 0.00488 1980 54 f white 0.00532 1980 55 f white 0.00579 1980 56 f white 0.00628 1980 57 f white 0.00681 1980 58 f white 0.00742 1980 59 f white 0.00811 1980 60 f white 0.00889 1980 61 f white 0.00975 1980 62 f white 0.01067 1980 63 f white 0.01162 1980 64 f white 0.01259 1980 65 f white 0.01359 1980 66 f white 0.0147 1980 67 f white 0.01595 1980 68 f white 0.0174 1980 69 f white 0.01907 1980 70 f white 0.02092 1980 71 f white 0.02294 1980 72 f white 0.02517 1980 73 f white 0.0276 1980 74 f white 0.03027 1980 75 f white 0.03315 1980 76 f white 0.03637 1980 77 f white 0.04015 1980 78 f white 0.04467 1980 79 f white 0.04995 1980 80 f white 0.05589 1980 81 f white 0.06239 1980 82 f white 0.06949 1980 83 f white 0.07713 1980 84 f white 0.08539 1980 85 f white 0.09463 1980 86 f white 0.10491 1980 87 f white 0.11534 1980 88 f white 0.12559 1980 89 f white 0.13617 1980 90 f white 0.14831 1980 91 f white 0.16231 1980 92 f white 0.17709 1980 93 f white 0.19198 1980 94 f white 0.2069 1980 95 f white 0.22228 1980 96 f white 0.23729 1980 97 f white 0.25173 1980 98 f white 0.26551 1980 99 f white 0.27859 1980 100 f white 0.29094 1980 101 f white 0.30255 1980 102 f white 0.31342 1980 103 f white 0.32355 1980 104 f white 0.33297 1980 105 f white 0.34168 1980 106 f white 0.34973 1980 107 f white 0.35715 1980 108 f white 0.36397 1980 109 f white 0.37022 1980 0-1d m nonwhite 0.00869 1980 1-7d m nonwhite 0.00421 1980 7-28d m nonwhite 0.0023 1980 0 m nonwhite 0.02061 1980 1 m nonwhite 0.00139 1980 2 m nonwhite 0.00101 1980 3 m nonwhite 0.00082 1980 4 m nonwhite 0.00066 1980 5 m nonwhite 0.00058 1980 6 m nonwhite 0.00051 1980 7 m nonwhite 0.00045 1980 8 m nonwhite 0.00039 1980 9 m nonwhite 0.00034 1980 10 m nonwhite 3e-04 1980 11 m nonwhite 0.00031 1980 12 m nonwhite 0.00039 1980 13 m nonwhite 0.00055 1980 14 m nonwhite 0.00076 1980 15 m nonwhite 0.00098 1980 16 m nonwhite 0.00119 1980 17 m nonwhite 0.0014 1980 18 m nonwhite 0.00162 1980 19 m nonwhite 0.00186 1980 20 m nonwhite 0.00212 1980 21 m nonwhite 0.00239 1980 22 m nonwhite 0.00262 1980 23 m nonwhite 0.00279 1980 24 m nonwhite 0.00291 1980 25 m nonwhite 0.00302 1980 26 m nonwhite 0.00314 1980 27 m nonwhite 0.00325 1980 28 m nonwhite 0.00335 1980 29 m nonwhite 0.00346 1980 30 m nonwhite 0.00356 1980 31 m nonwhite 0.00367 1980 32 m nonwhite 0.00379 1980 33 m nonwhite 0.00395 1980 34 m nonwhite 0.00413 1980 35 m nonwhite 0.00436 1980 36 m nonwhite 0.00461 1980 37 m nonwhite 0.00491 1980 38 m nonwhite 0.00523 1980 39 m nonwhite 0.00557 1980 40 m nonwhite 0.00595 1980 41 m nonwhite 0.00638 1980 42 m nonwhite 0.00687 1980 43 m nonwhite 0.00743 1980 44 m nonwhite 0.00807 1980 45 m nonwhite 0.00877 1980 46 m nonwhite 0.00952 1980 47 m nonwhite 0.01036 1980 48 m nonwhite 0.01128 1980 49 m nonwhite 0.01225 1980 50 m nonwhite 0.01323 1980 51 m nonwhite 0.01424 1980 52 m nonwhite 0.01531 1980 53 m nonwhite 0.01648 1980 54 m nonwhite 0.01774 1980 55 m nonwhite 0.01905 1980 56 m nonwhite 0.02039 1980 57 m nonwhite 0.02174 1980 58 m nonwhite 0.02312 1980 59 m nonwhite 0.02459 1980 60 m nonwhite 0.02619 1980 61 m nonwhite 0.02794 1980 62 m nonwhite 0.02981 1980 63 m nonwhite 0.03172 1980 64 m nonwhite 0.03361 1980 65 m nonwhite 0.03545 1980 66 m nonwhite 0.03733 1980 67 m nonwhite 0.03936 1980 68 m nonwhite 0.04171 1980 69 m nonwhite 0.04445 1980 70 m nonwhite 0.04754 1980 71 m nonwhite 0.05084 1980 72 m nonwhite 0.05421 1980 73 m nonwhite 0.05742 1980 74 m nonwhite 0.06046 1980 75 m nonwhite 0.06356 1980 76 m nonwhite 0.06699 1980 77 m nonwhite 0.07083 1980 78 m nonwhite 0.07538 1980 79 m nonwhite 0.08088 1980 80 m nonwhite 0.08772 1980 81 m nonwhite 0.09578 1980 82 m nonwhite 0.10433 1980 83 m nonwhite 0.1119 1980 84 m nonwhite 0.11781 1980 85 m nonwhite 0.12406 1980 86 m nonwhite 0.13154 1980 87 m nonwhite 0.13945 1980 88 m nonwhite 0.14805 1980 89 m nonwhite 0.15729 1980 90 m nonwhite 0.16621 1980 91 m nonwhite 0.17527 1980 92 m nonwhite 0.18599 1980 93 m nonwhite 0.19866 1980 94 m nonwhite 0.21229 1980 95 m nonwhite 0.22554 1980 96 m nonwhite 0.23274 1980 97 m nonwhite 0.23944 1980 98 m nonwhite 0.24563 1980 99 m nonwhite 0.25135 1980 100 m nonwhite 0.25662 1980 101 m nonwhite 0.26146 1980 102 m nonwhite 0.2659 1980 103 m nonwhite 0.26996 1980 104 m nonwhite 0.27367 1980 105 m nonwhite 0.27706 1980 106 m nonwhite 0.28014 1980 107 m nonwhite 0.28295 1980 108 m nonwhite 0.2855 1980 109 m nonwhite 0.28782 1980 0-1d f nonwhite 0.00741 1980 1-7d f nonwhite 0.00331 1980 7-28d f nonwhite 0.00207 1980 0 f nonwhite 0.01739 1980 1 f nonwhite 0.0012 1980 2 f nonwhite 8e-04 1980 3 f nonwhite 0.00063 1980 4 f nonwhite 0.00046 1980 5 f nonwhite 0.00041 1980 6 f nonwhite 0.00034 1980 7 f nonwhite 0.00029 1980 8 f nonwhite 0.00026 1980 9 f nonwhite 0.00024 1980 10 f nonwhite 0.00023 1980 11 f nonwhite 0.00024 1980 12 f nonwhite 0.00026 1980 13 f nonwhite 0.00031 1980 14 f nonwhite 0.00036 1980 15 f nonwhite 0.00043 1980 16 f nonwhite 0.00049 1980 17 f nonwhite 0.00055 1980 18 f nonwhite 6e-04 1980 19 f nonwhite 0.00066 1980 20 f nonwhite 0.00072 1980 21 f nonwhite 0.00078 1980 22 f nonwhite 0.00084 1980 23 f nonwhite 9e-04 1980 24 f nonwhite 0.00096 1980 25 f nonwhite 0.00102 1980 26 f nonwhite 0.00109 1980 27 f nonwhite 0.00115 1980 28 f nonwhite 0.00121 1980 29 f nonwhite 0.00127 1980 30 f nonwhite 0.00133 1980 31 f nonwhite 0.0014 1980 32 f nonwhite 0.00148 1980 33 f nonwhite 0.00159 1980 34 f nonwhite 0.00172 1980 35 f nonwhite 0.00187 1980 36 f nonwhite 0.00205 1980 37 f nonwhite 0.00224 1980 38 f nonwhite 0.00245 1980 39 f nonwhite 0.00266 1980 40 f nonwhite 0.0029 1980 41 f nonwhite 0.00316 1980 42 f nonwhite 0.00345 1980 43 f nonwhite 0.00378 1980 44 f nonwhite 0.00413 1980 45 f nonwhite 0.00451 1980 46 f nonwhite 0.00492 1980 47 f nonwhite 0.00537 1980 48 f nonwhite 0.00585 1980 49 f nonwhite 0.00636 1980 50 f nonwhite 0.00688 1980 51 f nonwhite 0.0074 1980 52 f nonwhite 0.00796 1980 53 f nonwhite 0.00858 1980 54 f nonwhite 0.00927 1980 55 f nonwhite 0.01001 1980 56 f nonwhite 0.01079 1980 57 f nonwhite 0.01161 1980 58 f nonwhite 0.01247 1980 59 f nonwhite 0.0134 1980 60 f nonwhite 0.01441 1980 61 f nonwhite 0.01552 1980 62 f nonwhite 0.01668 1980 63 f nonwhite 0.01785 1980 64 f nonwhite 0.01898 1980 65 f nonwhite 0.02007 1980 66 f nonwhite 0.0212 1980 67 f nonwhite 0.02253 1980 68 f nonwhite 0.02422 1980 69 f nonwhite 0.02631 1980 70 f nonwhite 0.02875 1980 71 f nonwhite 0.03138 1980 72 f nonwhite 0.03408 1980 73 f nonwhite 0.03659 1980 74 f nonwhite 0.03888 1980 75 f nonwhite 0.04114 1980 76 f nonwhite 0.04363 1980 77 f nonwhite 0.04648 1980 78 f nonwhite 0.05001 1980 79 f nonwhite 0.05442 1980 80 f nonwhite 0.05992 1980 81 f nonwhite 0.06626 1980 82 f nonwhite 0.07279 1980 83 f nonwhite 0.07834 1980 84 f nonwhite 0.08251 1980 85 f nonwhite 0.08685 1980 86 f nonwhite 0.09238 1980 87 f nonwhite 0.09881 1980 88 f nonwhite 0.10652 1980 89 f nonwhite 0.11547 1980 90 f nonwhite 0.12514 1980 91 f nonwhite 0.13529 1980 92 f nonwhite 0.14624 1980 93 f nonwhite 0.15791 1980 94 f nonwhite 0.17016 1980 95 f nonwhite 0.18279 1980 96 f nonwhite 0.1917 1980 97 f nonwhite 0.20022 1980 98 f nonwhite 0.20825 1980 99 f nonwhite 0.21577 1980 100 f nonwhite 0.22279 1980 101 f nonwhite 0.2293 1980 102 f nonwhite 0.23534 1980 103 f nonwhite 0.24091 1980 104 f nonwhite 0.24605 1980 105 f nonwhite 0.25077 1980 106 f nonwhite 0.2551 1980 107 f nonwhite 0.25907 1980 108 f nonwhite 0.26269 1980 109 f nonwhite 0.266 1980 0-1d m black 0.00768 1980 1-7d m black 0.00372 1980 7-28d m black 0.00206 1980 0 m black 0.02297 1980 1 m black 0.00148 1980 2 m black 0.0011 1980 3 m black 0.00086 1980 4 m black 7e-04 1980 5 m black 0.00063 1980 6 m black 0.00055 1980 7 m black 0.00049 1980 8 m black 0.00043 1980 9 m black 0.00037 1980 10 m black 0.00033 1980 11 m black 0.00034 1980 12 m black 0.00041 1980 13 m black 0.00057 1980 14 m black 0.00078 1980 15 m black 0.00099 1980 16 m black 0.0012 1980 17 m black 0.00142 1980 18 m black 0.00165 1980 19 m black 0.00191 1980 20 m black 0.00221 1980 21 m black 0.00251 1980 22 m black 0.00279 1980 23 m black 0.003 1980 24 m black 0.00315 1980 25 m black 0.0033 1980 26 m black 0.00346 1980 27 m black 0.00362 1980 28 m black 0.00377 1980 29 m black 0.00392 1980 30 m black 0.00408 1980 31 m black 0.00424 1980 32 m black 0.00441 1980 33 m black 0.0046 1980 34 m black 0.00483 1980 35 m black 0.00509 1980 36 m black 0.00539 1980 37 m black 0.00572 1980 38 m black 0.00609 1980 39 m black 0.00648 1980 40 m black 0.00691 1980 41 m black 0.00739 1980 42 m black 0.00794 1980 43 m black 0.00857 1980 44 m black 0.00929 1980 45 m black 0.01007 1980 46 m black 0.0109 1980 47 m black 0.01181 1980 48 m black 0.0128 1980 49 m black 0.01384 1980 50 m black 0.01488 1980 51 m black 0.01594 1980 52 m black 0.01709 1980 53 m black 0.01835 1980 54 m black 0.01972 1980 55 m black 0.02116 1980 56 m black 0.02262 1980 57 m black 0.02408 1980 58 m black 0.02556 1980 59 m black 0.02711 1980 60 m black 0.02877 1980 61 m black 0.03058 1980 62 m black 0.03252 1980 63 m black 0.03452 1980 64 m black 0.03651 1980 65 m black 0.03846 1980 66 m black 0.04044 1980 67 m black 0.0426 1980 68 m black 0.04511 1980 69 m black 0.04804 1980 70 m black 0.05141 1980 71 m black 0.05501 1980 72 m black 0.05866 1980 73 m black 0.06202 1980 74 m black 0.06508 1980 75 m black 0.06814 1980 76 m black 0.07154 1980 77 m black 0.07537 1980 78 m black 0.07999 1980 79 m black 0.08566 1980 80 m black 0.09268 1980 81 m black 0.10087 1980 82 m black 0.10953 1980 83 m black 0.11714 1980 84 m black 0.12302 1980 85 m black 0.12872 1980 86 m black 0.13559 1980 87 m black 0.14282 1980 88 m black 0.15071 1980 89 m black 0.15928 1980 90 m black 0.16761 1980 91 m black 0.17617 1980 92 m black 0.18648 1980 93 m black 0.19888 1980 94 m black 0.21236 1980 95 m black 0.22554 1980 96 m black 0.23274 1980 97 m black 0.23944 1980 98 m black 0.24563 1980 99 m black 0.25135 1980 100 m black 0.25662 1980 101 m black 0.26146 1980 102 m black 0.2659 1980 103 m black 0.26996 1980 104 m black 0.27367 1980 105 m black 0.27706 1980 106 m black 0.28014 1980 107 m black 0.28295 1980 108 m black 0.2855 1980 109 m black 0.28782 1980 0-1d f black 0.0066 1980 1-7d f black 0.00298 1980 7-28d f black 0.00186 1980 0 f black 0.01927 1980 1 f black 0.00127 1980 2 f black 0.00087 1980 3 f black 0.00066 1980 4 f black 0.00048 1980 5 f black 0.00044 1980 6 f black 0.00037 1980 7 f black 0.00031 1980 8 f black 0.00027 1980 9 f black 0.00025 1980 10 f black 0.00024 1980 11 f black 0.00024 1980 12 f black 0.00027 1980 13 f black 0.00031 1980 14 f black 0.00037 1980 15 f black 0.00043 1980 16 f black 0.00049 1980 17 f black 0.00056 1980 18 f black 0.00062 1980 19 f black 0.00068 1980 20 f black 0.00074 1980 21 f black 0.00081 1980 22 f black 0.00088 1980 23 f black 0.00095 1980 24 f black 0.00102 1980 25 f black 0.00109 1980 26 f black 0.00118 1980 27 f black 0.00126 1980 28 f black 0.00133 1980 29 f black 0.0014 1980 30 f black 0.00148 1980 31 f black 0.00157 1980 32 f black 0.00168 1980 33 f black 0.0018 1980 34 f black 0.00194 1980 35 f black 0.00211 1980 36 f black 0.00231 1980 37 f black 0.00252 1980 38 f black 0.00275 1980 39 f black 0.00298 1980 40 f black 0.00324 1980 41 f black 0.00352 1980 42 f black 0.00385 1980 43 f black 0.00421 1980 44 f black 0.00462 1980 45 f black 0.00505 1980 46 f black 0.00552 1980 47 f black 0.00602 1980 48 f black 0.00655 1980 49 f black 0.0071 1980 50 f black 0.00765 1980 51 f black 0.00821 1980 52 f black 0.00882 1980 53 f black 0.0095 1980 54 f black 0.01026 1980 55 f black 0.01107 1980 56 f black 0.01192 1980 57 f black 0.0128 1980 58 f black 0.01372 1980 59 f black 0.0147 1980 60 f black 0.01577 1980 61 f black 0.01695 1980 62 f black 0.01817 1980 63 f black 0.01936 1980 64 f black 0.0205 1980 65 f black 0.02158 1980 66 f black 0.02272 1980 67 f black 0.02408 1980 68 f black 0.02587 1980 69 f black 0.0281 1980 70 f black 0.03072 1980 71 f black 0.03354 1980 72 f black 0.03639 1980 73 f black 0.03899 1980 74 f black 0.04132 1980 75 f black 0.0436 1980 76 f black 0.04615 1980 77 f black 0.04909 1980 78 f black 0.05282 1980 79 f black 0.05754 1980 80 f black 0.0635 1980 81 f black 0.07041 1980 82 f black 0.07751 1980 83 f black 0.08335 1980 84 f black 0.08744 1980 85 f black 0.09106 1980 86 f black 0.09591 1980 87 f black 0.10168 1980 88 f black 0.10886 1980 89 f black 0.11738 1980 90 f black 0.12656 1980 91 f black 0.13619 1980 92 f black 0.14672 1980 93 f black 0.15816 1980 94 f black 0.17027 1980 95 f black 0.18279 1980 96 f black 0.1917 1980 97 f black 0.20022 1980 98 f black 0.20825 1980 99 f black 0.21577 1980 100 f black 0.22279 1980 101 f black 0.2293 1980 102 f black 0.23534 1980 103 f black 0.24091 1980 104 f black 0.24605 1980 105 f black 0.25077 1980 106 f black 0.2551 1980 107 f black 0.25907 1980 108 f black 0.26269 1980 109 f black 0.266 1990 0-1d m total 0.00381 1990 1-7d m total 0.00153 1990 7-28d m total 0.00116 1990 0 m total 0.01039 1990 1 m total 0.00078 1990 2 m total 0.00054 1990 3 m total 0.00042 1990 4 m total 0.00035 1990 5 m total 0.00031 1990 6 m total 0.00028 1990 7 m total 0.00026 1990 8 m total 0.00023 1990 9 m total 2e-04 1990 10 m total 0.00017 1990 11 m total 0.00017 1990 12 m total 0.00025 1990 13 m total 0.00042 1990 14 m total 0.00064 1990 15 m total 0.00089 1990 16 m total 0.00112 1990 17 m total 0.0013 1990 18 m total 0.00142 1990 19 m total 0.00148 1990 20 m total 0.00155 1990 21 m total 0.00161 1990 22 m total 0.00167 1990 23 m total 0.0017 1990 24 m total 0.00173 1990 25 m total 0.00174 1990 26 m total 0.00176 1990 27 m total 0.0018 1990 28 m total 0.00187 1990 29 m total 0.00196 1990 30 m total 0.00205 1990 31 m total 0.00215 1990 32 m total 0.00224 1990 33 m total 0.00234 1990 34 m total 0.00245 1990 35 m total 0.00257 1990 36 m total 0.0027 1990 37 m total 0.00282 1990 38 m total 0.00293 1990 39 m total 0.00304 1990 40 m total 0.00315 1990 41 m total 0.00328 1990 42 m total 0.00344 1990 43 m total 0.00365 1990 44 m total 0.0039 1990 45 m total 0.00421 1990 46 m total 0.00457 1990 47 m total 0.00496 1990 48 m total 0.00537 1990 49 m total 0.0058 1990 50 m total 0.0063 1990 51 m total 0.00689 1990 52 m total 0.00755 1990 53 m total 0.00828 1990 54 m total 0.00909 1990 55 m total 0.00995 1990 56 m total 0.01089 1990 57 m total 0.01197 1990 58 m total 0.0132 1990 59 m total 0.01455 1990 60 m total 0.01591 1990 61 m total 0.0173 1990 62 m total 0.01877 1990 63 m total 0.02039 1990 64 m total 0.02214 1990 65 m total 0.02397 1990 66 m total 0.02586 1990 67 m total 0.02793 1990 68 m total 0.0303 1990 69 m total 0.03301 1990 70 m total 0.03607 1990 71 m total 0.03945 1990 72 m total 0.0431 1990 73 m total 0.0469 1990 74 m total 0.05079 1990 75 m total 0.05492 1990 76 m total 0.05943 1990 77 m total 0.0643 1990 78 m total 0.06969 1990 79 m total 0.07576 1990 80 m total 0.08283 1990 81 m total 0.09078 1990 82 m total 0.09911 1990 83 m total 0.10718 1990 84 m total 0.11497 1990 85 m total 0.12378 1990 86 m total 0.13424 1990 87 m total 0.1456 1990 88 m total 0.1577 1990 89 m total 0.17058 1990 90 m total 0.1846 1990 91 m total 0.19998 1990 92 m total 0.21596 1990 93 m total 0.23158 1990 94 m total 0.24618 1990 95 m total 0.26004 1990 96 m total 0.27536 1990 97 m total 0.28943 1990 98 m total 0.3039 1990 99 m total 0.3191 1990 100 m total 0.33505 1990 101 m total 0.35181 1990 102 m total 0.3694 1990 103 m total 0.38787 1990 104 m total 0.40726 1990 105 m total 0.42762 1990 106 m total 0.449 1990 107 m total 0.47145 1990 108 m total 0.49503 1990 109 m total 0.51978 1990 0-1d f total 0.00318 1990 1-7d f total 0.00116 1990 7-28d f total 0.00092 1990 0 f total 0.00828 1990 1 f total 0.00068 1990 2 f total 0.00042 1990 3 f total 0.00032 1990 4 f total 0.00025 1990 5 f total 0.00024 1990 6 f total 0.00021 1990 7 f total 0.00019 1990 8 f total 0.00017 1990 9 f total 0.00016 1990 10 f total 0.00015 1990 11 f total 0.00015 1990 12 f total 0.00018 1990 13 f total 0.00022 1990 14 f total 0.00028 1990 15 f total 0.00035 1990 16 f total 0.00041 1990 17 f total 0.00046 1990 18 f total 0.00049 1990 19 f total 5e-04 1990 20 f total 0.00052 1990 21 f total 0.00054 1990 22 f total 0.00056 1990 23 f total 0.00057 1990 24 f total 0.00058 1990 25 f total 0.00059 1990 26 f total 6e-04 1990 27 f total 0.00062 1990 28 f total 0.00066 1990 29 f total 7e-04 1990 30 f total 0.00075 1990 31 f total 8e-04 1990 32 f total 0.00085 1990 33 f total 9e-04 1990 34 f total 0.00095 1990 35 f total 0.00101 1990 36 f total 0.00107 1990 37 f total 0.00115 1990 38 f total 0.00123 1990 39 f total 0.00132 1990 40 f total 0.00142 1990 41 f total 0.00153 1990 42 f total 0.00166 1990 43 f total 0.0018 1990 44 f total 0.00198 1990 45 f total 0.00218 1990 46 f total 0.00242 1990 47 f total 0.00268 1990 48 f total 0.00295 1990 49 f total 0.00324 1990 50 f total 0.00356 1990 51 f total 0.00394 1990 52 f total 0.00434 1990 53 f total 0.00476 1990 54 f total 0.0052 1990 55 f total 0.00566 1990 56 f total 0.00618 1990 57 f total 0.00677 1990 58 f total 0.00745 1990 59 f total 0.00819 1990 60 f total 0.00895 1990 61 f total 0.00972 1990 62 f total 0.01055 1990 63 f total 0.01146 1990 64 f total 0.01244 1990 65 f total 0.01348 1990 66 f total 0.01456 1990 67 f total 0.01574 1990 68 f total 0.01709 1990 69 f total 0.01865 1990 70 f total 0.02042 1990 71 f total 0.02239 1990 72 f total 0.02457 1990 73 f total 0.02688 1990 74 f total 0.0293 1990 75 f total 0.03181 1990 76 f total 0.03456 1990 77 f total 0.03772 1990 78 f total 0.04151 1990 79 f total 0.04599 1990 80 f total 0.05106 1990 81 f total 0.05659 1990 82 f total 0.06265 1990 83 f total 0.06919 1990 84 f total 0.07631 1990 85 f total 0.08446 1990 86 f total 0.09376 1990 87 f total 0.10379 1990 88 f total 0.11442 1990 89 f total 0.1259 1990 90 f total 0.13918 1990 91 f total 0.15417 1990 92 f total 0.16951 1990 93 f total 0.1844 1990 94 f total 0.19922 1990 95 f total 0.21475 1990 96 f total 0.23143 1990 97 f total 0.24775 1990 98 f total 0.26375 1990 99 f total 0.27957 1990 100 f total 0.29635 1990 101 f total 0.31413 1990 102 f total 0.33298 1990 103 f total 0.35296 1990 104 f total 0.37413 1990 105 f total 0.39658 1990 106 f total 0.42038 1990 107 f total 0.4456 1990 108 f total 0.47233 1990 109 f total 0.50068 1990 0-1d m white 0.00302 1990 1-7d m white 0.00134 1990 7-28d m white 0.001 1990 0 m white 0.00862 1990 1 m white 0.00066 1990 2 m white 0.00049 1990 3 m white 0.00037 1990 4 m white 0.00032 1990 5 m white 0.00028 1990 6 m white 0.00026 1990 7 m white 0.00024 1990 8 m white 0.00022 1990 9 m white 0.00019 1990 10 m white 0.00016 1990 11 m white 0.00017 1990 12 m white 0.00024 1990 13 m white 0.00039 1990 14 m white 0.00059 1990 15 m white 0.00081 1990 16 m white 0.00102 1990 17 m white 0.00118 1990 18 m white 0.00127 1990 19 m white 0.00132 1990 20 m white 0.00136 1990 21 m white 0.00141 1990 22 m white 0.00145 1990 23 m white 0.00148 1990 24 m white 0.0015 1990 25 m white 0.00151 1990 26 m white 0.00153 1990 27 m white 0.00156 1990 28 m white 0.00162 1990 29 m white 0.00169 1990 30 m white 0.00177 1990 31 m white 0.00185 1990 32 m white 0.00193 1990 33 m white 0.00201 1990 34 m white 0.0021 1990 35 m white 0.00219 1990 36 m white 0.0023 1990 37 m white 0.0024 1990 38 m white 0.0025 1990 39 m white 0.0026 1990 40 m white 0.00271 1990 41 m white 0.00283 1990 42 m white 0.00298 1990 43 m white 0.00317 1990 44 m white 0.00341 1990 45 m white 0.0037 1990 46 m white 0.00404 1990 47 m white 0.00441 1990 48 m white 0.00479 1990 49 m white 0.00518 1990 50 m white 0.00564 1990 51 m white 0.0062 1990 52 m white 0.00683 1990 53 m white 0.00753 1990 54 m white 0.00831 1990 55 m white 0.00913 1990 56 m white 0.01004 1990 57 m white 0.01109 1990 58 m white 0.01231 1990 59 m white 0.01366 1990 60 m white 0.01503 1990 61 m white 0.01641 1990 62 m white 0.01788 1990 63 m white 0.01947 1990 64 m white 0.02118 1990 65 m white 0.02297 1990 66 m white 0.02483 1990 67 m white 0.02689 1990 68 m white 0.02926 1990 69 m white 0.032 1990 70 m white 0.03509 1990 71 m white 0.03848 1990 72 m white 0.04215 1990 73 m white 0.04598 1990 74 m white 0.04993 1990 75 m white 0.05414 1990 76 m white 0.05875 1990 77 m white 0.06372 1990 78 m white 0.0692 1990 79 m white 0.07533 1990 80 m white 0.08246 1990 81 m white 0.09049 1990 82 m white 0.09891 1990 83 m white 0.10715 1990 84 m white 0.11519 1990 85 m white 0.12436 1990 86 m white 0.13522 1990 87 m white 0.14695 1990 88 m white 0.15927 1990 89 m white 0.17219 1990 90 m white 0.18617 1990 91 m white 0.20159 1990 92 m white 0.21773 1990 93 m white 0.23376 1990 94 m white 0.24893 1990 95 m white 0.26329 1990 96 m white 0.27914 1990 97 m white 0.29399 1990 98 m white 0.30869 1990 99 m white 0.32413 1990 100 m white 0.34033 1990 101 m white 0.35735 1990 102 m white 0.37522 1990 103 m white 0.39398 1990 104 m white 0.41368 1990 105 m white 0.43436 1990 106 m white 0.45608 1990 107 m white 0.47888 1990 108 m white 0.50282 1990 109 m white 0.52797 1990 0-1d f white 0.00249 1990 1-7d f white 0.00101 1990 7-28d f white 0.00077 1990 0 f white 0.00667 1990 1 f white 0.00059 1990 2 f white 0.00037 1990 3 f white 0.00029 1990 4 f white 0.00023 1990 5 f white 0.00021 1990 6 f white 0.00019 1990 7 f white 0.00017 1990 8 f white 0.00016 1990 9 f white 0.00015 1990 10 f white 0.00014 1990 11 f white 0.00014 1990 12 f white 0.00017 1990 13 f white 0.00021 1990 14 f white 0.00027 1990 15 f white 0.00034 1990 16 f white 4e-04 1990 17 f white 0.00045 1990 18 f white 0.00047 1990 19 f white 0.00048 1990 20 f white 0.00049 1990 21 f white 5e-04 1990 22 f white 0.00051 1990 23 f white 0.00051 1990 24 f white 0.00051 1990 25 f white 0.00051 1990 26 f white 0.00051 1990 27 f white 0.00053 1990 28 f white 0.00055 1990 29 f white 0.00058 1990 30 f white 0.00062 1990 31 f white 0.00066 1990 32 f white 7e-04 1990 33 f white 0.00074 1990 34 f white 0.00078 1990 35 f white 0.00082 1990 36 f white 0.00088 1990 37 f white 0.00094 1990 38 f white 0.00102 1990 39 f white 0.00111 1990 40 f white 0.00121 1990 41 f white 0.00131 1990 42 f white 0.00143 1990 43 f white 0.00157 1990 44 f white 0.00173 1990 45 f white 0.00193 1990 46 f white 0.00215 1990 47 f white 0.0024 1990 48 f white 0.00265 1990 49 f white 0.00291 1990 50 f white 0.00321 1990 51 f white 0.00356 1990 52 f white 0.00394 1990 53 f white 0.00434 1990 54 f white 0.00476 1990 55 f white 0.00521 1990 56 f white 0.00571 1990 57 f white 0.00628 1990 58 f white 0.00693 1990 59 f white 0.00764 1990 60 f white 0.00837 1990 61 f white 0.00912 1990 62 f white 0.00993 1990 63 f white 0.01081 1990 64 f white 0.01177 1990 65 f white 0.01278 1990 66 f white 0.01383 1990 67 f white 0.015 1990 68 f white 0.01634 1990 69 f white 0.01791 1990 70 f white 0.01969 1990 71 f white 0.02168 1990 72 f white 0.02386 1990 73 f white 0.02618 1990 74 f white 0.0286 1990 75 f white 0.03111 1990 76 f white 0.03387 1990 77 f white 0.03707 1990 78 f white 0.0409 1990 79 f white 0.04542 1990 80 f white 0.05053 1990 81 f white 0.05606 1990 82 f white 0.06215 1990 83 f white 0.06878 1990 84 f white 0.07607 1990 85 f white 0.08445 1990 86 f white 0.09402 1990 87 f white 0.10431 1990 88 f white 0.11512 1990 89 f white 0.12673 1990 90 f white 0.14015 1990 91 f white 0.15536 1990 92 f white 0.17101 1990 93 f white 0.18626 1990 94 f white 0.20148 1990 95 f white 0.21737 1990 96 f white 0.23434 1990 97 f white 0.25091 1990 98 f white 0.26715 1990 99 f white 0.28318 1990 100 f white 0.30017 1990 101 f white 0.31818 1990 102 f white 0.33727 1990 103 f white 0.3575 1990 104 f white 0.37895 1990 105 f white 0.40169 1990 106 f white 0.42579 1990 107 f white 0.45134 1990 108 f white 0.47842 1990 109 f white 0.50712 1990 0-1d m nonwhite 0.00681 1990 1-7d m nonwhite 0.00227 1990 7-28d m nonwhite 0.00176 1990 0 m nonwhite 0.01712 1990 1 m nonwhite 0.00121 1990 2 m nonwhite 0.00077 1990 3 m nonwhite 0.00063 1990 4 m nonwhite 0.00048 1990 5 m nonwhite 0.00042 1990 6 m nonwhite 0.00038 1990 7 m nonwhite 0.00034 1990 8 m nonwhite 3e-04 1990 9 m nonwhite 0.00024 1990 10 m nonwhite 2e-04 1990 11 m nonwhite 2e-04 1990 12 m nonwhite 0.00031 1990 13 m nonwhite 0.00055 1990 14 m nonwhite 0.00087 1990 15 m nonwhite 0.00121 1990 16 m nonwhite 0.00153 1990 17 m nonwhite 0.0018 1990 18 m nonwhite 0.00201 1990 19 m nonwhite 0.00217 1990 20 m nonwhite 0.00234 1990 21 m nonwhite 0.00252 1990 22 m nonwhite 0.00267 1990 23 m nonwhite 0.00276 1990 24 m nonwhite 0.00283 1990 25 m nonwhite 0.00287 1990 26 m nonwhite 0.00292 1990 27 m nonwhite 0.00301 1990 28 m nonwhite 0.00315 1990 29 m nonwhite 0.00333 1990 30 m nonwhite 0.00351 1990 31 m nonwhite 0.00369 1990 32 m nonwhite 0.00389 1990 33 m nonwhite 0.00411 1990 34 m nonwhite 0.00435 1990 35 m nonwhite 0.00462 1990 36 m nonwhite 0.00489 1990 37 m nonwhite 0.00516 1990 38 m nonwhite 0.00538 1990 39 m nonwhite 0.00558 1990 40 m nonwhite 0.00579 1990 41 m nonwhite 0.00603 1990 42 m nonwhite 0.00631 1990 43 m nonwhite 0.00665 1990 44 m nonwhite 0.00705 1990 45 m nonwhite 0.00752 1990 46 m nonwhite 0.00805 1990 47 m nonwhite 0.00864 1990 48 m nonwhite 0.00926 1990 49 m nonwhite 0.00991 1990 50 m nonwhite 0.01061 1990 51 m nonwhite 0.01138 1990 52 m nonwhite 0.01225 1990 53 m nonwhite 0.01326 1990 54 m nonwhite 0.01441 1990 55 m nonwhite 0.01566 1990 56 m nonwhite 0.01698 1990 57 m nonwhite 0.01838 1990 58 m nonwhite 0.01984 1990 59 m nonwhite 0.02134 1990 60 m nonwhite 0.02284 1990 61 m nonwhite 0.0244 1990 62 m nonwhite 0.02613 1990 63 m nonwhite 0.02809 1990 64 m nonwhite 0.03025 1990 65 m nonwhite 0.0325 1990 66 m nonwhite 0.03475 1990 67 m nonwhite 0.03706 1990 68 m nonwhite 0.0395 1990 69 m nonwhite 0.04218 1990 70 m nonwhite 0.04524 1990 71 m nonwhite 0.04867 1990 72 m nonwhite 0.0523 1990 73 m nonwhite 0.05586 1990 74 m nonwhite 0.05921 1990 75 m nonwhite 0.06251 1990 76 m nonwhite 0.06603 1990 77 m nonwhite 0.06988 1990 78 m nonwhite 0.07444 1990 79 m nonwhite 0.07989 1990 80 m nonwhite 0.08644 1990 81 m nonwhite 0.0937 1990 82 m nonwhite 0.10106 1990 83 m nonwhite 0.10749 1990 84 m nonwhite 0.11273 1990 85 m nonwhite 0.11827 1990 86 m nonwhite 0.12507 1990 87 m nonwhite 0.13318 1990 88 m nonwhite 0.14333 1990 89 m nonwhite 0.1556 1990 90 m nonwhite 0.16977 1990 91 m nonwhite 0.18502 1990 92 m nonwhite 0.19999 1990 93 m nonwhite 0.21198 1990 94 m nonwhite 0.22061 1990 95 m nonwhite 0.22903 1990 96 m nonwhite 0.24048 1990 97 m nonwhite 0.2525 1990 98 m nonwhite 0.26513 1990 99 m nonwhite 0.27838 1990 100 m nonwhite 0.2923 1990 101 m nonwhite 0.30692 1990 102 m nonwhite 0.32226 1990 103 m nonwhite 0.33837 1990 104 m nonwhite 0.35529 1990 105 m nonwhite 0.37306 1990 106 m nonwhite 0.39171 1990 107 m nonwhite 0.4113 1990 108 m nonwhite 0.43186 1990 109 m nonwhite 0.45345 1990 0-1d f nonwhite 0.00575 1990 1-7d f nonwhite 0.00174 1990 7-28d f nonwhite 0.00148 1990 0 f nonwhite 0.01428 1990 1 f nonwhite 0.00103 1990 2 f nonwhite 0.00062 1990 3 f nonwhite 0.00047 1990 4 f nonwhite 0.00035 1990 5 f nonwhite 0.00034 1990 6 f nonwhite 0.00029 1990 7 f nonwhite 0.00025 1990 8 f nonwhite 0.00022 1990 9 f nonwhite 2e-04 1990 10 f nonwhite 0.00019 1990 11 f nonwhite 2e-04 1990 12 f nonwhite 0.00022 1990 13 f nonwhite 0.00026 1990 14 f nonwhite 0.00031 1990 15 f nonwhite 0.00037 1990 16 f nonwhite 0.00043 1990 17 f nonwhite 0.00049 1990 18 f nonwhite 0.00055 1990 19 f nonwhite 0.00059 1990 20 f nonwhite 0.00065 1990 21 f nonwhite 7e-04 1990 22 f nonwhite 0.00076 1990 23 f nonwhite 0.00082 1990 24 f nonwhite 0.00088 1990 25 f nonwhite 0.00094 1990 26 f nonwhite 0.001 1990 27 f nonwhite 0.00107 1990 28 f nonwhite 0.00116 1990 29 f nonwhite 0.00126 1990 30 f nonwhite 0.00137 1990 31 f nonwhite 0.00147 1990 32 f nonwhite 0.00157 1990 33 f nonwhite 0.00167 1990 34 f nonwhite 0.00178 1990 35 f nonwhite 0.00189 1990 36 f nonwhite 0.002 1990 37 f nonwhite 0.00213 1990 38 f nonwhite 0.00226 1990 39 f nonwhite 0.00239 1990 40 f nonwhite 0.00254 1990 41 f nonwhite 0.00271 1990 42 f nonwhite 0.00289 1990 43 f nonwhite 0.0031 1990 44 f nonwhite 0.00335 1990 45 f nonwhite 0.00363 1990 46 f nonwhite 0.00396 1990 47 f nonwhite 0.00433 1990 48 f nonwhite 0.00473 1990 49 f nonwhite 0.00515 1990 50 f nonwhite 0.00561 1990 51 f nonwhite 0.00612 1990 52 f nonwhite 0.00665 1990 53 f nonwhite 0.00721 1990 54 f nonwhite 0.00781 1990 55 f nonwhite 0.00843 1990 56 f nonwhite 0.0091 1990 57 f nonwhite 0.00987 1990 58 f nonwhite 0.01077 1990 59 f nonwhite 0.01176 1990 60 f nonwhite 0.01278 1990 61 f nonwhite 0.01381 1990 62 f nonwhite 0.01491 1990 63 f nonwhite 0.0161 1990 64 f nonwhite 0.0174 1990 65 f nonwhite 0.01877 1990 66 f nonwhite 0.02018 1990 67 f nonwhite 0.02162 1990 68 f nonwhite 0.02312 1990 69 f nonwhite 0.02473 1990 70 f nonwhite 0.0265 1990 71 f nonwhite 0.02851 1990 72 f nonwhite 0.03075 1990 73 f nonwhite 0.03315 1990 74 f nonwhite 0.03564 1990 75 f nonwhite 0.03817 1990 76 f nonwhite 0.04082 1990 77 f nonwhite 0.04377 1990 78 f nonwhite 0.04726 1990 79 f nonwhite 0.05146 1990 80 f nonwhite 0.05647 1990 81 f nonwhite 0.06209 1990 82 f nonwhite 0.06803 1990 83 f nonwhite 0.0737 1990 84 f nonwhite 0.07896 1990 85 f nonwhite 0.08452 1990 86 f nonwhite 0.09105 1990 87 f nonwhite 0.09831 1990 88 f nonwhite 0.10667 1990 89 f nonwhite 0.11633 1990 90 f nonwhite 0.12752 1990 91 f nonwhite 0.13979 1990 92 f nonwhite 0.15196 1990 93 f nonwhite 0.16268 1990 94 f nonwhite 0.17245 1990 95 f nonwhite 0.18338 1990 96 f nonwhite 0.19682 1990 97 f nonwhite 0.21089 1990 98 f nonwhite 0.22557 1990 99 f nonwhite 0.23911 1990 100 f nonwhite 0.25346 1990 101 f nonwhite 0.26866 1990 102 f nonwhite 0.28478 1990 103 f nonwhite 0.30187 1990 104 f nonwhite 0.31998 1990 105 f nonwhite 0.33918 1990 106 f nonwhite 0.35953 1990 107 f nonwhite 0.3811 1990 108 f nonwhite 0.40397 1990 109 f nonwhite 0.42821 1990 0-1d m black 0.00811 1990 1-7d m black 0.00263 1990 7-28d m black 0.00201 1990 0 m black 0.01977 1990 1 m black 0.00134 1990 2 m black 0.00085 1990 3 m black 0.00069 1990 4 m black 0.00054 1990 5 m black 0.00048 1990 6 m black 0.00043 1990 7 m black 0.00039 1990 8 m black 0.00034 1990 9 m black 0.00027 1990 10 m black 0.00022 1990 11 m black 0.00023 1990 12 m black 0.00035 1990 13 m black 0.00062 1990 14 m black 0.00097 1990 15 m black 0.00137 1990 16 m black 0.00173 1990 17 m black 0.00205 1990 18 m black 0.00231 1990 19 m black 0.00252 1990 20 m black 0.00274 1990 21 m black 0.00298 1990 22 m black 0.00317 1990 23 m black 0.0033 1990 24 m black 0.00338 1990 25 m black 0.00344 1990 26 m black 0.00351 1990 27 m black 0.00363 1990 28 m black 0.00382 1990 29 m black 0.00407 1990 30 m black 0.00433 1990 31 m black 0.00458 1990 32 m black 0.00485 1990 33 m black 0.00513 1990 34 m black 0.00544 1990 35 m black 0.00577 1990 36 m black 0.00612 1990 37 m black 0.00645 1990 38 m black 0.00675 1990 39 m black 0.00702 1990 40 m black 0.0073 1990 41 m black 0.00762 1990 42 m black 0.00799 1990 43 m black 0.00841 1990 44 m black 0.0089 1990 45 m black 0.00946 1990 46 m black 0.0101 1990 47 m black 0.01081 1990 48 m black 0.01155 1990 49 m black 0.01232 1990 50 m black 0.01314 1990 51 m black 0.01404 1990 52 m black 0.01504 1990 53 m black 0.01619 1990 54 m black 0.01748 1990 55 m black 0.01885 1990 56 m black 0.02029 1990 57 m black 0.02181 1990 58 m black 0.0234 1990 59 m black 0.02506 1990 60 m black 0.02672 1990 61 m black 0.02842 1990 62 m black 0.03033 1990 63 m black 0.0325 1990 64 m black 0.03489 1990 65 m black 0.03739 1990 66 m black 0.03989 1990 67 m black 0.04244 1990 68 m black 0.04511 1990 69 m black 0.04801 1990 70 m black 0.05131 1990 71 m black 0.055 1990 72 m black 0.05885 1990 73 m black 0.06255 1990 74 m black 0.06599 1990 75 m black 0.06931 1990 76 m black 0.07285 1990 77 m black 0.07675 1990 78 m black 0.08145 1990 79 m black 0.08713 1990 80 m black 0.09403 1990 81 m black 0.10169 1990 82 m black 0.10937 1990 83 m black 0.11578 1990 84 m black 0.12062 1990 85 m black 0.12515 1990 86 m black 0.13086 1990 87 m black 0.13796 1990 88 m black 0.14736 1990 89 m black 0.15912 1990 90 m black 0.17285 1990 91 m black 0.18751 1990 92 m black 0.20162 1990 93 m black 0.21224 1990 94 m black 0.21915 1990 95 m black 0.22659 1990 96 m black 0.23792 1990 97 m black 0.24982 1990 98 m black 0.26231 1990 99 m black 0.27542 1990 100 m black 0.2892 1990 101 m black 0.30365 1990 102 m black 0.31884 1990 103 m black 0.33478 1990 104 m black 0.35152 1990 105 m black 0.36909 1990 106 m black 0.38755 1990 107 m black 0.40693 1990 108 m black 0.42727 1990 109 m black 0.44864 1990 0-1d f black 0.00675 1990 1-7d f black 0.002 1990 7-28d f black 0.00169 1990 0 f black 0.01644 1990 1 f black 0.00113 1990 2 f black 0.00069 1990 3 f black 0.00051 1990 4 f black 4e-04 1990 5 f black 0.00037 1990 6 f black 0.00032 1990 7 f black 0.00027 1990 8 f black 0.00024 1990 9 f black 0.00023 1990 10 f black 0.00022 1990 11 f black 0.00023 1990 12 f black 0.00025 1990 13 f black 0.00028 1990 14 f black 0.00033 1990 15 f black 0.00039 1990 16 f black 0.00045 1990 17 f black 0.00051 1990 18 f black 0.00058 1990 19 f black 0.00064 1990 20 f black 0.00072 1990 21 f black 8e-04 1990 22 f black 0.00088 1990 23 f black 0.00096 1990 24 f black 0.00103 1990 25 f black 0.0011 1990 26 f black 0.00118 1990 27 f black 0.00127 1990 28 f black 0.00138 1990 29 f black 0.00151 1990 30 f black 0.00165 1990 31 f black 0.00178 1990 32 f black 0.00191 1990 33 f black 0.00203 1990 34 f black 0.00216 1990 35 f black 0.00229 1990 36 f black 0.00243 1990 37 f black 0.00259 1990 38 f black 0.00275 1990 39 f black 0.00293 1990 40 f black 0.00313 1990 41 f black 0.00335 1990 42 f black 0.00359 1990 43 f black 0.00384 1990 44 f black 0.00411 1990 45 f black 0.00442 1990 46 f black 0.00478 1990 47 f black 0.00519 1990 48 f black 0.00564 1990 49 f black 0.00612 1990 50 f black 0.00664 1990 51 f black 0.00721 1990 52 f black 0.00781 1990 53 f black 0.00843 1990 54 f black 0.0091 1990 55 f black 0.00979 1990 56 f black 0.01054 1990 57 f black 0.01142 1990 58 f black 0.01247 1990 59 f black 0.01363 1990 60 f black 0.01482 1990 61 f black 0.01602 1990 62 f black 0.01727 1990 63 f black 0.01859 1990 64 f black 0.01997 1990 65 f black 0.02142 1990 66 f black 0.02291 1990 67 f black 0.02442 1990 68 f black 0.02601 1990 69 f black 0.02774 1990 70 f black 0.02965 1990 71 f black 0.03177 1990 72 f black 0.03411 1990 73 f black 0.03656 1990 74 f black 0.03904 1990 75 f black 0.04152 1990 76 f black 0.04412 1990 77 f black 0.04705 1990 78 f black 0.05061 1990 79 f black 0.05492 1990 80 f black 0.06008 1990 81 f black 0.06581 1990 82 f black 0.07179 1990 83 f black 0.07744 1990 84 f black 0.08264 1990 85 f black 0.08797 1990 86 f black 0.09428 1990 87 f black 0.10129 1990 88 f black 0.10933 1990 89 f black 0.1186 1990 90 f black 0.12942 1990 91 f black 0.14138 1990 92 f black 0.15318 1990 93 f black 0.16333 1990 94 f black 0.17232 1990 95 f black 0.18244 1990 96 f black 0.19556 1990 97 f black 0.20946 1990 98 f black 0.22414 1990 99 f black 0.23758 1990 100 f black 0.25184 1990 101 f black 0.26695 1990 102 f black 0.28297 1990 103 f black 0.29994 1990 104 f black 0.31794 1990 105 f black 0.33702 1990 106 f black 0.35724 1990 107 f black 0.37867 1990 108 f black 0.40139 1990 109 f black 0.42548 2000 0-1d m total 0.00298 2000 1-7d m total 0.00106 2000 7-28d m total 0.00102 2000 0 m total 0.00763 2000 1 m total 0.00055 2000 2 m total 0.00038 2000 3 m total 0.00029 2000 4 m total 0.00023 2000 5 m total 0.00021 2000 6 m total 0.00019 2000 7 m total 0.00018 2000 8 m total 0.00016 2000 9 m total 0.00014 2000 10 m total 0.00012 2000 11 m total 0.00012 2000 12 m total 0.00018 2000 13 m total 3e-04 2000 14 m total 0.00047 2000 15 m total 0.00065 2000 16 m total 0.00082 2000 17 m total 0.00097 2000 18 m total 0.00109 2000 19 m total 0.00118 2000 20 m total 0.00128 2000 21 m total 0.00138 2000 22 m total 0.00143 2000 23 m total 0.00143 2000 24 m total 0.00139 2000 25 m total 0.00133 2000 26 m total 0.00129 2000 27 m total 0.00127 2000 28 m total 0.00128 2000 29 m total 0.00132 2000 30 m total 0.00136 2000 31 m total 0.00142 2000 32 m total 0.00149 2000 33 m total 0.00158 2000 34 m total 0.00168 2000 35 m total 0.0018 2000 36 m total 0.00192 2000 37 m total 0.00206 2000 38 m total 0.00222 2000 39 m total 0.0024 2000 40 m total 0.00259 2000 41 m total 0.0028 2000 42 m total 0.00303 2000 43 m total 0.00329 2000 44 m total 0.00357 2000 45 m total 0.00388 2000 46 m total 0.00422 2000 47 m total 0.00457 2000 48 m total 0.0049 2000 49 m total 0.00522 2000 50 m total 0.00556 2000 51 m total 0.00593 2000 52 m total 0.00636 2000 53 m total 0.00688 2000 54 m total 0.00749 2000 55 m total 0.00823 2000 56 m total 0.00905 2000 57 m total 0.00994 2000 58 m total 0.01086 2000 59 m total 0.01179 2000 60 m total 0.01282 2000 61 m total 0.014 2000 62 m total 0.01529 2000 63 m total 0.01667 2000 64 m total 0.01816 2000 65 m total 0.01971 2000 66 m total 0.0213 2000 67 m total 0.02316 2000 68 m total 0.02531 2000 69 m total 0.02771 2000 70 m total 0.03026 2000 71 m total 0.03302 2000 72 m total 0.03613 2000 73 m total 0.03966 2000 74 m total 0.04359 2000 75 m total 0.04792 2000 76 m total 0.05255 2000 77 m total 0.05761 2000 78 m total 0.06312 2000 79 m total 0.06912 2000 80 m total 0.07564 2000 81 m total 0.08272 2000 82 m total 0.0904 2000 83 m total 0.09872 2000 84 m total 0.10771 2000 85 m total 0.11742 2000 86 m total 0.12787 2000 87 m total 0.13911 2000 88 m total 0.15117 2000 89 m total 0.16407 2000 90 m total 0.17784 2000 91 m total 0.1925 2000 92 m total 0.20806 2000 93 m total 0.22454 2000 94 m total 0.24191 2000 95 m total 0.26019 2000 96 m total 0.27933 2000 97 m total 0.29931 2000 98 m total 0.32009 2000 99 m total 0.3416 2000 100 m total 0.36379 2000 101 m total 0.38657 2000 102 m total 0.40986 2000 103 m total 0.43356 2000 104 m total 0.45757 2000 105 m total 0.48178 2000 106 m total 0.50607 2000 107 m total 0.53034 2000 108 m total 0.55446 2000 109 m total 0.57833 2000 0-1d f total 0.00252 2000 1-7d f total 0.00081 2000 7-28d f total 0.00088 2000 0 f total 0.00626 2000 1 f total 0.00046 2000 2 f total 0.00028 2000 3 f total 0.00023 2000 4 f total 0.00019 2000 5 f total 0.00017 2000 6 f total 0.00015 2000 7 f total 0.00014 2000 8 f total 0.00013 2000 9 f total 0.00012 2000 10 f total 0.00011 2000 11 f total 0.00012 2000 12 f total 0.00014 2000 13 f total 0.00018 2000 14 f total 0.00024 2000 15 f total 0.00031 2000 16 f total 0.00037 2000 17 f total 0.00042 2000 18 f total 0.00044 2000 19 f total 0.00045 2000 20 f total 0.00045 2000 21 f total 0.00046 2000 22 f total 0.00047 2000 23 f total 0.00048 2000 24 f total 0.00049 2000 25 f total 5e-04 2000 26 f total 0.00051 2000 27 f total 0.00053 2000 28 f total 0.00056 2000 29 f total 0.00059 2000 30 f total 0.00063 2000 31 f total 0.00068 2000 32 f total 0.00073 2000 33 f total 8e-04 2000 34 f total 0.00088 2000 35 f total 0.00096 2000 36 f total 0.00104 2000 37 f total 0.00113 2000 38 f total 0.00124 2000 39 f total 0.00135 2000 40 f total 0.00147 2000 41 f total 0.0016 2000 42 f total 0.00174 2000 43 f total 0.00187 2000 44 f total 0.00201 2000 45 f total 0.00216 2000 46 f total 0.00233 2000 47 f total 0.00252 2000 48 f total 0.00273 2000 49 f total 0.00297 2000 50 f total 0.00322 2000 51 f total 0.00349 2000 52 f total 0.00379 2000 53 f total 0.00414 2000 54 f total 0.00454 2000 55 f total 0.00501 2000 56 f total 0.00554 2000 57 f total 0.00612 2000 58 f total 0.00672 2000 59 f total 0.00734 2000 60 f total 0.00804 2000 61 f total 0.00883 2000 62 f total 0.00969 2000 63 f total 0.01059 2000 64 f total 0.01154 2000 65 f total 0.01256 2000 66 f total 0.01353 2000 67 f total 0.01464 2000 68 f total 0.01593 2000 69 f total 0.01739 2000 70 f total 0.01898 2000 71 f total 0.02079 2000 72 f total 0.02292 2000 73 f total 0.0254 2000 74 f total 0.02822 2000 75 f total 0.03137 2000 76 f total 0.03479 2000 77 f total 0.03857 2000 78 f total 0.04274 2000 79 f total 0.04733 2000 80 f total 0.0524 2000 81 f total 0.05797 2000 82 f total 0.06409 2000 83 f total 0.07082 2000 84 f total 0.07819 2000 85 f total 0.08625 2000 86 f total 0.09507 2000 87 f total 0.10468 2000 88 f total 0.11513 2000 89 f total 0.12649 2000 90 f total 0.13878 2000 91 f total 0.15207 2000 92 f total 0.16638 2000 93 f total 0.18175 2000 94 f total 0.19821 2000 95 f total 0.21575 2000 96 f total 0.2344 2000 97 f total 0.25414 2000 98 f total 0.27494 2000 99 f total 0.29677 2000 100 f total 0.31957 2000 101 f total 0.34326 2000 102 f total 0.36777 2000 103 f total 0.39297 2000 104 f total 0.41876 2000 105 f total 0.445 2000 106 f total 0.47154 2000 107 f total 0.49826 2000 108 f total 0.52498 2000 109 f total 0.55156 2000 0-1d m white 0.00236 2000 1-7d m white 0.00094 2000 7-28d m white 0.00087 2000 0 m white 0.00628 2000 1 m white 0.00048 2000 2 m white 0.00035 2000 3 m white 0.00026 2000 4 m white 0.00021 2000 5 m white 0.00019 2000 6 m white 0.00018 2000 7 m white 0.00017 2000 8 m white 0.00015 2000 9 m white 0.00013 2000 10 m white 0.00011 2000 11 m white 0.00011 2000 12 m white 0.00017 2000 13 m white 0.00028 2000 14 m white 0.00044 2000 15 m white 0.00062 2000 16 m white 0.00078 2000 17 m white 0.00091 2000 18 m white 0.00102 2000 19 m white 0.00109 2000 20 m white 0.00117 2000 21 m white 0.00125 2000 22 m white 0.00129 2000 23 m white 0.00128 2000 24 m white 0.00124 2000 25 m white 0.00119 2000 26 m white 0.00115 2000 27 m white 0.00113 2000 28 m white 0.00114 2000 29 m white 0.00118 2000 30 m white 0.00123 2000 31 m white 0.00128 2000 32 m white 0.00134 2000 33 m white 0.00143 2000 34 m white 0.00153 2000 35 m white 0.00164 2000 36 m white 0.00175 2000 37 m white 0.00188 2000 38 m white 0.00203 2000 39 m white 0.00219 2000 40 m white 0.00237 2000 41 m white 0.00256 2000 42 m white 0.00277 2000 43 m white 0.003 2000 44 m white 0.00325 2000 45 m white 0.00353 2000 46 m white 0.00383 2000 47 m white 0.00414 2000 48 m white 0.00445 2000 49 m white 0.00475 2000 50 m white 0.00507 2000 51 m white 0.00542 2000 52 m white 0.00583 2000 53 m white 0.00632 2000 54 m white 0.00692 2000 55 m white 0.00762 2000 56 m white 0.00842 2000 57 m white 0.00928 2000 58 m white 0.01017 2000 59 m white 0.01109 2000 60 m white 0.01212 2000 61 m white 0.01331 2000 62 m white 0.0146 2000 63 m white 0.01597 2000 64 m white 0.01743 2000 65 m white 0.01894 2000 66 m white 0.02051 2000 67 m white 0.02235 2000 68 m white 0.02449 2000 69 m white 0.02689 2000 70 m white 0.02941 2000 71 m white 0.03215 2000 72 m white 0.03525 2000 73 m white 0.03876 2000 74 m white 0.04267 2000 75 m white 0.047 2000 76 m white 0.05165 2000 77 m white 0.05674 2000 78 m white 0.0623 2000 79 m white 0.06837 2000 80 m white 0.07498 2000 81 m white 0.08217 2000 82 m white 0.08998 2000 83 m white 0.09846 2000 84 m white 0.10764 2000 85 m white 0.11756 2000 86 m white 0.12827 2000 87 m white 0.1398 2000 88 m white 0.15218 2000 89 m white 0.16545 2000 90 m white 0.17963 2000 91 m white 0.19475 2000 92 m white 0.21081 2000 93 m white 0.22782 2000 94 m white 0.24577 2000 95 m white 0.26465 2000 96 m white 0.28444 2000 97 m white 0.30509 2000 98 m white 0.32656 2000 99 m white 0.34878 2000 100 m white 0.37168 2000 101 m white 0.39517 2000 102 m white 0.41915 2000 103 m white 0.44352 2000 104 m white 0.46817 2000 105 m white 0.49297 2000 106 m white 0.51781 2000 107 m white 0.54256 2000 108 m white 0.5671 2000 109 m white 0.59132 2000 0-1d f white 0.00202 2000 1-7d f white 0.00071 2000 7-28d f white 0.00074 2000 0 f white 0.00513 2000 1 f white 0.00041 2000 2 f white 0.00025 2000 3 f white 2e-04 2000 4 f white 0.00017 2000 5 f white 0.00015 2000 6 f white 0.00014 2000 7 f white 0.00013 2000 8 f white 0.00012 2000 9 f white 0.00011 2000 10 f white 0.00011 2000 11 f white 0.00011 2000 12 f white 0.00013 2000 13 f white 0.00017 2000 14 f white 0.00024 2000 15 f white 0.00031 2000 16 f white 0.00037 2000 17 f white 0.00042 2000 18 f white 0.00044 2000 19 f white 0.00044 2000 20 f white 0.00043 2000 21 f white 0.00043 2000 22 f white 0.00043 2000 23 f white 0.00043 2000 24 f white 0.00044 2000 25 f white 0.00044 2000 26 f white 0.00045 2000 27 f white 0.00047 2000 28 f white 0.00049 2000 29 f white 0.00052 2000 30 f white 0.00055 2000 31 f white 0.00059 2000 32 f white 0.00064 2000 33 f white 7e-04 2000 34 f white 0.00077 2000 35 f white 0.00084 2000 36 f white 0.00091 2000 37 f white 0.00099 2000 38 f white 0.00108 2000 39 f white 0.00118 2000 40 f white 0.00129 2000 41 f white 0.0014 2000 42 f white 0.00152 2000 43 f white 0.00164 2000 44 f white 0.00176 2000 45 f white 0.00189 2000 46 f white 0.00205 2000 47 f white 0.00222 2000 48 f white 0.00243 2000 49 f white 0.00265 2000 50 f white 0.0029 2000 51 f white 0.00317 2000 52 f white 0.00346 2000 53 f white 0.0038 2000 54 f white 0.00418 2000 55 f white 0.00464 2000 56 f white 0.00516 2000 57 f white 0.00572 2000 58 f white 0.0063 2000 59 f white 0.00691 2000 60 f white 0.00759 2000 61 f white 0.00838 2000 62 f white 0.00922 2000 63 f white 0.0101 2000 64 f white 0.01102 2000 65 f white 0.012 2000 66 f white 0.01295 2000 67 f white 0.01406 2000 68 f white 0.01535 2000 69 f white 0.0168 2000 70 f white 0.01838 2000 71 f white 0.02018 2000 72 f white 0.0223 2000 73 f white 0.02475 2000 74 f white 0.02754 2000 75 f white 0.03068 2000 76 f white 0.03409 2000 77 f white 0.03787 2000 78 f white 0.04205 2000 79 f white 0.04667 2000 80 f white 0.05177 2000 81 f white 0.05739 2000 82 f white 0.06358 2000 83 f white 0.07039 2000 84 f white 0.07787 2000 85 f white 0.08607 2000 86 f white 0.09504 2000 87 f white 0.10484 2000 88 f white 0.11552 2000 89 f white 0.12714 2000 90 f white 0.13974 2000 91 f white 0.15336 2000 92 f white 0.16806 2000 93 f white 0.18386 2000 94 f white 0.20079 2000 95 f white 0.21886 2000 96 f white 0.23807 2000 97 f white 0.25841 2000 98 f white 0.27985 2000 99 f white 0.30234 2000 100 f white 0.32582 2000 101 f white 0.35021 2000 102 f white 0.37541 2000 103 f white 0.4013 2000 104 f white 0.42775 2000 105 f white 0.45463 2000 106 f white 0.48177 2000 107 f white 0.50902 2000 108 f white 0.53621 2000 109 f white 0.5632 2000 0-1d m black 0.00668 2000 1-7d m black 0.00186 2000 7-28d m black 0.00191 2000 0 m black 0.01571 2000 1 m black 0.00095 2000 2 m black 0.00052 2000 3 m black 0.00041 2000 4 m black 0.00034 2000 5 m black 3e-04 2000 6 m black 0.00028 2000 7 m black 0.00026 2000 8 m black 0.00024 2000 9 m black 2e-04 2000 10 m black 0.00018 2000 11 m black 0.00019 2000 12 m black 0.00026 2000 13 m black 0.00041 2000 14 m black 0.00063 2000 15 m black 0.00087 2000 16 m black 0.0011 2000 17 m black 0.00134 2000 18 m black 0.00158 2000 19 m black 0.00182 2000 20 m black 0.00208 2000 21 m black 0.00235 2000 22 m black 0.00253 2000 23 m black 0.00259 2000 24 m black 0.00255 2000 25 m black 0.00247 2000 26 m black 0.00242 2000 27 m black 0.00239 2000 28 m black 0.00241 2000 29 m black 0.00247 2000 30 m black 0.00255 2000 31 m black 0.00262 2000 32 m black 0.00273 2000 33 m black 0.00286 2000 34 m black 0.00301 2000 35 m black 0.00317 2000 36 m black 0.00336 2000 37 m black 0.00359 2000 38 m black 0.00388 2000 39 m black 0.00423 2000 40 m black 0.0046 2000 41 m black 0.00499 2000 42 m black 0.00544 2000 43 m black 0.00596 2000 44 m black 0.00655 2000 45 m black 0.00722 2000 46 m black 0.00793 2000 47 m black 0.00864 2000 48 m black 0.00931 2000 49 m black 0.00995 2000 50 m black 0.01062 2000 51 m black 0.01137 2000 52 m black 0.01217 2000 53 m black 0.01307 2000 54 m black 0.01408 2000 55 m black 0.01525 2000 56 m black 0.01656 2000 57 m black 0.01791 2000 58 m black 0.0192 2000 59 m black 0.02039 2000 60 m black 0.02156 2000 61 m black 0.02283 2000 62 m black 0.02429 2000 63 m black 0.02606 2000 64 m black 0.02812 2000 65 m black 0.03032 2000 66 m black 0.03267 2000 67 m black 0.03522 2000 68 m black 0.03799 2000 69 m black 0.04096 2000 70 m black 0.04409 2000 71 m black 0.04742 2000 72 m black 0.05101 2000 73 m black 0.05489 2000 74 m black 0.05903 2000 75 m black 0.06341 2000 76 m black 0.06801 2000 77 m black 0.07293 2000 78 m black 0.07816 2000 79 m black 0.08374 2000 80 m black 0.08968 2000 81 m black 0.096 2000 82 m black 0.10271 2000 83 m black 0.10984 2000 84 m black 0.11739 2000 85 m black 0.12539 2000 86 m black 0.13385 2000 87 m black 0.14279 2000 88 m black 0.15223 2000 89 m black 0.16216 2000 90 m black 0.17262 2000 91 m black 0.1836 2000 92 m black 0.19511 2000 93 m black 0.20717 2000 94 m black 0.21976 2000 95 m black 0.2329 2000 96 m black 0.24657 2000 97 m black 0.26077 2000 98 m black 0.27549 2000 99 m black 0.29072 2000 100 m black 0.30643 2000 101 m black 0.3226 2000 102 m black 0.33921 2000 103 m black 0.35623 2000 104 m black 0.37361 2000 105 m black 0.39133 2000 106 m black 0.40934 2000 107 m black 0.4276 2000 108 m black 0.44605 2000 109 m black 0.46466 2000 0-1d f black 0.00543 2000 1-7d f black 0.00138 2000 7-28d f black 0.00167 2000 0 f black 0.01282 2000 1 f black 0.00074 2000 2 f black 0.00041 2000 3 f black 0.00034 2000 4 f black 0.00028 2000 5 f black 0.00023 2000 6 f black 2e-04 2000 7 f black 0.00018 2000 8 f black 0.00017 2000 9 f black 0.00016 2000 10 f black 0.00016 2000 11 f black 0.00017 2000 12 f black 0.00019 2000 13 f black 0.00023 2000 14 f black 0.00027 2000 15 f black 0.00032 2000 16 f black 0.00038 2000 17 f black 0.00043 2000 18 f black 0.00049 2000 19 f black 0.00055 2000 20 f black 0.00061 2000 21 f black 0.00068 2000 22 f black 0.00074 2000 23 f black 0.00078 2000 24 f black 0.00082 2000 25 f black 0.00085 2000 26 f black 9e-04 2000 27 f black 0.00095 2000 28 f black 0.00102 2000 29 f black 0.0011 2000 30 f black 0.00118 2000 31 f black 0.00128 2000 32 f black 0.00139 2000 33 f black 0.00152 2000 34 f black 0.00167 2000 35 f black 0.00181 2000 36 f black 0.00196 2000 37 f black 0.00214 2000 38 f black 0.00235 2000 39 f black 0.00259 2000 40 f black 0.00285 2000 41 f black 0.00312 2000 42 f black 0.00339 2000 43 f black 0.00366 2000 44 f black 0.00394 2000 45 f black 0.00425 2000 46 f black 0.00458 2000 47 f black 0.00493 2000 48 f black 0.00528 2000 49 f black 0.00565 2000 50 f black 0.00605 2000 51 f black 0.00648 2000 52 f black 0.00695 2000 53 f black 0.00747 2000 54 f black 0.00805 2000 55 f black 0.00871 2000 56 f black 0.00948 2000 57 f black 0.0103 2000 58 f black 0.01113 2000 59 f black 0.01197 2000 60 f black 0.01282 2000 61 f black 0.01376 2000 62 f black 0.01481 2000 63 f black 0.01602 2000 64 f black 0.01739 2000 65 f black 0.01885 2000 66 f black 0.02026 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"98-99" 28828 25338 30473 27062 24915 24705 "99-100" 30360 26928 32290 29032 26031 26271 survival/noweb/survexp.Rnw0000644000175100001440000004100213017026563015461 0ustar hornikusers\section{Expected Survival} The expected survival routine creates the overall survival curve for a \emph{group} of people. It is possible to take the set of expected survival curves for each individual and average them, which is the \texttt{Ederer} method below, but this is not always the wisest choice: the Hakulinen and conditional methods average in anothers ways, both of which are more sophisticated ways to deal with censoring. The individual curves are dervived either from population rate tables such as the US annual life tables from the National Center for Health Statistics or the larger multi-national collection at mortality.org, or by using a previously fitted Cox model as the table. The arguments for [[survexp]] are \begin{description} \item[formula] The model formula. The right hand side consists of grouping variables, identically to [[survfit]] and an optional [[ratetable]] directive. The ``response'' varies by method: \begin{itemize} \item for the Hakulinen method it is a vector of censoring times. This is the actual censoring time for censored subjecs, and is what the censoring time `would have been' for each subject who died. %'` \item for the conditional method it is the usual Surv(time, status) code \item for the Ederer method no response is needed \end{itemize} \item[data, weights, subset, na.action] as usual \item[rmap] an optional mapping for rate table variables, see more below. \item[times] An optional vector of time points at which to compute the response. For the Hakulinen and conditional methods the program uses the vector of unique y values if this is missing. For the Ederer the component is not optional. \item[method] The method used for the calculation. Choices are individual survival, or the Ederer, Hakulinen, or conditional methods for cohort survival. \item[cohort, conditional] Older arguments that were used to select the method. \item[ratetable] the population rate table to use as a reference. This can either be a ratetable object or a previously fitted Cox model \item[scale] Scale the resulting output times, e.g., 365.25 to turn days into years. \item[se.fit] This has been deprecated. \item[model, x, y] usual \end{description} The output of survexp contains a subset of the elements in a [[survfit]] object, so many of the survfit methods can be applied. The result has a class of [[c('survexp', 'survfit')]]. <>= survexp <- function(formula, data, weights, subset, na.action, rmap, times, method=c("ederer", "hakulinen", "conditional", "individual.h", "individual.s"), cohort=TRUE, conditional=FALSE, ratetable=survival::survexp.us, scale=1, se.fit, model=FALSE, x=FALSE, y=FALSE) { <> <> <> <> } @ The first few lines are standard. Keep a copy of the call, then manufacture a call to [[model.frame]] that contains only the arguments relevant to that function. <>= Call <- match.call() m <- match.call(expand.dots=FALSE) # keep the first element (the call), and the following selected arguments m <- m[c(1, match(c('formula', 'data', 'weights', 'subset', 'na.action'), names(m), nomatch=0))] m[[1L]] <- quote(stats::model.frame) Terms <- if(missing(data)) terms(formula, 'ratetable') else terms(formula, 'ratetable',data=data) @ The function works with two data sets, the user's data on an actual set of %' subjects and the reference ratetable. This leads to a particular nuisance, that the variable names in the data set may not match those in the ratetable. For instance the United States overall death rate table [[survexp.us]] expects 3 variables, as shown by [[summary(survexp.us)]] \begin{itemize} \item age = age in days for each subject at the start of follow-up \item sex = sex of the subject, ``male'' or ``female'' (the routine accepts any unique abbreviation and is case insensitive) \item year = date of the start of follow-up \end{itemize} Up until the most recent revision, the formula contained any necessary mapping between the variables in the data set and the ratetable. For instance \begin{verbatim} survexp( ~ sex + ratetable(age=age*365.25, sex=sex, year=entry.dt), data=mydata, ratetable=survexp.us) \end{verbatim} In this case the user's data set has a variable `age' containing age in years, along with sex and an entry date. This had to be changed for two reasons. The primary one is that the data in a [[ratetable]] call had to be converted into a matrix in order to ``pass through'' the model.frame logic. With the recent updates to coxph so that it remembers factor codings correctly in new data sets, it is advantageous to keep factors as factors. The second is that a coxph model with a large number of covariates induces a very long ratetable clause; at about 40 variable it caused one of the R internal routines to fail due to a long expression. A third reason, perhaps the most pressing in reality, is that I've always %' felt that the prior code was confusing since it used the same term 'ratetable' for two different tasks. The new process adds the [[rmap]] argument, an example would be [[rmap=list(age =age*365.25, year=entry.dt)]]. Any variables in the ratetable that are not found in [[rmap]] are assumed to not need a mapping, this would be [[sex]] in the above example. For backwards compatability we allow the old style argument, converting it into the new style. The [[rmap]] argument needs to be examined without evaluating it; we then add the appropriate extra variables into a temporary formula so that the model frame has all that is required. The ratetable variables then can be retrieved from the model frame. The [[pyears]] routine uses the same rmap argument; this segment of the code is given its own name so that it can be included there as well. <>= rate <- attr(Terms, "specials")$ratetable if(length(rate) > 1) stop("Can have only 1 ratetable() call in a formula") <> m <- eval(m, parent.frame()) @ <>= if(length(rate) == 1) { if (!missing(rmap)) stop("The ratetable() call in a formula is depreciated") stemp <- untangle.specials(Terms, 'ratetable') rcall <- as.call(parse(text=stemp$var)[[1]]) # as a call object rcall[[1]] <- as.name('list') # make it a call to list(.. Terms <- Terms[-stemp$terms] # remove from the formula } else if (!missing(rmap)) { rcall <- substitute(rmap) if (!is.call(rcall) || rcall[[1]] != as.name('list')) stop ("Invalid rcall argument") } else rcall <- NULL # A ratetable, but not rcall argument # Check that there are no illegal names in rcall, then expand it # to include all the names in the ratetable if(is.ratetable(ratetable)) varlist <- attr(ratetable, "dimid") else if(inherits(ratetable, "coxph")) { ## Remove "log" and such things, to get just the list of # variable names varlist <- all.vars(delete.response(ratetable$terms)) } else stop("Invalid rate table") temp <- match(names(rcall)[-1], varlist) # 2,3,... are the argument names if (any(is.na(temp))) stop("Variable not found in the ratetable:", (names(rcall))[is.na(temp)]) if (any(!(varlist %in% names(rcall)))) { to.add <- varlist[!(varlist %in% names(rcall))] temp1 <- paste(text=paste(to.add, to.add, sep='='), collapse=',') if (is.null(rcall)) rcall <- parse(text=paste("list(", temp1, ")"))[[1]] else { temp2 <- deparse(rcall) rcall <- parse(text=paste("c(", temp2, ",list(", temp1, "))"))[[1]] } } @ The formula below is used only in the call to [[model.frame]] to ensure that the frame has both the formula and the ratetable variables. We don't want to modify the original formula, since we use it to create the $X$ matrix and the response variable. The non-obvious bit of code is the addition of an environment to the formula. The [[model.matrix]] routine has a non-standard evaluation - it uses the frame of the formula, rather than the parent.frame() argument below, along with the [[data]] to look up variables. If a formula is long enough deparse() will give two lines, hence the extra paste call to re-collapse it into one. <>= # Create a temporary formula, used only in the call to model.frame newvar <- all.vars(rcall) if (length(newvar) > 0) { tform <- paste(paste(deparse(Terms), collapse=""), paste(newvar, collapse='+'), sep='+') m$formula <- as.formula(tform, environment(Terms)) } @ If the user data has 0 rows, e.g. from a mistaken [[subset]] statement that eliminated all subjects, we need to stop early. Otherwise the .C code fails in a nasty way. <>= n <- nrow(m) if (n==0) stop("Data set has 0 rows") if (!missing(se.fit) && se.fit) warning("se.fit value ignored") weights <- model.extract(m, 'weights') if (length(weights) ==0) weights <- rep(1.0, n) if (class(ratetable)=='ratetable' && any(weights !=1)) warning("weights ignored") if (any(attr(Terms, 'order') >1)) stop("Survexp cannot have interaction terms") if (!missing(times)) { if (any(times<0)) stop("Invalid time point requested") if (length(times) >1 ) if (any(diff(times)<0)) stop("Times must be in increasing order") } @ If a response variable was given, we only need the times and not the status. To be correct, computations need to be done for each of the times given in the [[times]] argument as well as for each of the unique y values. This ends up as the vector [[newtime]]. If a [[times]] argument was given we will subset down to only those values at the end. For a population rate table and the Ederer method the times argument is required. <>= Y <- model.extract(m, 'response') no.Y <- is.null(Y) if (no.Y) { if (missing(times)) { if (is.ratetable(ratetable)) stop("either a times argument or a response is needed") } else newtime <- times } else { if (is.matrix(Y)) { if (is.Surv(Y) && attr(Y, 'type')=='right') Y <- Y[,1] else stop("Illegal response value") } if (any(Y<0)) stop ("Negative follow up time") # if (missing(npoints)) temp <- unique(Y) # else temp <- seq(min(Y), max(Y), length=npoints) temp <- unique(Y) if (missing(times)) newtime <- sort(temp) else newtime <- sort(unique(c(times, temp[temp>= ovars <- attr(Terms, 'term.labels') # rdata contains the variables matching the ratetable rdata <- data.frame(eval(rcall, m), stringsAsFactors=TRUE) if (is.ratetable(ratetable)) { israte <- TRUE if (no.Y) { Y <- rep(max(times), n) } rtemp <- match.ratetable(rdata, ratetable) R <- rtemp$R } else if (inherits(ratetable, 'coxph')) { israte <- FALSE Terms <- ratetable$terms # if (!is.null(attr(Terms, 'offset'))) # stop("Cannot deal with models that contain an offset") # strats <- attr(Terms, "specials")$strata # if (length(strats)) # stop("survexp cannot handle stratified Cox models") # if (any(names(m[,rate]) != attr(ratetable$terms, 'term.labels'))) stop("Unable to match new data to old formula") } else stop("Invalid ratetable") @ Now for some calculation. If cohort is false, then any covariates on the right hand side (other than the rate table) are irrelevant, the function returns a vector of expected values rather than survival curves. <>= if (substring(method, 1, 10) == "individual") { #individual survival if (no.Y) stop("for individual survival an observation time must be given") if (israte) temp <- survexp.fit (1:n, R, Y, max(Y), TRUE, ratetable) else { rmatch <- match(names(data), names(rdata)) if (any(is.na(rmatch))) rdata <- cbind(rdata, data[,is.na(rmatch)]) temp <- survexp.cfit(1:n, rdata, Y, 'individual', ratetable) } if (method == "individual.s") xx <- temp$surv else xx <- -log(temp$surv) names(xx) <- row.names(m) na.action <- attr(m, "na.action") if (length(na.action)) return(naresid(na.action, xx)) else return(xx) } @ Now for the more commonly used case: returning a survival curve. First see if there are any grouping variables. The results of the [[tcut]] function are often used in person-years analysis, which is somewhat related to expected survival. However tcut results aren't relevant here and we put in a check for the %' confused user. The strata command creates a single factor incorporating all the variables. <>= if (length(ovars)==0) X <- rep(1,n) #no categories else { odim <- length(ovars) for (i in 1:odim) { temp <- m[[ovars[i]]] ctemp <- class(temp) if (!is.null(ctemp) && ctemp=='tcut') stop("Can't use tcut variables in expected survival") } X <- strata(m[ovars]) } #do the work if (israte) temp <- survexp.fit(as.numeric(X), R, Y, newtime, method=="conditional", ratetable) else { temp <- survexp.cfit(as.numeric(X), rdata, Y, method, ratetable, weights) newtime <- temp$time } @ Now we need to package up the curves properly All the results can be returned as a single matrix of survivals with a common vector of times. If there was a times argument we need to subset to selected rows of the computation. <>= if (missing(times)) { n.risk <- temp$n surv <- temp$surv } else { if (israte) keep <- match(times, newtime) else { # The result is from a Cox model, and it's list of # times won't match the list requested in the user's call # Interpolate the step function, giving survival of 1 # for requested points that precede the Cox fit's # first downward step. The code is like summary.survfit. n <- length(temp$time) keep <- approx(temp$time, 1:n, xout=times, yleft=0, method='constant', f=0, rule=2)$y } if (is.matrix(temp$surv)) { surv <- (rbind(1,temp$surv))[keep+1,,drop=FALSE] n.risk <- temp$n[pmax(1,keep),,drop=FALSE] } else { surv <- (c(1,temp$surv))[keep+1] n.risk <- temp$n[pmax(1,keep)] } newtime <- times } newtime <- newtime/scale if (is.matrix(surv)) { dimnames(surv) <- list(NULL, levels(X)) out <- list(call=Call, surv= drop(surv), n.risk=drop(n.risk), time=newtime) } else { out <- list(call=Call, surv=c(surv), n.risk=c(n.risk), time=newtime) } @ Last do the standard things: add the model, x, or y components to the output if the user asked for them. (For this particular routine I can't think of %' a reason they every would.) Copy across summary information from the rate table computation if present, and add the method and class to the output. <>= if (model) out$model <- m else { if (x) out$x <- X if (y) out$y <- Y } if (israte && !is.null(rtemp$summ)) out$summ <- rtemp$summ if (no.Y) out$method <- 'Ederer' else if (conditional) out$method <- 'conditional' else out$method <- 'cohort' class(out) <- c('survexp', 'survfit') out @ survival/noweb/coxsurv.Rnw0000644000175100001440000006517213055105650015471 0ustar hornikusers \section{Cox models} \subsection{Predicted survival} The [[survfit]] method for a Cox model produces individual survival curves. As might be expected these have much in common with ordinary survival curves, and share many of the same methods. The primary differences are first that a predicted curve always refers to a particular set of covariate values. It is often the case that a user wants multiple values at once, in which case the result will be a matrix of survival curves with a row for each time and a column for each covariate set. The second is that the computations are somewhat more difficult. The input arguments are \begin{description} \item[formula] a fitted object of class 'coxph'. The argument name of 'formula' is historic, from when the survfit function was not a generic and only did Kaplan-Meier type curves. \item[newdata] contains the data values for which curves should be produced, one per row \item[se.fit] TRUE/FALSE, should standard errors be computed. \item[individual] a particular option for time-dependent covariates \item[type] computation type for the survival curve \item[vartype] computation type for the variance \item[censor] if FALSE, remove any times that have no events from the output. This is for backwards compatability with older versions of the code. \item[id] replacement and extension for the individual argument \item[start.time] Start a curve at a later timepoint than zero. \end{description} All the other arguments are common to all the methods, refer to the help pages. <>= survfit.coxph <- function(formula, newdata, se.fit=TRUE, conf.int=.95, individual=FALSE, type, vartype, conf.type=c("log", "log-log", "plain", "none"), censor=TRUE, id, start.time, na.action=na.pass, ...) { Call <- match.call() Call[[1]] <- as.name("survfit") #nicer output for the user object <- formula #'formula' because it has to match survfit <> <> <> } @ The third line [[as.name('survfit')]] causes the printout to say `survfit' instead of `survfit.coxph'. %' The setup for the routine is fairly pedestrian. If the newdata argument is missing we use [[object$means]] as the default value. This choice has lots of statistical shortcomings, particularly in a stratified model, but is common in other packages and a historic option here. If the type or vartype are missing we use the appropriate one for the method in the Cox model. That is, the [[coxph]] computation used for [[method=``exact'']] is the same approximation used in the Kalbfleish-Prentice estimate, that for the Breslow method matches the Aalen survival estimate, and the Efron approximation the Efron survival estimate. The other two rows of labels in [[temp1]] are historical; we include them for backwards compatability but they don't appear in the documentation. %' One particular special case (that gave me fits for a while) is when there are non-heirarchical models, for example [[~ age + age:sex]]. The fit of such a model will \emph{not} be the same using the variable [[age2 <- age-50]]; I originally thought it was a flaw induced by my subtraction. The routine simply cannot give a sensible curve for a model like this. The issue continued to surprise me each time I rediscovered it, leading to an error message for my own protection. I'm not convinced at this time that there is a sensible survival curve that \emph{could} be calculated for such a model. A model with \code{age + age:strata(sex)} will be ok, because the coxph routine treats this last term as though it had a * in it, i.e., fits a stratified model. <>= if (!is.null(attr(object$terms, "specials")$tt)) stop("The survfit function can not yet process coxph models with a tt term") if (missing(type)) { # Use the appropriate one from the model temp1 <- c("exact", "breslow", "efron") survtype <- match(object$method, temp1) } else { temp1 <- c("kalbfleisch-prentice", "aalen", "efron", "kaplan-meier", "breslow", "fleming-harrington", "greenwood", "tsiatis", "exact") survtype <- match(match.arg(type, temp1), temp1) survtype <- c(1,2,3,1,2,3,2,2,1)[survtype] } if (missing(vartype)) { vartype <- survtype } else { temp2 <- c("greenwood", "aalen", "efron", "tsiatis") vartype <- match(match.arg(vartype, temp2), temp2) if (vartype==4) vartype<- 2 } if (!se.fit) conf.type <- "none" else conf.type <- match.arg(conf.type) tfac <- attr(terms(object), 'factors') temp <- attr(terms(object), 'specials')$strata has.strata <- !is.null(temp) if (has.strata) { # Toss out strata terms in tfac before doing the test 1 line below, as # strata end up in the model with age:strat(grp) terms or *strata() terms # (There might be more than one strata term) for (i in temp) tfac <- tfac[,tfac[i,] ==0] # toss out strata terms } if (any(tfac >1)) stop("not able to create a curve for models that contain an interaction without the lower order effect") @ I need to retrieve a copy of the original data. We always need the $X$ matrix and $y$, both of which may be found in the data object. If the original call included either strata, offset, or weights, or if either $x$ or $y$ are missing from the [[coxph]] object, then the model frame will need to be reconstructed. We have to use [[object['x']]] instead of \texttt{object\$x} since the latter will pick off the [[xlevels]] component if the [[x]] component is missing (which is the default). <>= if (is.null(object$y) || is.null(object[['x']]) || !is.null(object$call$weights) || (has.strata && is.null(object$strata)) || !is.null(attr(object$terms, 'offset'))) { mf <- stats::model.frame(object) } else mf <- NULL #useful for if statements later @ If a model frame was created, then it is trivial to grab [[y]] from the new frame and compare it to [[object$y]] from the original one. This is to avoid nonsense results that arise when someone changes the data set under our feet. For instance <>= fit <- coxph(Surv(time,status) ~ age, data=lung) lung <- lung[1:100,] survfit(fit) @ <>= if (is.null(mf)) y <- object[['y']] else { y <- model.response(mf) y2 <- object[['y']] # Avoid issues with roundoff. The data set may have been saved and # then read back in, for instance if (!is.null(y2)) { if (ncol(y2) != ncol(y) || length(y2) != length(y)) stop("Could not reconstruct the y vector") if (FALSE) { # removed in 2.40-1. With the addition of aeqSurv # other packages were being flagged due to tiny discrpancies if (ncol(y2) != ncol(y) || length(y2) != length(y) || !(isTRUE(all.equal(y[,1], y2[,1]))) || !(isTRUE(all.equal(y[,2], y2[,2]))) || (ncol(y)==3 && any(y[,3] != y2[,3]))) stop("Could not reconstruct the y vector") } } } if (is.null(object[['x']])) x <- model.matrix.coxph(object, data=mf) else x <- object[['x']] missid <- missing(id) # I need this later, and setting id below makes # "missing(id)" always false if (!missid) individual <- TRUE else if (missid && individual) id <- rep(0,nrow(y)) #dummy value else id <- NULL if (!missing(start.time)) { if (!is.numeric(start.time) || length(start.time) > 1) stop("start.time must be a single numeric value") # Start the curves after start.time # To do so, remove any rows of the data with an endpoint before that # time. if (ncol(y)==3) { keep <- y[,2] > start.time y[keep,1] <- pmax(y[keep,1], start.time) } else keep <- y[,1] > start.time if (!any(y[keep, ncol(y)]==1)) stop("start.time argument has removed all endpoints") y <- y[keep,,drop=FALSE] x <- x[keep,,drop=FALSE] if (length(id) >0 ) id <- id[keep] n <- nrow(y) } else { n <- nrow(y) if (n != object$n[1] || nrow(x) !=n) stop("Failed to reconstruct the original data set") } if (is.null(mf)) wt <- rep(1., n) else { wt <- model.weights(mf) if (is.null(wt)) wt <- rep(1.0, n) } type <- attr(y, 'type') if (type != 'right' && type != 'counting') stop("Cannot handle \"", type, "\" type survival data") if (individual && missing(newdata)) { stop("the id and/or individual options only make sense with new data") } if (individual && type!= 'counting') stop("The individual option is only valid for start-stop data") if (is.null(mf)) offset <- 0 else { offset <- model.offset(mf) if (is.null(offset)) offset <- 0 } Terms <- object$terms if (!has.strata) strata <- rep(0L,n) else { stangle <- untangle.specials(Terms, 'strata') # used multiple times strata <- object$strata #try this first if (is.null(strata)){ if (length(stangle$vars) ==1) strata <- mf[[stangle$vars]] else strata <- strata(mf[, stangle$vars], shortlabel=TRUE) } if (!missing(start.time)) strata <- strata[keep] } @ In two places below we need to know if there are strata by covariate interactions, which requires looking at attributes of the terms object. The factors attribute will have a row for the strata variable, or maybe more than one (multiple strata terms are legal). If it has a 1 in a column that corresponds to something of order 2 or greater, that is a strata by covariate interaction. <>= if (has.strata) { temp <- attr(Terms, "specials")$strata factors <- attr(Terms, "factors")[temp,] strata.interaction <- any(t(factors)*attr(Terms, "order") >1) } @ If a variable is deemed redundant the [[coxph]] routine will have set its coefficient to NA as a marker. We want to ignore that coefficient: treating it as a zero has the desired effect. Another special case is a null model, having either ~1 or only an offset on the right hand side. In that case we create a dummy covariate to allow the rest of the code to work without special if/else. The last special case is a model with a sparse frailty term. We treat the frailty coefficients as 0 variance (in essence as an offset). The frailty is removed from the model variables but kept in the risk score. This isn't statistically very defensible, but it is backwards compatatble. %' A non-sparse frailty does not need special code and works out like any other variable. We also remove the means from each column of the $X$ matrix. The reason for this is to avoid huge values when calculating $\exp(X\beta)$; this would happen if someone had a variable with a mean of 1000 and a variance of 1. Any constant can be subtracted, mathematically the results are identical as long as the same values are subtracted from the old and new $X$ data. The mean is used because it is handy, we just need to get $X\beta$ in the neighborhood of zero. <>= if (is.null(x) || ncol(x)==0) { # a model with ~1 on the right hand side # Give it a dummy x so the rest of the code goes through # (This case is really rare) x <- matrix(0., nrow=n) coef <- 0.0 varmat <- matrix(0.0,1,1) risk <- rep(exp(offset- mean(offset)), length=n) } else { varmat <- object$var coef <- ifelse(is.na(object$coefficients), 0, object$coefficients) xcenter <- object$means if (is.null(object$frail)) { x <- scale(x, center=xcenter, scale=FALSE) risk <- c(exp(x%*% coef + offset - mean(offset))) } else { keep <- !grepl("frailty(", dimnames(x)[[2]], fixed=TRUE) x <- x[,keep, drop=F] # varmat <- varmat[keep,keep] #coxph already has trimmed it risk <- exp(object$linear.predictor) x <- scale(x, center=xcenter, scale=FALSE) } } @ The [[risk]] vector and [[x]] matrix come from the original data, and are the raw data for the survival curve and its variance. We also need the risk score $\exp(X\beta)$ for the target subject(s). \begin{itemize} \item For predictions with time-dependent covariates the user will have either included an [[id]] statement (newer style) or specified the [[individual=TRUE]] option. If the latter, then [[newdata]] is presumed to contain only a single indivual represented by multiple rows. If the former then the [[id]] variable marks separate individuals. In either case we need to retrieve the covariates, strata, and repsonse from the new data set. \item For ordinary predictions only the covariates are needed. \item If newdata is not present we assume that this is the ordinary case, and use the value of [[object$means]] as the default covariate set. This is not ideal statistically since many users view this as an ``average'' survival curve, which it is not. \end{itemize} When grabbing [newdata] we want to use model.frame processing, both to handle missing values correctly and, perhaps more importantly, to correctly map any factor variables between the original fit and the new data. (The new data will often have only one of the original levels represented.) Also, we want to correctly handle data-dependent nonlinear terms such as ns and pspline. However, the simple call found in predict.lm, say, [[model.frame(Terms, data=newdata, ..]] isn't used here for a few reasons. The first is a decision on our part that the user should not have to include unused terms in the model. The second is that if there are strata, the user may or may not have included strata variables in their data set and we need to act accordingly. The third is that we might have an [[id]] statement in this call, which is another variable to be fetched. Last, there is no ability to use sparse frailties and newdata together; it is a hard case and so rare as to not be worth it. First, remove unnecessary terms from the orginal model formula. Any [[cluster]] terms can be deleted, If [[individual]] is false then the repsonse variable can go. The dataClasses and predvars attributes, if present, have elements in the same order as the first dimension of the ``factors'' attribute of the terms. Subscripting the terms argument does not preserve dataClasses or predvars, however. Use the pre and post subscripting factors attribute to determine what elements of them to keep. The predvars component is a call objects with one element for each term in the formula, so y ~ age + ns(height) would lead to a predvars of length 4, element 1 is the call itself, 2 would be y, etc. The dataClasses object is a simple list. <>= subterms <- function(tt, i) { dataClasses <- attr(tt, "dataClasses") predvars <- attr(tt, "predvars") oldnames <- dimnames(attr(tt, 'factors'))[[1]] tt <- tt[i] index <- match(dimnames(attr(tt, 'factors'))[[1]], oldnames) if (length(index) >0) { if (!is.null(predvars)) attr(tt, "predvars") <- predvars[c(1, index+1)] if (!is.null(dataClasses)) attr(tt, "dataClasses") <- dataClasses[index] } tt } temp <- untangle.specials(Terms, 'cluster') if (length(temp$terms)) Terms <- subterms(Terms, -temp$terms) if (missing(newdata)) { mf2 <- as.list(object$means) #create a dummy newdata names(mf2) <- names(object$coefficients) mf2 <- as.data.frame(mf2) found.strata <- FALSE } else { if (!is.null(object$frail)) stop("Newdata cannot be used when a model has frailty terms") Terms2 <- Terms if (!individual) Terms2 <- delete.response(Terms) <> } @ For backwards compatability, I allow someone to give an ordinary vector instead of a data frame (when only one curve is required). In this case I also need to verify that the elements have a name. Then turn it into a data frame, like it should have been from the beginning. (Documentation of this ability has been suppressed, however. I'm hoping people forget it ever existed.) <>= if (is.vector(newdata, "numeric")) { if (individual) stop("newdata must be a data frame") if (is.null(names(newdata))) { stop("Newdata argument must be a data frame") } newdata <- data.frame(as.list(newdata)) } @ Finally get my new model frame mf2. There are two cases. If the call does not has an ``id'' argument then we use the semantics of top-level functions like coxph: get a copy of the call, keep what we need, change the called function's name to ``model.fram'' and evalutate it. then we If all is particularly simple we can use a simple call. Otherwise get an abbreviated form of the original call that has only the calling function, na.action, and id. The calling function is always element 1, the others are found by name. Now manipulate it: add the formula, data and xlev components (the last might be NULL), and then change the name of the call. If the original call was [[survfit(fit1, newdata=mydat, conf.int=.9)]] the result is [[model.frame(data= copy of newdat, formula=Terms2, xlev=myxlev)]]. If there is no id argument we use a simple call, except that we allow the user to leave out any strata() variables if they so desire, \emph{if} there are no strata by covariate interactions. How does one check if the strata variables are or are not available in the call? My first attempt at this was to wrap the call in a try() construct and see if it failed. This doesn't work. \begin{itemize} \item What if there is no strata variable in newdata, but they do have, by bad luck, a variable of the same name in their main directory? \item It would seem like changing the environment to NULL would be wise, so that we don't find variables anywhere but in the data argument, a sort of sandboxing. Not wise: you then won't find functions like ``log''. \item We don't dare modify the environment of the formula at all. It is needed for the sneaky caller who uses his own function inside the formula, 'mycosine' say, and that function can only be found if we retain the environment. \end{itemize} One way out of this is to evaluate each of the strata terms (there can be more than one) one at a time, in an environment that knows nothing except "list" and a fake definition of "strata", and newdata. Variables that are part of the global environment won't be found. I even watch out for the case of either "strata" or "list" is the name of the stratification variable, which causes my fake strata function to return a function when said variable is not in newdata. <>= if (missid) { if (has.strata && !strata.interaction) { found.strata <- TRUE tempenv <- new.env(, parent=emptyenv()) assign("strata", function(..., na.group, shortlabel, sep) list(...), envir=tempenv) assign("list", list, envir=tempenv) for (svar in stangle$vars) { temp <- try(eval(parse(text=svar), newdata, tempenv), silent=TRUE) if (!is.list(temp) || any(unlist(lapply(temp, class))== "function")) found.strata <- FALSE } if (found.strata) mf2 <- stats::model.frame(Terms2, data=newdata, na.action=na.action, xlev=object$xlevels) else { Terms2 <- subterms(Terms2, -attr(Terms2, 'specials')$strata) if (!is.null(object$xlevels)) { myxlev <- object$xlevels[match(attr(Terms2, "term.labels"), names(object$xlevels), nomatch=0)] if (length(myxlev)==0) myxlev <- NULL } else myxlev <- NULL mf2 <- stats::model.frame(Terms2, data=newdata, na.action=na.action, xlev=myxlev) } } else { mf2 <- stats::model.frame(Terms2, data=newdata, na.action=na.action, xlev=object$xlevels) found.strata <- has.strata #would have failed otherwise } } else { tcall <- Call[c(1, match(c('id', "na.action"), names(Call), nomatch=0))] tcall$data <- newdata tcall$formula <- Terms2 tcall$xlev <- object$xlevels tcall[[1L]] <- quote(stats::model.frame) mf2 <- eval(tcall) found.strata <- has.strata # would have failed otherwise } @ Now, finally, extract the [[x2]] matrix from the just-created frame. <>= if (has.strata && found.strata) { #pull them off temp <- untangle.specials(Terms2, 'strata') strata2 <- strata(mf2[temp$vars], shortlabel=TRUE) strata2 <- factor(strata2, levels=levels(strata)) if (any(is.na(strata2))) stop("New data set has strata levels not found in the original") # An expression like age:strata(sex) will have temp$vars= "strata(sex)" # and temp$terms = integer(0). This does not work as a subscript if (length(temp$terms) >0) Terms2 <- Terms2[-temp$terms] } else strata2 <- factor(rep(0, nrow(mf2))) if (individual) { if (missing(newdata)) stop("The newdata argument must be present when individual=TRUE") if (!missid) { #grab the id variable id <- model.extract(mf2, "id") if (is.null(id)) stop("id=NULL is an invalid argument") } else id <- rep(1, nrow(mf2)) x2 <- model.matrix(Terms2, mf2)[,-1, drop=FALSE] #no intercept if (length(x2)==0) stop("Individual survival but no variables") x2 <- scale(x2, center=xcenter, scale=FALSE) offset2 <- model.offset(mf2) if (length(offset2) >0) offset2 <- offset2 - mean(offset) else offset2 <- 0 y2 <- model.extract(mf2, 'response') if (attr(y2,'type') != type) stop("Survival type of newdata does not match the fitted model") if (attr(y2, "type") != "counting") stop("Individual=TRUE is only valid for counting process data") y2 <- y2[,1:2, drop=F] #throw away status, it's never used newrisk <- exp(c(x2 %*% coef) + offset2) result <- survfitcoxph.fit(y, x, wt, x2, risk, newrisk, strata, se.fit, survtype, vartype, varmat, id, y2, strata2) } @ If there is no newdata argument, the centering means that we need to predict for x2=0. The second the most common call to the routine. <>= else { if (missing(newdata)) { if (has.strata && strata.interaction) stop ("Models with strata by covariate interaction terms require newdata") x2 <- matrix(0.0, nrow=1, ncol=ncol(x)) offset2 <- 0 } else { offset2 <- model.offset(mf2) if (length(offset2) >0) offset2 <- offset2 - mean(offset) else offset2 <- 0 x2 <- model.matrix(Terms2, mf2)[,-1, drop=FALSE] #no intercept x2 <- scale(x2, center=xcenter, scale=FALSE) } newrisk <- exp(c(x2 %*% coef) + offset2) result <- survfitcoxph.fit(y, x, wt, x2, risk, newrisk, strata, se.fit, survtype, vartype, varmat) if (has.strata && found.strata) { if (is.matrix(result$surv)) { <> } } } @ The final bit of work. If the newdata arg contained strata then the user should not get a matrix of survival curves containing every newdata obs * strata combination, but rather a vector of curves, each one with the appropriate strata. It was faster to compute them all, however, than to use the individual=T logic. So now pick off the bits we want. The names of the curves will be the rownames of the newdata arg, if they exist. <>= nr <- nrow(result$surv) #a vector if newdata had only 1 row indx1 <- split(1:nr, rep(1:length(result$strata), result$strata)) rows <- indx1[as.numeric(strata2)] #the rows for each curve indx2 <- unlist(rows) #index for time, n.risk, n.event, n.censor indx3 <- as.integer(strata2) #index for n and strata for(i in 2:length(rows)) rows[[i]] <- rows[[i]]+ (i-1)*nr #linear subscript indx4 <- unlist(rows) #index for surv and std.err temp <- result$strata[indx3] names(temp) <- row.names(mf2) new <- list(n = result$n[indx3], time= result$time[indx2], n.risk= result$n.risk[indx2], n.event=result$n.event[indx2], n.censor=result$n.censor[indx2], strata = temp, surv= result$surv[indx4], cumhaz = result$cumhaz[indx4]) if (se.fit) new$std.err <- result$std.err[indx4] result <- new @ Finally, the last (somewhat boring) part of the code. First, if given the argument [[censor=FALSE]] we need to remove all the time points from the output at which there was only censoring activity. This action is mostly for backwards compatability with older releases that never returned censoring times. Second, add in the variance and the confidence intervals to the result. The code is nearly identical to that in survfitKM. <>= if (!censor) { kfun <- function(x, keep){ if (is.matrix(x)) x[keep,,drop=F] else if (length(x)==length(keep)) x[keep] else x} keep <- (result$n.event > 0) if (!is.null(result$strata)) { temp <- factor(rep(names(result$strata), result$strata), levels=names(result$strata)) result$strata <- c(table(temp[keep])) } result <- lapply(result, kfun, keep) } if (se.fit) { zval <- qnorm(1- (1-conf.int)/2, 0,1) if (conf.type=='plain') { temp1 <- result$surv + zval* result$std.err * result$surv temp2 <- result$surv - zval* result$std.err * result$surv result <- c(result, list(upper=pmin(temp1,1), lower=pmax(temp2,0), conf.type='plain', conf.int=conf.int)) } if (conf.type=='log') { xx <- ifelse(result$surv==0,1,result$surv) #avoid some "log(0)" messages temp1 <- ifelse(result$surv==0, 0*result$std.err, exp(log(xx) + zval* result$std.err)) temp2 <- ifelse(result$surv==0, 0*result$std.err, exp(log(xx) - zval* result$std.err)) result <- c(result, list(upper=pmin(temp1,1), lower=temp2, conf.type='log', conf.int=conf.int)) } if (conf.type=='log-log') { who <- (result$surv==0 | result$surv==1) #special cases xx <- ifelse(who, .1,result$surv) #avoid some "log(0)" messages temp1 <- exp(-exp(log(-log(xx)) + zval*result$std.err/log(xx))) temp1 <- ifelse(who, result$surv + 0*result$std.err, temp1) temp2 <- exp(-exp(log(-log(xx)) - zval*result$std.err/log(xx))) temp2 <- ifelse(who, result$surv + 0*result$std.err, temp2) result <- c(result, list(upper=temp1, lower=temp2, conf.type='log-log', conf.int=conf.int)) } } if (!missing(start.time)) result$start.time <- start.time result$call <- Call # The "type" component is in the middle -- match history indx <- match('surv', names(result)) result <- c(result[1:indx], type=attr(y, 'type'), result[-(1:indx)]) class(result) <- c('survfit.cox', 'survfit') result @ survival/noweb/survfit.Rnw0000644000175100001440000002573513026501446015464 0ustar hornikusers\section{Survival curves} The survfit function was set up as a method so that we could apply the function to both formulas (to compute the Kaplan-Meier) and to coxph objects. The downside to this is that the manual pages get a little odd, but from a programming perspective it was a good idea. At one time, long long ago, we allowed the function to be called with ``Surv(time, status)'' as the formula, i.e., without a tilde. That was a bad idea, now abandoned. A note on times: one of the things that drove me nuts was the problem of ``tied but not quite tied'' times. As an example consider two values of 24173 = 23805 + 368. These are values from an actual study with times in days. However, the user chose to use age in years, and saved those values out in a CSV file, resulting in values for the above of 66.18206708000000 and 66.18206708000001. The R phrase \code{unique(x)} sees these two values as distinct but \code{table(x)} and \code{tapply} see it as a single value since they first apply \code{factor} to the values, and that in turn uses \code{as.character}. As an even more relvant example consider the following code: <>= tfun <- function(start, gap) { as.numeric(start)/365.25 - as.numeric(start + gap)/365.25 } test <- logical(200) for (i in 1:200) { test[i] <- tfun(as.Date("2010/01/01"), 29) == tfun(as.Date("2010/01/01") + i, 29) } table(test) @ The number of FALSE entries in the table depends on machine, compiler, and a host of other issues. There is discussion of this general issue in the R FAQ: ``why doesn't R think these numbers are equal''. The Kaplan-Meier and Cox model both pay careful attention to ties, and so both now use the \code{aeqSurv} routine to first preprocess the time data. It uses the same rules as \code{all.equal} to adjudicate ties and near ties. <>= survfit <- function(formula, ...) { UseMethod("survfit", formula) } <> <> <> @ The result of a survival curve can have a [[surv]] component that is a vector or a matrix, and an optional strata component. A dual subscript to a survfit object always associates the first subscript with the strata and the second with the matrix. When a survfit object has only one or the other of the two, we allow a single subscript to be used and map it appropriately. <>= dim.survfit <- function(x) { if (is.null(x$strata)) { if (is.matrix(x$surv)) c(1L, ncol(x$surv)) else 1L } else { nr <- length(x$strata) if (is.matrix(x$surv)) c(nr, ncol(x$surv)) else nr } } "[.survfit" <- function(x, ..., drop=TRUE) { nmatch <- function(indx, target) { # This function lets R worry about character, negative, or logical subscripts # It always returns a set of positive integer indices temp <- 1:length(target) names(temp) <- target temp[indx] } if (missing(..1)) i<- NULL else i <- ..1 if (missing(..2)) j<- NULL else j <- ..2 if (is.null(i) && is.null(j)) return (x) #no subscripts present! if (!is.matrix(x$surv) && !is.null(j)) stop("survfit object does not have 2 dimensions") if (is.null(x$strata)) { if (is.matrix(x$surv)) { if (is.null(j) && !is.null(i)) j <- i #special case noted above x$surv <- x$surv[,j,drop=drop] if (!is.null(x$std.err)) x$std.err <- x$std.err[,j,drop=drop] if (!is.null(x$upper)) x$upper <- x$upper[,j,drop=drop] if (!is.null(x$lower)) x$lower <- x$lower[,j,drop=drop] if (!is.null(x$cumhaz)) x$cumhaz <- x$cumhaz[,j,drop=drop] } else warning("survfit object has only a single survival curve") } else { if (is.null(i)) keep <- seq(along.with=x$time) else { indx <- nmatch(i, names(x$strata)) #strata to keep if (any(is.na(indx))) stop(paste("strata", paste(i[is.na(indx)], collapse=' '), 'not matched')) # Now, indx may not be in order: some can use curve[3:2] to reorder # The list/unlist construct will reorder the data temp <- rep(1:length(x$strata), x$strata) keep <- unlist(lapply(indx, function(x) which(temp==x))) if (length(indx) <=1 && drop) x$strata <- NULL else x$strata <- x$strata[i] x$n <- x$n[indx] x$time <- x$time[keep] x$n.risk <- x$n.risk[keep] x$n.event <- x$n.event[keep] x$n.censor<- x$n.censor[keep] if (!is.null(x$n.enter)) x$n.enter <- x$n.enter[keep] } if (is.matrix(x$surv)) { # If the curve has been selected by strata and keep has only # one row, we don't want to lose the second subscript too if (!is.null(i) && (is.null(j) ||length(j) >1)) drop <- FALSE if (is.null(j)) { x$surv <- x$surv[keep,,drop=drop] if (!is.null(x$std.err)) x$std.err <- x$std.err[keep,,drop=drop] if (!is.null(x$upper)) x$upper <-x$upper[keep,,drop=drop] if (!is.null(x$lower)) x$lower <-x$lower[keep,,drop=drop] if (!is.null(x$cumhaz)) x$cumhaz <-x$cumhaz[keep,,drop=drop] } else { x$surv <- x$surv[keep,j, drop=drop] if (!is.null(x$std.err)) x$std.err <- x$std.err[keep,j, drop=drop] if (!is.null(x$upper)) x$upper <- x$upper[keep,j, drop=drop] if (!is.null(x$lower)) x$lower <- x$lower[keep,j, drop=drop] if (!is.null(x$cumhaz)) x$cumhaz <- x$cumhaz[keep,j, drop=drop] } } else { x$surv <- x$surv[keep] if (!is.null(x$std.err)) x$std.err <- x$std.err[keep] if (!is.null(x$upper)) x$upper <- x$upper[keep] if (!is.null(x$lower)) x$lower <- x$lower[keep] if (!is.null(x$cumhaz)) x$cumhaz <- x$cumhaz[keep] } } x } @ \subsection{Kaplan-Meier} The most common use of the survfit function is with a formula as the first argument, and the most common outcome of such a call is a Kaplan-Meier curve. The id argument is from an older version of the competing risks code; most people will use [[cluster(id)]] in the formula instead. The istate argument only applies to competing risks, but don't print an error message if it is accidentally there. <>= survfit.formula <- function(formula, data, weights, subset, na.action, etype, id, istate, timefix=TRUE, ...) { Call <- match.call() Call[[1]] <- as.name('survfit') #make nicer printout for the user # create a copy of the call that has only the arguments we want, # and use it to call model.frame() indx <- match(c('formula', 'data', 'weights', 'subset','na.action', 'istate', 'id', "etype"), names(Call), nomatch=0) #It's very hard to get the next error message other than malice # eg survfit(wt=Surv(time, status) ~1) if (indx[1]==0) stop("a formula argument is required") temp <- Call[c(1, indx)] temp[[1L]] <- quote(stats::model.frame) m <- eval.parent(temp) Terms <- terms(formula, c("strata", "cluster")) ord <- attr(Terms, 'order') if (length(ord) & any(ord !=1)) stop("Interaction terms are not valid for this function") n <- nrow(m) Y <- model.extract(m, 'response') if (!is.Surv(Y)) stop("Response must be a survival object") casewt <- model.extract(m, "weights") if (is.null(casewt)) casewt <- rep(1,n) if (!is.null(attr(Terms, 'offset'))) warning("Offset term ignored") id <- model.extract(m, 'id') istate <- model.extract(m,"istate") temp <- untangle.specials(Terms, "cluster") if (length(temp$vars)>0) { if (length(temp$vars) > 1) stop("can not have two cluster terms") if (!is.null(id)) stop("can not have both a cluster term and an id variable") id <- m[[temp$vars]] Terms <- Terms[-temp$terms] } ll <- attr(Terms, 'term.labels') if (length(ll) == 0) X <- factor(rep(1,n)) # ~1 on the right else X <- strata(m[ll]) if (!is.Surv(Y)) stop("y must be a Surv object") # Backwards support for the now-depreciated etype argument etype <- model.extract(m, "etype") if (!is.null(etype)) { if (attr(Y, "type") == "mcounting" || attr(Y, "type") == "mright") stop("cannot use both the etype argument and mstate survival type") if (length(istate)) stop("cannot use both the etype and istate arguments") status <- Y[,ncol(Y)] etype <- as.factor(etype) temp <- table(etype, status==0) if (all(rowSums(temp==0) ==1)) { # The user had a unique level of etype for the censors newlev <- levels(etype)[order(-temp[,2])] #censors first } else newlev <- c(" ", levels(etype)[temp[,1] >0]) status <- factor(ifelse(status==0,0, as.numeric(etype)), labels=newlev) if (attr(Y, 'type') == "right") Y <- Surv(Y[,1], status, type="mstate") else if (attr(Y, "type") == "counting") Y <- Surv(Y[,1], Y[,2], status, type="mstate") else stop("etype argument incompatable with survival type") } # Deal with the near-ties problem if (!is.logical(timefix) || length(timefix) > 1) stop("invalid value for timefix option") if (timefix) newY <- aeqSurv(Y) # Call the appropriate helper function if (attr(Y, 'type') == 'left' || attr(Y, 'type') == 'interval') temp <- survfitTurnbull(X, newY, casewt, ...) else if (attr(Y, 'type') == "right" || attr(Y, 'type')== "counting") temp <- survfitKM(X, newY, casewt, ...) else if (attr(Y, 'type') == "mright" || attr(Y, "type")== "mcounting") temp <- survfitCI(X, newY, weights=casewt, id=id, istate=istate, ...) else { # This should never happen stop("unrecognized survival type") } if (is.null(temp$states)) class(temp) <- 'survfit' else class(temp) <- c("survfitms", "survfit") if (!is.null(attr(m, 'na.action'))) temp$na.action <- attr(m, 'na.action') temp$call <- Call temp } @ Once upon a time I allowed survfit to be called without the `\textasciitilde 1' portion of the formula. This was a mistake for multiple reasons, but the biggest problem is timing. If the subject has a data statement but the first argument is not a formula, R needs to evaluate Surv(t,s) to know that it is a survival object, but it also needs to know that this is a survival object before evaluation in order to dispatch the correct method. The method below helps give a useful error message in some cases. <>= survfit.Surv <- function(formula, ...) stop("the survfit function requires a formula as its first argument") @ survival/noweb/pyears2.Rnw0000644000175100001440000004310013046705744015342 0ustar hornikusers\subsection{Print and summary} The print function for pyear gives a very abbreviated printout: just a few lines. It works with pyears objects with or without a data component. <>= print.pyears <- function(x, ...) { if (!is.null(cl<- x$call)) { cat("Call:\n") dput(cl) cat("\n") } if (is.null(x$data)) { if (!is.null(x$event)) cat("Total number of events:", format(sum(x$event)), "\n") cat ( "Total number of person-years tabulated:", format(sum(x$pyears)), "\nTotal number of person-years off table:", format(x$offtable), "\n") } else { if (!is.null(x$data$event)) cat("Total number of events:", format(sum(x$data$event)), "\n") cat ( "Total number of person-years tabulated:", format(sum(x$data$pyears)), "\nTotal number of person-years off table:", format(x$offtable), "\n") } if (!is.null(x$summary)) { cat("Matches to the chosen rate table:\n ", x$summary) } cat("Observations in the data set:", x$observations, "\n") if (!is.null(x$na.action)) cat(" (", naprint(x$na.action), ")\n", sep='') cat("\n") invisible(x) } @ The summary function attempts to create output that looks like a pandoc table, which in turn makes it mesh nicely with Rstudio. Pandoc has 4 types of tables: with and without vertical bars and with single or multiple rows per cell. If the pyears object has only a single dimension then our output will be a simple table with a row or column for each of the output types (see the vertical argument). The result will be a simple table or a ``pipe'' table depending on the vline argument. For two or more dimensions the output follows the usual R strategy for printing an array, but with each ``cell'' containing all of the summaries for that combination of predictors, thus giving either a ``multiline'' or ``grid'' table. The default values of no vertical lines makes the tables appropriate for non-pandoc output such as a terminal session. <>= summary.pyears <- function(object, header=TRUE, call=header, n= TRUE, event=TRUE, pyears=TRUE, expected = TRUE, rate = FALSE, rr = expected, ci.r = FALSE, ci.rr = FALSE, totals=FALSE, legend=TRUE, vline = FALSE, vertical = TRUE, nastring=".", conf.level=0.95, scale= 1, ...) { # Usual checks if (!inherits(object, "pyears")) stop("input must be a pyears object") temp <- c(is.logical(header), is.logical(call), is.logical(n), is.logical(event) , is.logical(pyears), is.logical(expected), is.logical(rate), is.logical(ci.r), is.logical(rr), is.logical(ci.rr), is.logical(vline), is.logical(vertical), is.logical(legend), is.logical(totals)) tname <- c("header", "call", "n", "event", "pyears", "expected", "rate", "ci.r", "rr", "ci.rr", "vline", "vertical", "legend", "totals") if (any(!temp) || length(temp) != 14 || any(is.na(temp))) { stop("the ", paste(tname[!temp], collapse=", "), "argument(s) must be single logical values") } if (!is.numeric(conf.level) || conf.level <=0 || conf.level >=1 | length(conf.level) > 1 || is.na(conf.level) > 1) stop("conf.level must be a single numeric between 0 and 1") if (is.na(scale) || !is.numeric(scale) || length(scale) !=1 || scale <=0) stop("scale must be a value > 0") vname <- attr(terms(object), "term.labels") #variable names if (!is.null(object$data)) { # Extra work: restore the tables which had been unpacked into a df # All of the categories are factors in this case tdata <- object$data[vname] # the conditioning variables dname <- lapply(tdata, function(x) { if (is.factor(x)) levels(x) else sort(unique(x))}) # dimnames dd <- sapply(dname, length) # dim of arrays index <- tapply(tdata[,1], tdata) restore <- c('n', 'event', 'pyears', 'expected') #do these, if present restore <- restore[restore %in% names(object$data)] new <- lapply(object$data[restore], function(x) { temp <- array(0L, dim=dd, dimnames=dname) temp[index] <- x temp} ) object <- c(object, new) } if (is.null(object$expected)) { expected <- FALSE rr <- FALSE ci.rr <- FALSE } if (is.null(object$event)) { event <- FALSE rate <- FALSE ci.r <- FALSE rr <- FALSE ci.rr <- FALSE } # print out the front matter if (call && !is.null(object$call)) { cat("Call: ") dput(object$call) cat("\n") } if (header) { cat("number of observations =", object$observations) if (length(object$omit)) cat(" (", naprint(object$omit), ")\n", sep="") else cat("\n") if (object$offtable > 0) cat(" Total time lost (off table)", format(object$offtable), "\n") cat("\n") } # Add in totals if requested if (totals) { # if the pyear object was based on any time dependent cuts, then # the "n" component cannot be totaled up. tcut <- if (is.null(object$tcut)) TRUE else object$tcut object$n <- pytot(object$n, na=tcut) object$pyears <- pytot(object$pyears) if (event) object$event <- pytot(object$event) if (expected) object$expected <- pytot(object$expected) } dd <- dim(object$n) vname <- attr(terms(object), "term.labels") #variable names <> if (length(dd) ==1) { # 1 dimensional table <> } else { # more than 1 dimension <> } invisible(object) } <> @ <>= # Put the elements to be printed onto a list pname <- (tname[3:6])[c(n, event, pyears, expected)] plist <- object[pname] if (rate) { pname <- c(pname, "rate") plist$r <- scale* object$event/object$pyears } if (ci.r) { pname <- c(pname, "ci.r") plist$ci.r <- cipoisson(object$event, object$pyears, p=conf.level) *scale } if (rr) { pname <- c(pname, "rr") plist$rr <- object$event/object$expected } if (ci.rr) { pname <- c(pname, "ci.rr") plist$ci.rr <- cipoisson(object$event, object$expected, p=conf.level) } rname <- c(n = "N", event="Events", pyears= "Time", expected= "Expected events", rate = "Event rate", ci.r = "CI (rate)", rr= "Obs/Exp", ci.rr= "CI (O/E)") rname <- rname[pname] @ If there is only one dimension to the table we can forgo the top legend and use the object names as one of the margins. If \code{vertical=TRUE} the output types are vertical, otherwise they are horizontal. Format each element of the output separately. <>= cname <- names(object$n) #category names if (vertical) { # The person-years objects list across the top, categories up and down # This makes columns line up in a standard "R" way # The first column label is the variable name, content is the categories plist <- lapply(plist, pformat, nastring, ...) # make it character pcol <- sapply(plist, function(x) nchar(x[1])) #width of each one colwidth <- pmax(pcol, nchar(rname)) +2 for (i in 1:length(plist)) plist[[i]] <- strpad(plist[[i]], colwidth[i]) colwidth <- c(max(nchar(vname), nchar(cname)) +2, colwidth) leftcol <- list(strpad(cname, colwidth[1])) header <- strpad(c(vname, rname), colwidth) } else { # in this case each column will have different types of objects in it # alignment is the nuisance newmat <- pybox(plist, length(plist[[1]]), nastring, ...) colwidth <- pmax(nchar(cname), apply(nchar(newmat), 1, max)) +2 # turn the list sideways plist <- split(newmat, row(newmat)) for (i in 1:length(plist)) plist[[i]] <- strpad(plist[[i]], colwidth[i]) colwidth <- c(max(nchar(vname), nchar(rname)) +2, colwidth) leftcol <- list(strpad(rname, colwidth[1])) header <- strpad(c(vname, cname), colwidth) } # Now print it if (vline) { # use a pipe table cat(paste(header, collapse = "|"), "\n") cat(paste(strpad("-", colwidth, "-"), collapse="|"), "\n") temp <- do.call("paste", c(leftcol, plist, list(sep ="|"))) cat(temp, sep= '\n') } else { cat(paste(header, collapse = " "), "\n") cat(paste(strpad("-", colwidth, "-"), collapse=" "), "\n") temp <- do.call("paste", c(leftcol, plist, list(sep =" "))) cat(temp, sep='\n') } @ When there are more than one category in the pyears object then we use a special layout. Each 'cell' of the printed table has all of the values in it. <>= if (header) { # the header is itself a table width <- max(nchar(rname)) if (vline) { cat('+', strpad('-', width, '-'), "+\n", sep="") cat(paste0('|',strpad(rname, width), '|'), sep='\n') cat('+', strpad('-', width, '-'), "+\n\n", sep="") } else { cat(strpad('-', width, '-'), "\n") cat(strpad(rname, width), sep='\n') cat(strpad('-', width, '-'), "\n\n") } } tname <- vname[1:2] #names for the row and col rowname <- dimnames(object$n)[[1]] colname <- dimnames(object$n)[[2]] if (length(dd) > 2) newmat <- pybox(plist, c(dd[1],dd[2], prod(dd[-(1:2)])), nastring, ...) else newmat <- pybox(plist, dd, nastring, ...) if (length(dd) > 2) { newmat <- pybox(plist, c(dd[1],dd[2], prod(dd[-(1:2)])), nastring, ...) outer.label <- do.call("expand.grid", dimnames(object$n)[-(1:2)]) temp <- names(outer.label) for (i in 1:nrow(outer.label)) { # first the caption, then data cat(paste(":", paste(temp, outer.label[i,], sep="=")), '\n') pyshow(newmat[,,i,], tname, rowname, colname, vline) } } else { newmat <- pybox(plist, dd, nastring, ...) pyshow(newmat, tname, rowname, colname, vline) } @ Here are some character manipulation functions. The stringi package has more elegant versions of the pad function, but we don't need the speed. No one is going to print out thousands of lines. <>= strpad <- function(x, width, pad=' ') { # x = the string(s) to be padded out # width = width of desired string. nc <- nchar(x) added <- width - nc left <- pmax(0, floor(added/2)) # can't add negative space right <- pmax(0, width - (nc + left)) # right will be >= left if (all(right <=0)) { if (length(x) >= length(width)) x # nothing needs to be done else rep(x, length=length(width)) } else { # Each pad could be a different length. # Make a long string from which we can take a portion longpad <- paste(rep(pad, max(right)), collapse='') paste0(substring(longpad, 1, left), x, substring(longpad,1, right)) } } pformat <- function(x, nastring, ...) { # This is only called for single index tables, in vertical mode # Any matrix will be a confidence interval if (is.matrix(x)) ret <- paste(ifelse(is.na(x[,1]), nastring, format(x[,1], ...)), "-", ifelse(is.na(x[,2]), nastring, format(x[,2], ...))) else ret <- ifelse(is.na(x), nastring, format(x, ...)) } @ Create formatted boxes. We want all the decimal points to line up, so the format calls are in 3 parts: integer, real, and confidence interval. If there are confidence intervals, format their values and then paste together the left-right ends. The intermediag form \code{final} is a matrix with one column per statistic. At the end, reformat it as an array whose last dimension is the components. <>= pybox <- function(plist, dd, nastring, ...) { ci <- (substring(names(plist), 1,3) == "ci.") # the CI components int <- sapply(plist, function(x) all(x == floor(x) | is.na(x))) int <- (!ci & int) real<- (!ci & !int) nc <- prod(dd) final <- matrix("", nrow=nc, ncol=length(ci)) if (any(int)) { # integers if (any(sapply(plist[int], length) != nc)) stop("programming length error, notify package author") temp <- unlist(plist[int]) final[,int] <- ifelse(is.na(temp), nastring, format(temp)) } if (any(real)) { # floating point if (any(sapply(plist[real], length) != nc)) stop("programming length error, notify package author") temp <- unlist(plist[real]) final[,real] <- ifelse(is.na(temp), nastring, format(temp, ...)) } if (any(ci)) { if (any(sapply(plist[ci], length) != nc*2)) stop("programming length error, notify package author") temp <- unlist(plist[ci]) temp <- array(ifelse(is.na(temp), nastring, format(temp, ...)), dim=c(nc, 2, sum(ci))) final[,ci] <- paste(temp[,1,], temp[,2,], sep='-') } array(final, dim=c(dd, length(ci))) } @ This function prints out a box table. Each cell contains the full set of statistics that were requested. Most of the work is the creation of the appropriate spacing and special characters to create a valid pandoc table. <>= pyshow <- function(dmat, labels, rowname, colname, vline) { # Every column is the same width, except the first colwidth <- c(max(nchar(rowname), nchar(labels[1])), rep(max(nchar(dmat[1,1,]), nchar(colname)), length(colname))) colwidth[2] <- max(colwidth[2], nchar(labels[2])) ncol <- length(colwidth) dd <- dim(dmat) # vector of length 3, third dim is the statistics rline <- ceiling(dd[3]/2) #which line to put the row label on. if (vline) { # use a grid table cat("+", paste(strpad('-', colwidth, pad='-'), collapse='+'), "+\n", sep='') temp <- rep(' ', ncol); temp[2] <- labels[2] cat("|", paste(strpad(temp, colwidth), collapse="|"), "|\n", sep='') cat("|", paste(strpad(c(labels[1], colname), colwidth), collapse="|"), "|\n", sep='') cat("+", paste(strpad('=', colwidth, pad='='), collapse="+"), "+\n", sep='') for (i in 1:dd[1]) { for (j in 1:dd[3]) { #one printout line per stat if (j==rline) temp <- c(rowname[i], dmat[i,,j]) else temp <- c("", dmat[i,,j]) cat("|", paste(strpad(temp, colwidth), collapse='|'), "|\n", sep='') } cat("+", paste(strpad('-', colwidth, '-'), collapse='+'), "+\n", sep='') } } else { # use a multiline table cat(paste(strpad('-', colwidth, '-'), collapse='-'), "\n") temp <- rep(' ', ncol); temp[2] <- labels[2] cat(paste(strpad(temp, colwidth), collapse=" "), "\n") cat(paste(strpad(c(labels[1], colname), colwidth), collapse=" "), "\n") cat(paste(strpad('-', colwidth, pad='-'), collapse=" "), "\n") for (i in 1:dd[1]) { for (j in 1:dd[3]) { #one printout line per stat if (j==rline) temp <- c(rowname[i], dmat[i,,j]) else temp <- c("", dmat[i,,j]) cat(paste(strpad(temp, colwidth), collapse=' '), "\n") } if (i< dd[1]) cat(" \n") #blank line } cat(paste(strpad('-', colwidth, '-'), collapse='-'), "\n") } } @ This function adds a totals row to the data, for either the first or first and second dimensions. The ``n'' component can't be totaled, so we turn that into NA. <>= pytot <- function(x, na=FALSE) { dd <- dim(x) if (length(dd) ==1) { if (na) array(c(x, NA), dim= length(x) +1, dimnames=list(c(dimnames(x)[[1]], "Total"))) else array(c(x, sum(x)), dim= length(x) +1, dimnames=list(c(dimnames(x)[[1]], "Total"))) } else if (length(dd) ==2) { if (na) new <- rbind(cbind(x, NA), NA) else { new <- rbind(x, colSums(x)) new <- cbind(new, rowSums(new)) } array(new, dim=dim(x) + c(1,1), dimnames=list(c(dimnames(x)[[1]], "Total"), c(dimnames(x)[[2]], "Total"))) } else { # The general case index <- 1:length(dd) if (na) sum1 <- sum2 <- sum3 <- NA else { sum1 <- apply(x, index[-1], sum) # row sums sum2 <- apply(x, index[-2], sum) # col sums sum3 <- apply(x, index[-(1:2)], sum) # total sums } # create a new matrix and then fill it in d2 <- dd d2[1:2] <- dd[1:2] +1 dname <- dimnames(x) dname[[1]] <- c(dname[[1]], "Total") dname[[2]] <- c(dname[[2]], "Total") new <- array(x[1], dim=d2, dimnames=dname) # say dim(x) =(5,8,4); we want new[6,-9,] <- sum1; new[-6,9,] <- sum2 # and new[6,9,] <- sum3 # if dim is longer, we need to add more commas commas <- rep(',', length(dd) -2) eval(parse(text=paste("new[1:dd[1], 1:dd[2]", commas, "] <- x"))) eval(parse(text=paste("new[ d2[1],-d2[2]", commas, "] <- sum1"))) eval(parse(text=paste("new[-d2[1], d2[2]", commas, "] <- sum2"))) eval(parse(text=paste("new[ d2[1], d2[2]", commas, "] <- sum3"))) new } } @ survival/noweb/tail0000644000175100001440000000007611773344220014137 0ustar hornikusers\bibliographystyle{plain} \bibliography{refer} \end{document} survival/noweb/exact.nw0000644000175100001440000004101212514444605014732 0ustar hornikusers\section{Exact partial likelihood} Let $r_i = \exp(X_i\beta)$ be the risk score for observation $i$. For one of the time points assume that there that there are $d$ tied deaths among $n$ subjects at risk. For convenience we will index them as $i= 1,\ldots,d$ in the $n$ at risk. Then for the exact parial likelihood, the contribution at this time point is \begin{align*} L &= \sum_{i=1}^d \log(r_i) - \log(D) \\ \frac{\partial L}{\partial \beta_j} &= x_{ij} - (1/D) \frac{\partial D}{\partial \beta_j} \\ \frac{\partial^2 L}{\partial \beta_j \partial \beta_k} &= (1/D^2)\left[D\frac{\partial^2D}{\partial \beta_j \partial \beta_k} - \frac{\partial D}{\partial \beta_j}\frac{\partial D}{\partial \beta_k} \right] \end{align*} The hard part of this computation is $D$, which is a sum \begin{equation*} D = \sum_{S(d,n)} r_{s_1}r_{s_2} \ldots r_{s_d} \end{equation*} where $S(d,n)$ is the set of all possible subsets of size $d$ from $n$ objects, and $s_1, s_2, \ldots$ indexes the current selection. So if $n=6$ and $d=2$ we would have the 15 pairs 12, 13, .... 56; for $n=5$ and $d=3$ there would be 10 triples 123, 124, 125, \ldots, 345. The brute force computation of all subsets can take a very long time. Gail et al \cite{Gail81} show simple recursion formulas that speed this up considerably. Let $D(d,n)$ be the denominator with $d$ deaths and $n$ subjects. Then \begin{align} D(d,n) &= r_nD(d-1, n-1) + D(d, n-1) \label{d0}\\ \frac{\partial D(d,n)}{\partial \beta_j} &= \frac{\partial D(d, n-1)}{\partial \beta_j} + r_n \frac{\partial D(d-1, n-1)}{\partial \beta_j} + x_{nj}r_n D(d-1, n-1) \label{d1}\\ \frac{\partial^2D(d,n}{\partial \beta_j \partial \beta_k} &= \frac{\partial^2D(d,n-1)}{\partial \beta_j \partial \beta_k} + r_n\frac{\partial^2D(d-1,n-1)}{\partial \beta_j \partial \beta_k} + x_{nj}r_n\frac{\partial D(d-1, n-1)}{\partial \beta_k} + \nonumber \\ & x_{nk}r_n\frac{\partial D(d-1, n-1)}{\partial \beta_j} + x_{nj}x_{nk}r_n D(d-1, n-1) \label{d2} \end{align} The above recursion is captured in the three routines below. The first calculates $D$. It is called with $d$, $n$, an array that will contain all the values of $D(d,n)$ computed so far, and the the first dimension of the array. The intial condition $D(0,n)=1$ is important to all three routines. <>= double coxd0(int d, int n, double *score, double *dmat, int dmax) { double *dn; if (d==0) return(1.0); dn = dmat + (n-1)*dmax + d -1; /* pointer to dmat[d,n] */ if (*dn ==0) { /* still to be computed */ *dn = score[n-1]* coxd0(d-1, n-1, score, dmat, dmax); if (d>= double coxd1(int d, int n, double *score, double *dmat, double *d1, double *covar, int dmax) { int indx; indx = (n-1)*dmax + d -1; /*index to the current array member d1[d.n]*/ if (d1[indx] ==0) { /* still to be computed */ d1[indx] = score[n-1]* covar[n-1]* coxd0(d-1, n-1, score, dmat, dmax); if (d1) d1[indx] += score[n-1]* coxd1(d-1, n-1, score, dmat, d1, covar, dmax); } return(d1[indx]); } double coxd2(int d, int n, double *score, double *dmat, double *d1j, double *d1k, double *d2, double *covarj, double *covark, int dmax) { int indx; indx = (n-1)*dmax + d -1; /*index to the current array member d1[d,n]*/ if (d2[indx] ==0) { /*still to be computed */ d2[indx] = coxd0(d-1, n-1, score, dmat, dmax)*score[n-1] * covarj[n-1]* covark[n-1]; if (d1) d2[indx] += score[n-1] * ( coxd2(d-1, n-1, score, dmat, d1j, d1k, d2, covarj, covark, dmax) + covarj[n-1] * coxd1(d-1, n-1, score, dmat, d1k, covark, dmax) + covark[n-1] * coxd1(d-1, n-1, score, dmat, d1j, covarj, dmax)); } return(d2[indx]); } @ Now for the main body. Start with the dull part of the code: declarations. I use [[maxiter2]] for the S structure and [[maxiter]] for the variable within it, and etc for the other input arguments. All the input arguments except strata are read-only. The output beta vector starts as a copy of ibeta. <>= #include #include "survS.h" #include "survproto.h" #include <> SEXP coxexact(SEXP maxiter2, SEXP y2, SEXP covar2, SEXP offset2, SEXP strata2, SEXP ibeta, SEXP eps2, SEXP toler2) { int i,j,k; int iter; double **covar, **imat; /*ragged arrays */ double *time, *status; /* input data */ double *offset; int *strata; int sstart; /* starting obs of current strata */ double *score; double *oldbeta; double zbeta; double newlk=0; double temp; int halving; /*are we doing step halving at the moment? */ int nrisk; /* number of subjects in the current risk set */ int dsize, /* memory needed for one coxc0, coxc1, or coxd2 array */ dmemtot, /* amount needed for all arrays */ ndeath; /* number of deaths at the current time point */ double maxdeath; /* max tied deaths within a strata */ double dtime; /* time value under current examiniation */ double *dmem0, **dmem1, *dmem2; /* pointers to memory */ double *dtemp; /* used for zeroing the memory */ double *d1; /* current first derivatives from coxd1 */ double d0; /* global sum from coxc0 */ /* copies of scalar input arguments */ int nused, nvar, maxiter; double eps, toler; /* returned objects */ SEXP imat2, beta2, u2, loglik2; double *beta, *u, *loglik; SEXP rlist, rlistnames; int nprotect; /* number of protect calls I have issued */ <> <> <> <> } @ Setup is ordinary. Grab S objects and assign others. I use \verb!R_alloc! for temporary ones since it is released automatically on return. <>= nused = LENGTH(offset2); nvar = ncols(covar2); maxiter = asInteger(maxiter2); eps = asReal(eps2); /* convergence criteria */ toler = asReal(toler2); /* tolerance for cholesky */ /* ** Set up the ragged array pointer to the X matrix, ** and pointers to time and status */ covar= dmatrix(REAL(covar2), nused, nvar); time = REAL(y2); status = time +nused; strata = INTEGER(PROTECT(duplicate(strata2))); offset = REAL(offset2); /* temporary vectors */ score = (double *) R_alloc(nused+nvar, sizeof(double)); oldbeta = score + nused; /* ** create output variables */ PROTECT(beta2 = duplicate(ibeta)); beta = REAL(beta2); PROTECT(u2 = allocVector(REALSXP, nvar)); u = REAL(u2); PROTECT(imat2 = allocVector(REALSXP, nvar*nvar)); imat = dmatrix(REAL(imat2), nvar, nvar); PROTECT(loglik2 = allocVector(REALSXP, 5)); /* loglik, sctest, flag,maxiter*/ loglik = REAL(loglik2); nprotect = 5; @ The data passed to us has been sorted by strata, and reverse time within strata (longest subject first). The variable [[strata]] will be 1 at the start of each new strata. Separate strata are completely separate computations: time 10 in one strata and time 10 in another are not comingled. Compute the largest product (size of strata)* (max tied deaths in strata) for allocating scratch space. When computing $D$ it is advantageous to create all the intermediate values of $D(d,n)$ in an array since they will be used in the derivative calculation. Likewise, the first derivatives are used in calculating the second. Even more importantly, say we have a large data set. It will be sorted with the longest times first. If there is a death with 30 at risk and another with 40 at risk, the intermediate sums we computed for the n=30 case are part of the computation for n=40. To make this work we need to index our matrices, within any strata, by the maximum number of tied deaths in the strata. We save this in the strata variable: first obs of a new strata has the number of events. And what if a strata had 0 events? We mark it with a 1. Note that the maxdeath variable is floating point. I had someone call this routine with a data set that gives an integer overflow in that situation. We now keep track of this further below and fail with a message. Such a run would take longer than forever to complete even if integer subscripts did not overflow. <>= strata[0] =1; /* in case the parent forgot */ temp = 0; /* temp variable for dsize */ maxdeath =0; j=0; /* start of the strata */ for (i=0; i0) { /* If maxdeath <2 leave the strata alone at it's current value of 1 */ if (maxdeath >1) strata[j] = maxdeath; j = i; if (maxdeath*nrisk > temp) temp = maxdeath*nrisk; } maxdeath =0; /* max tied deaths at any time in this strata */ nrisk=0; ndeath =0; } dtime = time[i]; ndeath =0; /*number tied here */ while (time[i] ==dtime) { nrisk++; ndeath += status[i]; i++; if (i>=nused || strata[i] >0) break; /*tied deaths don't cross strata */ } if (ndeath > maxdeath) maxdeath=ndeath; } if (maxdeath*nrisk > temp) temp = maxdeath*nrisk; if (maxdeath >1) strata[j] = maxdeath; /* Now allocate memory for the scratch arrays Each per-variable slice is of size dsize */ dsize = temp; temp = temp * ((nvar*(nvar+1))/2 + nvar + 1); dmemtot = dsize * ((nvar*(nvar+1))/2 + nvar + 1); if (temp != dmemtot) { /* the subscripts will overflow */ error("(number at risk) * (number tied deaths) is too large"); } dmem0 = (double *) R_alloc(dmemtot, sizeof(double)); /*pointer to memory */ dmem1 = (double **) R_alloc(nvar, sizeof(double*)); dmem1[0] = dmem0 + dsize; /*points to the first derivative memory */ for (i=1; i>= for (i=0; i0) { /* first obs of a new strata */ maxdeath= strata[i]; dtemp = dmem0; for (j=0; j=nused || strata[i] >0) break; } /* We have added up over the death time, now process it */ if (ndeath >0) { /* Add to the loglik */ d0 = coxd0(ndeath, nrisk, score+sstart, dmem0, maxdeath); R_CheckUserInterrupt(); newlk -= log(d0); dmem2 = dmem0 + (nvar+1)*dsize; /*start for the second deriv memory */ for (j=0; j 3) R_CheckUserInterrupt(); u[j] -= d1[j]; for (k=0; k<= j; k++) { /* second derivative*/ temp = coxd2(ndeath, nrisk, score+sstart, dmem0, dmem1[j], dmem1[k], dmem2, covar[j] + sstart, covar[k] + sstart, maxdeath); if (ndeath > 5) R_CheckUserInterrupt(); imat[k][j] += temp/d0 - d1[j]*d1[k]; dmem2 += dsize; } } } } @ Do the first iteration of the solution. The first iteration is different in 3 ways: it is used to set the initial log-likelihood, to compute the score test, and we pay no attention to convergence criteria or diagnositics. (I expect it not to converge in one iteration). <>= /* ** do the initial iteration step */ newlk =0; for (i=0; i> loglik[0] = newlk; /* save the loglik for iteration zero */ loglik[1] = newlk; /* and it is our current best guess */ /* ** update the betas and compute the score test */ for (i=0; i> } /* ** Never, never complain about convergence on the first step. That way, ** if someone has to they can force one iter at a time. */ for (i=0; i>= halving =0 ; /* =1 when in the midst of "step halving" */ for (iter=1; iter<=maxiter; iter++) { newlk =0; for (i=0; i> /* am I done? ** update the betas and test for convergence */ loglik[3] = cholesky2(imat, nvar, toler); if (fabs(1-(loglik[1]/newlk))<= eps && halving==0) { /* all done */ loglik[1] = newlk; <> } if (iter==maxiter) break; /*skip the step halving and etc */ if (newlk < loglik[1]) { /*it is not converging ! */ halving =1; for (i=0; i> @ The common code for finishing. 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toler.chol= toler.chol, debug=debug, maxiter=maxiter, outer.max=outer.max) } survival/R/print.summary.coxph.S0000644000175100001440000000415213016105374016442 0ustar hornikusersprint.summary.coxph <- function(x, digits = max(getOption('digits')-3, 3), signif.stars = getOption("show.signif.stars"), ...) { if (!is.null(x$call)) { cat("Call:\n") dput(x$call) cat("\n") } if (!is.null(x$fail)) { cat(" Coxreg failed.", x$fail, "\n") return() } savedig <- options(digits = digits) on.exit(options(savedig)) omit <- x$na.action cat(" n=", x$n) if (!is.null(x$nevent)) cat(", number of events=", x$nevent, "\n") else cat("\n") if (length(omit)) cat(" (", naprint(omit), ")\n", sep="") if (nrow(x$coef)==0) { # Null model cat (" Null model\n") return() } if(!is.null(x$coefficients)) { cat("\n") printCoefmat(x$coefficients, digits=digits, signif.stars=signif.stars, ...) } if(!is.null(x$conf.int)) { cat("\n") print(x$conf.int) } cat("\n") if (!is.null(x$concordance)) { cat("Concordance=", format(round(x$concordance[1],3)), " (se =", format(round(x$concordance[2], 3)),")\n") } cat("Rsquare=", format(round(x$rsq["rsq"],3)), " (max possible=", format(round(x$rsq["maxrsq"],3)), ")\n" ) cat("Likelihood ratio test= ", format(round(x$logtest["test"], 2)), " on ", x$logtest["df"], " df,", " p=", format(x$logtest["pvalue"]), "\n", sep = "") cat("Wald test = ", format(round(x$waldtest["test"], 2)), " on ", x$waldtest["df"], " df,", " p=", format(x$waldtest["pvalue"]), "\n", sep = "") cat("Score (logrank) test = ", format(round(x$sctest["test"], 2)), " on ", x$sctest["df"]," df,", " p=", format(x$sctest["pvalue"]), sep ="") if (is.null(x$robscore)) cat("\n\n") else cat(", Robust = ", format(round(x$robscore["test"], 2)), " p=", format(x$robscore["pvalue"]), "\n\n", sep="") if (x$used.robust) cat(" (Note: the likelihood ratio and score tests", "assume independence of\n observations within a cluster,", "the Wald and robust score tests do not).\n") invisible() } survival/R/print.coxph.penal.S0000644000175100001440000000730312536376005016054 0ustar hornikusersprint.coxph.penal <- function(x, terms=FALSE, maxlabel=25, digits=max(options()$digits - 4, 3), ...) { if (!inherits(x, 'coxph.penal')) stop("Invalid object") if (!is.null(x$call)) { cat("Call:\n") dput(x$call) cat("\n") } if (!is.null(x$fail)) { cat(" Coxph failed.", x$fail, "\n") return() } savedig <- options(digits = digits) on.exit(options(savedig)) coef <- x$coefficients if (length(coef)==0 && length(x$frail)==0) stop("Penalized print function can't be used for a null model") # # Map terms to special print functions, and the list of iteration histories # pterms <- x$pterms nterms <- length(pterms) npenal <- sum(pterms>0) print.map <- rep(0,nterms) if (!is.null(x$printfun)) { temp <- unlist(lapply(x$printfun, is.null)) #which ones are missing print.map[pterms>0] <- (1:npenal) * (!temp) } # Tedious, but build up the coef matrix a term at a time print1 <- NULL pname1 <- NULL if (is.null(x$assign2)) alist <- x$assign[-1] else alist <- x$assign2 print2 <- NULL for (i in 1:nterms) { kk <- alist[[i]] if (print.map[i] >0) { j <- print.map[i] if (pterms[i]==2) temp <- (x$printfun[[j]])(x$frail, x$fvar, ,x$df[i], x$history[[j]]) else temp <- (x$printfun[[j]])(coef[kk], x$var[kk,kk], x$var2[kk,kk], x$df[i], x$history[[j]]) print1 <- rbind(print1, temp$coef) if (is.matrix(temp$coef)) { xx <- dimnames(temp$coef)[[1]] if (is.null(xx)) xx <- rep(names(pterms)[i], nrow(temp$coef)) else xx <- paste(names(pterms)[i], xx, sep=', ') pname1 <- c(pname1, xx) } else pname1 <- c(pname1, names(pterms)[i]) print2 <- c(print2, temp$history) } else if (terms && length(kk)>1) { pname1 <- c(pname1, names(pterms)[i]) temp <- coxph.wtest(x$var[kk,kk], coef[kk])$test print1 <- rbind(print1, c(NA, NA, NA, temp, x$df[i], 1-pchisq(temp, 1))) } else { pname1 <- c(pname1, names(coef)[kk]) tempe<- (diag(x$var))[kk] temp <- coef[kk]^2/ tempe print1 <- rbind(print1, cbind(coef[kk], sqrt(tempe), sqrt((diag(x$var2))[kk]), temp, 1, 1-pchisq(temp, 1))) } } # Format out the NA's # temp <- cbind(format(print1[,1]), format(print1[,2]), # format(print1[,3]), # format(round(print1[,4], 2)), # format(round(print1[,5], 2)), # format(signif(print1[,6], 2))) # temp <- ifelse(is.na(print1), "", temp) # dimnames(temp) <- list(substring(pname1,1, maxlabel), # c("coef","se(coef)", "se2", "Chisq","DF","p")) # print(temp, quote=FALSE) dimnames(print1) <- list(substring(pname1,1, maxlabel), c("coef","se(coef)", "se2", "Chisq","DF","p")) printCoefmat(print1, signif.stars=FALSE, P.values=TRUE, has.Pvalue=TRUE, na.print="") # # Write out the remaider of the info # cat("\nIterations:", x$iter[1], "outer,", x$iter[2], "Newton-Raphson\n") if (length(print2)) { # cat("Penalized terms:\n") for (i in 1:length(print2)) cat(" ", print2[i], "\n") } logtest <- -2 * (x$loglik[1] - x$loglik[2]) if (is.null(x$df)) df <- sum(!is.na(coef)) else df <- round(sum(x$df),2) # cat("\n") cat("Degrees of freedom for terms=", format(round(x$df,1)), "\n") # cat("Cox PL (initial,final) = ", format(round(x$loglik,2)), # " Penalty = ", format(x$penalty), "\n") cat("Likelihood ratio test=", format(round(logtest, 2)), " on ", df, " df,", " p=", format(1 - pchisq(logtest, df)), sep="") omit <- x$na.action if (length(omit)) cat("\n n=", x$n, " (", naprint(omit), ")\n", sep="") else cat(" n=", x$n, "\n") invisible() } survival/R/summary.coxph.S0000644000175100001440000000573413016105374015316 0ustar hornikuserssummary.coxph <- function(object, conf.int = 0.95, scale = 1, ...) { cox<-object beta <- cox$coefficients if (is.null(cox$coefficients)) { # Null model return(object) #The summary method is the same as print in this case } nabeta <- !(is.na(beta)) #non-missing coefs beta2 <- beta[nabeta] if(is.null(beta) | is.null(cox$var)) stop("Input is not valid") se <- sqrt(diag(cox$var)) if (!is.null(cox$naive.var)) nse <- sqrt(diag(cox$naive.var)) rval<-list(call=cox$call,fail=cox$fail, na.action=cox$na.action, n=cox$n, loglik=cox$loglik) if (!is.null(cox$nevent)) rval$nevent <- cox$nevent if (is.null(cox$naive.var)) { tmp <- cbind(beta, exp(beta), se, beta/se, 1 - pchisq((beta/ se)^2, 1)) dimnames(tmp) <- list(names(beta), c("coef", "exp(coef)", "se(coef)", "z", "Pr(>|z|)")) } else { tmp <- cbind(beta, exp(beta), nse, se, beta/se, 1 - pchisq((beta/ se)^2, 1)) dimnames(tmp) <- list(names(beta), c("coef", "exp(coef)", "se(coef)", "robust se", "z", "Pr(>|z|)")) } rval$coefficients <- tmp if (conf.int) { z <- qnorm((1 + conf.int)/2, 0, 1) beta <- beta * scale se <- se * scale tmp <- cbind(exp(beta), exp(-beta), exp(beta - z * se), exp(beta + z * se)) dimnames(tmp) <- list(names(beta), c("exp(coef)", "exp(-coef)", paste("lower .", round(100 * conf.int, 2), sep = ""), paste("upper .", round(100 * conf.int, 2), sep = ""))) rval$conf.int <- tmp } df <- length(beta2) logtest <- -2 * (cox$loglik[1] - cox$loglik[2]) rval$logtest <- c(test=logtest, df=df, pvalue=1 - pchisq(logtest, df)) rval$sctest <- c(test=cox$score, df=df, pvalue=1 - pchisq(cox$score, df)) rval$rsq<-c(rsq=1-exp(-logtest/cox$n), maxrsq=1-exp(2*cox$loglik[1]/cox$n)) rval$waldtest<-c(test=as.vector(round(cox$wald.test, 2)), df=df, pvalue=1 - pchisq(as.vector(cox$wald.test), df)) if (!is.null(cox$rscore)) rval$robscore<-c(test=cox$rscore, df=df, pvalue=1 - pchisq(cox$rscore, df)) rval$used.robust<-!is.null(cox$naive.var) if (!is.null(cox$concordance)) { # A stratified model has a matrix of values, one row per strata if (is.matrix(cox$concordance)) temp <- colSums(cox$concordance) else temp <- cox$concordance # C= (concordant + tied/2)/(concordant + discordant + tied) rval$concordance <- c((temp[1] + temp[3]/2)/sum(temp[1:3]), temp[5]/(2*sum(temp[1:3]))) names(rval$concordance) <- c("C", "se(C)") } class(rval) <-"summary.coxph" rval } survival/R/residuals.survreg.penal.S0000644000175100001440000000063311732700061017254 0ustar hornikusers# $Id: residuals.survreg.penal.S 11166 2008-11-24 22:10:34Z therneau $ # This routine just stops disastrous arithmetic for models with sparse # terms. A placeholder until the proper sparse terms actions are inserted. residuals.survreg.penal <- function(object, ...) { pterms <- object$pterms if (any(pterms==2)) stop("Residualss not available for sparse models") NextMethod('residuals') } survival/R/frailty.gaussian.S0000644000175100001440000000752713016105374015766 0ustar hornikusers# # Defining function for gaussian frailty fits # frailty.gaussian <- function(x, sparse=(nclass >5), theta, df, method=c("reml", "aic", "df", "fixed"), ...) { # Check for consistency of the arguments if (missing(method)) { if (!missing(theta)) { method <- 'fixed' if (!missing(df)) stop("Cannot give both a df and theta argument") } else if (!missing(df)) { if (df==0) method <- "aic" else method <- 'df' } } method <- match.arg(method) if (method=='df' && missing(df)) stop("Method = df but no df argument") if (method=='fixed' && missing(theta)) stop("Method= fixed but no theta argument") if (method !='fixed' && !missing(theta)) stop("Method is not 'fixed', but have a theta argument") nclass <- length(unique(x[!is.na(x)])) if (sparse){ x <- as.numeric(factor(x)) #if there are missing levels, drop them class(x) <- "coxph.penalty" } else{ x <- factor(x) nclass <- length(levels(x)) class(x) <- c("coxph.penalty", class(x)) attr(x, 'contrasts') <- contr.treatment(nclass, contrasts=FALSE) } if (!missing(theta) & !missing(df)) stop("Cannot give both a df and theta argument") pfun<- function(coef, theta, ndead){ if (theta==0) list(recenter=0, penalty=0, flag=TRUE) else { recenter <- mean(coef) coef <- coef - recenter list(recenter = recenter, first= coef/theta, second= rep(1, length(coef))/theta, # penalty= -sum(log(dnorm(coef,0, sqrt(theta))), penalty= 0.5* sum(coef^2/theta + log(2*pi*theta)), flag=FALSE) } } printfun <- function(coef, var, var2, df, history) { if (!is.null(history$history)) theta <- history$history[nrow(history$history),1] else theta <- history$theta if (is.matrix(var)) test <- coxph.wtest(var, coef)$test else test <- sum(coef^2/var) df2 <- max(df, .5) # Stop silly p-values list(coef=c(NA, NA, NA, test, df, 1-pchisq(test, df2)), history=paste("Variance of random effect=", format(theta))) } # The final coxph object will contain a copy of printfun. Stop it from # also containing huge unnecessary variables, e.g. 'x', known at this # point in time. Not an issue for pfun, which does not get saved. # Setting to globalenv() will not suffice since coxph.wtest is not visible # outside the survival library's name space. temp <- new.env(parent=globalenv()) assign("cox.zph", cox.zph, envir=temp) #make a private copy environment(printfun) <- temp if (method=='reml') { temp <- list(pfun=pfun, printfun=printfun, diag =TRUE, sparse= sparse, cargs = c('coef', 'trH', 'loglik'), cfun = frailty.controlgauss, cparm= list( ...)) } else if (method=='fixed') { temp <- list(pfun=pfun, printfun = printfun, diag =TRUE, sparse= sparse, cfun = function(parms, iter, old){ list(theta=parms$theta, done=TRUE)}, cparm= list(theta=theta, ...)) } else if (method=='aic') { temp <- list(pfun=pfun, printfun=printfun, diag =TRUE, sparse= sparse, cargs = c("neff", "df", "plik"), cparm=list(lower=0, init=c(.1,1), ...), cfun = frailty.controlaic) } else { #df method temp <- list(pfun=pfun, printfun =printfun, diag =TRUE, sparse= sparse, cargs=('df'), cparm=list(df=df, thetas=0, dfs=0, guess=3*df/length(unclass(x)), ...), cfun = frailty.controldf) } # If not sparse, give shorter names to the coefficients, so that any # printout of them is readable. if (!sparse) { vname <- paste("gauss", levels(x), sep=':') temp <- c(temp, list(varname=vname)) } attributes(x) <- c(attributes(x), temp) x } survival/R/survpenal.fit.S0000644000175100001440000005105513016105374015276 0ustar hornikusers# # fit a penalized parametric model # survpenal.fit<- function(x, y, weights, offset, init, controlvals, dist, scale=0, nstrat=1, strata, pcols, pattr, assign, parms=NULL) { iter.max <- controlvals$iter.max outer.max <- controlvals$outer.max eps <- controlvals$rel.tolerance toler.chol <- controlvals$toler.chol if (!is.matrix(x)) stop("Invalid X matrix ") n <- nrow(x) nvar <- ncol(x) ny <- ncol(y) if (is.null(offset)) offset <- rep(0,n) if (missing(weights)|| is.null(weights)) weights<- rep(1.0,n) else if (any(weights<=0)) stop("Invalid weights, must be >0") # The strata() term in survreg signals one scale parameter is # to be fit per strata. Here strata contains the strata level of each # subject (variable not needed for only one strata), nstrat= # of strata. # Set nstrat2 = the number of coefficients I need to fit (which is 0 # if the scale is pre-fixed). if (scale <0) stop("Invalid scale") if (scale >0 && nstrat >1) stop("Cannot have both a fixed scale and strata") if (nstrat>1 && (missing(strata) || length(strata)!= n)) stop("Invalid strata variable") if (nstrat==1) strata <- rep(1,n) if (scale >0) nstrat2 <- 0 else nstrat2 <- nstrat if (is.character(dist)) { sd <- survreg.distributions[[dist]] if (is.null(sd)) stop ("Unrecognized distribution") } else sd <- dist dnum <- match(sd$name, c("Extreme value", "Logistic", "Gaussian")) if (is.na(dnum)) { # Not one of the three distributions built in to the C code # We need to set up a callback routine # This returns the 5 number distribution summary (see the density # functions in survreg.distributions). Interval censored obs require # 2 evals and all others 1, so the call to the routine will have n2 # values. dnum <- 4 # flag for the C routine n2 <- n + sum(y[,ny]==3) # # Create an expression that will be evaluated by the C-code, # but with knowledge of some current variables # In the R doc, this would be "body(function(z) {" # in Splus (Chambers book): "functionBody(function(z)" # same action, different name. Luckily 'quote' exists in both # We make very sure the result is the right type and length here, # rather than in the C code, for simplicity. fdensity <- quote({ if (length(parms)) temp <- sd$density(z, parms) else temp <- sd$density(z) if (!is.matrix(temp) || any(dim(temp) != c(n2,5)) || !is.numeric(temp)) stop("Density function returned an invalid matrix") as.vector(as.double(temp)) }) } else { fdensity <-1 #dummy value for the .Call n2 <- n #a dummy value for inclusion in rho } # This is a subset of residuals.survreg: define the first and second # derivatives at z=0 for the 4 censoring types # Used below for starting estimates derfun <- function(y, eta, sigma, density, parms) { ny <- ncol(y) status <- y[,ny] z <- (y[,1] - eta)/sigma dmat <- density(z,parms) dtemp<- dmat[,3] * dmat[,4] #f' if (any(status==3)) { z2 <- (y[,2] - eta)/sigma dmat2 <- density(z2) } else { dmat2 <- matrix(0,1,5) #dummy values z2 <- 0 } tdenom <- ((status==0) * dmat[,2]) + ((status==1) * 1 ) + ((status==2) * dmat[,1]) + ((status==3) * ifelse(z>0, dmat[,2]-dmat2[,2], dmat2[,1] - dmat[,1])) tdenom <- 1/(tdenom* sigma) dg <- -tdenom *(((status==0) * (0-dmat[,3])) + ((status==1) * dmat[,4]) + ((status==2) * dmat[,3]) + ((status==3) * (dmat2[,3]- dmat[,3]))) ddg <- (tdenom/sigma)*(((status==0) * (0- dtemp)) + ((status==1) * dmat[,5]) + ((status==2) * dtemp) + ((status==3) * (dmat2[,3]*dmat2[,4] - dtemp))) list(dg = dg, ddg = ddg - dg^2) } status <- y[,ny] # # are there any sparse frailty terms? # npenal <- length(pattr) #total number of penalized terms if (npenal == 0 || length(pcols) != npenal) stop("Invalid pcols or pattr arg") sparse <- sapply(pattr, function(x) !is.null(x$sparse) && x$sparse) if (sum(sparse) >1) stop("Only one sparse penalty term allowed") # # Create a marking vector for the terms, the same length as assign # with pterms == 0=ordinary term, 1=penalized, 2=sparse, # pindex = length of pcols = position in pterms # # Make sure that pcols is a strict subset of assign, so that the # df computation (and printing) can unambiguously decide which cols of # X are penalized and which are not when doing "terms" like actions. # To make some downstream things easier, order pcols and pattr to be # in the same relative order as the terms in 'assign' # pterms <- rep(0, length(assign)) names(pterms) <- names(assign) pindex <- rep(0, npenal) for (i in 1:npenal) { temp <- unlist(lapply(assign, function(x,y) (length(x) == length(y) && all(x==y)), pcols[[i]])) if (sparse[i]) pterms[temp] <- 2 else pterms[temp] <- 1 pindex[i] <- (seq(along.with=temp))[temp] } if ((sum(pterms==2) != sum(sparse)) || (sum(pterms>0) != npenal)) stop("pcols and assign arguments disagree") if (any(pindex != sort(pindex))) { temp <- order(pindex) pindex <- pindex[temp] pcols <- pcols[temp] pattr <- pattr[temp] } # ptype= 1 or 3 if a sparse term exists, 2 or 3 if a non-sparse exists ptype <- any(sparse) + 2*(any(!sparse)) if (any(sparse)) { sparse.attr <- (pattr[sparse])[[1]] #can't use [[sparse]] directly # if 'sparse' is a T/F vector fcol <- unlist(pcols[sparse]) if (length(fcol) > 1) stop("Sparse term must be single column") # Remove the sparse term from the X matrix frailx <- x[, fcol] x <- x[, -fcol, drop=FALSE] for (i in 1:length(assign)){ j <- assign[[i]] if (j[1] > fcol) assign[[i]] <- j-1 } for (i in 1:npenal) { j <- pcols[[i]] if (j[1] > fcol) pcol[[i]] <- j-1 } frailx <- match(frailx, sort(unique(frailx))) nfrail <- max(frailx) nvar <- nvar - 1 #Set up the callback for the sparse frailty term # (At most one sparse term is allowed). The calling code will # first set 'coef1' to the current value of the sparse coefficients, # then call the expression below. It uses a separate context (Splus # frame or R environment), so there is no conflict between that # variable name and the rest of the code. Thus, think of the below as # a funcion of the temporary variable coef1 (current value found # in the calling C code), theta1 (current value in the S code # below, using calls to cfun), and fixed known values of pfun1 etc. # The expression will constantly replace components of "coxlist1". By # creating it first, we assure the order of the components, again # to make it simpler for the C code (it can grab the first component # and know that that is 'coef', etc). # pfun1 <- sparse.attr$pfun coxlist1 <- list(coef=0, first=0, second=0, penalty=0, flag=F) f.expr1 <- quote({ if (is.null(extra1)) temp <- pfun1(coef1, theta1, n.eff) else temp <- pfun1(coef1, theta1, n.eff, extra1) if (!is.null(temp$recenter)) coxlist1$coef <- coef1 - as.double(temp$recenter) else coxlist1$coef <- coef1 if (!temp$flag) { coxlist1$first <- -as.double(temp$first) coxlist1$second <- as.double(temp$second) } else { coxlist1$first <- double(nfrail) coxlist1$second <- double(nfrail) } coxlist1$penalty <- -as.double(temp$penalty) coxlist1$flag <- as.logical(temp$flag) # Make sure the list has exactly the right structure, so # the the C code can be simple. The first line below is # probably unnecessary (belt AND suspenders); the second is # checking a possibly user-supplied penaly function if (any(names(coxlist1) != c('coef', 'first', 'second', 'penalty', 'flag'))) stop("Invalid coxlist1") if (any(sapply(coxlist1, length) != c(rep(nfrail,3), 1, 1))) stop("Incorrect length in coxlist1") coxlist1 }) } else { # no sparse terms frailx <- 0 nfrail <- 0 f.expr1 <- NULL #dummy value pfun1 <- NULL #dummy coxlist1 <- NULL # " } nvar2 <- nvar + nstrat2 if (nvar2 ==0) { # There are no non-sparse coefficients, and no scale parameters # A strange model, leading to an hmat with 0 columns. The # underlying C code will choke, since this case is not built in. stop("Cannot fit a model with no coefficients other than sparse ones") } # Now the non-sparse penalties # There can be multiple penalized terms if (sum(!sparse) >0) { full.imat <- !all(unlist(lapply(pattr, function(x) x$diag))) ipenal <- (1:length(pattr))[!sparse] #index for non-sparse terms if (full.imat) { coxlist2 <- list(coef=double(nvar), first=double(nvar), second= double(nvar^2), penalty=0.0, flag=rep(FALSE,nvar)) length2 <- c(nvar, nvar, nvar*nvar, 1, nvar) } else { coxlist2 <- list(coef=double(nvar), first=double(nvar), second=double(nvar), penalty= 0.0, flag=rep(FALSE,nvar)) length2 <- c(nvar, nvar, nvar, 1, nvar) } # The C code will set the variable coef2, containing the concatonation # of all the non-sparse penalized coefs. Think of the below as # a function of coef (from the C code), thetalist (set further # below), and unchanging variables such as pattr. f.expr2 <- quote({ pentot <- 0 newcoef <- coef2 for (i in ipenal) { pen.col <- pcols[[i]] tcoef <- coef2[pen.col] if (is.null(extralist[[i]])) temp <- ((pattr[[i]])$pfun)(tcoef, thetalist[[i]], n.eff) else temp <- ((pattr[[i]])$pfun)(tcoef, thetalist[[i]], n.eff,extralist[[i]]) if (!is.null(temp$recenter)) newcoef[pen.col] <- tcoef - temp$recenter if (temp$flag) coxlist2$flag[pen.col] <- TRUE else { coxlist2$flag[pen.col] <- FALSE coxlist2$first[pen.col] <- -temp$first if (full.imat) { tmat <- matrix(coxlist2$second, nvar, nvar) tmat[pen.col,pen.col] <- temp$second coxlist2$second <- c(tmat) } else coxlist2$second[pen.col] <- temp$second } pentot <- pentot - temp$penalty } coxlist2$penalty <- as.double(pentot) coxlist2$coef <- newcoef if (any(sapply(coxlist2, length) != length2)) stop("Length error in coxlist2") coxlist2 }) } else { full.imat <- FALSE # no non-sparse penalties length2 <- 0 #dummy value f.expr2 <- NULL coxlist2 <- NULL ipenal <- NULL } # Create the frame for penalized evaluation rho <- new.env() # # "Unpack" the passed in paramter list, # and make the initial call to each of the external routines # cfun <- lapply(pattr, function(x) x$cfun) parmlist <- lapply(pattr, function(x,eps) c(x$cparm, eps2=eps), sqrt(eps)) extralist<- lapply(pattr, function(x) x$pparm) iterlist <- vector('list', length(cfun)) thetalist <- vector('list', length(cfun)) printfun <- lapply(pattr, function(x) x$printfun) extra1 <- NULL theta1 <- NULL for (i in 1:length(cfun)) { temp <- (cfun[[i]])(parmlist[[i]], iter=0) if (sparse[i]) { assign('theta1', temp$theta, rho) assign('extra1', extralist[[i]], rho) } thetalist[[i]] <- temp$theta iterlist[[i]] <- temp } # # Manufacture the list of calls to cfun, with appropriate arguments # temp1 <- c('x', 'coef', 'plik', 'loglik', 'status', 'neff', 'df', 'trH') temp2 <- c('frailx', 'fcoef', 'fit$loglik-fit$penalty', 'fit$loglik', 'status', 'n.eff') temp3 <- c('x[,pen.col]', 'coef[pen.col]', 'fit$loglik-fit$penalty', 'fit$loglik', 'status', 'n.eff') calls <- vector('expression', length(cfun)) cargs <- lapply(pattr, function(x) x$cargs) for (i in 1:length(cfun)) { tempchar <- paste("(cfun[[", i, "]])(parmlist[[", i, "]], iter,", "iterlist[[", i, "]]") temp2b <- c(temp2, paste('pdf[', i, ']'), paste('trH[', i, ']')) temp3b <- c(temp3, paste('pdf[', i, ']'), paste('trH[', i, ']')) if (length(cargs[[i]])==0) calls[i] <- parse(text=paste(tempchar, ")")) else { temp <- match(cargs[[i]], temp1) if (any(is.na(temp))) stop(paste((cargs[[i]])[is.na(temp)], "not matched")) if (sparse[i]) temp4 <- paste(temp2b[temp], collapse=',') else temp4 <- paste(temp3b[temp], collapse=',') calls[i] <- parse(text=paste(paste(tempchar,temp4,sep=','),')')) } } need.df <- any(!is.na(match(c('df', 'trH'), unlist(cargs))))#do any use df? # # Last of the setup: create the vector of variable names # varnames <- dimnames(x)[[2]] for (i in 1:npenal) { if (!is.null(pattr[[i]]$varname)) varnames[pcols[[i]]] <- pattr[[i]]$varname } nvar2 <- nvar + nstrat2 nvar3 <- nvar2 + nfrail # # A good initial value of the scale turns out to be critical for successful # iteration, in a surprisingly large number of data sets. # The best way we've found to get one is to fit a model with only the # mean and the scale. We also the loglik of the mean-only model in the # result # Even this model needs starting guesses... yy <- ifelse(status !=3, y[,1], (y[,1]+y[,2])/2 ) coef <- sd$init(yy, weights,parms) # We sometimes get into trouble with a small initial estimate of sigma, # (the surface isn't SPD), but never with a large one. Double it. if (scale >0) vars <- log(scale) else vars <- log(4*coef[2])/2 # init gives \sigma^2, I need log(sigma) coef <- c(coef[1], rep(vars, nstrat)) # get a better initial value for the mean using the "glim" trick deriv <- derfun(y, yy, exp(vars), sd$density, parms) wt <- -1*deriv$ddg*weights coef[1] <- sum(weights*deriv$dg + wt*(yy -offset)) / sum(wt) fit0 <- .Call(Csurvreg6, iter = as.integer(20), nvar = as.integer(1), as.double(y), as.integer(ny), x = as.double(rep(1.0, n)), as.double(weights), as.double(offset), coef= as.double(coef), as.integer(nstrat2), as.integer(strata), as.double(eps), as.double(toler.chol), as.integer(dnum), fdensity, rho) # The "effective n" of the model temp <- mean(exp(fit0$coef[-1])) #overall sd n.eff <- sd$variance(temp^2) * (solve(matrix(fit0$var,1+nstrat2)))[1,1] # # Fit the model with all covariates # Start with initial values # if (is.numeric(init)) { if (length(init) == nvar) { if (scale >0) init <- c(init, log(scale)) else init <-c(rep(0, nfrail), init, fit0$coef[-1]) } else if (length(init) == nvar2) init <- c(rep(0,nfrail), init) else if (length(init) != nvar3) stop("Wrong length for inital values") if (scale >0) init <- c(init, log(scale)) } else { # The algebra behind the 'glim' trick just doesn't work here # Use the intercept fit + zeros # coef order = frailty, intercept, other covariates, sigmas init <- c(rep(0, nfrail), fit0$coef[1], rep(0, nvar-1), fit0$coef[-1]) } # # Tack on the sigmas to "assign", so that the df component includes # the sigmas if (nstrat2 >0) assign <- c(assign, list(sigma=(1+nvar):nvar2)) iter2 <- 0 iterfail <- NULL thetasave <- unlist(thetalist) for (iterx in 1:outer.max) { fit <- .Call(Csurvreg7, iter = as.integer(iter.max), as.integer(nvar), as.double(y), as.integer(ny), as.double(x), as.double(weights), as.double(offset), coef= as.double(init), as.integer(nstrat2), as.integer(strata), as.double(eps), as.double(toler.chol), as.integer(dnum), fdensity, rho, as.integer(ptype), as.integer(full.imat), as.integer(nfrail), as.integer(frailx), f.expr1, f.expr2) iter <- iterx iter2 <- iter2 + fit$iter if (fit$flag == 1000) iterfail <- c(iterfail, iter) if (nfrail >0) { fcoef <- fit$coef[1:nfrail] coef <- fit$coef[nfrail + 1:nvar2] } else coef <- fit$coef[1:nvar2] # We need to fetch back some of the results from the # evaluation area of f.expr1 and f.expr2 if (nfrail >0) coxlist1 <- get('coxlist1', envir=rho) if (ptype >1 ) coxlist2 <- get('coxlist2', envir=rho) # If any penalties were infinite, the C code has made hdiag=1 out # of self-preservation (avoid zero divides). But such coefs are # guarranteed to be zero so the variance should be too. temp <- rep(FALSE, nvar2+nfrail) if (nfrail>0) temp[1:nfrail] <- coxlist1$flag if (ptype >1) temp[nfrail+ 1:nvar] <- coxlist2$flag hdiag <- ifelse(temp, 0, fit$hdiag) if (need.df) { #get the penalty portion of the second derive matrix if (nfrail>0) temp1 <- coxlist1$second else temp1 <- 0 if (ptype>1) { if (full.imat) { temp2 <- matrix(0., nvar2, nvar2) temp2[1:nvar, 1:nvar] <- coxlist2$second } else temp2 <- diag(c(coxlist2$second, rep(0, nstrat2))) } else temp2 <- 0 dftemp <-coxpenal.df(matrix(fit$hmat, ncol=nvar2), matrix(fit$hinv, ncol=nvar2), hdiag, assign, ptype, nvar2, temp1, temp2, pindex[sparse]) df <- dftemp$df var <- dftemp$var var2 <- dftemp$var2 pdf <- df[pterms>0] # df's for penalized terms trH <- dftemp$trH[pterms>0] # trace H } # # Call the control function(s) # done <- TRUE for (i in 1:length(cfun)) { pen.col <- pcols[[i]] temp <- eval(calls[i]) if (sparse[i]) assign('theta1', temp$theta, rho) thetalist[[i]] <- temp$theta iterlist[[i]] <- temp done <- done & temp$done } if (done) break # # Choose starting estimates for the next iteration # if (iter==1) { init <- coefsave <- fit$coef thetasave <- cbind(thetasave, unlist(thetalist)) } else { temp <- unlist(thetalist) coefsave <- cbind(coefsave, fit$coef) # temp = next guess for theta # *save = prior thetas and the resultant fits # choose as initial values the result for the closest old theta howclose <- apply((thetasave-temp)^2,2, sum) which <- min((1:iter)[howclose==min(howclose)]) init <- coefsave[,which] thetasave <- cbind(thetasave, temp) } } #end of the iteration loop if (!need.df) { #didn't need it iteration by iteration, but do it now #get the penalty portion of the second derive matrix if (nfrail>0) temp1 <- coxlist1$second else temp1 <- 0 if (ptype>1) { if (full.imat) { temp2 <- matrix(0., nvar2, nvar2) temp2[1:nvar, 1:nvar] <- coxlist2$second } else temp2 <- diag(c(coxlist2$second, rep(0, nstrat2))) } else temp2 <- 0 dftemp <-coxpenal.df(matrix(fit$hmat,ncol=nvar2), matrix(fit$hinv,ncol=nvar2), hdiag, assign, ptype, nvar2, temp1, temp2, pindex[sparse]) df <- dftemp$df trH <- dftemp$trH var <- dftemp$var var2 <- dftemp$var2 } if (iter.max >1 && length(iterfail)>0) warning(paste("Inner loop failed to coverge for iterations", paste(iterfail, collapse=' '))) which.sing <- (hdiag[nfrail + 1:nvar] ==0) coef[which.sing] <- NA names(iterlist) <- names(pterms[pterms>0]) cname <- varnames cname <- c(cname, rep("Log(scale)", nstrat2)) dimnames(var) <- list(cname, cname) names(coef) <- cname if (nfrail >0) { lp <- offset + fcoef[frailx] lp <- lp + x %*%coef[1:nvar] list(coefficients = coef, icoef = fit0$coef, var = var, var2 = var2, loglik = c(fit0$loglik, fit$loglik- fit$penalty), iter = c(iter, iter2), linear.predictors = as.vector(lp), frail = fcoef, fvar = dftemp$fvar, df = df, penalty= c(fit0$penalty, -fit$penalty), pterms = pterms, assign2=assign, history= iterlist, printfun=printfun, score = fit$u) } else { #no sparse terms list(coefficients = coef, icoef = fit0$coef, var = var, var2 = var2, loglik = c(fit0$loglik, fit$loglik- fit$penalty), iter = c(iter, iter2), linear.predictors = as.vector(x%*%coef[1:nvar]), df = df, df2=dftemp$df2, penalty= c(0, -fit$penalty), pterms = pterms, assign2=assign, history= iterlist, printfun= printfun, score = fit$u) } } survival/R/tcut.S0000644000175100001440000000236013016105374013450 0ustar hornikuserstcut <- function (x, breaks, labels, scale=1){ # avoid some problems with dates x <- as.numeric(x) breaks <- as.numeric(breaks) if(length(breaks) == 1) { if(breaks < 1) stop("Must specify at least one interval") if(missing(labels)) labels <- paste("Range", seq(length = breaks)) else if(length(labels) != breaks) stop("Number of labels must equal number of intervals") r <- range(x[!is.na(x)]) r[is.na(r)] <- 1 if((d <- diff(r)) == 0) { r[2] <- r[1] + 1 d <- 1 } breaks <- seq(r[1] - 0.01 * d, r[2] + 0.01 * d, length = breaks +1) } else { if(is.na(adb <- all(diff(breaks) >= 0)) || !adb) stop("breaks must be given in ascending order and contain no NA's") if(missing(labels)) labels <- paste(format(breaks[ - length(breaks)]), "+ thru ", format(breaks[-1]), sep = "") else if(length(labels) != length(breaks) - 1) stop("Number of labels must be 1 less than number of break points") } temp <- structure(x*scale, cutpoints=breaks*scale, labels=labels) class(temp) <- 'tcut' temp } "[.tcut" <- function(x, ..., drop=FALSE) { atts <- attributes(x) x <- unclass(x)[..1] attributes(x) <- atts class(x) <- 'tcut' x } levels.tcut <- function(x) attr(x, 'labels') survival/R/print.coxph.S0000644000175100001440000000302512656662135014760 0ustar hornikusersprint.coxph <- function(x, digits=max(options()$digits - 4, 3), ...) { if (!is.null(cl<- x$call)) { cat("Call:\n") dput(cl) cat("\n") } if (!is.null(x$fail)) { cat(" Coxph failed.", x$fail, "\n") return() } savedig <- options(digits = digits) on.exit(options(savedig)) coef <- x$coefficients se <- sqrt(diag(x$var)) if(is.null(coef) | is.null(se)) stop("Input is not valid") if (is.null(x$naive.var)) { tmp <- cbind(coef, exp(coef), se, coef/se, # signif(1 - pchisq((coef/ se)^2, 1), digits -1)) 1- pchisq((coef/se)^2, 1)) dimnames(tmp) <- list(names(coef), c("coef", "exp(coef)", "se(coef)", "z", "p")) } else { nse <- sqrt(diag(x$naive.var)) tmp <- cbind(coef, exp(coef), nse, se, coef/se, # signif(1 - pchisq((coef/se)^2, 1), digits -1)) 1 - pchisq((coef/se)^2, 1)) dimnames(tmp) <- list(names(coef), c("coef", "exp(coef)", "se(coef)", "robust se", "z", "p")) } printCoefmat(tmp, signif.stars=FALSE, P.values=TRUE, has.Pvalue=TRUE) logtest <- -2 * (x$loglik[1] - x$loglik[2]) if (is.null(x$df)) df <- sum(!is.na(coef)) else df <- round(sum(x$df),2) cat("\n") cat("Likelihood ratio test=", format(round(logtest, 2)), " on ", df, " df,", " p=", format(1 - pchisq(logtest, df)), "\n", sep="") omit <- x$na.action cat("n=", x$n) if (!is.null(x$nevent)) cat(", number of events=", x$nevent, "\n") else cat("\n") if (length(omit)) cat("\ (", naprint(omit), ")\n", sep="") invisible(x) } survival/R/survSplit.R0000644000175100001440000001242113046712712014505 0ustar hornikuserssurvSplit <- function(formula, data, subset, na.action=na.pass, cut, start="tstart", id, zero=0, episode, end="tstop", event="event") { Call <- match.call() if (missing(formula) || is.data.frame(formula)) { # an old style call # match arguments and build a formula if (missing(data)) { if (!missing(formula)) { names(Call)[[2]] <- "data" # The line above is sneaky: it makes model.frame() work later data <- formula } else stop("a data frame is required") } if (missing(end) || missing(event)) stop("either a formula or the end and event arguments are required") if (!(is.character(event) && length(event) ==1 && event %in% names(data))) stop("'event' must be a variable name in the data set") if (!(is.character(end) && length(end) ==1 && end %in% names(data))) stop("'end' must be a variable name in the data set") if (!(is.character(start) && length(start)==1)) stop("'start' must be a variable name") if (start %in% names(data)) temp <- paste(start, end, event, sep=',') else temp <- paste(end, event, sep=',') formula <- as.formula(paste("Surv(", temp, ")~ .")) } else if (missing(formula)) stop("either a formula or the end and event arguments are required") # create a call to model.frame() that contains the formula (required) # and any other of the relevant optional arguments # then evaluate it in the proper frame indx <- match(c("data", "weights", "subset"), names(Call), nomatch=0) temp <- Call[c(1L,indx)] # only keep the arguments we wanted temp$formula <- formula temp$na.action <- na.action temp[[1L]] <- quote(stats::model.frame) # change the function called mf <- eval.parent(temp) Y <- model.response(mf) states <- attr(Y, "states") if (!is.Surv(Y)) stop ("the model must have a Surv object as the response") if (!(attr(Y, "type") %in% c("right", "mright", "counting", "mcounting"))) stop(paste("not valid for", attr(Y, "type"), "censored survival data")) nY <- ncol(Y) if (nY ==2) Y <- cbind(zero, Y) temp <- (Y[,1] >= Y[,2]) if (any(temp & !is.na(temp))) stop("start time must be < stop time") if (!is.numeric(cut) || any(!is.finite(cut))) stop("cut must be a vector of finite numbers") cut <- sort(cut) ntimes <- length(cut) n <- nrow(data) if (!missing(id)) { if (!is.character(id)) stop("id must be a variable name") if (id %in% names(mf)) stop("the suggested id name is already present") id <- make.names(id) if (id %in% names(mf)) stop("the suggested id name is already present") mf[[id]] <- 1:nrow(mf) } storage.mode(Y) <- "double" index <- .Call(Csurvsplit, Y[,1], Y[,2], as.double(cut)) newdata <- mf[index$row, -1, drop=FALSE] row.names(newdata) <- NULL # erase R's manufactured row names attr(newdata, "terms") <- NULL status <- Y[index$row, 3] status[index$censor] <- 0 if (!is.null(states)) status <- factor(status, labels=c("censor", states)) # Did the user hand me a Surv call with multiple variables, or a # premade Surv object? if (class(formula[[2]]) == "call" && formula[[2]][[1]]== as.name("Surv")){ # it was a call, figure out the names # The user might have used something like Surv(status=abc, time=fred), # so use match.call to find "abc" and "fred". But give up if there # is anything complex. temp <- match.call(Surv, formula[[2]]) if (nY==2) { if (missing(end) && !is.null(temp[["time"]]) && is.name(temp[["time"]])) end <- as.character(temp[["time"]]) # $time might match 'time2' if (missing(event) && !is.null(temp$time2) && is.name(temp$time2)) event <- as.character(temp$time2) if (missing(event) && !is.null(temp$event) && is.name(temp$event)) event <- as.character(temp$event) } else { if (missing(end) && !is.null(temp[["time"]]) && is.name(temp["time"])) start <- as.character(temp[["time"]]) if (missing(end) && !is.null(temp$time2) && is.name(temp$time2)) end <- as.character(temp$time2) if (missing(event) && !is.null(temp$event) && is.name(temp$event)) event <- as.character(temp$event) if (missing(start) && !is.null(temp$time) && is.name(temp$time)) start <- as.character(temp$time) } newdata[[start]] <- index$start newdata[[end]] <- index$end newdata[[event]] <- status } else { if (class(formula[[2]]) != "name") stop("left hand side not recognized") temp <- as.character(formula[[2]]) newdata[temp] <- Surv(index$start, index$end, status) } if (!missing(episode)) { if (!is.character(episode)) stop("episode must be a character string") newdata[[make.names(episode)]] <- index$interval +1 } newdata } survival/R/print.aareg.S0000644000175100001440000000200411732700061014673 0ustar hornikusers# $Id: print.aareg.S 11250 2009-03-19 13:44:59Z tlumley $ print.aareg <- function(x, maxtime, test=c('aalen', 'nrisk'), scale=1, ...) { if (!inherits(x, 'aareg')) stop ("Must be an addreg object") if (!is.null(cl<- x$call)) { cat("Call:\n") dput(cl) cat("\n") } if (missing(test)) test <- x$test else test <- match.arg(test) if (missing(maxtime)) summ <- summary(x, test=test, scale=scale) else summ <- summary(x, maxtime=maxtime, test=test, scale=scale) omit <- x$na.action if (length(omit)) cat(" n=", x$n[1], " (", naprint(omit), ")\n", sep="") else cat(" n=", x$n[1], "\n") cat(" ", summ$n[2], "out of", x$n[3], "unique event times used\n\n") print(signif(summ$table,3)) chi <- summ$chisq df <- nrow(summ$table) -1 cat("\nChisq=", format(round(chi,2)), " on ", df, " df, p=", signif(1- pchisq(chi,df),2), "; test weights=", x$test, "\n", sep="") invisible(x) } survival/R/plot.aareg.S0000644000175100001440000000453711732700061014532 0ustar hornikusers# $Id: plot.aareg.S 11166 2008-11-24 22:10:34Z therneau $ plot.aareg <- function(x, se=TRUE, maxtime, type='s', ...) { if (!inherits(x, 'aareg')) stop ("Must be an aareg object") if (missing(maxtime)) keep <- 1:length(x$time) else keep <- 1:sum(x$time <= maxtime) yylab <- names(x$test.statistic) if (is.matrix(x$coefficient) && ncol(x$coefficient)>1) { yy <- apply(x$coefficient[keep,], 2,cumsum) yy <- rbind(0,yy) # make the plot start at 0,0 if (se) { if (!is.null(x$dfbeta)) { # There was a cluster term, so use the robust variance # dfbeta will be of dimension (n, nvar, n-unique-times) # The first variance increment is apply(dfbeta[,,1]^2,2,sum) # second is apply(dfbeta[,,2]^2,2,sum) # ... , apply(dfbeta[,,ndeath]..... # By being sneaky, it can be done quickly dd <- dim(x$dfbeta) keep2 <- 1:length(unique(x$time[keep])) temp <- matrix(x$dfbeta[,,keep2], nrow=dd[1]) se.increment <- matrix(apply(temp^2, 2, sum), nrow=dd[2]) se.yy <- sqrt(apply(t(se.increment), 2, cumsum)) } else se.yy <- sqrt(apply(x$coefficient[keep,]^2, 2,cumsum)) se.yy <- rbind(0, se.yy) } ncurve <- ncol(yy) } else { # this is the branch most often called, when someone has done # plot(fit[3]), so that only 1 coefficient remains yy <- cumsum(c(0, x$coefficient[keep])) if (se) { if (!is.null(x$dfbeta)) { dd <- dim(x$dfbeta) keep2 <- 1:length(unique(x$time[keep])) temp <- matrix(x$dfbeta[,,keep2], nrow=dd[1]) se.yy <- sqrt(cumsum(c(0, apply(temp^2, 2, sum)))) } else se.yy <- sqrt(cumsum(c(0, x$coefficient[keep]^2))) } ncurve <- 1 } xx <- c(0, x$time[keep]) # There may be multiplicities in x$times. Only plot the last of # each of them indx <- 1 + length(xx) - rev(match(unique(rev(xx)), rev(xx))) xx <- xx[indx] yy <- as.matrix(yy)[indx,] if (se) { if (is.null(x$dfbeta)) se.yy<- as.matrix(se.yy)[indx,] yy <- cbind(yy, yy + 1.96*se.yy, yy - 1.96*se.yy) if (ncurve >1) { for (i in 1:ncurve) { j <- c(i, i+ncurve, i+2*ncurve) matplot(xx, yy[,j], type=type, ..., col=1, lty=c(1,2,2), xlab='Time', ylab=yylab[i]) } } else matplot(xx, yy, type=type, ..., col=1, lty=c(1,2,2), xlab='Time', ylab=yylab) } else { matplot(xx, yy, type=type, ..., xlab='Time') } } survival/R/print.survexp.S0000644000175100001440000000366512464750557015370 0ustar hornikusersprint.survexp <- function(x, scale=1, digits = max(options()$digits - 4, 3), naprint=FALSE, ...) { if (!inherits(x, 'survexp')) stop("Invalid data") savedig <- options(digits=digits) on.exit(options(savedig)) if (!is.null(cl<- x$call)) { cat("Call:\n") dput(cl) cat("\n") } if (!is.null(x$summ)) cat(x$summ) omit <- x$na.action if (length(omit)) cat(naprint(omit), "\n") else cat("\n") if (is.null(x$strata)) { #print it as a matrix mat <- cbind(x$time/scale, x$n.risk, x$surv, x$std.err) if (!naprint) { miss <- (is.na(mat)) %*% rep(1,ncol(mat)) mat <- mat[miss<(ncol(mat)-2),,drop=FALSE] } if (is.matrix(x$surv)) cname <- dimnames(x$surv)[[2]] else cname <- "survival" if (is.matrix(x$n.risk)) cname <- c(paste("nrisk", 1:ncol(x$n.risk), sep=''), cname) else cname <- c("n.risk", cname) cname <- c("time", cname) if (!is.null(x$std.err)) cname <- c(cname, paste("se(", cname, ")", sep='')) dimnames(mat) <- list(rep("", nrow(mat)), cname) print(mat) } else { #print it out one strata at a time, since n's differ if (is.null(x$std.err)) tname <- 'survival' else tname <- c('survival', 'se(surv)') nstrat <- length(x$strata) levs <- names(x$strata) if (nrow(x$surv)==1) { mat <- cbind(c(x$n.risk), c(x$surv), c(x$std.err*x$surv)) dimnames(mat) <- list(levs, c("n.risk", tname)) cat(" Survival at time", x$time, "\n") print(mat) } else { for (i in 1:nstrat) { cat(" ", levs[i], "\n") mat <- cbind(x$time/scale, x$n.risk[,i], x$surv[,i]) if (!is.null(x$std.err)) mat<- cbind(mat, x$std.err[,i] * x$surv[,i]) if (!naprint) mat <- mat[!is.na(mat[,3]),,drop=FALSE] dimnames(mat) <- list(rep("",nrow(mat)), c("Time", "n.risk", tname)) print(mat) cat("\n") } } } invisible(x) } survival/R/cox.zph.S0000644000175100001440000000501511732700061014057 0ustar hornikusers# $Id: cox.zph.S 11218 2009-02-09 12:09:29Z therneau $ # Test proportional hazards # cox.zph <- function(fit, transform='km', global=TRUE) { call <- match.call() if (!inherits(fit, 'coxph')) stop ("Argument must be the result of coxph") if (inherits(fit, 'coxph.null')) stop("The are no score residuals for a Null model") sresid <- resid(fit, 'schoenfeld') varnames <- names(fit$coefficients) nvar <- length(varnames) ndead<- length(sresid)/nvar if (nvar==1) times <- as.numeric(names(sresid)) else times <- as.numeric(dimnames(sresid)[[1]]) # Next line is no longer necessary: survfit.km can handle (start,stop] data # if (missing(transform) && attr(fit$y, 'type') != 'right') # transform <- 'identity' if (is.character(transform)) { tname <- transform ttimes <- switch(transform, 'identity'= times, 'rank' = rank(times), 'log' = log(times), 'km' = { temp <- survfitKM(factor(rep(1,nrow(fit$y))), fit$y, se.fit=FALSE) # A nuisance to do left cont KM t1 <- temp$surv[temp$n.event>0] t2 <- temp$n.event[temp$n.event>0] km <- rep(c(1,t1), c(t2,0)) if (is.null(attr(sresid, 'strata'))) 1-km else (1- km[sort.list(sort.list(times))]) }, stop("Unrecognized transform")) } else { tname <- deparse(substitute(transform)) if (length(tname) >1) tname <- 'user' ttimes <- transform(times) } xx <- ttimes - mean(ttimes) r2 <- sresid %*% fit$var * ndead test <- xx %*% r2 # time weighted col sums corel <- c(cor(xx, r2)) z <- c(test^2 /(diag(fit$var)*ndead* sum(xx^2))) Z.ph <- cbind(corel, z, 1- pchisq(z,1)) if (global && nvar>1) { test <- c(xx %*% sresid) z <- c(test %*% fit$var %*% test) * ndead / sum(xx^2) Z.ph <- rbind(Z.ph, c(NA, z, 1-pchisq(z, ncol(sresid)))) dimnames(Z.ph) <- list(c(varnames, "GLOBAL"), c("rho", "chisq", "p")) } else dimnames(Z.ph) <- list(varnames, c("rho", "chisq", "p")) dimnames(r2) <- list(times, names(fit$coefficients)) temp <-list(table=Z.ph, x=ttimes, y=r2 + outer(rep(1,ndead), fit$coefficients), var=fit$var, call=call, transform=tname) if (is.R()) class(temp) <- "cox.zph" else oldClass(temp) <- "cox.zph" temp } "[.cox.zph" <- function(x, ..., drop=FALSE) { i <- ..1 z<- list(table=x$table[i,,drop=FALSE], x=x$x, y=x$y[ ,i,drop=FALSE], var=x$var[i,i, drop=FALSE], call=x$call, transform=x$transform) attributes(z) <- attributes(x) z } survival/R/survregDtest.S0000644000175100001440000000511611732700061015171 0ustar hornikusers# $Id$ # # Test out if a distribution object found in survreg is legal. Mostly called # by the survreg routine, but a user might use it when developing a new # distribution object # # Short form, returns just T or F # Long form, returns all of the issues with the object, or T if it is ok # survregDtest <- function(dlist, verbose=F) { errlist <- NULL if (is.null(dlist$name)) errlist <- c(errlist, "Missing a name") else if (length(dlist$name) !=1 || !is.character(dlist$name)) errlist <- c(errlist, "Invalid name") # # First case, the object is a reference to another distribution # if (!is.null(dlist$dist)) { if (!is.character(dlist$dist) || is.null(match(dlist$dist, names(survreg.distributions)))) errlist <- c(errlist, "Reference distribution not found") else { if (!is.function(dlist$trans)) errlist <- c(errlist, "Missing or invalid trans component") if (!is.function(dlist$itrans)) errlist <- c(errlist, "Missing or invalid itrans component") if (!is.function(dlist$dtrans)) errlist <- c(errlist, "Missing or invalid dtrans component") } if (is.null(errlist)) { if (!all.equal(dlist$itrans(dlist$trans(1:10)), 1:10)) errlist <- c(errlist, "trans and itrans must be inverses of each other") if (length(dlist$dtrans(1:10)) != 10) errlist <- c(errlist, "dtrans must be a 1-1 function") } } # Second case, the actual definition of a distribution else { # Comment out the next line, until some function uses the variance #if (!is.function(dlist$variance)) # errlist <- c(errlist, "Missing or invalid variance function") if (!is.function(dlist$init)) errlist <- c(errlist, "Missing or invalid init function") if (!is.function(dlist$deviance)) errlist <- c(errlist, "Missing or invalid deviance function") if (!is.function(dlist$density)) errlist <- c(errlist, "Missing or invalid density function") else { if (is.null(dlist$parms)) temp <- dlist$density(1:10/10) else temp <- dlist$density(1:10/10, unlist(dlist$parms)) if (!is.numeric(temp) || !is.matrix(temp) || nrow(temp) != 10 || ncol(temp) != 5) errlist <- c(errlist, "Density function must return a 5 column matrix") } if (!is.function(dlist$quantile)) errlist <- c(errlist, "Missing or invalid quantile function") } if (is.null(errlist)) T else if (verbose) errlist else F } survival/R/survdiff.S0000644000175100001440000000523413016105374014324 0ustar hornikuserssurvdiff <- function(formula, data, subset, na.action, rho=0) { call <- match.call() m <- match.call(expand.dots=FALSE) m$rho <- NULL if (!inherits(formula, 'formula')) stop("The 'formula' argument is not a formula") Terms <- if(missing(data)) terms(formula, 'strata') else terms(formula, 'strata', data=data) m$formula <- Terms m[[1L]] <- quote(stats::model.frame) m <- eval(m, parent.frame()) y <- model.extract(m, "response") if (!inherits(y, "Surv")) stop("Response must be a survival object") if (attr(y, 'type') != 'right') stop("Right censored data only") ny <- ncol(y) n <- nrow(y) offset<- attr(Terms, "offset") if (!is.null(offset)) { #one sample test offset <- as.numeric(m[[offset]]) if (length(attr(Terms,"factors"))>0) stop("Cannot have both an offset and groups") if (any(offset <0 | offset >1)) stop("The offset must be a survival probability") expected <- sum(-log(offset)) #sum of expected events observed <- sum(y[,ny]) if (rho!=0) { num <- sum(1/rho - ((1/rho + y[,ny])*offset^rho)) var <- sum(1- offset^(2*rho))/(2*rho) } else { var <- sum(-log(offset)) num <- var - observed } chi <- num*num/var rval <-list(n= n, obs = observed, exp=expected, var=var, chisq= chi) } else { #k sample test strats <- attr(Terms, "specials")$strata if (length(strats)) { temp <- untangle.specials(Terms, 'strata', 1) dropx <- temp$terms if (length(temp$vars)==1) strata.keep <- m[[temp$vars]] else strata.keep <- strata(m[,temp$vars], shortlabel=TRUE) } else strata.keep <- rep(1,nrow(m)) #Now create the group variable if (length(strats)) ll <- attr(Terms[-dropx], 'term.labels') else ll <- attr(Terms, 'term.labels') if (length(ll) == 0) stop("No groups to test") else groups <- strata(m[ll]) fit <- survdiff.fit(y, groups, strata.keep, rho) if (is.matrix(fit$observed)){ otmp <- apply(fit$observed,1,sum) etmp <- apply(fit$expected,1,sum) } else { otmp <- fit$observed etmp <- fit$expected } df <- (etmp >0) #remove groups with exp=0 if (sum(df) <2) chi <- 0 # No test, actually else { temp2 <- ((otmp - etmp)[df])[-1] vv <- (fit$var[df,df])[-1,-1, drop=FALSE] chi <- sum(solve(vv, temp2) * temp2) } rval <-list(n= table(groups), obs = fit$observed, exp = fit$expected, var=fit$var, chisq=chi) if (length(strats)) rval$strata <- table(strata.keep) } na.action <- attr(m, "na.action") if (length(na.action)) rval$na.action <- na.action rval$call <- call class(rval) <- 'survdiff' rval } survival/R/coxph.fit.S0000644000175100001440000000726312377170071014407 0ustar hornikuserscoxph.fit <- function(x, y, strata, offset, init, control, weights, method, rownames) { n <- nrow(y) if (is.matrix(x)) nvar <- ncol(x) else { if (length(x)==0) nvar <-0 else nvar <-1 } time <- y[,1] status <- y[,2] # Sort the data (or rather, get a list of sorted indices) if (length(strata)==0) { sorted <- order(time) strata <- NULL newstrat <- as.integer(rep(0,n)) } else { sorted <- order(strata, time) strata <- strata[sorted] newstrat <- as.integer(c(1*(diff(as.numeric(strata))!=0), 1)) } if (missing(offset) || is.null(offset)) offset <- rep(0,n) if (missing(weights)|| is.null(weights))weights<- rep(1,n) else { if (any(weights<=0)) stop("Invalid weights, must be >0") weights <- weights[sorted] } stime <- as.double(time[sorted]) sstat <- as.integer(status[sorted]) if (nvar==0) { # A special case: Null model. # (This is why I need the rownames arg- can't use x' names) # Set things up for 0 iterations on a dummy variable x <- as.matrix(rep(1.0, n)) nullmodel <- TRUE nvar <- 1 init <- 0 maxiter <- 0 } else { nullmodel <- FALSE maxiter <- control$iter.max if (!missing(init) && length(init)>0) { if (length(init) != nvar) stop("Wrong length for inital values") } else init <- rep(0,nvar) } storage.mode(weights) <- storage.mode(init) <- "double" coxfit <- .Call(Ccoxfit6, as.integer(maxiter), stime, sstat, x[sorted,], as.double(offset[sorted]), weights, newstrat, as.integer(method=="efron"), as.double(control$eps), as.double(control$toler.chol), as.vector(init), as.integer(1)) # internally rescale if (nullmodel) { score <- exp(offset[sorted]) coxres <- .C(Ccoxmart, as.integer(n), as.integer(method=='efron'), stime, sstat, newstrat, as.double(score), as.double(weights), resid=double(n)) resid <- double(n) resid[sorted] <- coxres$resid names(resid) <- rownames list( loglik = coxfit$loglik[1], linear.predictors = offset, residuals = resid, method= c('coxph.null', 'coxph') ) } else { var <- matrix(coxfit$imat,nvar,nvar) coef <- coxfit$coef if (coxfit$flag < nvar) which.sing <- diag(var)==0 else which.sing <- rep(FALSE,nvar) infs <- abs(coxfit$u %*% var) if (maxiter >1) { if (coxfit$flag == 1000) warning("Ran out of iterations and did not converge") else { infs <- ((infs > control$eps) & infs > control$toler.inf*abs(coef)) if (any(infs)) warning(paste("Loglik converged before variable ", paste((1:nvar)[infs],collapse=","), "; beta may be infinite. ")) } } names(coef) <- dimnames(x)[[2]] lp <- c(x %*% coef) + offset - sum(coef*coxfit$means) score <- exp(lp[sorted]) coxres <- .C(Ccoxmart, as.integer(n), as.integer(method=='efron'), stime, sstat, newstrat, as.double(score), as.double(weights), resid=double(n)) resid <- double(n) resid[sorted] <- coxres$resid names(resid) <- rownames if (maxiter > 0) coef[which.sing] <- NA #leave it be if iter=0 is set concordance <- survConcordance.fit(Surv(stime, sstat), lp[sorted], strata, weights) list(coefficients = coef, var = var, loglik = coxfit$loglik, score = coxfit$sctest, iter = coxfit$iter, linear.predictors = as.vector(lp), residuals = resid, means = coxfit$means, concordance=concordance, method='coxph') } } survival/R/coxph.control.S0000644000175100001440000000140613006115603015264 0ustar hornikusers# # Gather all of the control parameters for coxph into one spot # coxph.control <- function(eps=1e-9, toler.chol = .Machine$double.eps ^ .75, iter.max=20, toler.inf= sqrt(eps), outer.max=10, timefix =TRUE) { if (iter.max <0) stop("Invalid value for iterations") if (eps <=0) stop ("Invalid convergence criteria") if (eps <= toler.chol) warning("For numerical accuracy, tolerance should be < eps") if (toler.inf <=0) stop ("The inf.warn setting must be >0") if (!is.logical(timefix)) stop("timefix must be TRUE or FALSE") list(eps=eps, toler.chol=toler.chol, iter.max=as.integer(iter.max), toler.inf=toler.inf, outer.max=as.integer(outer.max), timefix=timefix) } survival/R/frailty.controlgam.S0000644000175100001440000000427611732700061016314 0ustar hornikusers# $Id: frailty.controlgam.S 11166 2008-11-24 22:10:34Z therneau $ # # The control function for a single Gamma frailty term. # frailty.controlgam <- function(opt, iter, old, group, status, loglik){ if (iter==0) { # initial call if (!is.null(opt$theta)) theta <- opt$theta #fixed theta case else { if (is.null(opt$init)) theta <- 0 #no initial value -- use 0 else theta <- opt$init[1] } list(theta=theta) } else { if (is.null(opt$trace)) trace <-FALSE else trace <- opt$trace theta <- old$theta #compute correction to the loglik if (theta==0) correct <- 0 else { if (is.matrix(group)) group <- c(group %*% 1:ncol(group)) d <- tapply(status,group,sum) correct <- frailty.gammacon(d, 1/theta) } if (!is.null(opt$theta)) # fixed theta case list(theta=theta, done=TRUE, c.loglik=loglik + correct) else { # save history of the iteration, and get the next theta if (iter==1) history <- c(theta=theta, loglik=loglik, c.loglik=loglik + correct) else history <- rbind(old$history, as.vector(c(theta, loglik, loglik + correct))) if (iter==1) { if (is.null(opt$init )) theta <-1 else theta <- opt$init[2] list(theta=theta, done=FALSE, history=history, c.loglik= loglik+correct) } else if (iter ==2) { if (history[2,3] < (history[1,3] +1)) theta <- mean(history[1:2,1]) else theta <- 2*history[2,1] if (trace) { print(history) cat(" new theta=", theta, "\n\n") } list(theta=theta, done=FALSE, history=history, c.loglik= loglik+correct) } else { #Now, history has iter rows, each row contains the value # of theta, the Cox PL, and the full LL done <- (abs(1- history[iter,3]/history[iter-1,3]) < opt$eps) x <- history[,1] y <- history[,3] if (y[iter]== max(y) && x[iter]==max(x)) newtheta <- 2* max(x) else newtheta <- frailty.brent(sqrt(x), y, lower=0)^2 if (trace) { print(history) cat(" new theta=", format(newtheta), "\n\n") } list(theta=newtheta, done=done, history=history, c.loglik = loglik + correct) } } } } survival/R/statefig.R0000644000175100001440000001551313065013241014275 0ustar hornikusers# Automatically generated from the noweb directory statefig <- function(layout, connect, margin=.03, box=TRUE, cex=1, col=1, lwd=1, lty=1, bcol= col, acol=col, alwd = lwd, alty= lty) { # set up an empty canvas frame(); # new environment par(usr=c(0,1,0,1)) if (!is.numeric(layout)) stop("layout must be a numeric vector or matrix") if (!is.matrix(connect) || nrow(connect) != ncol(connect)) stop("connect must be a square matrix") nstate <- nrow(connect) dd <- dimnames(connect) if (!is.null(dd[[1]])) statenames <- dd[[1]] else if (is.null(dd[[2]])) stop("connect must have the state names as dimnames") else statenames <- dd[[2]] if (is.matrix(layout) && ncol(layout)==2 && nrow(layout) > 1) { # the user provided their own if (any(layout <0) || any(layout >1)) stop("layout coordinates must be between 0 and 1") if (nrow(layout) != nstate) stop("layout matrix should have one row per state") cbox <- layout } else { if (any(layout <=0 | layout != floor(layout))) stop("non-integer number of states in layout argument") space <- function(n) (1:n -.5)/n # centers of the boxes if (sum(layout) != nstate) stop("number of boxes != number of states") cbox <- matrix(0, ncol=2, nrow=nstate) #coordinates will be here n <- length(layout) ix <- rep(seq(along=layout), layout) if (is.vector(layout) || ncol(layout)> 1) { #left to right cbox[,1] <- space(n)[ix] for (i in 1:n) cbox[ix==i,2] <- 1 -space(layout[i]) } else { # top to bottom cbox[,2] <- 1- space(n)[ix] for (i in 1:n) cbox[ix==i,1] <- space(layout[i]) } } text(cbox[,1], cbox[,2], statenames, cex=cex, col=col) # write the labels textwd <- strwidth(statenames, cex=cex) textht <- strheight(statenames, cex=cex) temp <- par("pin") #plot region in inches dx <- margin * temp[2]/mean(temp) # extra to add in the x dimension dy <- margin * temp[1]/mean(temp) # extra to add in y if (box) { drawbox <- function(x, y, dx, dy, col) { lines(x+ c(-dx, dx, dx, -dx, -dx), y+ c(-dy, -dy, dy, dy, -dy), lwd=lwd, lty=lty, col=col) } bcol <- rep(bcol, length=nstate) for (i in 1:nstate) drawbox(cbox[i,1], cbox[i,2], textwd[i]/2 + dx, textht[i]/2 + dy, col=bcol[i]) dx <- 2*dx; dy <- 2*dy # move arrows out from the box } arrow2 <- function(...) arrows(..., angle=20, length=.1) doline <- function(x1, x2, d, delta1, delta2, lwd, lty, col) { if (d==0 && x1[1] ==x2[1]) { # vertical line if (x1[2] > x2[2]) # downhill arrow2(x1[1], x1[2]- delta1[2], x2[1], x2[2] + delta2[2], lwd=lwd, lty=lty, col=col) else arrow2(x1[1], x1[2]+ delta1[2], x2[1], x2[2] - delta2[2], lwd=lwd, lty=lty, col=col) } else if (d==0 && x1[2] == x2[2]) { # horizontal line if (x1[1] > x2[1]) # right to left arrow2(x1[1]-delta1[1], x1[2], x2[1] + delta2[1], x2[2], lwd=lwd, lty=lty, col=col) else arrow2(x1[1]+delta1[1], x1[2], x2[1] - delta2[1], x2[2], lwd=lwd, lty=lty, col=col) } else { temp <- phi(x1[1], x1[2], x2[1], x2[2], d, delta1, delta2) phi <- seq(temp$angle[1], temp$angle[2], length=21) lines(temp$center[1] + temp$r*cos(phi), temp$center[2] + temp$r*sin(phi), lwd=lwd, lty=lty, col=col) arrow2(temp$center[1] + temp$r*cos(phi[20]), temp$center[2] + temp$r*sin(phi[20]), temp$center[1] + temp$r*cos(phi[21]), temp$center[2] + temp$r*sin(phi[21]), lwd=lwd, lty=lty, col=col) } } for (i in 1:nstate) { for (j in 1:nstate) { if (i != j && connect[i,j] !=0) { doline(cbox[i,], cbox[j,], connect[i,j]-1, delta1 = c(textwd[i]/2 + dx, textht[i]/2 + dy), delta2 = c(textwd[j]/2 + dx, textht[j]/2 + dy), lty=alty[1], lwd=alwd[1], col=acol[1]) } } } invisible(cbox) } statefigx <- function(x, C, r, a1, a2) { amax <- max(a1, a2) amin <- min(a1, a2) temp <-(x - C[1])/r if (abs(temp) >1) return(NULL) # no intersection of the arc and x phi <- acos(temp) # this will be from 0 to pi # Add reflection about the X axis, in both forms phi <- c(phi, -phi, 2*pi - phi) phi[phi amin] } statefigy <- function(y, C, r, a1, a2) { amax <- max(a1, a2) amin <- min(a1, a2) temp <-(y - C[2])/r if (abs(temp) >1) return(NULL) # no intersection of the arc and y phi <- asin(temp) # will be from -pi/2 to pi/2 phi <- c(phi, sign(phi)*pi -phi) # reflect about the vertical phi <- c(phi, phi + 2*pi) phi[phi amin] } phi <- function(x1, y1, x2, y2, d, delta1, delta2) { # d = height above the line theta <- atan2(y2-y1, x2-x1) # angle from center to center if (abs(d) < .001) d=.001 # a really small arc looks like a line z <- sqrt((x2-x1)^2 + (y2 - y1)^2) /2 # half length of chord ab <- c((x1 + x2)/2, (y1 + y2)/2) # center of chord r <- abs(z*(1 + d^2)/ (2*d)) if (d >0) C <- ab + (r - d*z)* c(-sin(theta), cos(theta)) # center of arc else C <- ab + (r + d*z)* c( sin(theta), -cos(theta)) a1 <- atan2(y1-C[2], x1-C[1]) a2 <- atan2(y2-C[2], x2-C[1]) if (abs(a2-a1) > pi) a2 <- a2 + 2*pi if (d > 0) { #counterclockwise phi1 <- min(statefigx(x1 + delta1[1], C, r, a1, a2), statefigx(x1 - delta1[1], C, r, a1, a2), statefigy(y1 + delta1[2], C, r, a1, a2), statefigy(y1 - delta1[2], C, r, a1, a2), na.rm=TRUE) phi2 <- max(statefigx(x2 + delta2[1], C, r, a1, a2), statefigx(x2 - delta2[1], C, r, a1, a2), statefigy(y2 + delta2[2], C, r, a1, a2), statefigy(y2 - delta2[2], C, r, a1, a2), na.rm=TRUE) } else { # clockwise phi1 <- max(statefigx(x1 + delta1[1], C, r, a1, a2), statefigx(x1 - delta1[1], C, r, a1, a2), statefigy(y1 + delta1[2], C, r, a1, a2), statefigy(y1 - delta1[2], C, r, a1, a2), na.rm=TRUE) phi2 <- min(statefigx(x2 + delta2[1], C, r, a1, a2), statefigx(x2 - delta2[1], C, r, a1, a2), statefigy(y2 + delta2[2], C, r, a1, a2), statefigy(y2 - delta2[2], C, r, a1, a2), na.rm=TRUE) } list(center=C, angle=c(phi1, phi2), r=r) } survival/R/anova.survreglist.S0000644000175100001440000000406712666345774016217 0ustar hornikusersanova.survreglist <- function(object, ..., test = c("Chisq", "none")) { diff.term <- function(term.labels, i) { t1 <- term.labels[[1]] t2 <- term.labels[[2]] m1 <- match(t1, t2, FALSE) m2 <- match(t2, t1, FALSE) if(all(m1)) { if(all(m2)) return("=") else return(paste(c("", t2[ - m1]), collapse = "+")) } else { if(all(m2)) return(paste(c("", t1[ - m2]), collapse = "-")) else return(paste(i - 1, i, sep = " vs. ")) } } test <- match.arg(test) rt <- length(object) if(rt == 1) { object <- object[[1]] UseMethod("anova") } forms <- sapply(object, function(x) as.character(formula(x))) subs <- as.logical(match(forms[2, ], forms[2, 1], FALSE)) if(!all(subs)) warning("Some fit objects deleted because response differs from the first model") if(sum(subs) == 1) stop("The first model has a different response from the rest") forms <- forms[, subs] object <- object[subs] ## older survival objects might have df.resid: recent ones have df.residual dfres <- sapply(object, "[[", "df.resid", exact=FALSE) m2loglik <- -2 * sapply(object, "[[", "loglik")[2, ] tl <- lapply(object, labels) rt <- length(m2loglik) effects <- character(rt) for(i in 2:rt) effects[i] <- diff.term(tl[c(i - 1, i)], i) dm2loglik <- - diff(m2loglik) ddf <- - diff(dfres) heading <- c("Analysis of Deviance Table", paste("\nResponse: ", forms[2, 1], "\n", sep = "")) aod <- data.frame(Terms = forms[3, ], "Resid. Df" = dfres, "-2*LL" = m2loglik, Test = effects, Df = c(NA, ddf), Deviance = c(NA, dm2loglik), check.names = FALSE) aod<-structure(aod,heading=heading,class=c("anova","data.frame")) if(test != "none") { n <- length(object[[1]]$residuals) o <- order(dfres) ## R uses scale argument even for "Chisq" if (test=="Chisq") scale<-1 else scale<-sum(object$residuals^2)/dfres[o[1]] stat.anova(aod, test, scale, dfres[o[1]], n) } else aod } survival/R/survfitms.R0000644000175100001440000005620013065013251014530 0ustar hornikusers# Automatically generated from the noweb directory # Methods for survfitms objects dim.survfitms <- function(x) { if (is.null(x$strata)) { if (is.matrix(x$pstate)) c(1L, ncol(x$pstate)) else 1L } else { nr <- length(x$strata) if (is.matrix(x$pstate)) c(nr, ncol(x$pstate)) else nr } } summary.survfit <- function(object, times, censored=FALSE, scale=1, extend=FALSE, rmean=getOption('survfit.rmean'), ...) { fit <- object #make a local copy if (!inherits(fit, 'survfit')) stop("summary.survfit can only be used for survfit objects") # The print.rmean option is depreciated, it is still listened # to in print.survfit, but ignored here if (is.null(rmean)) rmean <- "common" if (is.numeric(rmean)) { if (is.null(object$start.time)) { if (rmean < min(object$time)) stop("Truncation point for the mean is < smallest survival") } else if (rmean < object$start.time) stop("Truncation point for the mean is < smallest survival") } else { rmean <- match.arg(rmean, c('none', 'common', 'individual')) if (length(rmean)==0) stop("Invalid value for rmean option") } temp <- survmean(fit, scale=scale, rmean) table <- temp$matrix #for inclusion in the output list rmean.endtime <- temp$end.time fit$time <- fit$time/scale if (!is.null(fit$strata)) { nstrat <- length(fit$strata) } delta <- function(x, indx) { # sums between chosen times if (is.logical(indx)) indx <- which(indx) if (!is.null(x) && length(indx) >0) { fx <- function(x, indx) diff(c(0, c(0, cumsum(x))[indx+1])) if (is.matrix(x)) { temp <- apply(x, 2, fx, indx=indx) # don't return a vector when only 1 time point is given if (is.matrix(temp)) temp else matrix(temp, nrow=1) } else fx(x, indx) } else NULL } if (missing(times)) { if (!censored) { index <- (rowSums(as.matrix(fit$n.event)) >0) for (i in c("time","n.risk", "n.event", "surv", "pstate", "std.err", "upper", "lower", "cumhaz")) { if (!is.null(fit[[i]])) { # not all components in all objects temp <- fit[[i]] if (!is.array(temp)) temp <- temp[index] #simple vector else if (is.matrix(temp)) temp <- temp[index,,drop=FALSE] else temp <- temp[,,index, drop=FALSE] # 3 way fit[[i]] <- temp } } # The n.enter and n.censor values are accumualated # both of these are simple vectors if (is.null(fit$strata)) { for (i in c("n.enter", "n.censor")) if (!is.null(fit[[i]])) fit[[i]] <- delta(fit[[i]], index) } else { sindx <- rep(1:nstrat, fit$strata) for (i in c("n.enter", "n.censor")) { if (!is.null(fit[[i]])) fit[[i]] <- unlist(sapply(1:nstrat, function(j) delta(fit[[i]][sindx==j], index[sindx==j]))) } # the "factor" is needed for the case that a strata has no # events at all, and hence 0 lines of output fit$strata[] <- as.vector(table(factor(sindx[index], 1:nstrat))) } } #if missing(times) and censored=TRUE, the fit object is ok as it is } else { ssub <- function(x, indx, init=0) { #select an object and index if (!is.null(x) && length(indx)>0) { # the as.vector() is a way to keep R from adding "init" as a row name if (is.matrix(x)) rbind(as.vector(init), x)[indx+1,,drop=FALSE] else c(init, x)[indx+1] } else NULL } # The left.open argument was added to findInterval in R 3.3, but # our local servers are version 3.2.x. Work around it. find2 <- function(x, vec, left.open=FALSE, ...) { if (!left.open) findInterval(x, vec, ...) else length(vec) - findInterval(-x, rev(-vec), ...) } findrow <- function(fit, times, extend, init=1) { # First, toss any printing times that are outside our range if (is.null(fit$start.time)) mintime <- min(fit$time, 0) else mintime <- fit$start.time ptimes <- times[times >= mintime] if (!extend) { maxtime <- max(fit$time) ptimes <- ptimes[ptimes <= maxtime] } ntime <- length(fit$time) index1 <- find2(ptimes, fit$time) index2 <- 1 + find2(ptimes, fit$time, left.open=TRUE) # The pmax() above encodes the assumption that n.risk for any # times before the first observation = n.risk at the first obs fit$time <- ptimes for (i in c("surv", "pstate", "upper", "lower")) { if (!is.null(fit[[i]])) fit[[i]] <- ssub(fit[[i]], index1, init) } for (i in c("std.err", "cumhaz")) { if (!is.null(fit[[i]])) fit[[i]] <- ssub(fit[[i]], index1, 0) } if (is.matrix(fit$n.risk)) { # Every observation in the data has to end with a censor or event. # So by definition the number at risk after the last observed time # value must be 0. fit$n.risk <- rbind(fit$n.risk,0)[index2,,drop=FALSE] } else fit$n.risk <- c(fit$n.risk, 0)[index2] for (i in c("n.event", "n.censor", "n.enter")) fit[[i]] <- delta(fit[[i]], index1) fit } # For a single component, turn it from a list into a single vector, matrix # or array unlistsurv <- function(x, name) { temp <- lapply(x, function(x) x[[name]]) if (is.vector(temp[[1]])) unlist(temp) else if (is.matrix(temp[[1]])) do.call("rbind", temp) else { # the cumulative hazard is the only component that is an array # it's third dimension is n xx <- unlist(temp) dd <- dim(temp[[1]]) dd[3] <- length(xx)/prod(dd[1:2]) array(xx, dim=dd) } } # unlist all the components built by a set of calls to findrow # and remake the strata unpacksurv <- function(fit, ltemp) { keep <- c("time", "surv", "pstate", "upper", "lower", "std.err", "cumhaz", "n.risk", "n.event", "n.censor", "n.enter") for (i in keep) if (!is.null(fit[[i]])) fit[[i]] <- unlistsurv(ltemp, i) fit$strata[] <- sapply(ltemp, function(x) length(x$time)) fit } times <- sort(times) #in case the user forgot if (is.null(fit$strata)) fit <- findrow(fit, times, extend) else { ltemp <- vector("list", nstrat) for (i in 1:nstrat) ltemp[[i]] <- findrow(fit[i], times, extend) fit <- unpacksurv(fit, ltemp) } } # finish off the output structure fit$table <- table if (length(rmean.endtime)>0 && !is.na(rmean.endtime)) fit$rmean.endtime <- rmean.endtime # An ordinary survfit object contains std(cum hazard), change scales if (!is.null(fit$std.err)) fit$std.err <- fit$std.err * fit$surv # Expand the strata if (!is.null(fit$strata)) fit$strata <- factor(rep(1:nstrat, fit$strata), 1:nstrat, labels= names(fit$strata)) class(fit) <- "summary.survfit" fit } summary.survfitms <- function(object, times, censored=FALSE, scale=1, extend=FALSE, rmean= getOption("survfit.rmean"), ...) { fit <- object if (!inherits(fit, 'survfitms')) stop("summary.survfitms can only be used for survfitms objects") # The print.rmean option is depreciated, it is still listened # to in print.survfit, but ignored here if (is.null(rmean)) rmean <- "common" if (is.numeric(rmean)) { if (is.null(object$start.time)) { if (rmean < min(object$time)) stop("Truncation point for the mean is < smallest survival") } else if (rmean < object$start.time) stop("Truncation point for the mean is < smallest survival") } else { rmean <- match.arg(rmean, c('none', 'common', 'individual')) if (length(rmean)==0) stop("Invalid value for rmean option") } temp <- survmean2(fit, scale=scale, rmean) table <- temp$matrix #for inclusion in the output list rmean.endtime <- temp$end.time if (!missing(times)) { if (!is.numeric(times)) stop ("times must be numeric") times <- sort(times) } fit$time <- fit$time/scale if (!is.null(fit$strata)) { nstrat <- length(fit$strata) sindx <- rep(1:nstrat, fit$strata) } delta <- function(x, indx) { # sums between chosen times if (is.logical(indx)) indx <- which(indx) if (!is.null(x) && length(indx) >0) { fx <- function(x, indx) diff(c(0, c(0, cumsum(x))[indx+1])) if (is.matrix(x)) { temp <- apply(x, 2, fx, indx=indx) if (is.matrix(temp)) temp else matrix(temp, nrow=1) } else fx(x, indx) } else NULL } if (missing(times)) { if (!censored) { index <- (rowSums(as.matrix(fit$n.event)) >0) for (i in c("time","n.risk", "n.event", "surv", "pstate", "std.err", "upper", "lower", "cumhaz")) { if (!is.null(fit[[i]])) { # not all components in all objects temp <- fit[[i]] if (!is.array(temp)) temp <- temp[index] #simple vector else if (is.matrix(temp)) temp <- temp[index,,drop=FALSE] else temp <- temp[,,index, drop=FALSE] # 3 way fit[[i]] <- temp } } # The n.enter and n.censor values are accumualated # both of these are simple vectors if (is.null(fit$strata)) { for (i in c("n.enter", "n.censor")) if (!is.null(fit[[i]])) fit[[i]] <- delta(fit[[i]], index) } else { sindx <- rep(1:nstrat, fit$strata) for (i in c("n.enter", "n.censor")) { if (!is.null(fit[[i]])) fit[[i]] <- unlist(sapply(1:nstrat, function(j) delta(fit[[i]][sindx==j], index[sindx==j]))) } # the "factor" is needed for the case that a strata has no # events at all, and hence 0 lines of output fit$strata[] <- as.vector(table(factor(sindx[index], 1:nstrat))) } } #if missing(times) and censored=TRUE, the fit object is ok as it is } else { ssub <- function(x, indx, init=0) { #select an object and index if (!is.null(x) && length(indx)>0) { # the as.vector() is a way to keep R from adding "init" as a row name if (is.matrix(x)) rbind(as.vector(init), x)[indx+1,,drop=FALSE] else c(init, x)[indx+1] } else NULL } # The left.open argument was added to findInterval in R 3.3, but # our local servers are version 3.2.x. Work around it. find2 <- function(x, vec, left.open=FALSE, ...) { if (!left.open) findInterval(x, vec, ...) else length(vec) - findInterval(-x, rev(-vec), ...) } findrow <- function(fit, times, extend, init=1) { # First, toss any printing times that are outside our range if (is.null(fit$start.time)) mintime <- min(fit$time, 0) else mintime <- fit$start.time ptimes <- times[times >= mintime] if (!extend) { maxtime <- max(fit$time) ptimes <- ptimes[ptimes <= maxtime] } ntime <- length(fit$time) index1 <- find2(ptimes, fit$time) index2 <- 1 + find2(ptimes, fit$time, left.open=TRUE) # The pmax() above encodes the assumption that n.risk for any # times before the first observation = n.risk at the first obs fit$time <- ptimes for (i in c("surv", "pstate", "upper", "lower")) { if (!is.null(fit[[i]])) fit[[i]] <- ssub(fit[[i]], index1, init) } for (i in c("std.err", "cumhaz")) { if (!is.null(fit[[i]])) fit[[i]] <- ssub(fit[[i]], index1, 0) } if (is.matrix(fit$n.risk)) { # Every observation in the data has to end with a censor or event. # So by definition the number at risk after the last observed time # value must be 0. fit$n.risk <- rbind(fit$n.risk,0)[index2,,drop=FALSE] } else fit$n.risk <- c(fit$n.risk, 0)[index2] for (i in c("n.event", "n.censor", "n.enter")) fit[[i]] <- delta(fit[[i]], index1) fit } # For a single component, turn it from a list into a single vector, matrix # or array unlistsurv <- function(x, name) { temp <- lapply(x, function(x) x[[name]]) if (is.vector(temp[[1]])) unlist(temp) else if (is.matrix(temp[[1]])) do.call("rbind", temp) else { # the cumulative hazard is the only component that is an array # it's third dimension is n xx <- unlist(temp) dd <- dim(temp[[1]]) dd[3] <- length(xx)/prod(dd[1:2]) array(xx, dim=dd) } } # unlist all the components built by a set of calls to findrow # and remake the strata unpacksurv <- function(fit, ltemp) { keep <- c("time", "surv", "pstate", "upper", "lower", "std.err", "cumhaz", "n.risk", "n.event", "n.censor", "n.enter") for (i in keep) if (!is.null(fit[[i]])) fit[[i]] <- unlistsurv(ltemp, i) fit$strata[] <- sapply(ltemp, function(x) length(x$time)) fit } times <- sort(times) if (is.null(fit$strata)) fit <- findrow(fit, times, extend, fit$p0) else { ltemp <- vector("list", nstrat) for (i in 1:nstrat) ltemp[[i]] <- findrow(fit[i], times, extend, fit$p0[i,]) fit <- unpacksurv(fit, ltemp) } } # finish off the output structure fit$table <- table if (length(rmean.endtime)>0 && !is.na(rmean.endtime)) fit$rmean.endtime <- rmean.endtime if (!is.null(fit$strata)) fit$strata <- factor(rep(names(fit$strata), fit$strata)) class(fit) <- "summary.survfitms" fit } print.survfitms <- function(x, scale=1, rmean = getOption("survfit.rmean"), ...) { if (!is.null(cl<- x$call)) { cat("Call: ") dput(cl) cat("\n") } omit <- x$na.action if (length(omit)) cat(" ", naprint(omit), "\n") if (is.null(rmean)) rmean <- "common" if (is.numeric(rmean)) { if (is.null(x$start.time)) { if (rmean < min(x$time)) stop("Truncation point for the mean is < smallest survival") } else if (rmean < x$start.time) stop("Truncation point for the mean is < smallest survival") } else { rmean <- match.arg(rmean, c('none', 'common', 'individual')) if (length(rmean)==0) stop("Invalid value for rmean option") } temp <- survmean2(x, scale=scale, rmean) if (is.null(temp$end.time)) print(temp$matrix, ...) else { etime <- temp$end.time dd <- dimnames(temp$matrix) cname <- dd[[2]] cname[length(cname)] <- paste0(cname[length(cname)], '*') dd[[2]] <- cname dimnames(temp$matrix) <- dd print(temp$matrix, ...) if (length(etime) ==1) cat(" *mean time in state, restricted (max time =", format(etime, ...), ")\n") else cat(" *mean time in state, restricted (per curve cutoff)\n") } invisible(x) } survmean2 <- function(x, scale, rmean) { nstate <- length(x$states) #there will always be at least 1 state ngrp <- max(1, length(x$strata)) if (ngrp >1) { igrp <- rep(1:ngrp, x$strata) rname <- names(x$strata) } else { igrp <- rep(1, length(x$time)) rname <- NULL } # The n.event matrix may not have nstate columms. Its # colnames are the first elements of states, however if (is.matrix(x$n.event)) { nc <- ncol(x$n.event) nevent <- tapply(x$n.event, list(rep(igrp, nc), col(x$n.event)), sum) dimnames(nevent) <- list(rname, x$states[1:nc]) } else { nevent <- tapply(x$n.event, igrp, sum) names(nevent) <- rname } outmat <- matrix(0., nrow=nstate*ngrp , ncol=2) outmat[,1] <- rep(x$n, nstate) outmat[1:length(nevent), 2] <- c(nevent) if (ngrp >1) rowname <- c(outer(rname, x$states, paste, sep=", ")) else rowname <- x$states # Caculate the mean time in each state if (rmean != "none") { if (is.numeric(rmean)) maxtime <- rep(rmean, ngrp) else if (rmean=="common") maxtime <- rep(max(x$time), ngrp) else maxtime <- tapply(x$time, igrp, max) meantime <- matrix(0., ngrp, nstate) p0 <- matrix(x$p0, nrow=ngrp) #in case there is only one row if (!is.null(x$influence)) stdtime <- meantime for (i in 1:ngrp) { if (is.matrix(x$pstate)) temp <- rbind(p0[i,], x$pstate[igrp==i,, drop=FALSE]) else temp <- matrix(c(p0[i], x$pstate[igrp==i]), ncol=1) if (is.null(x$start.time)) tt <- c(0, x$time[igrp==i]) else tt <- c(x$start.time, x$time[igrp==i]) # Now cut it off at maxtime delta <- diff(c(tt[tt nrow(temp)) delta <- delta[1:nrow(temp)] if (length(delta) < nrow(temp)) delta <- c(delta, rep(0, nrow(temp) - length(delta))) meantime[i,] <- colSums(delta*temp) if (!is.null(x$influence)) { # calculate the variance if (is.list(x$influence)) itemp <- apply(x$influence[[i]], 1, function(x) colSums(x*delta)) else itemp <- apply(x$influence, 1, function(x) colSums(x*delta)) stdtime[i,] <- sqrt(rowSums(itemp^2)) } } outmat <- cbind(outmat, c(meantime)/scale) cname <- c("n", "nevent", "rmean") if (!is.null(x$influence)) { outmat <- cbind(outmat, c(stdtime)/scale) cname <- c(cname, "std(rmean)") } # report back a single time, if there is only one if (all(maxtime == maxtime[1])) maxtime <- maxtime[1] } else cname <- c("n", "nevent") dimnames(outmat) <- list(rowname, cname) if (rmean=='none') list(matrix=outmat) else list(matrix=outmat, end.time=maxtime/scale) } "[.survfitms" <- function(x, ..., drop=TRUE) { nmatch <- function(indx, target) { # This function lets R worry about character, negative, or logical subscripts # It always returns a set of positive integer indices temp <- 1:length(target) names(temp) <- target temp[indx] } if (missing(..1)) i<- NULL else i <- ..1 # rows if (missing(..2)) j<- NULL else j <- ..2 # cols n <- length(x$time) if (is.null(x$strata) && is.matrix(x$pstate)) { # No strata, but a matrix of P(state) values # In this case, allow them to use a single i subscript as well if (is.null(j) && !is.null(i)) { j <- i i <- NULL } } # 'i' is the subscript from the user's point of view, 'i2' is the # subscript from the program's view, i.e, the row indices to keep if (is.null(i)) { i2 <- 1:n if (is.null(x$strata)) i <- 1 else i <- seq(along=x$strata) } else { if (is.null(x$strata) && (length(i) > 1 || i != 1)) stop("subscript out of bounds") indx <- nmatch(i, names(x$strata)) #strata to keep if (any(is.na(indx))) stop(paste("strata", paste(i[is.na(indx)], collapse=' '), 'not matched')) # Now, i may not be in order: a user has curve[3:2] to reorder # a plot. Hence the "unlist(lapply(" construct which will reorder # the data in the curves temp <- rep(1:length(x$strata), x$strata) i2 <- unlist(lapply(i, function(x) which(temp==x))) if (length(i) <=1 && drop) x$strata <- NULL else x$strata <- x$strata[indx] } if (!is.null(j)) { indx <- nmatch(j, x$states) if (any(is.na(indx))) stop("subscript out of bounds", j[is.na(indx)]) else j <- as.vector(indx) } # if only one state is kept, still retain the data as a matrix if (length(i2) ==1 && !is.null(j) && missing(drop)) drop <- FALSE # all the elements that can have "nstate" elements or columns # The n.event variable can have fewer temp <- c("n.risk", "n.event", "n.censor", "pstate", "cumhaz", "std.err", "lower", "upper") sfun <- function(z) { if (is.null(j)) { if (is.array(z)) { if (length(dim(z)) > 2) z[,,i2, drop=drop] else z[i2,,drop=drop] } else z[i2] } else { if (is.array(z)) { if (length(dim(z)) > 2) z[j,j,i2, drop=drop] else z[i2,j, drop=drop] } else z[i2] } } for (k in temp) x[[k]] <- sfun(x[[k]]) if (!is.null(j)) x$states <- x$states[j] x$n <- x$n[i] x$time <- x$time[i2] x$transitions <- NULL # this is incorrect after subscripting if (is.matrix(x$p0)) { if (is.null(j)) x$p0<- x$p0[i,] else x$p0 <- x$p0[i,j] } else if (!is.null(j)) x$p0 <- x$p0[j] if (!is.null(x$influence)) { if (length(i) >1) x$influence <- x$influence[i] else if (is.list(x$influence)) x$influence <- x$influence[[i]] if (!is.null(j)) { if (is.list(x$influence)) x$influence <- lapply(x$influence, function(x) x[,j,]) else x$influence <- x$influence[,j,] } } x } survival/R/survfit.matrix.R0000644000175100001440000001473613026560673015517 0ustar hornikusers# Create the Aalen-Johansen estimate by joining a set of # survival curves. Actually the cumulative hazard estimates are used. # survfit.matrix <- function(formula, p0, method=c("discrete", "matexp"), ...) { Call <- match.call() curves <- formula if (!is.matrix(curves)) stop("input must be a square matrix of survival curves") if (!is.list(curves)) stop("input must be a matrix of survival curves") if (nrow(curves) != ncol(curves)) stop("input must be a square matrix survival curves") nstate <- nrow(curves) states <- names(p0) if (is.null(states)) { dname <- dimnames(curves) if (!is.null(dname)[[1]]) states <- dname[[1]] else if (!is.null(dname[[2]])) states <- dname[[2]] else states <- 1:nstate } nonzero <- sapply(curves, function(x) length(x) > 0) # transitions curves <- curves[nonzero] #toss away the NULLS if (any(sapply(curves, function(z) !inherits(z, 'survfit')))) stop("input must be a square matrix survival curves") if (sum(nonzero) < 2) stop("input must have at least 2 transitions") classes <- lapply(curves, class) # Make sure we were sent the right things. If any of the curves inherit # from "survfitms", they are the result of a prior AJ computation; # such recursion does not lead to valid estimates. dd <- dim(curves[[1]]) ncurve <- prod(dd) for (i in 1:length(classes)) { if (length(classes[[i]]) != length(classes[[1]]) || any(classes[[i]] != classes[[1]])) stop("all curves must be the same type") if (length(dim(curves[[i]])) != length(dd) || any(dim(curves[[i]]) != dd)) stop("all curves must be of the same dimension") } if (any(sapply(curves, function(x) inherits(x, "survfitms")))) stop("multi-state curves are not a valid input") type <- classes[[1]][1] # 'survfit' or 'survfit.cox' temp <- sapply(curves, function(x) x$start.time) tlen <- sapply(temp, length) if (any(tlen >0)) { # at least one curve with start.time if (any(tlen != 1) || any(temp != temp[1])) stop("all curves must have a consistent start.time value") start.time <- temp[1] } else start.time <- NULL if (missing(method)) { if (type=='survfit.cox') method <- "matexp" else method <- "discrete" } else method <- match.arg(method) if (missing(p0)) p0 <- c(1, rep(0, nstate-1)) if (!is.matrix(p0)) p0 <- matrix(rep(p0, ncurve), ncol=nstate, byrow=TRUE) else if (nrow(p0) != ncurve) stop("wrong number of rows for p0") if (ncol(p0) != nstate) stop("incorrect number of states in p0") if (any( rowSums(p0) !=1) || any(p0<0)) stop("invalid elements in p0") docurve <- function(z, nonzero, nstate, p0) { # z is a list of survival curves utime <- lapply(z, function(x) x$time[x$n.event>0]) utime <- sort(unique(unlist(utime))) # set of unique times cumhaz<- lapply(z, function(x) summary(x, times=utime, extend=TRUE)$cumhaz) jumps <- matrix(unlist(lapply(cumhaz, function(x) diff(c(0, x)))), ncol= sum(nonzero)) Tmat <- diag(nstate) pstate <- matrix(0., nrow= 1+length(utime), ncol=nstate) pstate[1,] <- p0 for (i in 1:length(utime)) { Tmat[nonzero] <- jumps[i,] if (method == "matrix") { temp <- pmin(1, rowSums(Tmat) - diag(Tmat)) # failsafe diag(Tmat) <- 1 - temp #rows sum to 1 pstate[i+1,] <- pstate[i,] %*% Tmat } else { diag(Tmat) <- diag(Tmat) - rowSums(Tmat) #rows sum to 0 pstate[i+1,] <- as.vector(pstate[i,] %*% expm(Tmat)) } } # Fill in the n.risk and n.event matrices zz <- matrix(0, nstate, nstate) from <- (row(zz))[nonzero] to <- (col(zz))[nonzero] n.risk <- n.event <- matrix(0, length(utime), ncol= nstate) # the n.risk matrix is based on "from", n.event on "to" # If multiple curves come from the same source, we blithely # assume that they will agree on the sample size. If multiples # go to the same ending, add the events. for (i in 1:length(z)) { index <- findInterval(utime, z[[i]]$time) n.risk[,from[i]] <- c(0, z[[i]]$n.risk)[index +1] n.event[, to[i]] <- n.event[,to[i]] + c(0, z[[i]]$n.event)[index+1] } # All the curves should have the same n list(n = z[[1]]$n, time = utime, pstate= pstate[-1,], n.risk= n.risk, n.event=n.event) } # The output will have nstate columns, one for each state, and # prod(dim(curves)) strata. If the input has strata and # columns, the output strata will repeat the original strata, once # for each column of the input, adding "new1", "new2", etc to the # end to recognize the rows of the newdata frame that gave rise to it. # nstrat <- length(curves[[1]]$strata) tlist <- vector("list", prod(dd)) k <- 1 if (length(dd) ==1) { tname <- paste0("new", 1:dd[1]) for (j in 1:dd[1]) { tlist[[j]] <- docurve(lapply(curves, function(x) x[j]), nonzero, nstate, p0[j,]) } } else { tname <- paste0("new", 1:dd[2]) for (j in 1:dd[2]) { for (i in 1:dd[1]) { tlist[[k]] <- docurve(lapply(curves, function(x) x[i,j]), nonzero, nstate, p0[k,]) k <- k+1 } } } fit <- list() fit$n <- tlist[[1]]$n fit$time <- unlist(lapply(tlist, function(x) x$time)) fit$pstate <- do.call("rbind", lapply(tlist, function(x) x$pstate)) fit$n.risk <- do.call("rbind", lapply(tlist, function(x) x$n.risk)) fit$n.event<- do.call("rbind", lapply(tlist, function(x) x$n.event)) ntemp <- unlist(lapply(tlist, function(x) length(x$time))) if (nstrat > 0 && length(dd)==2) names(ntemp) <- as.vector(outer(names(curves[[1]]$strata), tname, paste, sep=", ")) else names(ntemp) <- tname fit$strata <- ntemp ns <- length(fit$strata) fit$p0 <- p0 fit$states <- states fit$n <- curves[[1]]$n if (!is.null(start.time)) fit$start.time <- start.time fit$call <- Call class(fit) <- c("survfitms", "survfit") fit } survival/R/tmerge.R0000644000175100001440000004275513065013252013764 0ustar hornikusers# Automatically generated from the noweb directory tmerge <- function(data1, data2, id, ..., tstart, tstop, options) { Call <- match.call() # The function wants to recognize special keywords in the # arguments, so define a set of functions which will be used to # mark objects new <- new.env(parent=parent.frame()) assign("tdc", function(time, value=NULL) { x <- list(time=time, value=value); class(x) <- "tdc"; x}, envir=new) assign("cumtdc", function(time, value=NULL) { x <- list(time=time, value=value); class(x) <-"cumtdc"; x}, envir=new) assign("event", function(time, value=NULL, censor=NULL) { x <- list(time=time, value=value, censor=censor); class(x) <-"event"; x}, envir=new) assign("cumevent", function(time, value=NULL, censor=NULL) { x <- list(time=time, value=value, censor=censor); class(x) <-"cumevent"; x}, envir=new) if (missing(data1) || missing(data2) || missing(id)) stop("the data1, data2, and id arguments are required") if (!inherits(data1, "data.frame")) stop("data1 must be a data frame") tmerge.control <- function(idname="id", tstartname="tstart", tstopname="tstop", delay =0, na.rm=TRUE, tdcstart=NA, ...) { extras <- list(...) if (length(extras) > 0) stop("unrecognized option(s):", paste(names(extras), collapse=', ')) if (length(idname) != 1 || make.names(idname) != idname) stop("idname option must be a valid variable name") if (!is.null(tstartname) && (length(tstartname) !=1 || make.names(tstartname) != tstartname)) stop("tstart option must be NULL or a valid variable name") if (length(tstopname) != 1 || make.names(tstopname) != tstopname) stop("tstop option must be a valid variable name") if (length(delay) !=1 || !is.numeric(delay) || delay < 0) stop("delay option must be a number >= 0") if (length(na.rm) !=1 || ! is.logical(na.rm)) stop("na.rm option must be TRUE or FALSE") if (length(tdcstart) !=1) stop("tdcstart must be a single value") list(idname=idname, tstartname=tstartname, tstopname=tstopname, delay=delay, na.rm=na.rm, tdcstart=tdcstart) } tname <- attr(data1, "tname") firstcall <- is.null(tname) #first call to the function if (!firstcall && any(is.null(match(unlist(tname), names(data1))))) stop("data1 does not match its own tname attribute") if (!missing(options)) { if (!is.list(options)) stop("options must be a list") if (!is.null(tname)) { # If an option name matches one already in tname, don't confuse # the tmerge.control routine with duplicate arguments temp <- match(names(options), names(tname), nomatch=0) topt <- do.call(tmerge.control, c(options, tname[temp==0])) if (any(temp >0)) { # A variable name is changing midstream, update the # variable names in data1 varname <- tname[c("idname", "tstartname", "tstopname")] temp2 <- match(varname, names(data1)) names(data1)[temp2] <- varname } } else topt <- do.call(tmerge.control, options) } else if (length(tname)) topt <- do.call(tmerge.control, tname) else topt <- tmerge.control() # id, tstart, tstop are found in data2 if (missing(id)) stop("the id argument is required") if (missing(data1) || missing(data2)) stop("two data sets are required") id <- eval(Call[["id"]], data2, enclos=emptyenv()) #don't find it elsewhere if (is.null(id)) stop("id variable not found in data2") if (firstcall) { if (!missing(tstop)) { tstop <- eval(Call[["tstop"]], data2) if (length(tstop) != length(id)) stop("tstop and id must be the same length") # The neardate routine will check for legal tstop data type } if (!missing(tstart)) { tstart <- eval(Call[["tstart"]], data2) if (length(tstart)==1) tstart <- rep(tstart, length(id)) if (length(tstart) != length(id)) stop("tstart and id must be the same length") if (any(tstart >= tstop)) stop("tstart must be < tstop") } } else { if (!missing(tstart) || !missing(tstop)) stop("tstart and tstop arguments only apply to the first call") } # grab the... arguments notdot <- c("data1", "data2", "id", "tstart", "tstop", "options") dotarg <- Call[is.na(match(names(Call), notdot))] dotarg[[1]] <- as.name("list") # The as-yet dotarg arguments if (missing(data2)) args <- eval(dotarg, envir=new) else args <- eval(dotarg, data2, enclos=new) argclass <- sapply(args, function(x) (class(x))[1]) argname <- names(args) if (any(argname== "")) stop("all additional argments must have a name") check <- match(argclass, c("tdc", "cumtdc", "event", "cumevent")) if (any(is.na(check))) stop(paste("argument(s)", argname[is.na(check)], "not a recognized type")) # The tcount matrix is useful for debugging tcount <- matrix(0L, length(argname), 8) dimnames(tcount) <- list(argname, c("early","late", "gap", "within", "boundary", "leading", "trailing", "tied")) tevent <- attr(data1, "tevent") # event type variables tcens <- attr(data1, "tcensor")# censor code for variables if (is.null(tcens)) tcens <- vector('list', 0) newdata <- data1 #make a copy if (firstcall) { # We don't look for topt$id. What if the user had id=clinic, but their # starting data set also had a variable named "id". We want clinic for # this first call. idname <- Call[["id"]] if (!is.name(idname)) stop("on the first call 'id' must be a single variable name") # The line below finds tstop and tstart variables in data1 indx <- match(c(topt$idname, topt$tstartname, topt$tstopname), names(data1), nomatch=0) if (any(indx[1:2]>0) && FALSE) { # warning currently turned off. Be chatty? overwrite <- c(topt$tstartname, topt$tstopname)[indx[2:3]] warning("overwriting data1 variables", paste(overwrite, collapse=' ')) } temp <- as.character(idname) if (!is.na(match(temp, names(data1)))) { data1[[topt$idname]] <- data1[[temp]] baseid <- data1[[temp]] } else stop("id variable not found in data1") if (any(duplicated(baseid))) stop("for the first call (that establishes the time range) data1 must have no duplicate identifiers") if (length(baseid)== length(id) && all(baseid == id)) newdata <- data1 else { # Note: 'id' is the idlist for data 2 indx2 <- match(id, baseid) if (any(is.na(indx2))) stop("'id' has values not in data1") newdata <- data1[indx2,] } if (missing(tstop)) { # case 2 if (length(argclass)==0 || argclass[1] != "event") stop("neither a tstop argument nor an initial event argument was found") tstop <- args[[1]][[1]] } # at this point newdata and data2 are in the same order, same # rows if (any(is.na(tstop))) stop("missing time value, when that variable defines the span") if (missing(tstart)) tstart <- rep(0, length(id)) if (any(tstart >= tstop)) stop("tstart must be > tstop") newdata[[topt$tstartname]] <- tstart newdata[[topt$tstopname]] <- tstop if (any(duplicated(id))) { # sort by time within id indx1 <- match(id, unique(id)) newdata <- newdata[order(indx1, tstop),] } n <- nrow(newdata) temp <- newdata[[topt$idname]] if (any(tstart >= tstop)) stop("tstart must be < tstop") if (any(newdata$tstart[-n] > newdata$tstop[-1] & temp[-n] == temp[-1])) stop("there are overlapping time intervals") } else { #not a first call if (any(is.na(match(id, data1[[topt$idname]])))) stop("id values were found in data2 which are not in data1") } saveid <- id for (ii in seq(along.with=args)) { argi <- args[[ii]] baseid <- newdata[[topt$idname]] dstart <- newdata[[topt$tstartname]] dstop <- newdata[[topt$tstopname]] argcen <- argi$censor # if an event time is missing then skip that obs etime <- argi$time if (length(etime) != length(saveid)) stop("argument ", argname[ii], " is not the same length as id") if (!is.null(argi$value)) { if (length(argi$value) != length(saveid)) stop("argument", argname[ii], "is not the same length as id") if (topt$na.rm) keep <- !(is.na(etime) | is.na(argi$value)) else keep <- !is.na(etime) if (!all(keep)) { etime <- etime[keep] argi$value <- argi$value[keep] } } else { keep <- !is.na(etime) etime <- etime[keep] } id <- saveid[keep] # Later steps become easier if we sort the new data by id and time # The match() is critical when baseid is not in sorted order. The # etime part of the sort will change from one ii value to the next. indx <- order(match(id, baseid), etime) id <- id[indx] etime <- etime[indx] if (!is.null(argi$value)) yinc <- argi$value[indx] else yinc <- NULL # indx1 points to the closest start time in the baseline data (data1) # that is <= etime. indx2 to the closest end time that is >=etime. # If etime falls into a (tstart, tstop) interval, indx1 and indx2 # will match # If the "delay" argument is set and this event is of type tdc, then # move any etime that is after the entry time for a subject. if (topt$delay >0 && argclass[ii] %in% c("tdc", "cumtdc")) { mintime <- tapply(dstart, baseid, min) index <- match(id, names(mintime)) etime <- ifelse(etime <= mintime[index], etime, etime+ topt$delay) } indx1 <- neardate(id, baseid, etime, dstart, best="prior") indx2 <- neardate(id, baseid, etime, dstop, best="after") # The event times fall into one of 5 categories # 1. Before the first interval # 2. After the last interval # 3. Outside any interval but with time span, i.e, it falls into # a gap in follow-up # 4. Strictly inside an interval (does't touch either end) # 5. Inside an interval, but touching. itype <- ifelse(is.na(indx1), 1, ifelse(is.na(indx2), 2, ifelse(indx2 > indx1, 3, ifelse(etime== dstart[indx1] | etime== dstop[indx2], 5, 4)))) # Subdivide the events that touch on a boundary # 1: intervals of (a,b] (b,d], new count at b "tied edge" # 2: intervals of (a,b] (c,d] with c>b, new count at c, "front edge" # 3: intervals of (a,b] (c,d] with c>b, new count at b, "back edge" # subtype <- ifelse(itype!=5, 0, ifelse(indx1 == indx2+1, 1, ifelse(etime==dstart[indx1], 2, 3))) tcount[ii,1:7] <- table(factor(itype+subtype, levels=c(1:4, 6:8))) # count ties. id and etime are not necessarily sorted tcount[ii,8] <- sum(tapply(etime, id, function(x) sum(duplicated(x)))) if (is.null(yinc)) yinc <- rep(1.0, length(etime)) indx4 <- which(itype==4) n4 <- length(indx4) if (n4 > 0) { icount <- tapply(etime[indx4], indx1[indx4], function(x) sort(unique(x))) n.add <- sapply(icount, length) #number of rows to add # expand the data irep <- rep.int(1L, nrow(newdata)) erow <- unique(indx1[indx4]) # which rows in newdata to be expanded irep[erow] <- 1+ n.add # number of rows in new data jrep <- rep(1:nrow(newdata), irep) #stutter the duplicated rows newdata <- newdata[jrep,] #expand it out dstart <- dstart[jrep] dstop <- dstop[jrep] #fix up times nfix <- length(erow) temp <- vector("list", nfix) iend <- (cumsum(irep))[irep >1] #end row of each duplication set for (j in 1:nfix) temp[[j]] <- -(seq(n.add[j] -1, 0)) + iend[j] newrows <- unlist(temp) # icount is a list, each element of which is a vector # the natural way to turn that into a vector is unlist(), but that # leads to problems if etime is a date: we lose the time origin if (is.numeric(icount[[1]])) icount <- unlist(icount) else icount <- do.call('c', icount) dstart[newrows] <- dstop[newrows-1] <- icount newdata[[topt$tstartname]] <- dstart newdata[[topt$tstopname]] <- dstop for (ename in tevent) newdata[newrows-1, ename] <- tcens[[ename]] # refresh indices baseid <- newdata[[topt$idname]] indx1 <- neardate(id, baseid, etime, dstart, best="prior") indx2 <- neardate(id, baseid, etime, dstop, best="after") subtype[itype==4] <- 1 #all the "insides" are now on a tied edge itype[itype==4] <- 5 } # add it in if (argclass[ii] %in% c("cumtdc", "cumevent")) { if (!is.numeric(yinc)) stop("invalid increment for cumtdc or cumevent") yinc <- unlist(tapply(yinc, match(id, baseid), cumsum)) } newvar <- newdata[[argname[ii]]] #does the variable exist? if (argclass[ii] %in% c("event", "cumevent")) { if (is.null(newvar)) { if (is.factor(yinc)) newvar <- factor(rep(levels(yinc)[1], nrow(newdata)), levels(yinc)) else if (is.numeric(yinc)) newvar <- rep(0L, nrow(newdata)) else stop("invalid value for a status variable") } keep <- (subtype==1 | subtype==3) # all other events are thrown away newvar[indx2[keep]] <- yinc[keep] if (!(argname[ii] %in% tevent)) { tevent <- c(tevent, argname[[ii]]) if (is.factor(yinc)) tcens <- c(tcens, levels(yinc)[1]) else tcens <- c(tcens, 0) names(tcens) <- tevent } } else { keep <- itype != 2 # changes after the last interval are ignored indx <- ifelse(subtype==1, indx1, ifelse(subtype==3, indx2+1L, indx2)) # we want to pass the right kind of NA to the C code if (is.na(topt$tdcstart)) topt$tdcstart <- as.numeric(topt$tdcstart) if (is.null(newvar)) { # not overwriting a prior value if (is.null(argi$value)) newvar <- rep(0.0, nrow(newdata)) else newvar <- rep(topt$tdcstart, nrow(newdata)) } if (is.numeric(yinc)) { # this is the usual case if (!is.numeric(newvar)) stop("data and options$tdcstart do not agree on data type") # id can be any data type; feed integers to the C routine storage.mode(yinc) <- storage.mode(dstop) <- "double" storage.mode(newvar) <- storage.mode(etime) <- "double" newvar <- .Call(Ctmerge, match(baseid, baseid), dstop, newvar, match(id, baseid)[keep], etime[keep], yinc[keep], indx[keep]) } else { # deal with a factor or character if (!(is.factor(yinc) || is.factor(yinc))) stop("the second argument of tdc must be numeric, character, or factor") newlev <- unique(c(levels(as.factor(yinc)), levels(as.factor(newvar)))) y2 <- factor(yinc, levels=newlev) newvar <- factor(newvar, levels=newlev) storage.mode(dstop) <- storage.mode(etime) <- "double" new <- .Call(Ctmerge, match(baseid, baseid), dstop, as.numeric(newvar), match(id, baseid)[keep], etime[keep], as.numeric(yinc[keep]), indx[keep]) if (is.factor(yinc)) newvar <- factor(new, labels=newlev) else newvar <- newlev[new] } } newdata[[argname[ii]]] <- newvar } attr(newdata, "tname") <- topt[c("idname", "tstartname", "tstopname")] attr(newdata, "tcount") <- rbind(attr(data1, "tcount"), tcount) if (length(tevent)) { attr(newdata, "tevent") <- tevent attr(newdata, "tcensor" ) <- tcens } row.names(newdata) <- NULL #These are a mess; kill them off. # Not that it works: R just assigns new row names. class(newdata) <- c("data.frame") newdata } survival/R/predict.survreg.S0000644000175100001440000001507113016105374015622 0ustar hornikuserspredict.survreg <- function(object, newdata, type=c('response', "link", 'lp', 'linear', 'terms', 'quantile','uquantile'), se.fit=FALSE, terms=NULL, p=c(.1, .9), na.action=na.pass, ...) { # # What do I need to do predictions ? # # linear predictor: exists # +se : X matrix # newdata : new X matrix # # response -- same as lp, +transform, from distribution # # p -- density function from distribution # scale(s) -- if multiple I need the strata # +se : variance matrix # newdata: new X type <-match.arg(type) if (type=='link') type<- 'lp' #true until their are link functions if (type=='linear') type<- 'lp' n <- length(object$linear.predictors) Terms <- object$terms if(!inherits(Terms, "terms")) stop("invalid terms component of object") strata <- attr(Terms, 'specials')$strata Terms <- delete.response(Terms) coef <- object$coefficients intercept <- attr(Terms, "intercept") nvar <- length(object$coefficients) vv <- object$var[1:nvar, 1:nvar] fixedscale <- (nvar == ncol(object$var)) if (missing(newdata) && (type=='terms' || se.fit)) need.x <- TRUE else need.x <- FALSE if (!missing(newdata)){ newframe <- stats::model.frame(Terms, data=newdata, na.action= na.action, xlev=object$xlevels) na.action.used <- attr(newframe, 'na.action') } else na.action.used <- object$na.action if (length(strata) && (type=='quantile' || type=='uquantile') && !fixedscale) { # # We need to reconstruct the original "strata" variable # mf <- stats::model.frame(object) temp <- untangle.specials(Terms, 'strata', 1) if (length(temp$vars)==1) strata.keep <- mf[[temp$vars]] else strata.keep <- strata(mf[,temp$vars], shortlabel=TRUE) strata <- as.numeric(strata.keep) nstrata <- max(strata) if (missing(newdata) && need.x){ #need the old x x <- object[['x']] if (is.null(x)) x <- model.matrix(object, mf) } else if (!missing(newdata)) { #need the new x if (length(temp$vars)==1) newstrat <- newframe[[temp$vars]] else newstrat <- strata(newframe[,temp$vars], shortlabel=TRUE) strata <- match(newstrat, levels(strata.keep)) x <- model.matrix(object, newframe) offset <- model.offset(newframe) } } else { # per subject strata not needed nstrata <- 1 if (missing(newdata)) { strata <- rep(1L, n) if (need.x) x <- model.matrix(object) } else { x <- model.matrix(object, newframe) strata <- rep(1L, nrow(x)) offset <- 0 } } scale <- object$scale[strata] #center x if terms are to be computed if(type=='p' || (type == "terms" && intercept)) x <- sweep(x, 2, object$means) # # Grab the distribution # if (is.character(object$dist)) dd <- survreg.distributions[[object$dist]] else dd <- object$dist if (is.null(dd$itrans)) { itrans <- function(x) x # identity transformation dtrans <- function (x) 1 # derivative of the transformation } else { itrans <- dd$itrans dtrans <- dd$dtrans } if (!is.null(dd$dist)) dd <- survreg.distributions[[dd$dist]] # # Now, lay out the code one case at a time. # There is some repetition this way, but otherwise the code just gets # too complicated. # if (type=='lp' || type=='response') { if (missing(newdata)) { pred <- object$linear.predictors # names(pred) <- names(object$residuals) } else pred <- drop(x %*% coef) + offset if (se.fit) se <- sqrt(diag(x %*% vv %*% t(x))) if (type=='response') { pred <- itrans(pred) if (se.fit) se <- se/ dtrans(pred) } } else if (type=='quantile' || type=='uquantile') { if (missing(newdata)) pred <- object$linear.predictors else pred <- x %*% coef # "pred" is the mean of the distribution, # now add quantiles and then invert qq <- dd$quantile(p, object$parm) if (length(qq)==1 || length(pred)==1) { pred <- drop(pred) + qq*scale if (se.fit && fixedscale) { var <- ((x %*% vv) * x) %*% rep(1., ncol(x)) se <- rep(sqrt(drop(var)), length(qq)) } else if (se.fit) { x.strata <- outer(strata, 1:nstrata, function(x,y) 1*(x==y)) se <- matrix(0, ncol=length(qq), nrow=nrow(x)) for (i in 1:(length(qq))) { temp <- cbind(x, (qq[i]*scale)* x.strata) var <- ((temp %*% object$var) *temp) %*% rep(1, ncol(temp)) se[,i] <- sqrt(drop(var)) } se <- drop(se) } } else { pred <- c(pred) + outer(scale, qq) if (se.fit && fixedscale) { var <- ((x %*% vv) * x) %*% rep(1., ncol(x)) if (length(qq) >1) { se <- rep(sqrt(drop(var)), length(qq)) se <- matrix(se, ncol=length(qq)) } else se <- sqrt(drop(var)) } else if (se.fit) { x.strata <- outer(strata, 1:nstrata, function(x,y) 1*(x==y)) se <- pred nc <- rep(1., ncol(object$var)) for (i in 1:length(qq)) { temp <- cbind(x, (qq[i]*scale)*x.strata) var <- ((temp %*% object$var)* temp) %*% nc se[,i] <- sqrt(drop(var)) } se <- drop(se) } } pred <- drop(pred) if (type == 'quantile') { pred <- itrans(pred) if (se.fit) se <- se/dtrans(pred) } } else { #terms # In Splus we can use Build.terms, in R we have to do it ourselves asgn <- attrassign(x,Terms) hasintercept<-attr(Terms,"intercept")>0 if (hasintercept) asgn$"(Intercept)"<-NULL nterms<-length(asgn) pred<-matrix(ncol=nterms,nrow=NROW(x)) dimnames(pred)<-list(rownames(x),names(asgn)) if (se.fit){ se<-matrix(ncol=nterms,nrow=NROW(x)) dimnames(se)<-list(rownames(x),names(asgn)) R<-object$var } for (i in 1:nterms){ ii<-asgn[[i]] pred[,i]<-x[,ii,drop=FALSE]%*%(coef[ii]) if (se.fit){ for(j in (1:NROW(x))){ xi<-x[j,ii,drop=FALSE]*(coef[ii]) vci<-R[ii,ii] se[j,i]<-sqrt(sum(xi%*% vci %*%t( xi))) } } } if (!is.null(terms)){ pred<-pred[,terms,drop=FALSE] if (se.fit) se<-se[,terms,drop=FALSE] } } #Expand out the missing values in the result # if (!is.null(na.action.used)) { pred <- naresid(na.action.used, pred) if(se.fit) se <- naresid(na.action.used, se) } if (se.fit) list(fit=pred, se.fit=se) else pred } survival/R/print.survfit.S0000644000175100001440000002357413003732260015334 0ustar hornikusersprint.survfit <- function(x, scale=1, digits = max(options()$digits - 4, 3), print.rmean = getOption('survfit.print.rmean'), rmean = getOption('survfit.rmean'), ...) { if (!is.null(cl<- x$call)) { cat("Call: ") dput(cl) cat("\n") } omit <- x$na.action if (length(omit)) cat(" ", naprint(omit), "\n") savedig <- options(digits=digits) on.exit(options(savedig)) # The print.rmean option is depreciated, with the more general # rmean option taking its place. But if someone specifically # uses print.rmean in the call, or has it as an option without # the rmean option, listen to them. if (!missing(print.rmean) && is.logical(print.rmean) && missing(rmean)) { if (print.rmean) rmean <- 'common' else rmean <- 'none' } else { if (is.null(rmean)) { if (is.logical(print.rmean)) { if (print.rmean) rmean <- 'common' else rmean <- 'none' } else rmean <- 'none' #no option set } # Check validity: it can be numeric or character if (is.numeric(rmean)) { if (is.null(x$start.time)) { if (rmean < min(x$time)) stop("Truncation point for the mean is < smallest survival") } else if (rmean < x$start.time) stop("Truncation point for the mean is < smallest survival") } else { rmean <- match.arg(rmean, c('none', 'common', 'individual')) if (length(rmean)==0) stop("Invalid value for rmean option") } } temp <- survmean(x, scale=scale, rmean) # If the first columns of survmean are identical, suppress duplicates # mtemp <- if (is.matrix(temp$matrix)) temp$matrix else matrix(temp$matrix, nrow=1, dimnames=list(NULL, names(temp$matrix))) if (all(mtemp[,2] == mtemp[,3])){ cname <- dimnames(mtemp)[[2]] mtemp <- mtemp[,-2, drop=FALSE] cname <-cname[-2] cname[2] <- "n" dimnames(mtemp)[[2]] <- cname } if (all(mtemp[,1] == mtemp[,2])) mtemp <- mtemp[,-1, drop=FALSE] temp$matrix <- drop(mtemp) print(temp$matrix) if (rmean != 'none') { if (rmean == 'individual') cat(" * restricted mean with variable upper limit\n") else cat(" * restricted mean with upper limit = ", format(temp$end.time[1]), "\n") } invisible(x) } # # The function that does all of the actual work -- output is a matrix # Used by both print.survfit and summary.survfit # survmean <- function(x, scale=1, rmean) { # The starting point for the integration of the AUC if (!is.null(x$start.time)) start.time <- x$start.time else start.time <- min(0, x$time) # # The function below is called once for each line of output, # i.e., once per curve. It creates the line of output # pfun <- function(nused, time, surv, n.risk, n.event, lower, upper, start.time, end.time) { # # Start by defining a small utility function # Multiple times, we need to find the x corresponding to the first # y that is <.5. (The y's are in decreasing order, but may have # duplicates). # Nuisance 1: if one of the y's is exactly .5, we want the mean of # the corresponding x and the first x for which y<.5. We need to # use the equivalent of all.equal to check for a .5 however: # survfit(Surv(1:100)~1) gives a value of .5 + 1.1e-16 due to # roundoff error. # Nuisance 2: there may by an NA in the y's # Nuisance 3: if no y's are <=.5, then we should return NA # Nuisance 4: the obs (or many) after the .5 may be censored, giving # a stretch of values = .5 +- epsilon # minmin <- function(y, x) { tolerance <- .Machine$double.eps^.5 #same as used in all.equal() keep <- (!is.na(y) & y <(.5 + tolerance)) if (!any(keep)) NA else { x <- x[keep] y <- y[keep] if (abs(y[1]-.5) 1 Y/N # Repeat the code, with minor variations, for each one if (is.matrix(surv) && !is.matrix(x$n.event)) #make it easier x$n.event <- matrix(rep(x$n.event, ncol(surv)), ncol=ncol(surv)) if (is.null(x$strata)) { if (rmean=='none') end.time <- NA else if (is.numeric(rmean)) end.time <- rmean else end.time <- max(stime) if (is.matrix(surv)) { out <- matrix(0, ncol(surv), ncols) for (i in 1:ncol(surv)) { if (is.null(x$conf.int)) out[i,] <- pfun(x$n, stime, surv[,i], x$n.risk, x$n.event[,i], NULL, NULL, start.time, end.time) else out[i,] <- pfun(x$n, stime, surv[,i], x$n.risk, x$n.event[,i], x$lower[,i], x$upper[,i], start.time, end.time) } dimnames(out) <- list(dimnames(surv)[[2]], plab) } else { out <- matrix(pfun(x$n, stime, surv, x$n.risk, x$n.event, x$lower, x$upper, start.time, end.time), nrow=1) dimnames(out) <- list(NULL, plab) } } else { #strata case nstrat <- length(x$strata) stemp <- rep(1:nstrat,x$strata) # the index vector for strata1, 2, etc last.time <- (rev(stime))[match(1:nstrat, rev(stemp))] if (rmean=='none') end.time <- rep(NA, nstrat) else if (is.numeric(rmean)) end.time <- rep(rmean, nstrat) else if (rmean== 'common') end.time <- rep(median(last.time), nstrat) else end.time <- last.time if (is.matrix(surv)) { ns <- ncol(surv) out <- matrix(0, nstrat*ns, ncols) if (is.null(dimnames(surv)[[2]])) dimnames(out) <- list(rep(names(x$strata), ns), plab) else { cname <- outer(names(x$strata), dimnames(surv)[[2]], paste, sep=", ") dimnames(out) <- list(c(cname), plab) } k <- 0 for (j in 1:ns) { for (i in 1:nstrat) { who <- (stemp==i) k <- k+1 if (is.null(x$lower)) out[k,] <- pfun(x$n[i], stime[who], surv[who,j], x$n.risk[who], x$n.event[who,j], NULL, NULL, start.time, end.time[i]) else out[k,] <- pfun(x$n[i], stime[who], surv[who,j], x$n.risk[who], x$n.event[who,j], x$lower[who,j], x$upper[who,j], start.time, end.time[i]) } } } else { #non matrix case out <- matrix(0, nstrat, ncols) dimnames(out) <- list(names(x$strata), plab) for (i in 1:nstrat) { who <- (stemp==i) if (is.null(x$lower)) out[i,] <- pfun(x$n[i], stime[who], surv[who], x$n.risk[who], x$n.event[who], NULL, NULL, start.time, end.time[i]) else out[i,] <- pfun(x$n[i], stime[who], surv[who], x$n.risk[who], x$n.event[who], x$lower[who], x$upper[who], start.time, end.time[i]) } } } if (is.null(x$lower)) out <- out[,1:7, drop=F] #toss away the limits if (rmean=='none') out <- out[,-(5:6), drop=F] #toss away the mean & sem list(matrix=out[,,drop=T], end.time=end.time) } survival/R/predict.coxph.R0000644000175100001440000003325013065013236015243 0ustar hornikusers# Automatically generated from the noweb directory predict.coxph <- function(object, newdata, type=c("lp", "risk", "expected", "terms", "survival"), se.fit=FALSE, na.action=na.pass, terms=names(object$assign), collapse, reference=c("strata", "sample"), ...) { if (!inherits(object, 'coxph')) stop("Primary argument much be a coxph object") Call <- match.call() type <-match.arg(type) if (type=="survival") { survival <- TRUE type == "expected" #this is to stop lots of "or" statements } else survival <- FALSE n <- object$n Terms <- object$terms if (!missing(terms)) { if (is.numeric(terms)) { if (any(terms != floor(terms) | terms > length(object$assign) | terms <1)) stop("Invalid terms argument") } else if (any(is.na(match(terms, names(object$assign))))) stop("a name given in the terms argument not found in the model") } # I will never need the cluster argument, if present delete it. # Terms2 are terms I need for the newdata (if present), y is only # needed there if type == 'expected' if (length(attr(Terms, 'specials')$cluster)) { temp <- untangle.specials(Terms, 'cluster', 1) Terms <- object$terms[-temp$terms] } else Terms <- object$terms if (type != 'expected') Terms2 <- delete.response(Terms) else Terms2 <- Terms has.strata <- !is.null(attr(Terms, 'specials')$strata) has.offset <- !is.null(attr(Terms, 'offset')) has.weights <- any(names(object$call) == 'weights') na.action.used <- object$na.action n <- length(object$residuals) if (missing(reference) && type=="terms") reference <- "sample" else reference <- match.arg(reference) have.mf <- FALSE if (type == "expected") { y <- object[['y']] if (is.null(y)) { # very rare case mf <- stats::model.frame(object) y <- model.extract(mf, 'response') have.mf <- TRUE #for the logic a few lines below, avoid double work } } if (se.fit || type=='terms' || (!missing(newdata) && type=="expected") || (has.strata && (reference=="strata") || type=="expected")) { use.x <- TRUE if (is.null(object[['x']]) || has.weights || has.offset || (has.strata && is.null(object$strata))) { # I need the original model frame if (!have.mf) mf <- stats::model.frame(object) if (nrow(mf) != n) stop("Data is not the same size as it was in the original fit") x <- model.matrix(object, data=mf) if (has.strata) { if (!is.null(object$strata)) oldstrat <- object$strata else { stemp <- untangle.specials(Terms, 'strata') if (length(stemp$vars)==1) oldstrat <- mf[[stemp$vars]] else oldstrat <- strata(mf[,stemp$vars], shortlabel=TRUE) } } else oldstrat <- rep(0L, n) weights <- model.weights(mf) if (is.null(weights)) weights <- rep(1.0, n) offset <- model.offset(mf) if (is.null(offset)) offset <- 0 } else { x <- object[['x']] if (has.strata) oldstrat <- object$strata else oldstrat <- rep(0L, n) weights <- rep(1.,n) offset <- 0 } } else { # I won't need strata in this case either if (has.strata) { stemp <- untangle.specials(Terms, 'strata', 1) Terms2 <- Terms2[-stemp$terms] has.strata <- FALSE #remaining routine never needs to look } oldstrat <- rep(0L, n) offset <- 0 use.x <- FALSE } if (!missing(newdata)) { use.x <- TRUE #we do use an X matrix later tcall <- Call[c(1, match(c("newdata", "collapse"), names(Call), nomatch=0))] names(tcall)[2] <- 'data' #rename newdata to data tcall$formula <- Terms2 #version with no response tcall$na.action <- na.action #always present, since there is a default tcall[[1L]] <- quote(stats::model.frame) # change the function called if (!is.null(attr(Terms, "specials")$strata) && !has.strata) { temp.lev <- object$xlevels temp.lev[[stemp$vars]] <- NULL tcall$xlev <- temp.lev } else tcall$xlev <- object$xlevels mf2 <- eval(tcall, parent.frame()) collapse <- model.extract(mf2, "collapse") n2 <- nrow(mf2) if (has.strata) { if (length(stemp$vars)==1) newstrat <- mf2[[stemp$vars]] else newstrat <- strata(mf2[,stemp$vars], shortlabel=TRUE) if (any(is.na(match(newstrat, oldstrat)))) stop("New data has a strata not found in the original model") else newstrat <- factor(newstrat, levels=levels(oldstrat)) #give it all if (length(stemp$terms)) newx <- model.matrix(Terms2[-stemp$terms], mf2, contr=object$contrasts)[,-1,drop=FALSE] else newx <- model.matrix(Terms2, mf2, contr=object$contrasts)[,-1,drop=FALSE] } else { newx <- model.matrix(Terms2, mf2, contr=object$contrasts)[,-1,drop=FALSE] newstrat <- rep(0L, nrow(mf2)) } newoffset <- model.offset(mf2) if (is.null(newoffset)) newoffset <- 0 if (type== 'expected') { newy <- model.response(mf2) if (attr(newy, 'type') != attr(y, 'type')) stop("New data has a different survival type than the model") } na.action.used <- attr(mf2, 'na.action') } else n2 <- n if (type=="expected" || type== "surv") { if (missing(newdata)) pred <- y[,ncol(y)] - object$residuals if (!missing(newdata) || se.fit) { ustrata <- unique(oldstrat) risk <- exp(object$linear.predictors) x <- x - rep(object$means, each=nrow(x)) #subtract from each column if (missing(newdata)) #se.fit must be true se <- double(n) else { pred <- se <- double(nrow(mf2)) newx <- newx - rep(object$means, each=nrow(newx)) newrisk <- c(exp(newx %*% object$coef) + newoffset) } survtype<- ifelse(object$method=='efron', 3,2) for (i in ustrata) { indx <- which(oldstrat == i) afit <- agsurv(y[indx,,drop=F], x[indx,,drop=F], weights[indx], risk[indx], survtype, survtype) afit.n <- length(afit$time) if (missing(newdata)) { # In this case we need se.fit, nothing else j1 <- approx(afit$time, 1:afit.n, y[indx,1], method='constant', f=0, yleft=0, yright=afit.n)$y chaz <- c(0, afit$cumhaz)[j1 +1] varh <- c(0, cumsum(afit$varhaz))[j1 +1] xbar <- rbind(0, afit$xbar)[j1+1,,drop=F] if (ncol(y)==2) { dt <- (chaz * x[indx,]) - xbar se[indx] <- sqrt(varh + rowSums((dt %*% object$var) *dt)) * risk[indx] } else { j2 <- approx(afit$time, 1:afit.n, y[indx,2], method='constant', f=0, yleft=0, yright=afit.n)$y chaz2 <- c(0, afit$cumhaz)[j2 +1] varh2 <- c(0, cumsum(afit$varhaz))[j2 +1] xbar2 <- rbind(0, afit$xbar)[j2+1,,drop=F] dt <- (chaz * x[indx,]) - xbar v1 <- varh + rowSums((dt %*% object$var) *dt) dt2 <- (chaz2 * x[indx,]) - xbar2 v2 <- varh2 + rowSums((dt2 %*% object$var) *dt2) se[indx] <- sqrt(v2-v1)* risk[indx] } } else { #there is new data use.x <- TRUE indx2 <- which(newstrat == i) j1 <- approx(afit$time, 1:afit.n, newy[indx2,1], method='constant', f=0, yleft=0, yright=afit.n)$y chaz <-c(0, afit$cumhaz)[j1+1] pred[indx2] <- chaz * newrisk[indx2] if (se.fit) { varh <- c(0, cumsum(afit$varhaz))[j1+1] xbar <- rbind(0, afit$xbar)[j1+1,,drop=F] } if (ncol(y)==2) { if (se.fit) { dt <- (chaz * newx[indx2,]) - xbar se[indx2] <- sqrt(varh + rowSums((dt %*% object$var) *dt)) * newrisk[indx2] } } else { j2 <- approx(afit$time, 1:afit.n, newy[indx2,2], method='constant', f=0, yleft=0, yright=afit.n)$y chaz2 <- approx(-afit$time, afit$cumhaz, -newy[indx2,2], method="constant", rule=2, f=0)$y chaz2 <-c(0, afit$cumhaz)[j2+1] pred[indx2] <- (chaz2 - chaz) * newrisk[indx2] if (se.fit) { varh2 <- c(0, cumsum(afit$varhaz))[j1+1] xbar2 <- rbind(0, afit$xbar)[j1+1,,drop=F] dt <- (chaz * newx[indx2,]) - xbar dt2 <- (chaz2 * newx[indx2,]) - xbar2 v2 <- varh2 + rowSums((dt2 %*% object$var) *dt2) v1 <- varh + rowSums((dt %*% object$var) *dt) se[indx2] <- sqrt(v2-v1)* risk[indx2] } } } } } if (survival) { #it actually was type= survival, do one more step if (se.fit) se <- se * exp(-pred) pred <- exp(-pred) # probablility of being in state 0 } } else { if (is.null(object$coefficients)) coef<-numeric(0) else { # Replace any NA coefs with 0, to stop NA in the linear predictor coef <- ifelse(is.na(object$coefficients), 0, object$coefficients) } if (missing(newdata)) { offset <- offset - mean(offset) if (has.strata && reference=="strata") { # We can't use as.integer(oldstrat) as an index, if oldstrat is # a factor variable with unrepresented levels as.integer could # give 1,2,5 for instance. xmeans <- rowsum(x*weights, oldstrat)/c(rowsum(weights, oldstrat)) newx <- x - xmeans[match(oldstrat,row.names(xmeans)),] } else if (use.x) newx <- x - rep(object$means, each=nrow(x)) } else { offset <- newoffset - mean(offset) if (has.strata && reference=="strata") { xmeans <- rowsum(x*weights, oldstrat)/c(rowsum(weights, oldstrat)) newx <- newx - xmeans[match(newstrat, row.names(xmeans)),] } else newx <- newx - rep(object$means, each=nrow(newx)) } if (type=='lp' || type=='risk') { if (use.x) pred <- drop(newx %*% coef) + offset else pred <- object$linear.predictors if (se.fit) se <- sqrt(rowSums((newx %*% object$var) *newx)) if (type=='risk') { pred <- exp(pred) if (se.fit) se <- se * sqrt(pred) # standard Taylor series approx } } else if (type=='terms') { asgn <- object$assign nterms<-length(asgn) pred<-matrix(ncol=nterms,nrow=NROW(newx)) dimnames(pred) <- list(rownames(newx), names(asgn)) if (se.fit) se <- pred for (i in 1:nterms) { tt <- asgn[[i]] tt <- tt[!is.na(object$coefficients[tt])] xtt <- newx[,tt, drop=F] pred[,i] <- xtt %*% object$coefficient[tt] if (se.fit) se[,i] <- sqrt(rowSums((xtt %*% object$var[tt,tt]) *xtt)) } pred <- pred[,terms, drop=F] if (se.fit) se <- se[,terms, drop=F] attr(pred, 'constant') <- sum(object$coefficients*object$means, na.rm=T) } } if (type != 'terms') { pred <- drop(pred) if (se.fit) se <- drop(se) } if (!is.null(na.action.used)) { pred <- napredict(na.action.used, pred) if (is.matrix(pred)) n <- nrow(pred) else n <- length(pred) if(se.fit) se <- napredict(na.action.used, se) } if (!missing(collapse) && !is.null(collapse)) { if (length(collapse) != n2) stop("Collapse vector is the wrong length") pred <- rowsum(pred, collapse) # in R, rowsum is a matrix, always if (se.fit) se <- sqrt(rowsum(se^2, collapse)) if (type != 'terms') { pred <- drop(pred) if (se.fit) se <- drop(se) } } if (se.fit) list(fit=pred, se.fit=se) else pred } survival/R/model.matrix.coxph.R0000644000175100001440000002132413065013234016211 0ustar hornikusers# Automatically generated from the noweb directory # In internal use "data" will often be an already derived model frame. # We detect this via it having a terms attribute. model.matrix.coxph <- function(object, data=NULL, contrast.arg=object$contrasts, ...) { # # If the object has an "x" component, return it, unless a new # data set is given if (is.null(data) && !is.null(object[['x']])) return(object[['x']]) #don't match "xlevels" Terms <- delete.response(object$terms) if (is.null(data)) mf <- stats::model.frame(object) else { if (is.null(attr(data, "terms"))) mf <- stats::model.frame(Terms, data, xlev=object$xlevels) else mf <- data #assume "data" is already a model frame } cluster <- attr(Terms, "specials")$cluster if (length(cluster)) { temp <- untangle.specials(Terms, "cluster") dropterms <- temp$terms } else dropterms <- NULL attr(Terms, "intercept") <- 1 adrop <- 0 #levels of "assign" to be dropped; 0= intercept stemp <- untangle.specials(Terms, 'strata', 1) if (length(stemp$vars) > 0) { #if there is a strata statement hasinteractions <- FALSE for (i in stemp$vars) { #multiple strata terms are allowed # The factors attr has one row for each variable in the frame, one # col for each term in the model. Pick rows for each strata # var, and find if it participates in any interactions. if (any(attr(Terms, 'order')[attr(Terms, "factors")[i,] >0] >1)) hasinteractions <- TRUE } if (!hasinteractions) dropterms <- c(dropterms, stemp$terms) else adrop <- c(0, match(stemp$var, colnames(attr(Terms, 'factors')))) } if (length(dropterms)) { temppred <- attr(terms, "predvars") Terms2 <- Terms[ -dropterms] if (!is.null(temppred)) { # subscripting a Terms object currently drops predvars, in error attr(Terms2, "predvars") <- temppred[-(1+dropterms)] # "Call" object } X <- model.matrix(Terms2, mf, constrasts=contrast.arg) # we want to number the terms wrt the original model matrix # Do not forget the intercept, which will be a zero renumber <- match(colnames(attr(Terms2, "factors")), colnames(attr(Terms, "factors"))) attr(X, "assign") <- c(0, renumber)[1+attr(X, "assign")] } else X <- model.matrix(Terms, mf, contrasts=contrast.arg) # drop the intercept after the fact, and also drop strata if necessary Xatt <- attributes(X) xdrop <- Xatt$assign %in% adrop #columns to drop (always the intercept) X <- X[, !xdrop, drop=FALSE] attr(X, "assign") <- Xatt$assign[!xdrop] #if (any(adrop>0)) attr(X, "contrasts") <- Xatt$contrasts[-adrop] #else attr(X, "contrasts") <- Xatt$contrasts attr(X, "contrasts") <- Xatt$contrasts X } model.frame.coxph <- function(formula, ...) { dots <- list(...) nargs <- dots[match(c("data", "na.action", "subset", "weights"), names(dots), 0)] # If nothing has changed and the coxph object had a model component, # simply return it. if (length(nargs) ==0 && !is.null(formula$model)) return(formula$model) else { # Rebuild the original call to model.frame Terms <- terms(formula) fcall <- formula$call indx <- match(c("formula", "data", "weights", "subset", "na.action"), names(fcall), nomatch=0) if (indx[1] ==0) stop("The coxph call is missing a formula!") temp <- fcall[c(1,indx)] # only keep the arguments we wanted temp[[1]] <- quote(stats::model.frame) # change the function called temp$xlev <- formula$xlevels temp$formula <- Terms #keep the predvars attribute # Now, any arguments that were on this call overtake the ones that # were in the original call. if (length(nargs) >0) temp[names(nargs)] <- nargs # The documentation for model.frame implies that the environment arg # to eval will be ignored, but if we omit it there is a problem. if (is.null(environment(formula$terms))) mf <- eval(temp, parent.frame()) else mf <- eval(temp, environment(formula$terms), parent.frame()) if (!is.null(attr(formula$terms, "dataClasses"))) .checkMFClasses(attr(formula$terms, "dataClasses"), mf) if (!is.null(attr(Terms, "specials")$tt)) { # Do time transform tt <- eval(formula$call$tt) Y <- aeqSurv(model.response(mf)) strats <- attr(Terms, "specials")$strata if (length(strats)) { stemp <- untangle.specials(Terms, 'strata', 1) if (length(stemp$vars)==1) strata.keep <- mf[[stemp$vars]] else strata.keep <- strata(mf[,stemp$vars], shortlabel=TRUE) strats <- as.numeric(strata.keep) } timetrans <- untangle.specials(Terms, 'tt') ntrans <- length(timetrans$terms) if (is.null(tt)) { tt <- function(x, time, riskset, weights){ #default to O'Brien's logit rank obrien <- function(x) { r <- rank(x) (r-.5)/(.5+length(r)-r) } unlist(tapply(x, riskset, obrien)) } } if (is.function(tt)) tt <- list(tt) #single function becomes a list if (is.list(tt)) { if (any(!sapply(tt, is.function))) stop("The tt argument must contain function or list of functions") if (length(tt) != ntrans) { if (length(tt) ==1) { temp <- vector("list", ntrans) for (i in 1:ntrans) temp[[i]] <- tt[[1]] tt <- temp } else stop("Wrong length for tt argument") } } else stop("The tt argument must contain a function or list of functions") if (ncol(Y)==2) { if (length(strats)==0) { sorted <- order(-Y[,1], Y[,2]) newstrat <- rep.int(0L, nrow(Y)) newstrat[1] <- 1L } else { sorted <- order(strats, -Y[,1], Y[,2]) #newstrat marks the first obs of each strata newstrat <- as.integer(c(1, 1*(diff(strats[sorted])!=0))) } if (storage.mode(Y) != "double") storage.mode(Y) <- "double" counts <- .Call(Ccoxcount1, Y[sorted,], as.integer(newstrat)) tindex <- sorted[counts$index] } else { if (length(strats)==0) { sort.end <- order(-Y[,2], Y[,3]) sort.start<- order(-Y[,1]) newstrat <- c(1L, rep(0, nrow(Y) -1)) } else { sort.end <- order(strats, -Y[,2], Y[,3]) sort.start<- order(strats, -Y[,1]) newstrat <- c(1L, as.integer(diff(strats[sort.end])!=0)) } if (storage.mode(Y) != "double") storage.mode(Y) <- "double" counts <- .Call(Ccoxcount2, Y, as.integer(sort.start -1L), as.integer(sort.end -1L), as.integer(newstrat)) tindex <- counts$index } Y <- Surv(rep(counts$time, counts$nrisk), counts$status) type <- 'right' # new Y is right censored, even if the old was (start, stop] mf <- mf[tindex,] strats <- rep(1:length(counts$nrisk), counts$nrisk) weights <- model.weights(mf) if (!is.null(weights) && any(!is.finite(weights))) stop("weights must be finite") tcall <- attr(Terms, 'variables')[timetrans$terms+2] pvars <- attr(Terms, 'predvars') pmethod <- sub("makepredictcall.", "", as.vector(methods("makepredictcall"))) for (i in 1:ntrans) { newtt <- (tt[[i]])(mf[[timetrans$var[i]]], Y[,1], strats, weights) mf[[timetrans$var[i]]] <- newtt nclass <- class(newtt) if (any(nclass %in% pmethod)) { # It has a makepredictcall method dummy <- as.call(list(as.name(class(newtt)[1]), tcall[[i]][[2]])) ptemp <- makepredictcall(newtt, dummy) pvars[[timetrans$terms[i]+2]] <- ptemp } } attr(Terms, "predvars") <- pvars mf[[".strata."]] <- strats } mf } } survival/R/print.survreg.S0000644000175100001440000000252611732700061015322 0ustar hornikusers# $Id: print.survreg.S 11166 2008-11-24 22:10:34Z therneau $ print.survreg <- function(x, ...) { if(!is.null(cl <- x$call)) { cat("Call:\n") dput(cl) } if (!is.null(x$fail)) { cat(" Survreg failed.", x$fail, "\n") return(invisible(x)) } coef <- x$coef if(any(nas <- is.na(coef))) { if(is.null(names(coef))) names(coef) <- paste("b", 1:length(coef), sep = "") cat("\nCoefficients: (", sum(nas), " not defined because of singularities)\n", sep = "") } else cat("\nCoefficients:\n") print(coef, ...) if (nrow(x$var)==length(coef)) cat("\nScale fixed at",format(x$scale),"\n") else if (length(x$scale)==1) cat ("\nScale=", format(x$scale), "\n") else { cat("\nScale:\n") print(x$scale, ...) } nobs <- length(x$linear) chi <- 2*diff(x$loglik) df <- sum(x$df) - x$idf # The sum is for penalized models cat("\nLoglik(model)=", format(round(x$loglik[2],1)), " Loglik(intercept only)=", format(round(x$loglik[1],1))) if (df > 0) cat("\n\tChisq=", format(round(chi,2)), "on", round(df,1), "degrees of freedom, p=", format(signif(1-pchisq(chi, df),2)), "\n") else cat("\n") omit <- x$na.action if (length(omit)) cat("n=", nobs, " (", naprint(omit), ")\n", sep="") else cat("n=", nobs, "\n") invisible(x) } survival/R/coxph.detail.S0000644000175100001440000000614512676277274015104 0ustar hornikuserscoxph.detail <- function(object, riskmat=FALSE) { method <- object$method if (method!='breslow' && method!='efron') stop(paste("Detailed output is not available for the", method, "method")) n <- length(object$residuals) weights <- object$weights #always present if there are weights x <- object[['x']] y <- object$y strat <- object$strata Terms <- object$terms if (!inherits(Terms, 'terms')) stop("invalid terms component of object") strats <- attr(Terms, "specials")$strata if (is.null(y) || is.null(x)) { mf <- stats::model.frame(object) y <- model.response(mf) x <- model.matrix(object, data=mf) if (length(strats)) { stemp <- untangle.specials(object$terms, 'strata', 1) if (length(stemp$vars)==1) strat <- mf[[stemp$vars]] else strat <- strata(mf[,stemp$vars], shortlabel=TRUE) } } nvar <- ncol(x) if (ncol(y)==2) { mintime <- min(y[,1]) if (mintime < 0) y <- cbind( 2*mintime -1, y) else y <- cbind(-1,y) } if (is.null(strat)) { ord <- order(y[,2], -y[,3]) newstrat <- rep(0,n) } else { ord <- order(strat, y[,2], -y[,3]) newstrat <- c(diff(as.numeric(strat[ord]))!=0 ,1) } newstrat[n] <- 1 # sort the data x <- x[ord,] y <- y[ord,] storage.mode(y) <- 'double' score <- exp(object$linear.predictors)[ord] if (is.null(weights)) weights <- rep(1,n) else weights <- weights[ord] ndeath <- sum(y[,3]) if (riskmat) { rmat <- integer(ndeath*n) } else rmat <- as.integer(1) ff <- .C(Ccoxdetail, as.integer(n), as.integer(nvar), ndeath= as.integer(ndeath), y = y, as.double(x), index = as.integer(newstrat), event2 =as.double(score), weights = as.double(weights), means= c(method=='efron', double(ndeath*nvar-1)), u = double(ndeath*nvar), i = double(ndeath*nvar*nvar), rmat = rmat, nrisk2 = double(ndeath), double(nvar*(3 + 2*nvar))) keep <- 1:ff$ndeath vname<- dimnames(x)[[2]] time <- y[ff$index[keep],2] names(time) <- NULL means<- (matrix(ff$means,ndeath, nvar))[keep,] score<- matrix(ff$u, ndeath, nvar)[keep,] var <- array(ff$i, c(nvar, nvar, ndeath))[,,keep] if (riskmat) { rmat <- matrix(0, n, ff$ndeath) rmat[ord,] <- ff$rmat[1:(n*ff$ndeath)] # in the order of orig data dimnames(rmat) <- list(NULL, time) } if (nvar>1) { dimnames(means) <- list(time, vname) dimnames(score) <- list(time, vname) dimnames(var) <- list(vname, vname, time) } else { names(means) <- time names(score) <- time names(var) <- time } dimnames(ff$y) <- NULL temp <- list(time = time, means=means, nevent=ff$y[keep,1], nrisk = ff$y[keep,2], hazard= ff$y[keep,3], score= score, imat=var, varhaz=ff$weights[keep], y=y, x=x) if (length(strats)) temp$strata <- table((strat[ord])[ff$index[keep]]) if (riskmat) temp$riskmat <- rmat if (!all(weights==1)) { temp$weights <- weights temp$nevent.wt <- ff$event2[keep] temp$nrisk.wt <- ff$nrisk2[keep] } temp } survival/R/residuals.coxph.null.S0000644000175100001440000000053711732700061016556 0ustar hornikusers# $Id $ residuals.coxph.null <- function(object, type=c("martingale", "deviance", "score", "schoenfeld"), collapse=FALSE, weighted=FALSE, ...) { type <- match.arg(type) if (type=='martingale' || type=='deviance') NextMethod() else stop(paste("\'", type, "\' residuals are not defined for a null model", sep="")) } survival/R/model.frame.survreg.R0000644000175100001440000000513112676277464016401 0ustar hornikusersmodel.frame.survreg <- function (formula, ...) { dots <- list(...) nargs <- dots[match(c("data", "na.action", "subset"), names(dots), 0)] if (length(nargs) || is.null(formula$model)) { fcall <- formula$call indx <- match(c("formula", "data", "weights", "subset", "na.action"), names(fcall), nomatch = 0) if (indx[1] == 0) stop("The coxph call is missing a formula!") temp <- fcall[c(1, indx)] temp[[1L]] <- quote(stats::model.frame) temp$xlev <- formula$xlevels if (length(nargs) > 0) temp[names(nargs)] <- nargs if (is.null(environment(formula$terms))) eval(temp, parent.frame()) else eval(temp, environment(formula$terms), parent.frame()) } else formula$model } # model.matrix.survreg <- function(object, data, ...) { if (missing(data) && !is.null(object[["x"]])) object[["x"]] else { Terms <- delete.response(object$terms) strats <- attr(Terms, "specials")$strata cluster<- attr(Terms, "specials")$cluster dropx <- NULL if (length(cluster)) { tempc <- untangle.specials(Terms, 'cluster', 1:10) dropx <- tempc$terms } if (length(strats)) { temp <- untangle.specials(Terms, 'strata', 1) dropx <- c(dropx, temp$terms) } if (length(dropx)) { newTerms <- Terms[-dropx] # R (version 2.7.1) adds intercept=T anytime you drop something attr(newTerms, 'intercept') <- attr(Terms, 'intercept') # The predvars attribute, if present, is lost when we # subscript. The attribute is a Call, so has one more element # than term wrt subscripting, i.e., the called function "list" if (!is.null(attr(terms, "predvars"))) attr(newTerms, "predvars") <- attr(terms, "predvars")[-(dropx+1)] } else newTerms <- Terms # Grab the model frame. By using "newterms" for a new data set, # we allow the new data to be missing things we don't need: y, # strata, and cluster. For the original data we can assume they # are present. if (missing(data)) mf <- stats::model.frame(object, ...) else { if (is.null(attr(data, "terms"))) mf <- stats::model.frame(newTerms, data, xlev=object$xlevels) else mf <- data #assume we were given a model frame } model.matrix(newTerms, mf, contrasts.arg= object$contrasts) } } survival/R/residuals.survreg.R0000644000175100001440000001745713065013241016167 0ustar hornikusers# Automatically generated from the noweb directory # $Id$ # # Residuals for survreg objects residuals.survreg <- function(object, type=c('response', 'deviance', 'dfbeta', 'dfbetas', 'working', 'ldcase', 'ldresp', 'ldshape', 'matrix'), rsigma =TRUE, collapse=FALSE, weighted=FALSE, ...) { type <-match.arg(type) n <- length(object$linear.predictors) Terms <- object$terms if(!inherits(Terms, "terms")) stop("invalid terms component of object") # If the variance wasn't estimated then it has no error if (nrow(object$var) == length(object$coefficients)) rsigma <- FALSE # If there was a cluster directive in the model statment then remove # it. It does not correspond to a coefficient, and would just confuse # things later in the code. cluster <- untangle.specials(Terms,"cluster")$terms if (length(cluster) >0 ) Terms <- Terms[-cluster] strata <- attr(Terms, 'specials')$strata coef <- object$coefficients intercept <- attr(Terms, "intercept") response <- attr(Terms, "response") weights <- object$weights if (is.null(weights)) weighted <- FALSE if (is.character(object$dist)) dd <- survreg.distributions[[object$dist]] else dd <- object$dist if (is.null(dd$itrans)) { itrans <- dtrans <-function(x)x } else { itrans <- dd$itrans dtrans <- dd$dtrans } if (!is.null(dd$dist)) dd <- survreg.distributions[[dd$dist]] deviance <- dd$deviance dens <- dd$density if (is.null(object$naive.var)) vv <- object$var else vv <- object$naive.var need.x <- is.na(match(type, c('response', 'deviance', 'working'))) if (is.null(object$y) || !is.null(strata) || (need.x & is.null(object[['x']]))) mf <- stats::model.frame(object) y <- object$y if (is.null(y)) { y <- model.extract(mf, 'response') if (!is.null(dd$trans)) { tranfun <- dd$trans exactsurv <- y[,ncol(y)] ==1 if (any(exactsurv)) logcorrect <-sum(log(dd$dtrans(y[exactsurv,1]))) if (type=='interval') { if (any(y[,3]==3)) y <- cbind(tranfun(y[,1:2]), y[,3]) else y <- cbind(tranfun(y[,1]), y[,3]) } else if (type=='left') y <- cbind(tranfun(y[,1]), 2-y[,2]) else y <- cbind(tranfun(y[,1]), y[,2]) } else { if (type=='left') y[,2] <- 2- y[,2] else if (type=='interval' && all(y[,3]<3)) y <- y[,c(1,3)] } } if (!is.null(strata)) { temp <- untangle.specials(Terms, 'strata', 1) Terms2 <- Terms[-temp$terms] if (length(temp$vars)==1) strata.keep <- mf[[temp$vars]] else strata.keep <- strata(mf[,temp$vars], shortlabel=TRUE) strata <- as.numeric(strata.keep) nstrata <- max(strata) sigma <- object$scale[strata] } else { Terms2 <- Terms nstrata <- 1 sigma <- object$scale } if (need.x) { x <- object[['x']] #don't grab xlevels component if (is.null(x)) x <- model.matrix(Terms2, mf, contrasts.arg=object$contrasts) } if (type=='response') { yhat0 <- deviance(y, sigma, object$parms) rr <- itrans(yhat0$center) - itrans(object$linear.predictor) } else { status <- y[,ncol(y)] eta <- object$linear.predictors z <- (y[,1] - eta)/sigma dmat <- dens(z, object$parms) dtemp<- dmat[,3] * dmat[,4] #f' if (any(status==3)) { z2 <- (y[,2] - eta)/sigma dmat2 <- dens(z2, object$parms) } else { dmat2 <- dmat #dummy values z2 <- 0 } tdenom <- ((status==0) * dmat[,2]) + #right censored ((status==1) * 1 ) + #exact ((status==2) * dmat[,1]) + #left ((status==3) * ifelse(z>0, dmat[,2]-dmat2[,2], dmat2[,1] - dmat[,1])) #interval g <- log(ifelse(status==1, dmat[,3]/sigma, tdenom)) #loglik tdenom <- 1/tdenom dg <- -(tdenom/sigma) *(((status==0) * (0-dmat[,3])) + #dg/ eta ((status==1) * dmat[,4]) + ((status==2) * dmat[,3]) + ((status==3) * (dmat2[,3]- dmat[,3]))) ddg <- (tdenom/sigma^2) *(((status==0) * (0- dtemp)) + #ddg/eta^2 ((status==1) * dmat[,5]) + ((status==2) * dtemp) + ((status==3) * (dmat2[,3]*dmat2[,4] - dtemp))) ds <- ifelse(status<3, dg * sigma * z, tdenom*(z2*dmat2[,3] - z*dmat[,3])) dds <- ifelse(status<3, ddg* (sigma*z)^2, tdenom*(z2*z2*dmat2[,3]*dmat2[,4] - z * z*dmat[,3] * dmat[,4])) dsg <- ifelse(status<3, ddg* sigma*z, tdenom *(z2*dmat2[,3]*dmat2[,4] - z*dtemp)) deriv <- cbind(g, dg, ddg=ddg- dg^2, ds = ifelse(status==1, ds-1, ds), dds=dds - ds*(1+ds), dsg=dsg - dg*(1+ds)) if (type=='deviance') { yhat0 <- deviance(y, sigma, object$parms) rr <- (-1)*deriv[,2]/deriv[,3] #working residuals rr <- sign(rr)* sqrt(2*(yhat0$loglik - deriv[,1])) } else if (type=='working') rr <- (-1)*deriv[,2]/deriv[,3] else if (type=='dfbeta' || type== 'dfbetas' || type=='ldcase') { score <- deriv[,2] * x # score residuals if (rsigma) { if (nstrata > 1) { d4 <- matrix(0., nrow=n, ncol=nstrata) d4[cbind(1:n, strata)] <- deriv[,4] score <- cbind(score, d4) } else score <- cbind(score, deriv[,4]) } rr <- score %*% vv if (type=='dfbetas') rr <- rr %*% diag(1/sqrt(diag(vv))) if (type=='ldcase') rr<- rowSums(rr*score) } else if (type=='ldresp') { rscore <- deriv[,3] * (x * sigma) if (rsigma) { if (nstrata >1) { d6 <- matrix(0., nrow=n, ncol=nstrata) d6[cbind(1:n, strata)] <- deriv[,6]*sigma rscore <- cbind(rscore, d6) } else rscore <- cbind(rscore, deriv[,6] * sigma) } temp <- rscore %*% vv rr <- rowSums(rscore * temp) } else if (type=='ldshape') { sscore <- deriv[,6] *x if (rsigma) { if (nstrata >1) { d5 <- matrix(0., nrow=n, ncol=nstrata) d5[cbind(1:n, strata)] <- deriv[,5] sscore <- cbind(sscore, d5) } else sscore <- cbind(sscore, deriv[,5]) } temp <- sscore %*% vv rr <- rowSums(sscore * temp) } else { #type = matrix rr <- deriv } } #case weights if (weighted) rr <- rr * weights #Expand out the missing values in the result if (!is.null(object$na.action)) { rr <- naresid(object$na.action, rr) if (is.matrix(rr)) n <- nrow(rr) else n <- length(rr) } # Collapse if desired if (!missing(collapse)) { if (length(collapse) !=n) stop("Wrong length for 'collapse'") rr <- drop(rowsum(rr, collapse)) } rr } survival/R/finegray.R0000644000175100001440000001774413065013233014304 0ustar hornikusers# Automatically generated from the noweb directory finegray <- function(formula, data, subset, na.action= na.pass, etype, prefix="fg", count="", id, timefix=TRUE) { Call <- match.call() indx <- match(c("formula", "data", "subset", "id"), names(Call), nomatch=0) if (indx[1] ==0) stop("A formula argument is required") temp <- Call[c(1,indx)] # only keep the arguments we wanted temp$na.action <- na.action temp[[1L]] <- quote(stats::model.frame) # change the function called special <- c("strata", "cluster") temp$formula <- if(missing(data)) terms(formula, special) else terms(formula, special, data=data) mf <- eval(temp, parent.frame()) if (nrow(mf) ==0) stop("No (non-missing) observations") Terms <- terms(mf) Y <- model.extract(mf, "response") if (!inherits(Y, "Surv")) stop("Response must be a survival object") type <- attr(Y, "type") if (type!='mright' && type!='mcounting') stop("Fine-Gray model requires a multi-state survival") nY <- ncol(Y) states <- attr(Y, "states") if (timefix) Y <- aeqSurv(Y) strats <- attr(Terms, "specials")$strata if (length(strats)) { stemp <- untangle.specials(Terms, 'strata', 1) if (length(stemp$vars)==1) strata <- mf[[stemp$vars]] else strata <- survival::strata(mf[,stemp$vars], shortlabel=TRUE) istrat <- as.numeric(strata) mf[stemp$vars] <- NULL } else istrat <- rep(1, nrow(mf)) id <- model.extract(mf, "id") if (!is.null(id)) mf["(id)"] <- NULL # don't leave it in result cluster<- attr(Terms, "specials")$cluster if (length(cluster)) { if (!is.null(id)) stop("an id argument and a cluster() term are redundant") tempc <- untangle.specials(Terms, 'cluster', 1) id <- strata(mf[,tempc$vars], shortlabel=TRUE) #allow multiples mf[tempc$vars] <- NULL } # If there is start-stop data, then there needs to be a cluster() # argument or an id argument, and we check that this is indeed # a competing risks form of data. # Mark the first and last obs of each subject, as we need it later. # Observations may not be in time order within a subject delay <- FALSE # is there delayed entry? if (type=="mcounting") { if (is.null(id)) stop("(start, stop] data requires a subject id") else { index <- order(id, Y[,2]) # by time within id sorty <- Y[index,] first <- which(!duplicated(id[index])) last <- c(first[-1] -1, length(id)) if (any(sorty[-last, 3]) != 0) stop("a subject has a transition before their last time point") delta <- c(sorty[-1,1], 0) - sorty[,2] if (any(delta[-last] !=0)) stop("a subject has gaps in time") if (any(Y[first,1] > min(Y[,2]))) delay <- TRUE temp1 <- temp2 <- rep(FALSE, nrow(mf)) temp1[index[first]] <- TRUE temp2[index[last]] <- TRUE first <- temp1 #used later last <- temp2 } } else last <- rep(TRUE, nrow(mf)) if (missing(etype)) enum <- 1 #generate a data set for which endpoint? else { index <- match(etype, states) if (any(is.na(index))) stop ("etype argument has a state that is not in the data") enum <- index[1] if (length(index) > 1) warning("only the first endpoint was used") } # make sure count, if present is syntactically valid if (!missing(count)) count <- make.names(count) else count <- NULL oname <- paste0(prefix, c("start", "stop", "status", "wt")) find2 <- function(x, vec, left.open=FALSE, ...) { if (!left.open) findInterval(x, vec, ...) else { # the left.open arg is a recent addition to findInterval, and I want # this to work in 3.2.0 (my employer's default). In another cycle or # so we can drop this workaround and call findInterval directly # length(vec) - findInterval(-x, rev(-vec), ...) } } if (ncol(Y) ==2) { temp <- min(Y[,1], na.rm=TRUE) if (temp >0) zero <- 0 else zero <- 2*temp -1 # a value less than any observed y Y <- cbind(zero, Y) # add a start column } utime <- sort(unique(c(Y[,1:2]))) # all the unique times newtime <- matrix(findInterval(Y[,1:2], utime), ncol=2) status <- Y[,3] newtime[status !=0, 2] <- newtime[status !=0,2] - .2 Gsurv <- survfit(Surv(newtime[,1], newtime[,2], status==0) ~ istrat, se.fit=FALSE) if (delay) Hsurv <- survfit(Surv(-newtime[,2], -newtime[,1], first) ~ istrat, se.fit =FALSE) status <- Y[, 3] # Do computations separately for each stratum stratfun <- function(i) { keep <- (istrat ==i) times <- sort(unique(Y[keep & status == enum, 2])) #unique event times if (length(times)==0) return(NULL) #no events in this stratum tdata <- mf[keep, -1, drop=FALSE] maxtime <- max(Y[keep, 2]) if (dim(Gsurv)==1) { # the phrase Gsurv[1] gives a warning when there is only one curve # keep only the event times, and convert back to the original time units if (delay) { dtime <- rev(-Hsurv$time[Hsurv$n.event > 0]) dprob <- c(rev(Hsurv$surv[Hsurv$n.event > 0])[-1], 1) ctime <- Gsurv$time[Gsurv$n.event > 0] cprob <- c(1, Gsurv$surv[Gsurv$n.event > 0]) temp <- sort(unique(c(dtime, ctime))) # these will all be integers index1 <- findInterval(temp, dtime) index2 <- findInterval(temp, ctime) ctime <- utime[temp] cprob <- dprob[index1] * cprob[index2+1] # G(t)H(t), eq 11 Geskus } else { ctime <- utime[Gsurv$time[Gsurv$n.event > 0]] cprob <- Gsurv$surv[Gsurv$n.event > 0] } } else { Gtemp <- Gsurv[i] if (delay) { Htemp <- Hsurv[i] dtime <- rev(-Htemp$time[Htemp$n.event > 0]) dprob <- c(rev(Htemp$surv[Htemp$n.event > 0])[-1], 1) ctime <- Gtemp$time[Gtemp$n.event > 0] cprob <- c(1, Gtemp$surv[Gtemp$n.event > 0]) temp <- sort(unique(c(dtime, ctime))) # these will all be integers index1 <- findInterval(temp, dtime) index2 <- findInterval(temp, ctime) ctime <- utime[temp] cprob <- dprob[index1] * cprob[index2+1] # G(t)H(t), eq 11 Geskus } else { ctime <- utime[Gtemp$time[Gtemp$n.event > 0]] cprob <- Gtemp$surv[Gtemp$n.event > 0] } } ct2 <- c(ctime, maxtime) cp2 <- c(1.0, cprob) index <- find2(times, ct2, left.open=TRUE) index <- sort(unique(index)) # the intervals that were actually seen # times before the first ctime get index 0, those between 1 and 2 get 1 ckeep <- rep(FALSE, length(ct2)) ckeep[index] <- TRUE expand <- (Y[keep, 3] !=0 & Y[keep,3] != enum & last[keep]) #which rows to expand split <- .Call(Cfinegray, Y[keep,1], Y[keep,2], ct2, cp2, expand, c(TRUE, ckeep)) tdata <- tdata[split$row,,drop=FALSE] tstat <- ifelse((status[keep])[split$row]== enum, 1, 0) tdata[[oname[1]]] <- split$start tdata[[oname[2]]] <- split$end tdata[[oname[3]]] <- tstat tdata[[oname[4]]] <- split$wt if (!is.null(count)) tdata[[count]] <- split$add tdata } if (max(istrat) ==1) result <- stratfun(1) else { tlist <- lapply(1:max(istrat), stratfun) result <- do.call("rbind", tlist) } rownames(result) <- NULL #remove all the odd labels that R adds attr(result, "event") <- states[enum] result } survival/R/survreg.S0000644000175100001440000002141613016105374014171 0ustar hornikuserssurvreg <- function(formula, data, weights, subset, na.action, dist='weibull', init=NULL, scale=0, control, parms=NULL, model=FALSE, x=FALSE, y=TRUE, robust=FALSE, score=FALSE, ...) { Call <- match.call() # save a copy of the call indx <- match(c("formula", "data", "weights", "subset", "na.action"), names(Call), nomatch=0) if (indx[1] ==0) stop("A formula argument is required") temp <- Call[c(1,indx)] # only keep the arguments we wanted temp[[1L]] <- quote(stats::model.frame) # change the function called special <- c("strata", "cluster") temp$formula <- if(missing(data)) terms(formula, special) else terms(formula, special, data=data) m <- eval(temp, parent.frame()) Terms <- attr(m, 'terms') weights <- model.extract(m, 'weights') Y <- model.extract(m, "response") if (!inherits(Y, "Surv")) stop("Response must be a survival object") type <- attr(Y, "type") if (type== 'counting') stop ("start-stop type Surv objects are not supported") if (type=="mright" || type=="mcounting") stop("multi-state survival is not supported") strats <- attr(Terms, "specials")$strata cluster<- attr(Terms, "specials")$cluster dropx <- NULL if (length(cluster)) { if (missing(robust)) robust <- TRUE tempc <- untangle.specials(Terms, 'cluster', 1:10) ord <- attr(Terms, 'order')[tempc$terms] if (any(ord>1)) stop ("Cluster can not be used in an interaction") cluster <- strata(m[,tempc$vars], shortlabel=TRUE) #allow multiples dropx <- tempc$terms } if (length(strats)) { temp <- untangle.specials(Terms, 'strata', 1) dropx <- c(dropx, temp$terms) if (length(temp$vars)==1) strata.keep <- m[[temp$vars]] else strata.keep <- strata(m[,temp$vars], shortlabel=TRUE) strata <- as.numeric(strata.keep) nstrata <- max(strata) } else { nstrata <- 1 strata <- 0 } if (length(dropx)) { newTerms <- Terms[-dropx] # R (version 2.7.1) adds intercept=T anytime you drop something attr(newTerms, 'intercept') <- attr(Terms, 'intercept') } else newTerms <- Terms X <- model.matrix(newTerms, m) assign <- lapply(attrassign(X, newTerms)[-1], function(x) x-1) xlevels <- .getXlevels(newTerms, m) contr.save <- attr(X, 'contrasts') n <- nrow(X) nvar <- ncol(X) offset<- model.offset(m) # R returns NULL if no offset, Splus a zero if (length(offset)==0 || all(offset==0)) offset <- rep(0.,n) # The user can either give a distribution name, in which the distribution # is found in the object survreg.distributions, or include a list object # of the same format as is found there. if (is.character(dist)) { # partial matching of names in [[ is on its way out in R, so # first use match.arg, e.g. turn 'exp' into 'exponential' dist <- match.arg(dist, names(survreg.distributions)) dlist <- survreg.distributions[[dist]] if (is.null(dlist)) stop(paste(dist, ": distribution not found")) } else if (is.list(dist)) dlist <- dist else stop("Invalid distribution object") # # Make sure it is legal # if (!survregDtest(dlist)) stop("Invalid distribution object") # If the distribution is a transformation of another, perform # said transform. # logcorrect <- 0 #correction to the loglik due to transformations if (!is.null(dlist$trans)) { tranfun <- dlist$trans exactsurv <- Y[,ncol(Y)] ==1 if (any(exactsurv)) { if (is.null(weights)) logcorrect <- sum(log(dlist$dtrans(Y[exactsurv, 1]))) else logcorrect <- sum(weights[exactsurv]*log(dlist$dtrans(Y[exactsurv, 1]))) } if (type=='interval') { if (any(Y[,3]==3)) Y <- cbind(tranfun(Y[,1:2]), Y[,3]) else Y <- cbind(tranfun(Y[,1]), Y[,3]) } else if (type=='left') Y <- cbind(tranfun(Y[,1]), 2-Y[,2]) else Y <- cbind(tranfun(Y[,1]), Y[,2]) if (!all(is.finite(Y))) stop("Invalid survival times for this distribution") } else { if (type=='left') Y[,2] <- 2- Y[,2] else if (type=='interval' && all(Y[,3]<3)) Y <- Y[,c(1,3)] } if (!is.null(dlist$scale)) { if (!missing(scale)) warning(paste(dlist$name, "has a fixed scale, user specified value ignored")) scale <- dlist$scale } if (!is.null(dlist$dist)) if (is.atomic(dlist$dist)) dlist <- survreg.distributions[[dlist$dist]] else dlist <- dlist$dist # check for parameters ptemp <- dlist$parms if (is.null(ptemp)) { if (!is.null(parms)) stop(paste(dlist$name, "distribution has no optional parameters")) } else { if (!is.numeric(ptemp)) stop("Default parameters must be a numeric vector") if (!missing(parms)) { temp <- unlist(parms) # just in case they gave a list object indx <- match(names(temp), names(ptemp)) if (any(is.na(indx))) stop("Invalid parameter names") ptemp[names(ptemp)] <- temp } parms <- ptemp } # An idea originally from Brian R: if the user gave a list of # control values, use it, but if they did not give an explicit control # argument assume that they mistakenly wrote control parameters as a # part of the "..." or other arguments if (missing(control)) control <- survreg.control(...) else control <- do.call('survreg.control', control) # The any() construction below is to catch a user that mistakenly # thinks that 'scale' can be used in a model with multiple strata, and # so provided a vector of scale values. # (A 'perhaps should be be added someday' feature). if (any(scale < 0)) stop("Invalid scale value") if (any(scale >0) && nstrata >1) stop("The scale argument is not valid with multiple strata") # Check for penalized terms pterms <- sapply(m, inherits, 'coxph.penalty') if (any(pterms)) { pattr <- lapply(m[pterms], attributes) # # the 'order' attribute has the same components as 'term.labels' # pterms always has 1 more (response), sometimes 2 (offset) # drop the extra parts from pterms temp <- c(attr(Terms, 'response'), attr(Terms, 'offset')) if (length(dropx)) temp <- c(temp, dropx+1) pterms <- pterms[-temp] temp <- match((names(pterms))[pterms], attr(Terms, 'term.labels')) ord <- attr(Terms, 'order')[temp] if (any(ord>1)) stop ('Penalty terms cannot be in an interaction') assign <- attrassign(X, newTerms) pcols <- assign[match(names(pterms[pterms]), names(assign))] fit <- survpenal.fit(X, Y, weights, offset, init=init, controlvals = control, dist= dlist, scale=scale, strata=strata, nstrat=nstrata, pcols, pattr, parms=parms, assign) } else fit <- survreg.fit(X, Y, weights, offset, init=init, controlvals=control, dist= dlist, scale=scale, nstrat=nstrata, strata, parms=parms) if (is.character(fit)) fit <- list(fail=fit) #error message else { if (scale==0) { nvar <- length(fit$coefficients) - nstrata fit$scale <- exp(fit$coefficients[-(1:nvar)]) if (nstrata==1) names(fit$scale) <- NULL else names(fit$scale) <- levels(strata.keep) fit$coefficients <- fit$coefficients[1:nvar] fit$idf <- 1 + nstrata } else { fit$scale <- scale fit$idf <- 1 } fit$loglik <- fit$loglik + logcorrect } if (!score) fit$score <- NULL #do not return the score vector fit$df.residual <- n - sum(fit$df) fit$terms <- Terms fit$contrasts <- contr.save if (length(xlevels)) fit$xlevels <- xlevels fit$means <- apply(X,2, mean) if (!is.null(weights)) fit$weights <- weights fit$call <- Call fit$dist <- dist if (model) fit$model <- m if (x) fit$x <- X if (y) fit$y <- Y if (length(parms)) fit$parms <- parms # Do this before attaching the na.action, so that residuals() won't # reinsert missing values under na.exclude if (robust) { fit$naive.var <- fit$var if (!model) fit$model <- m #temporary addition, so resid doesn't # have to reconstruct if (length(cluster)) fit$var <- crossprod(rowsum(residuals.survreg(fit, 'dfbeta'), cluster)) else fit$var <- crossprod(residuals.survreg(fit, 'dfbeta')) if (!model) fit$model <- NULL # take it back out } na.action <- attr(m, "na.action") if (length(na.action)) fit$na.action <- na.action if (any(pterms)) class(fit) <- c('survreg.penal', 'survreg') else class(fit) <- 'survreg' fit } survival/R/summary.coxph.penal.S0000644000175100001440000000770412652732471016424 0ustar hornikuserssummary.coxph.penal <- function(object, conf.int = 0.95, scale=1, terms=FALSE, maxlabel=25, ...) { beta <- object$coefficients if (length(beta)==0 && length(object$frail)==0) stop("Penalized summary function can't be used for a null model") if (length(beta) > 0) { #has non-penalized coefs nacoef <- !(is.na(beta)) #non-missing coefs beta2 <- beta[nacoef] if(is.null(beta2) | is.null(object$var)) stop("Input is not valid") se <- sqrt(diag(object$var)) } # # Map terms to special print functions, and the list of iteration histories # pterms <- object$pterms nterms <- length(pterms) npenal <- sum(pterms>0) print.map <- rep(0,nterms) if (!is.null(object$printfun)) { temp <- unlist(lapply(object$printfun, is.null)) #which ones are missing print.map[pterms>0] <- (1:npenal) * (!temp) } # Tedious, but build up the coef matrix a term at a time print1 <- NULL pname1 <- NULL if (is.null(object$assign2)) alist <- object$assign[-1] else alist <- object$assign2 print2 <- NULL for (i in 1:nterms) { kk <- alist[[i]] if (print.map[i] >0) { j <- print.map[i] if (pterms[i]==2) temp <- (object$printfun[[j]])(object$frail, object$fvar, , object$df[i], object$history[[j]]) else temp <- (object$printfun[[j]])(beta[kk], object$var[kk,kk], object$var2[kk,kk], object$df[i], object$history[[j]]) print1 <- rbind(print1, temp$coef) if (is.matrix(temp$coef)) { xx <- dimnames(temp$coef)[[1]] if (is.null(xx)) xx <- rep(names(pterms)[i], nrow(temp$coef)) else xx <- paste(names(pterms)[i], xx, sep=', ') pname1 <- c(pname1, xx) } else pname1 <- c(pname1, names(pterms)[i]) print2 <- c(print2, temp$history) } else if (terms && length(kk)>1) { pname1 <- c(pname1, names(pterms)[i]) temp <- coxph.wtest(object$var[kk,kk], beta[kk])$test print1 <- rbind(print1, c(NA, NA, NA, temp, object$df[i], 1-pchisq(temp, 1))) } else { pname1 <- c(pname1, names(beta)[kk]) tempe<- (diag(object$var))[kk] temp <- beta[kk]^2/ tempe print1 <- rbind(print1, cbind(beta[kk], sqrt(tempe), sqrt((diag(object$var2))[kk]), temp, 1, 1-pchisq(temp, 1))) } } dimnames(print1) <- list(substring(pname1,1, maxlabel), c("coef","se(coef)", "se2", "Chisq","DF","p")) rval <- object[match(c("call", "fail", "na.action", "n", "nevent", "loglik", "iter", "df"), names(object), nomatch=0)] rval$coefficients <- print1 rval$print2 <- print2 if(conf.int & length(beta) >0 ) { z <- qnorm((1 + conf.int)/2, 0, 1) beta <- beta * scale se <- se * scale tmp <- cbind(exp(beta), exp(-beta), exp(beta - z * se), exp(beta + z * se)) dimnames(tmp) <- list(substring(names(beta),1, maxlabel), c("exp(coef)", "exp(-coef)", paste("lower .", round(100 * conf.int, 2), sep = ""), paste("upper .", round(100 * conf.int, 2), sep = ""))) rval$conf.int <- tmp } df <- sum(object$df) logtest <- -2 * (object$loglik[1] - object$loglik[2]) rval$logtest <- c(test = logtest, df=df, pvalue= pchisq(logtest,df, lower.tail=FALSE)) if (!is.null(object$waldtest)) rval$waldtest <- c(test= object$wald.test, df=df, pvalue = pchisq(object$wald.test, df, lower.tail=FALSE)) if (!is.null(object$concordance)) { # A stratified model has a matrix of values, one row per strata if (is.matrix(object$concordance)) temp <- colSums(object$concordance) else temp <- object$concordance rval$concordance <- c((temp[1] + temp[3]/2)/sum(temp[1:3]), temp[5]/(2*sum(temp[1:3]))) names(rval$concordance) <- c("C", "se(C)") } class(rval) <- "summary.coxph.penal" rval } survival/R/frailty.brent.S0000644000175100001440000000327511732700061015257 0ustar hornikusers# $Id: frailty.brent.S 11166 2008-11-24 22:10:34Z therneau $ # # Brent's method for finding a maximum # If upper and/or lower is given, it transforms x to stay out of trouble # during the "bracketing" phase # frailty.brent <- function(x, y, lower, upper) { n <- length(x) if (length(y) != n) stop ("Length mismatch for x and y") if (n<3) return(mean(x)) # First, is the solution bracketed? # If not, take big steps until it is ord <- order(x) xx <- x[ord] yy <- y[ord] best <- (1:n)[yy==max(y)] if (length(best) >1) stop("Ties for max(y), I surrender") #fix this later if (best==1) { new <- xx[1] - 3*(xx[2] - xx[1]) if (!missing(lower) && !is.null(lower) && new < lower) new <- lower + (min(xx[xx>lower])-lower)/10 return(new) } if (best==n) { new <- xx[n] + 3*(xx[n] - xx[n-1]) if (!missing(upper) && !is.null(upper) && new > upper) new <- upper + (max(xx[xx xx[3] || ( (n>4) && (new-x[n]) > .5*abs(x[n-1]-x[n-2]))) { if ((xx[2]-xx[1]) > (xx[3]-xx[2])) return(xx[2] - .38*(xx[2]-xx[1])) else return(xx[2] + .32*(xx[3]-xx[2])) } else return(new) } survival/R/plot.cox.zph.S0000644000175100001440000000535212656662135015057 0ustar hornikusers# $Id: plot.cox.zph.S 11275 2009-04-06 16:18:00Z therneau $ plot.cox.zph <- function(x, resid=TRUE, se=TRUE, df=4, nsmo=40, var, xlab="Time", ylab="", lty=1:2, col=1, lwd=1, ...) { xx <- x$x yy <- x$y d <- nrow(yy) df <- max(df) #error proofing nvar <- ncol(yy) pred.x <- seq(from=min(xx), to=max(xx), length=nsmo) temp <- c(pred.x, xx) lmat <- ns(temp, df=df, intercept=TRUE) pmat <- lmat[1:nsmo,] # for prediction xmat <- lmat[-(1:nsmo),] qmat <- qr(xmat) if (qmat$rank < df) stop("Spline fit is singular, try a smaller degrees of freedom") if (se) { bk <- backsolve(qmat$qr[1:df, 1:df], diag(df)) xtx <- bk %*% t(bk) seval <- d*((pmat%*% xtx) *pmat) %*% rep(1, df) } if (missing(ylab)) ylab <- paste("Beta(t) for", dimnames(yy)[[2]]) if (missing(var)) var <- 1:nvar else { if (is.character(var)) var <- match(var, dimnames(yy)[[2]]) if (any(is.na(var)) || max(var)>nvar || min(var) <1) stop("Invalid variable requested") } # # Figure out a 'good' set of x-axis labels. Find 8 equally spaced # values on the 'transformed' axis. Then adjust until they correspond # to rounded 'true time' values. Avoid the edges of the x axis, or # approx() may give a missing value if (x$transform == 'log') { xx <- exp(xx) pred.x <- exp(pred.x) } else if (x$transform != 'identity') { xtime <- as.numeric(dimnames(yy)[[1]]) indx <- !duplicated(xx) #avoid a warning message in R apr1 <- approx(xx[indx], xtime[indx], seq(min(xx), max(xx), length=17)[2*(1:8)]) temp <- signif(apr1$y,2) apr2 <- approx(xtime[indx], xx[indx], temp) xaxisval <- apr2$y xaxislab <- rep("",8) for (i in 1:8) xaxislab[i] <- format(temp[i]) } col <- rep(col, length=2) lwd <- rep(lwd, length=2) lty <- rep(lty, length=2) for (i in var) { y <- yy[,i] yhat <- pmat %*% qr.coef(qmat, y) if (resid) yr <-range(yhat, y) else yr <-range(yhat) if (se) { temp <- 2* sqrt(x$var[i,i]*seval) yup <- yhat + temp ylow<- yhat - temp yr <- range(yr, yup, ylow) } if (x$transform=='identity') plot(range(xx), yr, type='n', xlab=xlab, ylab=ylab[i], ...) else if (x$transform=='log') plot(range(xx), yr, type='n', xlab=xlab, ylab=ylab[i], log='x', ...) else { plot(range(xx), yr, type='n', xlab=xlab, ylab=ylab[i], axes=FALSE,...) axis(1, xaxisval, xaxislab) axis(2) box() } if (resid) points(xx, y) lines(pred.x, yhat, lty=lty[1], col=col[1], lwd=lwd[1]) if (se) { lines(pred.x, yup, col=col[2], lty=lty[2], lwd=lwd[2]) lines(pred.x, ylow, col=col[2], lty=lty[2], lwd=lwd[2]) } } } survival/R/survexp.fit.S0000644000175100001440000001104612111735600014763 0ustar hornikusers# Actually compute the expected survival for one or more cohorts # of subjects. If each subject is his/her own group, it gives individual # survival # group = groups (one curve per group) # x matrix contains the rate # table indices = starting point for each obs in the rate table. # y is the number of follow-up days for each subject # times = the time points at which survival is desired # death = T if we want the conditional estimate survexp.fit <- function(group, x, y, times, death, ratetable) { if (!is.matrix(x)) stop("x must be a matrix") if (ncol(x) != length(dim(ratetable))) stop("x matrix does not match the rate table") atts <- attributes(ratetable) ngrp <- max(group) times <- sort(unique(times)) if (any(times <0)) stop("Negative time point requested") if (missing(y)) y <- rep(max(times), nrow(x)) ntime <- length(times) if (!is.logical(death)) stop("Invalid value for death indicator") cuts <- atts$cutpoints if (is.null(atts$type)) { # old style rate table rfac <- atts$factor us.special <- (rfac >1) } else { rfac <- 1*(atts$type ==1) us.special <- (atts$type==4) } if (any(us.special)) { #special handling for US pop tables if (sum(us.special) >1) stop("Two columns marked for special handling as a US rate table") # Now, the 'entry' date on a US rate table is the number of days # since 1/1/1960, and the user data has been aligned to the # same system by match.ratetable and marked as "year". # US rate tables are odd: the entry for age (year=1970, age=55) # contains the daily rate for anyone who turns 55 in that year, # from their birthday forward for 365 days. So if your birthday # is on Oct 2, the 1970 table applies from 2Oct 1970 to 1Oct 1971. # The underlying C code wants to make the 1970 rate table apply # from 1Jan 1970 to 31Dec 1970. The easiest way to finess this is # to fudge everyone's enter-the-study date. If you were born # in March but entered in April, make it look like you entered in # Febuary; that way you get the first 11 months at the entry # year's rates, etc. This is the same as being born on Jan 1. # The birth date is entry date - age in days (based on 1/1/1960). # cols <- match(c("age", "year"), atts$dimid) if (any(is.na(cols))) stop("Ratetable does not have expected shape") if (exists("as.Date")) { # true for modern version of R bdate <- as.Date('1960/1/1') + (x[,cols[2]] - x[,cols[1]]) byear <- format(bdate, "%Y") # year of birth offset <- as.numeric(bdate - as.Date(paste(byear, '01/01', sep='/'))) } # The lines below were commented out to stop spurious warning # messages from "CMD check". They are very unlikely to ever # be needed, so no big loss. #else if (exists('month.day.year')) { # Splus, usually # bdate <- x[,cols[2]] - x[,cols[1]] # byear <- month.day.year(bdate)$year # offset <- bdate - julian(1,1,byear) # } #else if (exists('date.mdy')) { # the TMT date class is available # bdate <- as.date(x[,cols[2]] - x[,cols[1]]) # byear <- date.mdy(bdate)$year # offset <- bdate - mdy.date(1,1,byear) # } else stop("Can't find an appropriate date class\n") x[,cols[2]] <- x[,cols[2]] - offset # Doctor up "cutpoints" - only needed for old style rate tables # for which the C code does interpolation on the fly if (any(rfac >1)) { temp <- which(us.special) nyear <- length(cuts[[temp]]) nint <- rfac[temp] #intervals to interpolate over cuts[[temp]] <- round(approx(nint*(1:nyear), cuts[[temp]], nint:(nint*nyear))$y - .0001) } } storage.mode(x) <- storage.mode(y) <- "double" storage.mode(times) <- "double" temp <- .Call(Cpyears3b, as.integer(death), as.integer(rfac), as.integer(atts$dim), as.double(unlist(cuts)), ratetable, as.integer(group), x, y, times, as.integer(ngrp)) if (ntime==1) list(surv=temp$surv, n=temp$n) else if (ngrp >1) list(surv=apply(matrix(temp$surv, ntime, ngrp),2,cumprod), n= matrix(temp$n, ntime, ngrp)) else list(surv=cumprod(temp$surv), n=temp$n) } survival/R/coxph.rvar.S0000644000175100001440000000112111732700061014552 0ustar hornikusers# $Id: coxph.rvar.S 11166 2008-11-24 22:10:34Z therneau $ coxph.rvar <- function(fit, collapse) { rcall <- match.call() if (class(fit) != 'coxph') stop ("First argument must be a fitted Cox model") if (missing(collapse)) temp <- residuals.coxph(fit, type='dfbeta') else temp <- residuals.coxph(fit, type='dfbeta', collapse=collapse) if (any(is.na(temp))) if (ncol(temp)==1) temp<- temp[!is.na(temp),,drop=FALSE] else temp <- temp[!is.na(temp %*% rep(1,ncol(temp))),] fit$robust.var <- t(temp) %*% temp fit$rcall <- rcall fit } survival/R/print.coxph.null.S0000644000175100001440000000065211732700061015715 0ustar hornikusers# $Id: print.coxph.null.S 11166 2008-11-24 22:10:34Z therneau $ print.coxph.null <- function(x, digits=max(options()$digits - 4, 3), ...) { if (!is.null(cl<- x$call)) { cat("Call: ") dput(cl) cat("\n") } cat("Null model\n log likelihood=", format(x$loglik), "\n") omit <- x$na.action if (length(omit)) cat(" n=", x$n, " (", naprint(omit), ")\n", sep="") else cat(" n=", x$n, "\n") } survival/R/ratetableDate.S0000644000175100001440000000213411737410271015234 0ustar hornikusers# # survexp/pyears ratetables keep all dates as number of days since 1/1/1960 # convert other types of objects to this form # ratetableDate <- function(x) { UseMethod("ratetableDate", x) } # Normally used in R ratetableDate.Date <- function(x) as.numeric(x - as.Date("1960/01/01")) ratetableDate.POSIXt <- function(x) as.numeric(as.Date(x) - as.Date("1960/01/01")) # Normally Splus #ratetableDate.timeDate <- function(x) # as.numeric(x - timeDate('1/1/1960')) # Therneau's old "date" class (will someday wither away) ratetableDate.date <- function(x) as.numeric(x) # David James's old "chron" class (will someday wither away) # Support it without using the chron library, which may not be loaded. ratetableDate.chron <- function(x) { origin <- attr(x, "origin") x<- as.numeric(x) + as.Date(paste(origin["year"], origin["month"], origin["day"], sep='/')) ratetableDate(x) } ratetableDate.dates <- ratetableDate.chron # the routines that call this are responsible for a useful error message ratetableDate.default <- function(x) NULL survival/R/pspline.R0000644000175100001440000001753213016105374014151 0ustar hornikusers# # the p-spline function for a Cox model # pspline <- function(x, df=4, theta, nterm=2.5*df, degree=3, eps=0.1, method, Boundary.knots=range(x), intercept=FALSE, penalty=TRUE, combine, ...) { if (!missing(theta)) { method <- 'fixed' if (theta <=0 || theta >=1) stop("Invalid value for theta") } else if (df ==0 || (!missing(method) && method=='aic')) { method <- 'aic' nterm <- 15 #will be ok for up to 6-8 df if (missing(eps)) eps <- 1e-5 } else { method <- 'df' if (df <=1) stop ('Too few degrees of freedom') # The below used to say "df+1 > nterm", but we need some scope for # the smoother parameter to avoid strange conditions if (df > nterm) stop("`nterm' too small for df=",df) } xname <- deparse(substitute(x)) keepx <- !is.na(x) if (!all(keepx)) x <- x[keepx] #this is done before any reference to # Boundary.knots, so the default works nterm <- round(nterm) if (nterm < 3) stop("Too few basis functions") if (!missing(Boundary.knots)) { if (!is.numeric(Boundary.knots) || length(Boundary.knots) !=2 || Boundary.knots[1] >= Boundary.knots[2]) stop("Invalid values for Boundary.knots") # Check for data values outside the knot range outl <- (x < Boundary.knots[1]) outr<- (x > Boundary.knots[2]) outside <- outl | outr } else outside <- FALSE # Set up the evenly spaced knots dx <- (Boundary.knots[2] - Boundary.knots[1])/nterm knots <- c(Boundary.knots[1] + dx*((-degree):(nterm-1)), Boundary.knots[2]+ dx*(0:degree)) # Set up the basis. Inside the boundary knots we use spline.des. # Outside of them we use f(edge) + (x-edge)* f'(edge) if (any(outside)) { newx <- matrix(0., length(x), nterm + degree) if (any(outl)) { tt <- spline.des(knots, Boundary.knots[c(1,1)], degree+1, 0:1) newx[outl,] <- cbind(1, x[outl] - Boundary.knots[1]) %*% tt$design } if (any(outr)) { tt <- spline.des(knots, Boundary.knots[c(2,2)], degree+1, 0:1) newx[outr,] <- cbind(1, x[outr] - Boundary.knots[2]) %*% tt$design } if (any(inside <- !outside)) newx[inside,] <- spline.des(knots, x[inside], degree+1)$design } else newx <- spline.des(knots, x, degree+1, outer.ok=TRUE)$design # put missings back in so that the number of rows is right if (!all(keepx)) { temp <- matrix(NA, length(keepx), ncol(newx)) temp[keepx,] <- newx newx <- temp } # deal with the combine argument if (!missing(combine)) { if (any (combine != floor(combine) | combine < 0) || any(diff(combine) < 0)) stop("combine must be an increasing vector of positive integers") if (!intercept) combine <- c(0, combine) if (length(combine) != ncol(newx)) stop("wrong length for combine") uc <- sort(unique(combine)) tmat <- matrix(0., nrow=ncol(newx), ncol=length(uc)) for (i in 1:length(uc)) tmat[combine==uc[i], i] <- 1 newx <- newx %*% tmat } nvar <- ncol(newx) #should be nterm + degree dmat <- diag(nvar) dmat <- apply(dmat, 2, diff, 1, 2) dmat <- t(dmat) %*% dmat if (intercept) xnames <-paste('ps(', xname, ')', 1:nvar, sep='') else { newx <- newx[,-1, drop=FALSE] dmat <- dmat[-1,-1, drop=FALSE] # rows corresponding to the 0 coef xnames <-paste('ps(', xname, ')', 1+ 2:nvar, sep='') } if (!penalty) { attributes(newx) <- c(attributes(newx), list(intercept=intercept, nterm=nterm, Boundary.knots=Boundary.knots)) class(newx) <- "pspline" return(newx) } pfun <- function(coef, theta, n, dmat) { if (theta >=1) list(penalty= 100*(1-theta), flag=TRUE) else { if (theta <= 0) lambda <- 0 else lambda <- theta / (1-theta) list(penalty= c(coef %*% dmat %*% coef) * lambda/2, first = c(dmat %*% coef) * lambda , second = c(dmat * lambda), flag=FALSE ) } } printfun <- function(coef, var, var2, df, history, cbase) { test1 <- coxph.wtest(var, coef)$test # cbase contains the centers of the basis functions # do a weighted regression of these on the coefs to get a slope xmat <- cbind(1, cbase) xsig <- coxph.wtest(var, xmat)$solve # V X , where V = g-inverse(var) # [X' V X]^{-1} X' V cmat <- coxph.wtest(t(xmat)%*% xsig, t(xsig))$solve[2,] linear <- sum(cmat * coef) lvar1 <- c(cmat %*% var %*% cmat) lvar2 <- c(cmat %*% var2%*% cmat) test2 <- linear^2 / lvar1 # the "max(.5, df-1)" below stops silly (small) p-values for a # chisq of 0 on 0 df, when using AIC gives theta near 1 cmat <- rbind(c(linear, sqrt(lvar1), sqrt(lvar2), test2, 1, 1-pchisq(test2, 1)), c(NA, NA, NA, test1-test2, df-1, 1-pchisq(test1-test2, max(.5,df-1)))) dimnames(cmat) <- list(c("linear", "nonlin"), NULL) nn <- nrow(history$thetas) if (length(nn)) theta <- history$thetas[nn,1] else theta <- history$theta list(coef=cmat, history=paste("Theta=", format(theta))) } # The printfun needs to remember the spline's knots, # but I don't need (or want) to carry around the entire upteen # variables defined here as an environment # So fill in defaults for the cbase argument, and # force the function's environment to simplicity (amnesia) temp <- formals(printfun) temp$cbase <- knots[2:nvar] + (Boundary.knots[1] -knots[1]) formals(printfun) <- temp environment(printfun) <- .GlobalEnv if (method=='fixed') { temp <- list(pfun=pfun, printfun=printfun, pparm=dmat, diag =FALSE, cparm=list(theta=theta), varname=xnames, cfun = function(parms, iter, old) list(theta=parms$theta, done=TRUE)) } else if (method=='df') { temp <- list(pfun=pfun, printfun=printfun, diag =FALSE, cargs=('df'), cparm=list(df=df, eps=eps, thetas=c(1,0), dfs=c(1, nterm), guess=1 - df/nterm, ...), pparm= dmat, varname=xnames, cfun = frailty.controldf) } else { # use AIC temp <- list(pfun=pfun, printfun=printfun, pparm=dmat, diag =FALSE, cargs = c('neff', 'df', 'plik'), cparm=list(eps=eps, init=c(.5, .95), lower=0, upper=1, ...), varname=xnames, cfun = frailty.controlaic) } attributes(newx) <- c(attributes(newx), temp, list(intercept=intercept, nterm=nterm, Boundary.knots=Boundary.knots)) class(newx) <- c("pspline", 'coxph.penalty') newx } makepredictcall.pspline <- function(var, call) { if (call[[1]] != as.name("pspline")) return(call) #wrong phone number newcall <- call[1:2] #don't let the user override anything at <- attributes(var)[c("nterm", "intercept", "Boundary.knots", "combine")] newcall[names(at)] <- at newcall } predict.pspline <- function(object, newx, ...) { if (missing(newx)) return(object) a <- c(list(x=newx, penalty=FALSE), attributes(object)[c("intercept, Boundary.knots", "combine")]) do.call("pspline", a) } # Given a pspline basis, recover x psplineinverse <- function(x) { if (!inherits(x, "pspline")) stop("Argment must be the result of a call to pspline") intercept <- attr(x, "intercept") knots <- attr(x, "knots") nknot <- length(knots) if (!intercept) { indx <- 1:(ncol(x)+1) + (nknot- (ncol(x) +1))/2 as.vector(cbind(1-rowSums(x), x) %*% knots[indx]) } else { indx <- 1:ncol(x) + (nknot - ncol(x))/2 as.vector(x %*% knots) } } as.matrix.pspline <- function(x, ...) { temp <- attributes(x) attributes(x) <- temp['dim'] x } survival/R/anova.survreg.S0000644000175100001440000000400312676277156015310 0ustar hornikusers# $Id: anova.survreg.S 11230 2009-02-09 23:37:55Z therneau $ anova.survreg <- function(object, ..., test = c("Chisq", "none")) { test <- match.arg(test) margs <- function(...) nargs() if(margs(...)) return(anova.survreglist(list(object, ...), test = test)) Terms <- object$terms term.labels <- attr(Terms, "term.labels") nt <- length(term.labels) m <- stats::model.frame(object) family.obj <- object$family y <- model.extract(m, "response") if(!inherits(y, "Surv")) stop("Response must be a survival object") loglik <- numeric(nt + 1) df.res <- loglik if(nt) { loglik[nt + 1] <- -2 * object$loglik[2] df.res[nt + 1] <- object$df.residual fit <- object for(iterm in seq(from = nt, to = 1, by = -1)) { argslist <- list(object = fit, formula = eval(parse(text = paste("~ . -", term.labels[iterm])))) fit <- do.call("update", argslist) loglik[iterm] <- -2 * fit$loglik[2] df.res[iterm] <- fit$df.residual } dev <- c(NA, - diff(loglik)) df <- c(NA, -diff(df.res)) } else { loglik[1] <- -2 * object$loglik[2] df.res[1] <- object$df.residual #dim(y)[1] - attr(Terms, "intercept") dev <- df <- as.numeric(NA) } heading <- c("Analysis of Deviance Table\n", paste(family.obj[1], "distribution with", family.obj[2], "link\n"), paste("Response: ", as.character(formula(object))[2], "\n", sep = ""), if (nrow(fit$var) == length(fit$coefficients)) paste("Scale fixed at", format(object$scale, digits = getOption("digits")),"\n") else "Scale estimated\n", "Terms added sequentially (first to last)") aod <- data.frame(Df = df, Deviance = dev, "Resid. Df" = df.res, "-2*LL" = loglik, row.names = c("NULL", term.labels), check.names = FALSE) attr(aod, "heading") <- heading class(aod) <- c("anova", "data.frame") if(test == "none") return(aod) else stat.anova(aod, test, scale=1 ,n= nrow(y)) } survival/R/survexp.cfit.R0000644000175100001440000001063312257335007015136 0ustar hornikusers# Do expected survival based on a Cox model # This version relies on the survfit routine to do most of # the work. survexp.cfit <- function(group, ndata, y, method, coxfit, weights) { # If it is individual survival, call the predict method if (method=='individual') { temp <- predict(coxfit, newdata=ndata, type='expect', se=FALSE) return(list(surv= exp(-temp))) } # Get the set of survival curves on which I'll base my work # There is no id statement allowed yet, so no survexp for time-dependent # covariates sfit <- survfit.coxph(coxfit, newdata=ndata, se.fit=FALSE, censor=FALSE) # rare case: someone called survexp with a single-obs newdata # The average of n curves is just the curve, when n=1 if (length(group)==1) return(sfit) # number of curves to create & number of subjects ncurve <- max(group) #group was preset to contain integer group number n <- length(group) # matches nrow(ndata) # If the Cox model had strata then the newdata object also had to contain # the strata (needed to fully identify the new subjects), and the # n survival curves will be "strung out" as a single surv vector in # sfit, along with a strata component saying how many points for each. # If the Cox model did not have strata, sfit$surv and sfit$cumhaz will be # matrices with n columns. # The output should be a list with components time, n, and surv. # time = vector of unique time points # surv = matrix with 1 column per created curve (often just 1) # n = same shape as surv, containing the number of obs from ndata # that contribute to each row. newtime <- sort(unique(sfit$time)) # all of the unique times ntime <- length(newtime) newsurv <- list(time=newtime) # Each row of the input data is part of one and only one of the output # curves. Each column of gmat will contain the weights we need. # Each col sums to 1, and has zeros for those who belong to another curve gmat <- matrix(0., nrow=n, ncol=ncurve) for (i in 1:ncurve) { temp <- weights[group==i] gmat[group==i, i] <- temp/sum(temp) } # If the result is a set of curves with strata rather than a matrix, we # need to index into it, using a code trick taken from summary.survfit # Note that is is possible (though odd) for someone to specify a population # of subjects in survexp whose individual members come from different # strata in sfit. The result curves could have any of the times # that appear in any stratum. So we create a regular matrix of survivals. if (is.null(sfit$strata)) ssurv <- sfit$surv else { ssurv <- matrix(0., nrow=ntime, ncol=n) indx <- rep(1:length(sfit$strata), sfit$strata) for (i in 1:n) { itemp <- which(indx==i) ssurv[,i] <- approx(sfit$time[itemp], sfit$surv[itemp], newtime, yleft=0, method="constant", f=0, rule=2)$y } } if (method=="ederer") { # This is the most common call. We can work directly # with the returned survival curves, taking weighed averages. newsurv$n <- matrix(rep(table(group), each=ntime), nrow=ntime) newsurv$surv <- ssurv %*% gmat } else { # These are rarely used, so are implemented in S code rather than # C, even though it involves a loop over time points. # We need the hazard at each of the new time points, from which # a weighted average at each time point is computed # the Hakulinen also the survival at each time point. hazard <- apply(rbind(0, sfit$cumhaz), 2, diff) cmat <- matrix(0, ntime, ncurve) # Holds the result if (method== "conditional") { for (i in 1:ntime) { tmat <- ifelse(y >= newtime[i],1,0) * gmat #zero if not at risk cmat[i,] <- hazard[i,] %*% tmat / colSums(tmat) } } else { #Hakulinen method # Weights in this case are S(newtime) * I(newtime >=y) * gmat lsurv <- rbind(1.0, ssurv) #right continuous time for (i in 1:ntime) { tmat <- (ifelse(y>=newtime[i],1,0) * lsurv[i,]) * gmat cmat[i,] <- hazard[i,] %*% tmat / colSums(tmat) } } newsurv$surv <- exp(-apply(cmat, 2, cumsum)) } newsurv } survival/R/frailty.t.S0000644000175100001440000000763013016105374014412 0ustar hornikusers# $Id: frailty.t.S 11377 2009-12-14 22:59:56Z therneau $ # # Defining function for t-distribution frailty fits # frailty.t <- function(x, sparse=(nclass>5), theta, df, eps= 1e-5, tdf=5, method=c("aic", "df", "fixed"), ...) { nclass <- length(unique(x[!is.na(x)])) if (sparse){ x <-as.numeric(factor(x)) class(x) <- "coxph.penalty" } else{ x <- factor(x) class(x) <- c("coxph.penalty",class(x)) attr(x,'contrasts') <- contr.treatment(nclass, contrasts=FALSE) } if (tdf <=2) stop("Cannot have df <3 for the t-frailty") # Check for consistency of the arguments if (missing(method)) { if (!missing(theta)) { method <- 'fixed' if (!missing(df)) stop("Cannot give both a df and theta argument") } else if (!missing(df)) { if (df==0) method <- 'aic' else method <- 'df' } } method <- match.arg(method) if (method=='df' && missing(df)) stop("Method = df but no df argument") if (method=='fixed' && missing(theta)) stop("Method= fixed but no theta argument") if (method !='fixed' && !missing(theta)) stop("Method is not 'fixed', but have a theta argument") pfun<- function(coef, theta, ndead, tdf){ if (theta==0) list(recenter=0, penalty=0, flag=TRUE) else { sig <- theta* (tdf-2)/tdf #scale contant^2 in density formula # # Find the centering constant, using 1 NR step # temp <- 1 + coef^2/(tdf*sig) temp1 <- coef/temp temp2 <- 1/temp - (2/(tdf*sig))*coef^2/temp^2 recenter <- sum(temp1)/sum(temp2) #NR step towards MLE coef <- coef - recenter const <- (tdf+1)/(tdf*sig) temp <- 1 + coef^2/(tdf*sig) list(recenter=recenter, first= const*coef/temp, second= const*(1/temp - (2/(tdf*sig))*coef^2/temp^2), penalty= sum(.5*log(pi*tdf*sig) + ((tdf+1)/2)*log(temp) + lgamma(tdf/2) - lgamma((tdf+1)/2)), flag=FALSE) } } printfun <- function(coef, var, var2, df, history) { if (!is.null(history$history)) theta <- history$history[nrow(history$history),1] else theta <- history$theta if (is.matrix(var)) test <- coxph.wtest(var, coef)$test else test <- sum(coef^2/var) df2 <- max(df, .5) # Stop silly p-values list(coef=c(NA, NA, NA, test, df, 1-pchisq(test, df2)), history=paste("Variance of random effect=", format(theta))) } # The final coxph object will contain a copy of printfun. Stop it from # also containing huge unnecessary variables, e.g. 'x', known at this # point in time. Not an issue for pfun, which does not get saved. # The reason for using the survival namespace instead of globalenv() is # that we call coxph.wtest, which may not be visible outside the name space environment(printfun) <- asNamespace('survival') if (method=='fixed') { temp <- list(pfun=pfun, pparm=tdf, printfun=printfun, diag =TRUE, sparse= sparse, cfun = function(parms, iter, old){ list(theta=parms$theta, done=TRUE)}, cparm= list(theta=theta, ...)) } else if (method=='aic') { temp <- list(pfun=pfun, pparm=tdf, printfun=printfun, diag =TRUE, sparse= sparse, cargs = c("neff", "df", "plik"), cparm=list(lower=0, init=c(.1,1), eps=eps, ...), cfun = frailty.controlaic) } else { #df method if (missing(eps)) eps <- .1 temp <- list(pfun=pfun, pparm=tdf, printfun=printfun, diag =TRUE, sparse= sparse, cargs= c('df'), cparm=list(df=df, eps=eps, thetas=0, dfs=0, guess=3*df/length(unclass(x)), ...), cfun = frailty.controldf) } # If not sparse, give shorter names to the coefficients, so that any # printout of them is readable. if (!sparse) { vname <- paste("t", levels(x), sep=':') temp <- c(temp, list(varname=vname)) } attributes(x) <- c(attributes(x), temp) x } survival/R/residuals.coxph.S0000644000175100001440000001204313010362577015607 0ustar hornikusersresiduals.coxph <- function(object, type=c("martingale", "deviance", "score", "schoenfeld", "dfbeta", "dfbetas", "scaledsch","partial"), collapse=FALSE, weighted=FALSE, ...) { type <- match.arg(type) otype <- type if (type=='dfbeta' || type=='dfbetas') { otype <- type # used for error messge type <- 'score' if (missing(weighted)) weighted <- TRUE # different default for this case } if (type=='scaledsch') type<-'schoenfeld' n <- length(object$residuals) rr <- object$residuals y <- object$y x <- object[['x']] # avoid matching object$xlevels vv <- drop(object$naive.var) if (is.null(vv)) vv <- drop(object$var) weights <- object$weights if (is.null(weights)) weights <- rep(1,n) strat <- object$strata method <- object$method if (method=='exact' && (type=='score' || type=='schoenfeld')) stop(paste(otype, 'residuals are not available for the exact method')) if (type == 'martingale' || type == 'partial') rr <- object$residuals else { # I need Y, and perhaps the X matrix (and strata) Terms <- object$terms if (!inherits(Terms, 'terms')) stop("invalid terms component of object") strats <- attr(Terms, "specials")$strata if (is.null(y) || (is.null(x) && type!= 'deviance')) { temp <- coxph.getdata(object, y=TRUE, x=TRUE, stratax=TRUE) y <- temp$y x <- temp$x if (length(strats)) strat <- temp$strata } ny <- ncol(y) status <- y[,ny,drop=TRUE] if (type != 'deviance') { nstrat <- as.numeric(strat) nvar <- ncol(x) if (is.null(strat)) { ord <- order(y[,ny-1], -status) newstrat <- rep(0,n) } else { ord <- order(nstrat, y[,ny-1], -status) newstrat <- c(diff(as.numeric(nstrat[ord]))!=0 ,1) } newstrat[n] <- 1 # sort the data x <- x[ord,] y <- y[ord,] score <- exp(object$linear.predictors)[ord] } } # # Now I have gotton the data that I need-- do the work # if (type=='schoenfeld') { if (ny==2) { mintime <- min(y[,1]) if (mintime < 0) y <- cbind(2*mintime -1, y) else y <- cbind(-1,y) } temp <- .C(Ccoxscho, n=as.integer(n), as.integer(nvar), as.double(y), resid= as.double(x), as.double(score * weights[ord]), as.integer(newstrat), as.integer(method=='efron'), double(3*nvar) ) deaths <- y[,3]==1 if (nvar==1) rr <- temp$resid[deaths] else rr <- matrix(temp$resid[deaths], ncol=nvar) #pick rows if (weighted) rr <- rr * weights[deaths] if (length(strats)) attr(rr, "strata") <- table((strat[ord])[deaths]) time <- c(y[deaths,2]) # 'c' kills all of the attributes if (is.matrix(rr)) dimnames(rr)<- list(time, names(object$coefficients)) else names(rr) <- time if (otype=='scaledsch') { ndead <- sum(deaths) coef <- ifelse(is.na(object$coefficients), 0, object$coefficients) rr <- drop(rr %*% vv *ndead + rep(coef, each=nrow(rr))) } return(rr) } if (type=='score') { if (ny==2) { resid <- .C(Ccoxscore, as.integer(n), as.integer(nvar), as.double(y), x=as.double(x), as.integer(newstrat), as.double(score), as.double(weights[ord]), as.integer(method=='efron'), resid= double(n*nvar), double(2*nvar))$resid } else { resid<- .C(Cagscore, as.integer(n), as.integer(nvar), as.double(y), as.double(x), as.integer(newstrat), as.double(score), as.double(weights[ord]), as.integer(method=='efron'), resid=double(n*nvar), double(nvar*6))$resid } if (nvar >1) { rr <- matrix(0, n, nvar) rr[ord,] <- matrix(resid, ncol=nvar) dimnames(rr) <- list(names(object$residuals), names(object$coefficients)) } else rr[ord] <- resid if (otype=='dfbeta') { if (is.matrix(rr)) rr <- rr %*% vv else rr <- rr * vv } else if (otype=='dfbetas') { if (is.matrix(rr)) rr <- (rr %*% vv) %*% diag(sqrt(1/diag(vv))) else rr <- rr * sqrt(vv) } } # # Multiply up by case weights (which will be 1 for unweighted) # if (weighted) rr <- rr * weights #Expand out the missing values in the result if (!is.null(object$na.action)) { rr <- naresid(object$na.action, rr) if (is.matrix(rr)) n <- nrow(rr) else n <- length(rr) if (type=='deviance') status <- naresid(object$na.action, status) } if (type=="partial"){ # This needs to be done after the naresid expansion, since the # predict function will have done naresid expansion, so that # the lengths match rr <- rr + predict(object,type="terms") } # Collapse if desired if (!missing(collapse)) { if (length(collapse) !=n) stop("Wrong length for 'collapse'") rr <- drop(rowsum(rr, collapse)) if (type=='deviance') status <- drop(rowsum(status, collapse)) } # Deviance residuals are computed after collapsing occurs if (type=='deviance') sign(rr) *sqrt(-2* (rr+ ifelse(status==0, 0, status*log(status-rr)))) else rr } survival/R/is.ratetable.S0000644000175100001440000000751213003730610015043 0ustar hornikusersis.ratetable <- function(x, verbose=FALSE) { dlist <- c("dim", "dimnames", "dimid", "cutpoints") if (!verbose) { if (!inherits(x, 'ratetable')) return(FALSE) att <- attributes(x) if (any(is.na(match(dlist, names(att))))) return(FALSE) nd <- length(att$dim) if (length(x) != prod(att$dim)) return(FALSE) if (!(is.list(att$dimnames) && is.list(att$cutpoints))) return(FALSE) if (length(att$dimnames)!=nd || length(att$cutpoints)!=nd) return(FALSE) # One of 'factor' (old style table) or 'type' (new style) should exist if (!is.null(att$factor)) { fac <- as.numeric(att$factor) if (any(is.na(fac))) return(FALSE) if (any(fac <0)) return(FALSE) if (length(att$factor)!=nd ) return(FALSE) } else if (!is.null(att$type)) { if (any(is.na(match(att$type, 1:4)))) return(FALSE) fac <- 1*(att$type==1) if (length(fac) != nd) return(FALSE) } else return(FALSE) if (length(att$dimid) != nd) return(FALSE) for (i in 1:nd) { n <- att$dim[i] if (length(att$dimnames[[i]]) !=n) return(FALSE) if (fac[i]!=1 && length(att$cutpoints[[i]])!=n) return(FALSE) if (fac[i]!=1 && any(order(att$cutpoints[[i]])!= 1:n)) return(FALSE) if (fac[i]==1 && !is.null(att$cutpoints[[i]])) return(FALSE) if (fac[i]>1 && i1) } else if (!is.null(att$type)) { if (any(is.na(match(att$type, 1:4)))) msg <- c(msg, 'type attribute must be 1, 2, 3, or 4') type <- att$type if (length(type)!=nd) msg <- c(msg, 'wrong length for type attribute') } else msg <- c(msg, "missing the 'type' attribute") for (i in 1:nd) { n <- att$dim[i] if (length(att$dimnames[[i]]) !=n) msg <- c(msg, paste('dimname', i, 'is the wrong length')) if (type[i] >1) { #continuous variable if (length(att$cutpoints[[i]]) != n) msg <- c(msg, paste('wrong length for cutpoints', i)) else if (any(order(att$cutpoints[[i]])!= 1:n)) msg <- c(msg, paste('unsorted cutpoints for dimension',i)) } if (type[i]==1 && !is.null(att$cutpoints[[i]])) msg <- c(msg, paste('type[', i, '] is 1; cutpoint should be null')) # This message only applies to old style rate table if (!is.null(att$fac) && type[i]==4 && i 0) { if (length(cluster$terms) >1) stop ("Can have only 1 cluster term") idvar <- m[[cluster$vars]] Terms2 <- Terms[-cluster$terms] } else { idvar <- 1:n Terms2 <- Terms } if (length(attr(Terms, "specials")$strata)) { stemp <- untangle.specials(Terms2, 'strata', 1) if (length(stemp$terms) >0) #beware strata by covariate interactions Terms2 <- Terms2[-stemp$terms] #not needed for model.matrix later if (length(stemp$vars)==1) strata.keep <- m[[stemp$vars]] else strata.keep <- strata(m[,stemp$vars], shortlabel=TRUE) } else strata.keep <- NULL if (any(attr(Terms2, "order") > 1)) stop("This function cannot deal with iteraction terms") # Figure out which are the continuous predictor variables myvars <- attr(Terms2, "term.labels") factors <- sapply(m[myvars], is.factor) protected <- sapply(m[myvars], function(x) inherits(x, "AsIs")) keepers <- factors | protected #variables to be left alone if (all(keepers)) stop ("No continuous variables to modify") if (ncol(y) ==3) { # counting process data if (is.null(strata.keep)) { etime <- sort(unique(y[y[,3]==1, 2])) #unique event times indx <- lapply(etime, function(x) which(y[,1]= x)) } else { temp <- unique(data.frame(y[,2], strata.keep)[y[,3]==1,]) etime <- temp[,1] indx <- lapply(1:nrow(temp), function(x) which(y[,1] < temp[x,1] & y[,2]>= temp[x,1] & !strata.keep == temp[x,2])) } } else { # Simple survival data if (is.null(strata.keep)) { etime <- sort(unique(y[y[,2]==1,1])) #unique event times indx <- lapply(etime, function(x) which(y[,1] >=x)) } else { temp <- unique(data.frame(y[,1], strata.keep)[y[,2]==1,]) etime <- temp[,1] indx <- lapply(1:nrow(temp), function(x) which(y[,2] >= temp[x,1] & strata.keep == temp[x,2])) } } # The indx list now has an entry for each event time containing the # row numbers of those at risk indx2 <- unlist(indx) # Create the new survival variables nrisk <- unlist(sapply(indx, length)) #number of obs at risk if (ncol(y)==3) { newdata <- list(y[indx2, 1], y[indx2,2]) newdata <- c(newdata, list(1L*(newdata[[2]]==rep(etime, nrisk) &y[indx2,3]==1))) } else { newdata <- list(y[indx2,1]) newdata <- c(newdata, list(1L*(newdata[[1]]==rep(etime, nrisk) &y[indx2,2]==1))) } names(newdata) <- dimnames(y)[[2]] # Add any untransformed variables if (any(keepers)) { temp <- lapply(myvars[keepers], function(x) all.vars(parse(text=x))) knames <- unlist(temp) } else knames <- NULL if (length(strata.keep)) { knames <- c(knames, unlist(lapply(names(m)[stemp$vars], function(x) all.vars(parse(text=x))))) } if (length(knames)) newdata <- c(newdata, lapply(data[knames], function(x) x[indx2])) # Add the identifier variable if (length(cluster$vars) >0) { clname <- all.vars(parse(text=names(m)[cluster$vars])) newdata <- c(newdata, lapply(data[clname], function(x) x[indx2])) } else newdata <- c(newdata, list(".id."=idvar[indx2])) # Add transformed variables tvars <- myvars[!keepers] newx <- lapply(m[tvars], function(z) unlist(lapply(indx, function(x) transform(z[x])))) data.frame(c(newdata, newx, list(".strata."=rep(1:length(indx), sapply(indx, length))))) } survival/R/print.ratetable.S0000644000175100001440000000035711732700061015570 0ustar hornikusers## $Id: print.ratetable.S 11166 2008-11-24 22:10:34Z therneau $ print.ratetable <- function(x, ...) { cat ("Rate table with dimension(s):", attr(x, 'dimid'), "\n") attributes(x) <- attributes(x)[c("dim", "dimnames")] NextMethod() } survival/R/summary.ratetable.S0000644000175100001440000000445411732700061016133 0ustar hornikusers# $Id: summary.ratetable.S 11437 2010-10-28 02:21:16Z therneau $ # # Print out information about a rate table: it's dimensions and keywords # summary.ratetable <- function(object, ...) { rtable<-object if (!inherits(rtable, 'ratetable')) stop("Argument is not a rate table") att <- attributes(rtable) ncat <- length(dim(rtable)) cat (" Rate table with", ncat, "dimensions:\n") for (i in 1:ncat) { # One of 'factor' (old style table) or "type" (new style) should exist if (!is.null(att$factor)) { if (att$factor[i]==0) { cat("\t", att$dimid[i], " ranges from ", format(min(att$cutpoints[[i]])), " to ", format(max(att$cutpoints[[i]])), "; with ", att$dim[i], " categories\n", sep='') } else if(att$factor[i]==1) { cat("\t", att$dimid[i], " has levels of: ", paste(att$dimnames[[i]], collapse=' '), "\n", sep='') } else { cat("\t", att$dimid[i], " ranges from " , format(min(att$cutpoints[[i]])), " to ", format(max(att$cutpoints[[i]])), "; with ", att$dim[i], " categories,\n\t\tlinearly interpolated in ", att$factor[i], " steps per division\n", sep='') } } else { if (att$type[i]==1) { cat("\t", att$dimid[i], " has levels of: ", paste(att$dimnames[[i]], collapse=' '), "\n", sep='') } else if (att$type[i]>2) { #date cat("\t", att$dimid[i], " ranges from " , format(as.Date(min(att$cutpoints[[i]]), origin='1960/01/01')), " to ", format(as.Date(max(att$cutpoints[[i]]), origin='1960/01/01')), "; with ", att$dim[i], " categories\n", sep='') } else { cat("\t", att$dimid[i], " ranges from ", format(min(att$cutpoints[[i]])), " to ", format(max(att$cutpoints[[i]])), "; with ", att$dim[i], " categories\n", sep='') } } } invisible(att) } survival/R/agsurv.R0000644000175100001440000000620413065013231013772 0ustar hornikusers# Automatically generated from the noweb directory agsurv <- function(y, x, wt, risk, survtype, vartype) { nvar <- ncol(as.matrix(x)) status <- y[,ncol(y)] dtime <- y[,ncol(y) -1] death <- (status==1) time <- sort(unique(dtime)) nevent <- as.vector(rowsum(wt*death, dtime)) ncens <- as.vector(rowsum(wt*(!death), dtime)) wrisk <- wt*risk rcumsum <- function(x) rev(cumsum(rev(x))) # sum from last to first nrisk <- rcumsum(rowsum(wrisk, dtime)) irisk <- rcumsum(rowsum(wt, dtime)) if (ncol(y) ==2) { temp2 <- rowsum(wrisk*x, dtime) xsum <- apply(temp2, 2, rcumsum) } else { delta <- min(diff(time))/2 etime <- c(sort(unique(y[,1])), max(y[,1])+delta) #unique entry times indx <- approx(etime, 1:length(etime), time, method='constant', rule=2, f=1)$y esum <- rcumsum(rowsum(wrisk, y[,1])) #not yet entered nrisk <- nrisk - c(esum,0)[indx] irisk <- irisk - c(rcumsum(rowsum(wt, y[,1])),0)[indx] xout <- apply(rowsum(wrisk*x, y[,1]), 2, rcumsum) #not yet entered xin <- apply(rowsum(wrisk*x, dtime), 2, rcumsum) # dtime or alive xsum <- xin - (rbind(xout,0))[indx,,drop=F] } ndeath <- rowsum(status, dtime) #unweighted death count ntime <- length(time) if (survtype ==1) { #Kalbfleisch-Prentice indx <- (which(status==1))[order(dtime[status==1])] #deaths km <- .C(Cagsurv4, as.integer(ndeath), as.double(risk[indx]), as.double(wt[indx]), as.integer(ntime), as.double(nrisk), inc = double(ntime)) } if (survtype==3 || vartype==3) { # Efron approx xsum2 <- rowsum((wrisk*death) *x, dtime) erisk <- rowsum(wrisk*death, dtime) #risk score sums at each death tsum <- .C(Cagsurv5, as.integer(length(nevent)), as.integer(nvar), as.integer(ndeath), as.double(nrisk), as.double(erisk), as.double(xsum), as.double(xsum2), sum1 = double(length(nevent)), sum2 = double(length(nevent)), xbar = matrix(0., length(nevent), nvar)) } haz <- switch(survtype, nevent/nrisk, nevent/nrisk, nevent* tsum$sum1) varhaz <- switch(vartype, nevent/(nrisk * ifelse(nevent>=nrisk, nrisk, nrisk-nevent)), nevent/nrisk^2, nevent* tsum$sum2) xbar <- switch(vartype, (xsum/nrisk)*haz, (xsum/nrisk)*haz, nevent * tsum$xbar) result <- list(n= nrow(y), time=time, n.event=nevent, n.risk=irisk, n.censor=ncens, hazard=haz, cumhaz=cumsum(haz), varhaz=varhaz, ndeath=ndeath, xbar=apply(matrix(xbar, ncol=nvar),2, cumsum)) if (survtype==1) result$surv <- km$inc result } survival/R/untangle.specials.S0000644000175100001440000000124611732700061016107 0ustar hornikusers# $Id: untangle.specials.S 11166 2008-11-24 22:10:34Z therneau $ # # This function takes a terms object, and extracts some aspects # of it into a "nice" list. It is simple an operation that # I do again and again in the modeling routines, so it was # made into a separate function # untangle.specials <- function(tt, special, order=1) { spc <- attr(tt, 'specials')[[special]] if (length(spc)==0) return(list(vars=character(0), terms=numeric(0))) facs <- attr(tt, 'factors') fname <- dimnames(facs) ff <- apply(facs[spc,,drop=FALSE], 2, sum) list(vars= (fname[[1]])[spc], terms= seq(ff)[ff & match(attr(tt, 'order'), order, nomatch=0)]) } survival/R/match.ratetable.S0000644000175100001440000000675511732700061015540 0ustar hornikusers# Do a set of error checks on whether any categorical vars match the # level set of the actual ratetable. If so they are mapped to the levels # found in the ratetable. Dates need to match dates, and others are set # to simple numerics with unclass(). A matrix is returned. # This is called by pyears and survexp, but not by users # # The categoricals are turned into integer subscripts # match.ratetable <- function(R, ratetable) { if (!is.ratetable(ratetable)) stop("Invalid rate table") dimid <- attr(ratetable, 'dimid') if (is.matrix(R)) { # older style call nd <- ncol(R) attR <- attributes(R) attributes(R) <- attR['dim'] #other attrs get in the way later Rnames <- attR$dimnames[[2]] isDate <- attR[["isDate"]] levlist <- attR[['levlist']] } else { # newer style is a dataframe nd <- length(R) Rnames <- names(R) isDate <- rep(FALSE, nd) levlist<- lapply(R, levels) for (i in 1:nd) { temp <- ratetableDate(R[[i]]) if (!is.null(temp)) { isDate[i] <- TRUE R[[i]] <- temp } } } ord <- match(dimid, Rnames) # This should not arise if (any(is.na(ord))) stop(paste("Argument '", dimid[is.na(ord)], "' needed by the ratetable was not found in the data", sep='')) # Neither should this -- two argments matched one of the dimids -- since # I demand an exact match if (any(duplicated(ord))) stop("A ratetable argument appears twice in the data") R <- R[,ord,drop=FALSE] #put cols in same order as the ratetable isDate <- isDate[ord] levlist <- levlist[ord] dtemp <-dimnames(ratetable) rtype <- attr(ratetable, 'type') # 1= class, 2=cont, 3=date, 4=US yr if (is.null(rtype)) { #old style ratetable, be backwards compatable temp <- attr(ratetable, 'factor') # we map 'old continuous' to 'new date'; since it might be a date rtype <- 1*(temp==1) + 3*(temp==0) + 4*(temp >1) } # Now, go through the dimensions of the ratetable 1 by 1, and # verify that the user's variable is compatable # with the rate table's dimensions # if (any(rtype<3 & isDate)) { indx <- which(rtype<1 & isDate) stop(paste("Data has a date type variable, but the reference", "ratetable is not a date for variable", dimid[indx])) } for (i in (1:nd)) { if (length(levlist[[i]]) >0) { #factor or character variable if (rtype[i]!=1) stop(paste("In ratetable(),", dimid[i], "must be a continuous variable")) temp <- charmatch(casefold(levlist[[i]]), casefold(dtemp[[i]])) if (any(is.na(temp))) stop(paste("Levels do not match for ratetable() variable", dimid[i])) if (any(temp==0)) stop(paste("Non-unique ratetable match for variable", dimid[i])) R[,i] <- temp[as.numeric(R[,i])] } else { # user's data isn't a factor or date R[,i] <- unclass(R[,i]) # get rid of difftimes & other such if (rtype[i]==1) { #ratetable is a factor: ok if data is integer temp <- R[,i] if (any(floor(temp)!=temp) || any(temp<=0) || max(temp) > length(dtemp[[i]])) stop(paste("The variable", dimid[i], "is out of range")) } } } R <- as.matrix(R) summ <- attr(ratetable, 'summary') if (is.null(summ)) list(R= R) else list(R= R, summ=summ(R)) } survival/R/ridge.S0000644000175100001440000000251211732700061013557 0ustar hornikusers# $Id: ridge.S 11166 2008-11-24 22:10:34Z therneau $ ridge <- function(..., theta, df=nvar/2, eps=.1, scale=TRUE) { x <- cbind(...) nvar <- ncol(x) xname <- as.character(parse(text=substitute(cbind(...))))[-1] vars <- apply(x, 2, function(z) var(z[!is.na(z)])) class(x) <- 'coxph.penalty' if (!missing(theta) && !missing(df)) stop("Only one of df or theta can be specified") if (scale) pfun <- function(coef,theta, ndead, scale) { list(penalty= sum(coef^2 *scale)*theta/2, first = theta*coef*scale, second = theta*scale, flag=FALSE) } else pfun <- function(coef,theta, ndead, scale) { list(penalty= sum(coef^2)*theta/2, first = theta*coef, second = theta, flag=FALSE) } if (!missing(theta)) { temp <- list(pfun=pfun, diag=TRUE, cfun=function(parms, iter, history) { list(theta=parms$theta, done=TRUE) }, cparm=list(theta= theta), pparm= vars, varname=paste('ridge(', xname, ')', sep='')) } else { temp <- list(pfun=pfun, diag=TRUE, cfun=frailty.controldf, cargs = 'df', cparm=list(df=df, eps=eps, thetas=0, dfs=nvar, guess=1), pparm= vars, varname=paste('ridge(', xname, ')', sep='')) } attributes(x) <- c(attributes(x), temp) x } survival/R/clogit.R0000644000175100001440000000441512676275373013776 0ustar hornikusers## conditional logistic regression ## ## case ~ exposure + strata(matching) ## clogit <- function(formula, data, weights, subset, na.action, method=c("exact","approximate", "efron", "breslow"), ... ) { Call <- match.call() # how we were called # Create a call to model.frame() that contains the formula (required) # and the data argument (if present). # It's only job is to find out the number of rows in the data # before subset or na.action are applied. indx <- match(c("formula", "data"), names(Call), nomatch=0) if (indx[1]==0) stop("A formula argument is required") mf <- Call[c(1,indx)] mf[[1L]] <- quote(stats::model.frame) mf$na.action <- "na.pass" nrows<-NROW(eval(mf, parent.frame())) # Now build a call to coxph with the formula fixed up to have # our special left hand side. coxcall <- Call coxcall[[1]] <- as.name("coxph") newformula <- formula newformula[[2]] <- substitute(Surv(rep(1,nn),case), list(case=formula[[2]],nn=nrows)) environment(newformula) <- environment(formula) coxcall$formula<-newformula # Set the method, with "approximate" matched to "breslow" method <- match.arg(method) coxcall$method <- switch(method, exact="exact", efron="efron", "breslow") # If the method is "exact", then case weights nor robust variance are # possible if (method =="exact") { if (missing(data)) temp <- terms(formula, special='cluster') else temp <- terms(formula, special="cluster", data=data) if (!is.null(attr(temp, 'specials')$cluster) && method=="exact") stop("robust variance plus the exact method is not supported") if (!is.null(coxcall$weights)) { coxcall$weights <- NULL warning("weights ignored: not possible for the exact method") } } coxcall<-eval(coxcall, sys.frame(sys.parent())) coxcall$userCall<-sys.call() class(coxcall)<-c("clogit","coxph") coxcall } print.clogit <- function(x,...){ x$call<-x$userCall NextMethod() } survfit.clogit <- function(formula, ...) stop("predicted survival curves are not defined for a clogit model") survival/R/survexp.R0000644000175100001440000002141013065013244014177 0ustar hornikusers# Automatically generated from the noweb directory survexp <- function(formula, data, weights, subset, na.action, rmap, times, method=c("ederer", "hakulinen", "conditional", "individual.h", "individual.s"), cohort=TRUE, conditional=FALSE, ratetable=survival::survexp.us, scale=1, se.fit, model=FALSE, x=FALSE, y=FALSE) { Call <- match.call() m <- match.call(expand.dots=FALSE) # keep the first element (the call), and the following selected arguments m <- m[c(1, match(c('formula', 'data', 'weights', 'subset', 'na.action'), names(m), nomatch=0))] m[[1L]] <- quote(stats::model.frame) Terms <- if(missing(data)) terms(formula, 'ratetable') else terms(formula, 'ratetable',data=data) rate <- attr(Terms, "specials")$ratetable if(length(rate) > 1) stop("Can have only 1 ratetable() call in a formula") if(length(rate) == 1) { if (!missing(rmap)) stop("The ratetable() call in a formula is depreciated") stemp <- untangle.specials(Terms, 'ratetable') rcall <- as.call(parse(text=stemp$var)[[1]]) # as a call object rcall[[1]] <- as.name('list') # make it a call to list(.. Terms <- Terms[-stemp$terms] # remove from the formula } else if (!missing(rmap)) { rcall <- substitute(rmap) if (!is.call(rcall) || rcall[[1]] != as.name('list')) stop ("Invalid rcall argument") } else rcall <- NULL # A ratetable, but not rcall argument # Check that there are no illegal names in rcall, then expand it # to include all the names in the ratetable if(is.ratetable(ratetable)) varlist <- attr(ratetable, "dimid") else if(inherits(ratetable, "coxph")) { ## Remove "log" and such things, to get just the list of # variable names varlist <- all.vars(delete.response(ratetable$terms)) } else stop("Invalid rate table") temp <- match(names(rcall)[-1], varlist) # 2,3,... are the argument names if (any(is.na(temp))) stop("Variable not found in the ratetable:", (names(rcall))[is.na(temp)]) if (any(!(varlist %in% names(rcall)))) { to.add <- varlist[!(varlist %in% names(rcall))] temp1 <- paste(text=paste(to.add, to.add, sep='='), collapse=',') if (is.null(rcall)) rcall <- parse(text=paste("list(", temp1, ")"))[[1]] else { temp2 <- deparse(rcall) rcall <- parse(text=paste("c(", temp2, ",list(", temp1, "))"))[[1]] } } # Create a temporary formula, used only in the call to model.frame newvar <- all.vars(rcall) if (length(newvar) > 0) { tform <- paste(paste(deparse(Terms), collapse=""), paste(newvar, collapse='+'), sep='+') m$formula <- as.formula(tform, environment(Terms)) } m <- eval(m, parent.frame()) n <- nrow(m) if (n==0) stop("Data set has 0 rows") if (!missing(se.fit) && se.fit) warning("se.fit value ignored") weights <- model.extract(m, 'weights') if (length(weights) ==0) weights <- rep(1.0, n) if (class(ratetable)=='ratetable' && any(weights !=1)) warning("weights ignored") if (any(attr(Terms, 'order') >1)) stop("Survexp cannot have interaction terms") if (!missing(times)) { if (any(times<0)) stop("Invalid time point requested") if (length(times) >1 ) if (any(diff(times)<0)) stop("Times must be in increasing order") } Y <- model.extract(m, 'response') no.Y <- is.null(Y) if (no.Y) { if (missing(times)) { if (is.ratetable(ratetable)) stop("either a times argument or a response is needed") } else newtime <- times } else { if (is.matrix(Y)) { if (is.Surv(Y) && attr(Y, 'type')=='right') Y <- Y[,1] else stop("Illegal response value") } if (any(Y<0)) stop ("Negative follow up time") # if (missing(npoints)) temp <- unique(Y) # else temp <- seq(min(Y), max(Y), length=npoints) temp <- unique(Y) if (missing(times)) newtime <- sort(temp) else newtime <- sort(unique(c(times, temp[temp1)) stop("Pyears cannot have interaction terms") rate <- attr(Terms, "specials")$ratetable if (length(rate) >0 || !missing(rmap) || !missing(ratetable)) { has.ratetable <- TRUE if(length(rate) > 1) stop("Can have only 1 ratetable() call in a formula") if (missing(ratetable)) stop("No rate table specified") if(length(rate) == 1) { if (!missing(rmap)) stop("The ratetable() call in a formula is depreciated") stemp <- untangle.specials(Terms, 'ratetable') rcall <- as.call(parse(text=stemp$var)[[1]]) # as a call object rcall[[1]] <- as.name('list') # make it a call to list(.. Terms <- Terms[-stemp$terms] # remove from the formula } else if (!missing(rmap)) { rcall <- substitute(rmap) if (!is.call(rcall) || rcall[[1]] != as.name('list')) stop ("Invalid rcall argument") } else rcall <- NULL # A ratetable, but not rcall argument # Check that there are no illegal names in rcall, then expand it # to include all the names in the ratetable if(is.ratetable(ratetable)) varlist <- attr(ratetable, "dimid") else if(inherits(ratetable, "coxph")) { ## Remove "log" and such things, to get just the list of # variable names varlist <- all.vars(delete.response(ratetable$terms)) } else stop("Invalid rate table") temp <- match(names(rcall)[-1], varlist) # 2,3,... are the argument names if (any(is.na(temp))) stop("Variable not found in the ratetable:", (names(rcall))[is.na(temp)]) if (any(!(varlist %in% names(rcall)))) { to.add <- varlist[!(varlist %in% names(rcall))] temp1 <- paste(text=paste(to.add, to.add, sep='='), collapse=',') if (is.null(rcall)) rcall <- parse(text=paste("list(", temp1, ")"))[[1]] else { temp2 <- deparse(rcall) rcall <- parse(text=paste("c(", temp2, ",list(", temp1, "))"))[[1]] } } # Create a temporary formula, used only in the call to model.frame newvar <- all.vars(rcall) if (length(newvar) > 0) { tform <- paste(paste(deparse(Terms), collapse=""), paste(newvar, collapse='+'), sep='+') m$formula <- as.formula(tform, environment(Terms)) } } else has.ratetable <- FALSE m <- eval(m, parent.frame()) Y <- model.extract(m, 'response') if (is.null(Y)) stop ("Follow-up time must appear in the formula") if (!is.Surv(Y)){ if (any(Y <0)) stop ("Negative follow up time") Y <- as.matrix(Y) if (ncol(Y) >2) stop("Y has too many columns") } else { stype <- attr(Y, 'type') if (stype == 'right') { if (any(Y[,1] <0)) stop("Negative survival time") nzero <- sum(Y[,1]==0 & Y[,2] ==1) if (nzero >0) warning(paste(nzero, "observations with an event and 0 follow-up time,", "any rate calculations are statistically questionable")) } else if (stype != 'counting') stop("Only right-censored and counting process survival types are supported") } n <- nrow(Y) if (is.null(n) || n==0) stop("Data set has 0 observations") weights <- model.extract(m, 'weights') if (is.null(weights)) weights <- rep(1.0, n) # rdata contains the variables matching the ratetable if (has.ratetable) { rdata <- data.frame(eval(rcall, m), stringsAsFactors=TRUE) if (is.ratetable(ratetable)) { israte <- TRUE rtemp <- match.ratetable(rdata, ratetable) R <- rtemp$R } else if (inherits(ratetable, 'coxph')) { israte <- FALSE Terms <- ratetable$terms if (!is.null(attr(Terms, 'offset'))) stop("Cannot deal with models that contain an offset") strats <- attr(Terms, "specials")$strata if (length(strats)) stop("pyears cannot handle stratified Cox models") if (any(names(m[,rate]) != attr(ratetable$terms, 'term.labels'))) stop("Unable to match new data to old formula") R <- model.matrix.coxph(ratetable, data=rdata) } else stop("Invalid ratetable") } ovars <- attr(Terms, 'term.labels') if (length(ovars)==0) { # no categories! X <- rep(1,n) ofac <- odim <- odims <- ocut <- 1 } else { odim <- length(ovars) ocut <- NULL odims <- ofac <- double(odim) X <- matrix(0, n, odim) outdname <- vector("list", odim) names(outdname) <- attr(Terms, 'term.labels') for (i in 1:odim) { temp <- m[[ovars[i]]] if (inherits(temp, 'tcut')) { X[,i] <- temp temp2 <- attr(temp, 'cutpoints') odims[i] <- length(temp2) -1 ocut <- c(ocut, temp2) ofac[i] <- 0 outdname[[i]] <- attr(temp, 'labels') } else { temp2 <- as.factor(temp) X[,i] <- temp2 temp3 <- levels(temp2) odims[i] <- length(temp3) ofac[i] <- 1 outdname[[i]] <- temp3 } } } ocut <-c(ocut,0) #just in case it were of length 0 osize <- prod(odims) if (has.ratetable) { #include expected atts <- attributes(ratetable) cuts <- atts$cutpoints if (is.null(atts$type)) { #old stlye table rfac <- atts$factor us.special <- (rfac >1) } else { rfac <- 1*(atts$type ==1) us.special <- (atts$type==4) } if (any(us.special)) { #special handling for US pop tables # Now, the 'entry' date on a US rate table is the number of days # since 1/1/1960, and the user data has been aligned to the # same system by match.ratetable and marked as "year". # The birth date is entry date - age in days (based on 1/1/1960). # I don't much care which date functions I use to do the arithmetic # below. Unfortunately R and Splus don't share one. My "date" # class is simple, but is also one of the earlier date class # attempts, has less features than others, and will one day fade # away; so I don't want to depend on it alone. # cols <- match(c("age", "year"), atts$dimid) if (any(is.na(cols))) stop("Ratetable does not have expected shape") if (exists("as.Date")) { # true for modern version of R bdate <- as.Date('1960/1/1') + (R[,cols[2]] - R[,cols[1]]) byear <- format(bdate, "%Y") offset <- bdate - as.Date(paste(byear, "01/01", sep='/'), origin="1960/01/01") } #else if (exists('month.day.year')) { # Splus, usually # bdate <- R[,cols[2]] - R[,cols[1]] # byear <- month.day.year(bdate)$year # offset <- bdate - julian(1,1,byear) # } #else if (exists('date.mdy')) { # Therneau's date class is available # bdate <- as.date(R[,cols[2]] - R[,cols[1]]) # byear <- date.mdy(bdate)$year # offset <- bdate - mdy.date(1,1,byear) # } else stop("Can't find an appropriate date class\n") R[,cols[2]] <- R[,cols[2]] - offset # Doctor up "cutpoints" - only needed for old style rate tables # for which the C code does interpolation on the fly if (any(rfac >1)) { temp <- which(us.special) nyear <- length(cuts[[temp]]) nint <- rfac[temp] #intervals to interpolate over cuts[[temp]] <- round(approx(nint*(1:nyear), cuts[[temp]], nint:(nint*nyear))$y - .0001) } } docount <- is.Surv(Y) temp <- .C(Cpyears1, as.integer(n), as.integer(ncol(Y)), as.integer(is.Surv(Y)), as.double(Y), as.double(weights), as.integer(length(atts$dim)), as.integer(rfac), as.integer(atts$dim), as.double(unlist(cuts)), as.double(ratetable), as.double(R), as.integer(odim), as.integer(ofac), as.integer(odims), as.double(ocut), as.integer(expect=='event'), as.double(X), pyears=double(osize), pn =double(osize), pcount=double(if(docount) osize else 1), pexpect=double(osize), offtable=double(1))[18:22] } else { #no expected docount <- as.integer(ncol(Y) >1) temp <- .C(Cpyears2, as.integer(n), as.integer(ncol(Y)), as.integer(docount), as.double(Y), as.double(weights), as.integer(odim), as.integer(ofac), as.integer(odims), as.double(ocut), as.double(X), pyears=double(osize), pn =double(osize), pcount=double(if (docount) osize else 1), offtable=double(1)) [11:14] } has.tcut <- any(sapply(m, function(x) inherits(x, 'tcut'))) if (data.frame) { # Create a data frame as the output, rather than a set of # rate tables keep <- (temp$pyears >0) # what rows to keep in the output names(outdname) <- ovars if (length(outdname) ==1) { # if there is only one variable, the call to "do.call" loses # the variable name, since expand.grid returns a factor df <- data.frame((outdname[[1]])[keep], pyears= temp$pyears[keep]/scale, n = temp$pn[keep]) names(df) <- c(names(outdname), 'pyears', 'n') } else { df <- cbind(do.call("expand.grid", outdname)[keep,], pyears= temp$pyears[keep]/scale, n = temp$pn[keep]) } row.names(df) <- 1:nrow(df) if (has.ratetable) df$expected <- temp$pexpect[keep] if (expect=='pyears') df$expected <- df$expected/scale if (docount) df$event <- temp$pcount[keep] out <- list(call=Call, data= df, offtable=temp$offtable/scale, tcut=has.tcut) if (has.ratetable && !is.null(rtemp$summ)) out$summary <- rtemp$summ } else if (prod(odims) ==1) { #don't make it an array out <- list(call=Call, pyears=temp$pyears/scale, n=temp$pn, offtable=temp$offtable/scale, tcut = has.tcut) if (has.ratetable) { out$expected <- temp$pexpect if (expect=='pyears') out$expected <- out$expected/scale if (!is.null(rtemp$summ)) out$summary <- rtemp$summ } if (docount) out$event <- temp$pcount } else { out <- list(call = Call, pyears= array(temp$pyears/scale, dim=odims, dimnames=outdname), n = array(temp$pn, dim=odims, dimnames=outdname), offtable = temp$offtable/scale, tcut=has.tcut) if (has.ratetable) { out$expected <- array(temp$pexpect, dim=odims, dimnames=outdname) if (expect=='pyears') out$expected <- out$expected/scale if (!is.null(rtemp$summ)) out$summary <- rtemp$summ } if (docount) out$event <- array(temp$pcount, dim=odims, dimnames=outdname) } out$observations <- nrow(m) out$terms <- Terms na.action <- attr(m, "na.action") if (length(na.action)) out$na.action <- na.action if (model) out$model <- m else { if (x) out$x <- X if (y) out$y <- Y } class(out) <- 'pyears' out } survival/R/summary.survreg.S0000644000175100001440000000442213016105374015663 0ustar hornikusers# $Id: summary.survreg.S 11166 2008-11-24 22:10:34Z therneau $ summary.survreg<- function(object, correlation = FALSE,...) { if (!is.null(object$fail)) { warning(" Survreg failed.", object$fail, " No summary provided\n") return(invisible(object)) } nvar0 <- length(object$coefficients) nvar <- nrow(object$var) if (nvar > nvar0) { coef <- c(object$coefficients, log(object$scale)) if ( (nvar-nvar0)==1) cname <- c(names(object$coefficients), "Log(scale)") else cname <- c(names(object$coefficients), names(object$scale)) } else { coef <- object$coefficients cname <- names(object$coefficients) } n <- length(object$linear.predictors) p <- sum(!is.na(coef)) if(!p) { warning("This model has zero rank --- no summary is provided") return(invisible(object)) } if (is.null(object$naive.var)){ table <- matrix(rep(coef, 4), ncol = 4) dimnames(table) <- list(cname, c("Value", "Std. Error", "z", "p")) stds <- sqrt(diag(object$var)) table[, 2] <- stds table[, 3] <- table[, 1]/stds table[, 4] <- 2*pnorm(-abs(table[,3])) } else { table <- matrix(rep(coef, 5), ncol = 5) dimnames(table) <- list(cname, c("Value", "Std. Err","(Naive SE)", "z", "p")) stds <- sqrt(diag(object$var)) table[, 2] <- stds table[, 3] <- sqrt(diag(object$naive.var)) table[, 4] <- table[, 1]/stds table[, 5] <- 2*pnorm(-abs(table[,4])) } if(correlation) { nas <- is.na(coef) stds <- stds[!nas] correl <- diag(1/stds) %*% object$var[!nas, !nas] %*% diag(1/stds) dimnames(correl) <- list(cname, cname) } else correl <- NULL dist <- object$dist if (is.character(dist)) sd <- survreg.distributions[[dist]] else sd <- dist if (length(object$parms)) pprint<- paste(sd$name, 'distribution: parmameters=', object$parms) else pprint<- paste(sd$name, 'distribution') x <- object[match(c('call', 'df', 'loglik', 'iter', 'na.action', 'idf', 'scale', 'coefficients', 'var'), names(object), nomatch=0)] x <- c(x, list(table=table, correlation=correl, parms=pprint, n=n, chi=2*diff(object$loglik)), robust=!is.null(object$naive.var)) class(x) <- 'summary.survreg' x } survival/R/coxph.wtest.S0000644000175100001440000000252112113164602014752 0ustar hornikusers# # A Wald test routine, used by the Cox model # Why not just do sum(b * solve(var, b))? -- because the solve # function chokes on singular matrices. # coxph.wtest <- function(var, b, toler.chol=1e-9) { if (is.matrix(b)) { nvar <- nrow(b) ntest<- ncol(b) } else { nvar <- length(b) ntest<- 1 } if (length(var)==0) { #special case added by Tom Lumley if (nvar==0) return(list(test=numeric(0), df=0, solve=0)) else stop("Argument lengths do not match") } if (length(var)==1) { if (nvar ==1) return(list(test=b*b/var, df=1, solve=b/var)) else stop("Argument lengths do not match") } if (!is.matrix(var) || (nrow(var) != ncol(var))) stop("First argument must be a square matrix") if (nrow(var) != nvar) stop("Argument lengths do not match") temp <- .C(Ccoxph_wtest, df=as.integer(nvar), as.integer(ntest), as.double(var), tests= as.double(b), solve= double(nvar*ntest), as.double(toler.chol)) if (ntest==1) list(test=temp$tests[1], df=temp$df, solve=temp$solve) else list(test=temp$tests[1:ntest], df=temp$df, solve=matrix(temp$solve, nvar, ntest)) } survival/R/survcallback.S0000644000175100001440000001670711732700061015154 0ustar hornikusers# # This is common code for survpenal.fit and coxpenal.fit. # It's all the bookkeeping to set up the penalized callbacks # This code is in development, and not yet used by anything, the if(FALSE) # keeps it out of the distribution if(FALSE){ survcallback <- function(pcols, pattr, assign, x) { # # are there any sparse frailty terms? # npenal <- length(pattr) #total number of penalized terms if (npenal == 0 || length(pcols) != npenal) stop("Invalid pcols or pattr arg") sparse <- sapply(pattr, function(x) !is.null(x$sparse) && x$sparse) if (sum(sparse) >1) stop("Only one sparse penalty term allowed") # # Create a marking vector for the terms, the same length as assign # with pterms == 0=ordinary term, 1=penalized, 2=sparse, # pindex = length of pcols = position in pterms # # Make sure that pcols is a strict subset of assign, so that the # df computation (and printing) can unambiguously decide which cols of # X are penalized and which are not when doing "terms" like actions. # To make some downstream things easier, order pcols and pattr to be # in the same relative order as the terms in 'assign' # pterms <- rep(0, length(assign)) names(pterms) <- names(assign) pindex <- rep(0, npenal) for (i in 1:npenal) { temp <- unlist(lapply(assign, function(x,y) (length(x) == length(y) && all(x==y)), pcols[[i]])) if (sparse[i]) pterms[temp] <- 2 else pterms[temp] <- 1 pindex[i] <- (seq(along.with=temp))[temp] } if ((sum(pterms==2) != sum(sparse)) || (sum(pterms>0) != npenal)) stop("pcols and assign arguments disagree") if (any(pindex != sort(pindex))) { temp <- order(pindex) pindex <- pindex[temp] pcols <- pcols[temp] pattr <- pattr[temp] } # ptype= 1 or 3 if a sparse term exists, 2 or 3 if a non-sparse exists ptype <- any(sparse) + 2*(any(!sparse)) if (any(sparse)) { sparse.attr <- (pattr[sparse])[[1]] #can't use [[sparse]] directly # if 'sparse' is a T/F vector fcol <- unlist(pcols[sparse]) if (length(fcol) > 1) stop("Sparse term must be single column") # Remove the sparse term from the X matrix frailx <- x[, fcol] x <- x[, -fcol, drop=FALSE] for (i in 1:length(assign)){ j <- assign[[i]] if (j[1] > fcol) assign[[i]] <- j-1 } for (i in 1:npenal) { j <- pcols[[i]] if (j[1] > fcol) pcol[[i]] <- j-1 } frailx <- match(frailx, sort(unique(frailx))) nfrail <- max(frailx) nvar <- nvar - 1 #Set up the callback for the sparse frailty term # (At most one sparse term is allowed). The calling code will # first set 'coef' to the current value of the sparse coefficients, # then call the expression below. It uses a separate context (Splus # frame or R environment), so there is no conflict between that # variable name and the rest of the code. Thus, think of the below as # a funcion of the temporary variable coef (current value found # in the calling C code), theta1 (current value in the S code # below, using calls to cfun), and fixed known values of pfun1 etc. # The expression will constantly replace components of "coxlist1". By # creating it first, we assure the order of the components, again # to make it simpler for the C code (it can grab the first component # and know that that is 'coef', etc). # pfun1 <- sparse.attr$pfun coxlist1 <- list(coef=0, first=0, second=0, penalty=0, flag=F) f.expr1 <- quote({ if (is.null(extra1)) temp <- pfun1(coef1, theta1, n.eff) else temp <- pfun1(coef1, theta1, n.eff, extra1) if (!is.null(temp$recenter)) coxlist1$coef <- coef1 - as.double(temp$recenter) else coxlist1$coef <- coef1 if (!temp$flag) { coxlist1$first <- -as.double(temp$first) coxlist1$second <- as.double(temp$second) } else { coxlist1$first <- double(nfrail) coxlist1$second <- double(nfrail) } coxlist1$penalty <- -as.double(temp$penalty) coxlist1$flag <- as.logical(temp$flag) # Make sure the list has exactly the right structure, so # the the C code can be simple. The first line below is # probably unnecessary (belt AND suspenders); the second is # checking a possibly user-supplied penaly function if (any(names(coxlist1) != c('coef', 'first', 'second', 'penalty', 'flag'))) stop("Invalid coxlist1") if (any(sapply(coxlist1, length) != c(rep(nfrail,3), 1, 1))) stop("Incorrect length in coxlist1") coxlist1 }) } else { # no sparse terms frailx <- 0 nfrail <- 0 f.expr1 <- NULL #dummy value pfun1 <- NULL #dummy coxlist1 <- NULL # " } nvar2 <- nvar + nstrat2 if (nvar2 ==0) { # There are no non-sparse coefficients, and no scale parameters # A strange model, leading to an hmat with 0 columns. The # underlying C code will choke, since this case is not built in. stop("Cannot fit a model with no coefficients other than sparse ones") } # Now the non-sparse penalties # There can be multiple penalized terms if (sum(!sparse) >0) { full.imat <- !all(unlist(lapply(pattr, function(x) x$diag))) ipenal <- (1:length(pattr))[!sparse] #index for non-sparse terms if (full.imat) { coxlist2 <- list(coef=double(nvar), first=double(nvar), second= double(nvar^2), penalty=0.0, flag=rep(FALSE,nvar)) length2 <- c(nvar, nvar, nvar*nvar, 1, nvar) } else { coxlist2 <- list(coef=double(nvar), first=double(nvar), second=double(nvar), penalty= 0.0, flag=rep(FALSE,nvar)) length2 <- c(nvar, nvar, nvar, 1, nvar) } # The C code will set the variable coef, containing the concatonation # of all the non-sparse penalized coefs. Think of the below as # a function of coef (from the C code), thetalist (set further # below), and unchanging variables such as pattr. f.expr2 <- quote({ pentot <- 0 newcoef <- coef2 for (i in ipenal) { pen.col <- pcols[[i]] tcoef <- coef2[pen.col] if (is.null(extralist[[i]])) temp <- ((pattr[[i]])$pfun)(tcoef, thetalist[[i]], n.eff) else temp <- ((pattr[[i]])$pfun)(tcoef, thetalist[[i]], n.eff,extralist[[i]]) if (!is.null(temp$recenter)) newcoef[pen.col] <- tcoef - temp$recenter if (temp$flag) coxlist2$flag[pen.col] <- TRUE else { coxlist2$flag[pen.col] <- FALSE coxlist2$first[pen.col] <- -temp$first if (full.imat) { tmat <- matrix(coxlist2$second, nvar, nvar) tmat[pen.col,pen.col] <- temp$second coxlist2$second <- c(tmat) } else coxlist2$second[pen.col] <- temp$second } pentot <- pentot - temp$penalty } coxlist2$penalty <- as.double(pentot) coxlist2$coef <- newcoef if (any(sapply(coxlist2, length) != length2)) stop("Length error in coxlist2") coxlist2 }) } else { full.imat <- FALSE # no non-sparse penalties length2 <- 0 #dummy value f.expr2 <- NULL coxlist2 <- NULL ipenal <- NULL } list(f.expr1=f.expr1, f.expr2=f.expr2, coxlist1=coxlist1, coxlist2=coxlist2, full.imat=full.imat, ipenal=ipenal, length2=length2, pfun1=pfun1, pindex=pindex, pcols=pcols, pattr=pattr, sparse=sparse, frailx=frailx, nfrail=nfrail, nvar=nvar) } } survival/R/Surv.S0000644000175100001440000002501513065013161013426 0ustar hornikusers# # Package up surivival type data as a structure # Surv <- function(time, time2, event, type=c('right', 'left', 'interval', 'counting', 'interval2', "mstate"), origin=0) { if (missing(time)) stop ("Must have a time argument") if (inherits(time ,"difftime")) time <- unclass(time) if (!missing(time2) && class(time2)=="difftime") time2 <-as.numeric(time2) if (!is.numeric(time)) stop ("Time variable is not numeric") nn <- length(time) # ng = number of the first 3 arguments that are present ng <- (!missing(time)) + (!missing(time2)) + (!missing(event)) # The logic below uses "ng" throughout; why not use "missing(time2)" # and missing(event) instead? Because we want to assume that # "Surv(a,b)" has the variable b matched to event rather than time2. # mtype <- match.arg(type) # If type is missing or it is "mstate", I need to figure out for myself # whether I have (time, time2, status) or (time, status) data if (missing(type) || mtype=="mstate") { if (ng==1 || ng==2) type <- 'right' else if (ng==3) type <- 'counting' else stop ("No time variable!") # no time variable at all! } else { type <- mtype if (ng!=3 && (type=='interval' || type =='counting')) stop("Wrong number of args for this type of survival data") if (ng!=2 && (type=='right' || type=='left' || type=='interval2')) stop("Wrong number of args for this type of survival data") } if (ng==1) { # only a time variable given if (!is.numeric(time)) stop("Time variable is not numeric") ss <- cbind(time=time-origin, status=1) type <- "right" } else if (type=='right' || type=='left') { if (!is.numeric(time)) stop("Time variable is not numeric") if (missing(event)) { event <- time2 # treat time2 as event time2 <- NULL # force any inputAttributes to attach to "event" } if (length(event) != nn) stop ("Time and status are different lengths") if (mtype=="mstate" || (is.factor(event))) { mstat <- as.factor(event) status <- as.numeric(mstat) -1 type <- "mright" } else { if (is.logical(event)) status <- as.numeric(event) else if (is.numeric(event)) { who2 <- !is.na(event) if (max(event[who2]) ==2) status <- event -1 else status <- event temp <- (status==0 | status==1) status <- ifelse(temp, status, NA) if (!all(temp[who2], na.rm=TRUE)) warning("Invalid status value, converted to NA") } else stop("Invalid status value, must be logical or numeric") } ss <- cbind(time=time-origin, status=status) } else if (type=='counting') { if (length(time2) !=nn) stop ("Start and stop are different lengths") if (length(event)!=nn) stop ("Start and event are different lengths") if (!is.numeric(time)) stop("Start time is not numeric") if (!is.numeric(time2)) stop("Stop time is not numeric") temp <- (time >= time2) if (any(temp & !is.na(temp))) { time[temp] <- NA warning("Stop time must be > start time, NA created") } if (mtype=="mstate" || (is.factor(event) && length(levels(event))>2)) { mstat <- as.factor(event) status <- as.numeric(mstat) -1 type <- "mcounting" } else { if (is.logical(event)) status <- as.numeric(event) else if (is.numeric(event)) { who2 <- !is.na(event) if (max(event[who2])==2) status <- event - 1 else status <- event temp <- (status==0 | status==1) status <- ifelse(temp, status, NA) if (!all(temp[who2], na.rm=TRUE)) warning("Invalid status value, converted to NA") } else stop("Invalid status value") } ss <- cbind(start=time-origin, stop=time2-origin, status=status) } else { #interval censored data if (type=='interval2') { # convert to "interval" type, infer the event code if (!is.numeric(time2)) stop("Time2 must be numeric") if (length(time2) !=nn) stop ("time and time2 are different lengths") backwards <- (!is.na(time) & !is.na(time2) & time > time2) # allow for infinite times (important to do the backwards check # first) time <- ifelse(is.finite(time), time, NA) time2 <- ifelse(is.finite(time2), time2, NA) unknown <- (is.na(time) & is.na(time2)) status <- ifelse(is.na(time), 2, ifelse(is.na(time2), 0, ifelse(time==time2, 1,3))) time <- ifelse(status!=2, time, time2) if (any(backwards)) { warning("Invalid interval: start > stop, NA created") status[backwards] <- NA } if (any(unknown)) status[unknown] <- NA type <- 'interval' } else { #check legality of event code if (length(event)!=nn) stop("Time and status are different lengths") if (!is.numeric(event)) stop("Invalid status value, must be logical or numeric") temp <- (event==0 | event==1| event==2 | event==3) status <- ifelse(temp, event, NA) if (!all(temp, na.rm=TRUE)) warning("Status must be 0, 1, 2 or 3; converted to NA") if (any(event==3, na.rm=T)) { if (!is.numeric(time2)) stop("Time2 must be numeric") if (length(time2) !=nn) stop ("time and time2 are different lengths") temp <- (status==3 & time>time2) if (any(temp & !is.na(temp))) { status[temp] <- NA warning("Invalid interval: start > stop, NA created") } } else time2 <- 1 #dummy value, time2 is never used } ss <- cbind(time1=time-origin, time2=ifelse(!is.na(status) & status==3, time2-origin, 1), status=status) } # Retain any attributes of the input arguments. Originally requested # by the rms package inputAttributes <- list() if (!is.null(attributes(time))) inputAttributes$time <-attributes(time) if (!missing(time2) && !is.null(attributes(time2))) inputAttributes$time2 <- attributes(time2) if (!missing(event) && !is.null(attributes(event))) inputAttributes$event <- attributes(event) # In rare cases there are no column names, and I have discovered that # people depend on them. cname <- dimnames(ss)[[2]] if (length(cname) ==0) { if (ncol(ss)==2) cname <- c("time", "status") else if (type=="counting") cname <- c("start", "stop", "status") else cname <- c("time1", "time2", "status") } dimnames(ss) <- list(NULL, cname) #kill extraneous row names attr(ss, "type") <- type if (type=="mright" || type=="mcounting") { states <- levels(mstat)[-1] if (any(is.na(states) | states=='') ) stop("each state must have a non-blank name") attr(ss, "states") <- states } if (length(inputAttributes) > 0) attr(ss, "inputAttributes") <- inputAttributes class(ss) <- 'Surv' ss } print.Surv <- function(x, quote=FALSE, ...) { invisible(print(as.character.Surv(x), quote=quote, ...)) } as.character.Surv <- function(x, ...) { switch(attr(x, "type"), "right"={ temp <- x[,2] temp <- ifelse(is.na(temp), "?", ifelse(temp==0, "+"," ")) paste(format(x[,1]), temp, sep='') }, "counting"= { temp <- x[,3] temp <- ifelse(is.na(temp), "?", ifelse(temp==0, "+","")) paste('(', format(x[,1]), ',', format(x[,2]), temp, ']', sep='') }, "left" ={ temp <- x[,2] temp <- ifelse(is.na(temp), "?", ifelse(temp==0, "<"," ")) paste(temp, format(x[,1]), sep='') }, "interval"= { stat <- x[,3] temp <- c("+", "", "-", "]")[stat+1] temp2 <- ifelse(stat==3, paste("[", format(x[,1]), ", ",format(x[,2]), sep=''), format(x[,1])) ifelse(is.na(stat), "NA", paste(temp2, temp, sep='')) }, "mright" = { #multi-state temp <- x[,2] end <- c("+", paste(":", attr(x, "states"), sep='')) #endpoint temp <- ifelse(is.na(temp), "?", end[temp+1]) paste(format(x[,1]), temp, sep='') }, "mcounting"= { temp <- x[,3] end <- c("+", paste(":", attr(x, "states"), sep='')) #endpoint temp <- ifelse(is.na(temp), "?", end[temp+1]) paste('(', format(x[,1]), ',', format(x[,2]), temp, ']', sep='') }) } "[.Surv" <- function(x, i, j, drop=FALSE) { # If only 1 subscript is given, the result will still be a Surv object, # and the drop argument is ignored. # I would argue that x[3:4,,drop=FALSE] should return a matrix, since # the user has implicitly specified that they want a matrix. # However, [.dataframe calls [.Surv with the extra comma; its # behavior drives the choice of default. if (missing(j)) { xattr <- attributes(x) x <- unclass(x)[i,, drop=FALSE] # treat it as a matrix: handles dimnames attr(x, 'type') <- xattr$type if (!is.null(xattr$states)) attr(x, "states") <- xattr$states if (!is.null(xattr$inputAttributes)) { # If I see "names" subscript it, leave all else alone attr(x, 'inputAttributes') <- lapply(xattr$inputAttributes, function(z) { if (any(names(z)=="names")) z$names <- z$names[i] z }) } class(x) <- "Surv" #restore the class x } else { # return a matrix or vector class(x) <- 'matrix' NextMethod("[") } } is.na.Surv <- function(x) { as.vector(rowSums(is.na(unclass(x))) >0) } Math.Surv <- function(...) stop("Invalid operation on a survival time") Ops.Surv <- function(...) stop("Invalid operation on a survival time") Summary.Surv<-function(...) stop("Invalid operation on a survival time") is.Surv <- function(x) inherits(x, 'Surv') as.matrix.Surv <- function(x, ...) { y <- unclass(x) attr(y, "type") <- NULL attr(y, "states") <- NULL attr(y, "inputAttributes") <- NULL y } length.Surv <- function(x) nrow(x) format.Surv <- function(x, ...) format(as.character.Surv(x), ...) as.data.frame.Surv <- as.data.frame.model.matrix survival/R/cipoisson.R0000644000175100001440000000243013017026563014477 0ustar hornikuserscipoisson <- function(k, time=1, p=0.95, method=c('exact', 'anscombe')) { nn <- max(length(k), length(time), length(p)) if (nn>1) { k <- rep(k, length=nn) time <- rep(time, length=nn) p <- rep(p, length=nn) } p <- (1-p)/2 method <- match.arg(method) if (method=='exact') { dummy1 <- ifelse(k==0, 1, k) #avoid an error message of qgamma lower <- ifelse(k==0, 0, qgamma(p, dummy1)) upper <- qgamma(1-p, k+1) } else if (method=='anscombe'){ # anscombe's method upper <- (sqrt(k + 7/8) - qnorm(p)/2)^2 lower <- (sqrt(k - 1/8) + qnorm(p)/2)^2 } else stop("Invalid method") # The summary.pyears routine sometimes calls this with time=0 if (any(time<=0)) { lower <- ifelse(time<=0, NA, lower) upper <- ifelse(time<=0, NA, upper) } if (nn==1) c(lower=lower, upper=upper)/time else { temp <- cbind(lower=lower, upper=upper)/time if (is.array(k)) { if (is.null(dd <- dimnames(k))) array(temp, dim=c(dim(k), 2), dimnames=list(NULL, NULL, c("lower", "upper"))) else array(temp, dim=c(dim(k), 2), dimnames=list(dd, c("lower", "upper"))) } else temp } } survival/R/is.na.coxph.penalty.S0000644000175100001440000000216211732700061016271 0ustar hornikusers# $Id: is.na.coxph.penalty.S 11447 2010-11-12 15:10:18Z therneau $ # The subscript function for coxph.penalty objects # without it the "subset" arg of a model statement tosses # away all of the attributes # "[.coxph.penalty" <- function(x, ..., drop=FALSE) { attlist <- attributes(x) attributes(x) <- attlist[match(c('dim', 'dimnames', 'levels', 'class'), names(attlist), 0)] x <- NextMethod('[') #let the default method do actual subscripting # Tack back on all of the old attributes, except dim and dimnames # which will have been properly modified by the standard [ method, # "levels" which may have dropped some, and "class" which is special attributes(x) <- c(attributes(x), attlist[is.na(match(names(attlist), c("dim", "dimnames", "levels", "class")))]) # The class will have lost it's first level oldClass(x) <- attlist$class return(x) } is.na.coxph.penalty <- function(x) { if (is.matrix(x)) is.na(c(unclass(x) %*% rep(1,ncol(x)))) else is.na(unclass(x)) } survival/R/neardate.R0000644000175100001440000000551412650522315014260 0ustar hornikusers# Create a "nearest date" index # date1: the trial date # date2: target to match to # # result: an index vector for data set 1, which shows the row in data set # 2 that has the same id, and the best date. # # best = "after" The closest date in #2 that is on or after the date in #1 # "prior" The closest date in #2 that is on or before the date in #1 # neardate <- function(id1, id2, y1, y2, best=c("after", "prior"), nomatch=NA_integer_) { if (missing(id1)) stop("id1 argument is required") if (missing(id2)) stop("id2 argument is required") if (missing(y1)) stop("y1 argument is required") if (missing(y2)) stop("y2 argument is required") if (length(id1) != length(y1)) stop("id1 and y1 have different lengths") if (length(id2) != length(y2)) stop("id2 and y2 have different lengths") best <- match.arg(best) # This check could be more sophisticated (though I don't see how to do it) # We want to make sure that the "alldate" line below makes sense for the # data types that the user passed in. if (is.factor(y1) || is.factor(y2)) stop("y1 and y2 must be sortable") if (inherits(y1, 'POSIXt')) if (!inherits(y2, 'POSIXt')) y2 <- as(y2, class(y1)) else if (inherits(y2, 'POSIXt')) y1 <- as(y1, class(y2)) alldate <- sort(unique(c(y1, y2))) y1 <- match(y1, alldate) y2 <- match(y2, alldate) # Throw out lines with missing y2, but remember which ones rowid <- 1:length(y2) if (any(is.na(y2))) { toss <- is.na(y2) y2 <- y2[!toss] if (!missing(id2)) id2 <- id2[!toss] rowid <- rowid[!toss] } n2 <- length(y2) if (n2 ==0) stop("No valid entries in data set 2") # Toss out any rows in id2 that are not possible targets for id1 # (id2 is usually the larger data set, thinning speeds it up) indx1 <- match(id2, id1) toss <- is.na(indx1) if (any(toss)) { id2 <- id2[!toss] y2 <- y2[!toss] indx1 <- indx1[!toss] rowid <- rowid[!toss] } n2 <- length(y2) if (n2 ==0) stop("No valid entries in data set 2") # We need to create a merging id. A minimal amount of # spread for the dates keeps numeric overflow at bay delta <- 1.0 + length(alldate) #numeric, not integer, on purpose hash1 <- match(id1, id1)*delta + y1 hash2 <- indx1*delta + y2 if (best=="prior") indx2 <- approx(hash2, 1:n2, hash1, method="constant", yleft=NA, rule=2, f=0)$y else indx2 <- approx(hash2, 1:n2, hash1, method="constant", yright=NA, rule=2, f=1)$y temp <- (!is.na(indx2) & id1== id2[indx2]) ifelse(temp, rowid[ifelse(is.na(indx2), 1, indx2)], nomatch) } survival/R/survfitCI.R0000644000175100001440000003242113065013246014407 0ustar hornikusers# Automatically generated from the noweb directory docurve2 <- function(entry, etime, status, istate, wt, states, id, se.fit, influence=FALSE) { timeset <- sort(unique(etime)) nstate <- length(states) uid <- sort(unique(id)) index <- match(id, uid) first <- match(uid, id) # first row for each subject cstate <- istate[first] # The influence matrix can be huge, make sure we have enough memory if (influence) { needed <- nstate * (1.0 + length(timeset)) * length(first) if (needed > .Machine$integer.max) stop("length of the influence matrix is > the maximum integer") } storage.mode(wt) <- "double" # just in case someone had integer weights # Compute p0 if (all(status==0)) t0 <- max(etime) #failsafe else t0 <- min(etime[status!=0]) # first transition event at.zero <- (entry < t0 & etime >= t0) wtsum <- sum(wt[at.zero]) # weights for a subject may change p0 <- tapply(wt[at.zero], factor(istate[at.zero], levels=states), sum) / wtsum p0 <- ifelse(is.na(p0), 0, p0) #for a state not in at.zero, tapply gives NA # initial leverage matrix nid <- length(uid) i0 <- matrix(0., nid, nstate) if (all(p0 <1)) { #actually have to compute it who <- index[at.zero] # this will have no duplicates for (j in 1:nstate) i0[who,j] <- (ifelse(istate[at.zero]==j, 1, 0) - p0[j])/wtsum } storage.mode(cstate) <- "integer" storage.mode(status) <- "integer" # C code has 0 based subscripts if (influence) se.fit <- TRUE # se.fit is free in this case fit <- .Call(Csurvfitci, c(entry, etime), order(entry) - 1L, order(etime) - 1L, length(timeset), status, cstate - 1L, wt, index -1L, p0, i0, as.integer(se.fit) + 2L*as.integer(influence)) if (se.fit) out <- list(n=length(etime), time= timeset, p0 = p0, sp0= sqrt(colSums(i0^2)), pstate = fit$p, std.err=fit$std, n.risk = fit$nrisk, n.event= fit$nevent, n.censor=fit$ncensor, cumhaz=array(fit$cumhaz, dim=c(nstate, nstate, length(timeset)))) else out <- list(n=length(etime), time= timeset, p0=p0, pstate = fit$p, n.risk = fit$nrisk, n.event = fit$nevent, n.censor= fit$ncensor, cumhaz=array(fit$cumhaz, dim=c(nstate, nstate, length(timeset)))) if (influence) { temp <- array(fit$influence, dim=c(length(uid), nstate, 1+ length(timeset)), dimnames=list(uid, NULL, NULL)) out$influence <- aperm(temp, c(1,3,2)) } out } survfitCI <- function(X, Y, weights, id, istate, type=c('kaplan-meier', 'fleming-harrington', 'fh2'), se.fit=TRUE, conf.int= .95, conf.type=c('log', 'log-log', 'plain', 'none'), conf.lower=c('usual', 'peto', 'modified'), influence = FALSE, start.time){ method <- match.arg(type) # error <- match.arg(error) # if (error != "inf") # warning("Only the infinetesimal jackknife error is supported for CI curves") conf.type <- match.arg(conf.type) conf.lower<- match.arg(conf.lower) if (is.logical(conf.int)) { # A common error is for users to use "conf.int = FALSE" # it's illegal per documentation, but be kind if (!conf.int) conf.type <- "none" conf.int <- .95 } type <- attr(Y, "type") # This line should be unreachable, unless they call "surfitCI" if (type !='mright' && type!='mcounting') stop(paste("multi-state computation doesn't support \"", type, "\" survival data", sep='')) # If there is a start.time directive, start by removing those observations if (!missing(start.time)) { if (!is.numeric(start.time) || length(start.time) !=1 || !is.finite(start.time)) stop("start.time must be a single numeric value") toss <- which(Y[,ncol(Y)] <= start.time) if (length(toss)) { n <- nrow(Y) Y <- Y[-toss,,drop=FALSE] X <- X[-toss] weights <- weights[-toss] if (length(id) ==n) id <- id[-toss] if (!missing(istate) && length(istate)==n) istate <- istate[-toss] } } n <- nrow(Y) status <- Y[,ncol(Y)] ncurve <- length(levels(X)) state.names <- attr(Y, "states") nstate <- length(state.names) has.istate <- !missing(istate) if (missing(istate) || is.null(istate)) { istate <- rep(nstate+ 1L, n) state.names <- c(state.names, "") } else { if (is.factor(istate) || is.character(istate)) { # Match levels with the survival variable temp <- as.factor(istate) # append any starting states not found in Y, but remember that # if istate was a factor then not all its levels might appear appear <- (levels(temp))[unique(as.numeric(temp))] state.names <- unique(c(attr(Y, "states"), appear)) istate <- as.numeric(factor(as.character(temp), levels=state.names)) } else { if (!is.numeric(istate) || any(istate != floor(istate)) || any(istate < 1)) stop("istate should be a vector of positive integers or a factor") if (max(istate) > nstate) state.names <- c(state.names, (1+nstate):max(istate)) } } if (length(id) ==0) id <- 1:n # these next two lines should be impossible, since istate came from # the data frame if (length(istate) ==1) istate <- rep(istate,n) if (length(istate) !=n) stop ("wrong length for istate") # The states of the status variable are the first columns in the output states <- unique(c(1:nstate, istate)) curves <- vector("list", ncurve) names(curves) <- levels(X) if (ncol(Y)==2) { # 1 transition per subject indx <- which(status == istate & status!=0) if (length(indx)) { warning("an observation transitions to it's starting state, transition ignored") status[indx] <- 0 } if (length(id) && any(duplicated(id))) stop("Cannot have duplicate id values with (time, status) data") # make a table of transitions. Variable 'from' can range across # all of the states, 'to' can only have nstate categories nst <- length(state.names) transitions <- table(factor(istate, 1:nst), factor(Y[,2], 1:nstate)) dimnames(transitions) <-list(from=state.names, to=state.names[1:nstate]) # dummy entry time that is < any event time t0 <- min(0, Y[,1]) entry <- rep(t0-1, nrow(Y)) for (i in levels(X)) { indx <- which(X==i) curves[[i]] <- docurve2(entry[indx], Y[indx,1], status[indx], istate[indx], weights[indx], states, id[indx], se.fit) } } else { if (missing(id) || is.null(id)) stop("the id argument is required for start:stop data") indx <- order(id, Y[,2]) #ordered event times within subject indx1 <- indx[-length(indx)] #a pair of lagged indices indx2 <- indx[-1] #if indx1[5] == index2[5] that means that the 5th and 6th are the same id same <- (id[indx1] == id[indx2]) if (any(same & X[indx1] != X[indx2])) { who <- min(which(same & X[indx1] != X[indx2])) stop("subject is in two different groups, id ", id[indx1[who]]) } if (any(same & Y[indx1,2] != Y[indx2,1])) { who <- min(which(same & Y[indx1,2] != Y[indx2,1])) stop("gap in follow-up, id ", id[indx1[who]]) } if (any(Y[,1] == Y[,2])) stop("cannot have start time == stop time") if (any(same & (Y[indx1,3] == Y[indx2,3]) & (Y[indx1,3] !=0))) { who <- min(which(same & (Y[indx1,3] == Y[indx2,3]) & (Y[indx1,3] !=0))) warning("subject changes to the same state, id ", id[indx1[who]]) } # Make the table of transitions nst <- length(state.names) first <- indx[!duplicated(id[indx])] transitions <- table(factor(istate[first], 1:nst), factor(Y[first,3], 1:nstate)) if (any(same)) transitions <- transitions + table(factor(Y[indx1[same],3], 1:nst), factor(Y[indx2[same],3], 1:nstate)) dimnames(transitions) = list(from=state.names, to=state.names[1:nstate]) # We only want to pay attention to the istate variable for the very first # observation of any given subject, but the program logic does better with # a full one. So construct one that will do this indx <- order(Y[,2]) uid <- unique(id) temp <- (istate[indx])[match(uid, id[indx])] #first istate for each subject istate <- temp[match(id, uid)] #replicate it to full length # Now to work for (i in levels(X)) { indx <- which(X==i) # temp <- docurve1(Y[indx,1], Y[indx,2], status[indx], # istate[indx], weights[indx], states, id[indx]) curves[[i]] <- docurve2(Y[indx,1], Y[indx,2], status[indx], istate[indx], weights[indx], states, id[indx], se.fit, influence) } } # Turn the result into a survfit type object grabit <- function(clist, element) { temp <-(clist[[1]][[element]]) if (is.matrix(temp)) { do.call("rbind", lapply(clist, function(x) x[[element]])) } else { xx <- as.vector(unlist(lapply(clist, function(x) x[element]))) if (class(temp)=="table") matrix(xx, byrow=T, ncol=length(temp)) else xx } } if (length(curves) ==1) { keep <- c("n", "time", "n.risk", "n.event", "n.censor", "pstate", "p0", "cumhaz", "influence") if (se.fit) keep <- c(keep, "std.err", "sp0") kfit <- (curves[[1]])[match(keep, names(curves[[1]]), nomatch=0)] names(kfit$p0) <- state.names } else { kfit <- list(n = as.vector(table(X)), #give it labels time = grabit(curves, "time"), n.risk= grabit(curves, "n.risk"), n.event= grabit(curves, "n.event"), n.censor=grabit(curves, "n.censor"), pstate = grabit(curves, "pstate"), p0 = grabit(curves, "p0"), transitions = transitions, strata= unlist(lapply(curves, function(x) length(x$time)))) kfit$p0 <- matrix(kfit$p0, ncol=nst, byrow=TRUE, dimnames=list(names(curves), state.names)) if (se.fit) { kfit$std.err <- grabit(curves, "std.err") kfit$sp0<- matrix(grabit(curves, "sp0"), ncol=nst, byrow=TRUE) } kfit$cumhaz <- array(unlist(lapply(curves, function(x) x$cumhaz)), dim=c(nst, nst, length(kfit$time))) if (influence) kfit$influence <- lapply(curves, function(x) x$influence) if (!missing(start.time)) kfit$start.time <- start.time } kfit$transitions <- transitions # # Last bit: add in the confidence bands: # modeled on survfit.km, though for P instead of S # # if (se.fit) { std.err <- kfit$std.err zval <- qnorm(1- (1-conf.int)/2, 0,1) if (conf.type=='plain') { temp <- zval* kfit$std.err kfit <- c(kfit, list(lower =pmax(kfit$pstate-temp, 0), upper=pmin(kfit$pstate+temp, 1), conf.type='plain', conf.int=conf.int)) } if (conf.type=='log') { #avoid some "log(0)" messages xx <- ifelse(kfit$pstate==1, 1, 1- kfit$pstate) temp1 <- ifelse(kfit$pstate==1, NA, exp(log(xx) + zval* kfit$std.err/xx)) temp2 <- ifelse(kfit$pstate==1, NA, exp(log(xx) - zval* kfit$std.err/xx)) kfit <- c(kfit, list(lower=pmax(1-temp1,0), upper= 1- temp2, conf.type='log', conf.int=conf.int)) } if (conf.type=='log-log') { who <- (kfit$pstate==0 | kfit$pstate==1) #special cases temp3 <- ifelse(kfit$pstate==1, NA, 1) xx <- ifelse(who, .1,kfit$pstate) #avoid some "log(0)" messages temp1 <- exp(-exp(log(-log(xx)) + zval*kfit$std.err/(xx*log(xx)))) temp1 <- ifelse(who, temp3, temp1) temp2 <- exp(-exp(log(-log(xx)) - zval*kfit$std.err/(xx*log(xx)))) temp2 <- ifelse(who, temp3, temp2) kfit <- c(kfit, list(lower=1-temp1, upper=1-temp2, conf.type='log-log', conf.int=conf.int)) } } kfit$states <- state.names kfit$type <- attr(Y, "type") kfit } survival/R/quantile.survfit.R0000644000175100001440000001562712703163037016027 0ustar hornikusers# # quantile function for survfit objects # # First a little function to find quantiles in a CDF # curve. It would be a trivial use of approx, except that # once in a while the survival curve has a flat spot exactly # at the requested quantile. Then we use the median of the # flat. findq <- function(x, y, p, tol) { # This case occurs for a survival curve whose upper limit never drops below 1 if (max(y, na.rm=T) < min(p)) return(rep(NA, length(p))) # Remove duplicate y values, i.e., the censors, since dups cause # issues for approx xmax <- x[length(x)] dups <- duplicated(y) if (any(dups)) { x <- x[!dups] y <- y[!dups] } n <- length(y) # quantile = where a horzontal line at p intercects the curve. At each # x the curve of 1-y jumps up to a new level # The most work is to check for horizontal lines in the survival # curve that match one of our quantiles within tolerance. If any # p matches, then our quantile is the average of the given x and # the x value of the next jump point, i.e., the usual midpoint rule # used for medians. # A flat at the end of the curve is a special case, as is the quantile # of 0. indx1 <- approx(y+tol, 1:n, p, method="constant", f=1)$y indx2 <- approx(y-tol, 1:n, p, method="constant", f=1)$y quant <- (x[indx1] + x[indx2])/2 quant[p==0] <- x[1] if (!is.na(y[n])) { lastpt <- (abs(p- y[n]) < tol) # end of the curve if (any(lastpt)) quant[lastpt] <- (x[indx1[lastpt]] + xmax)/2 } quant } doquant <- function(p, time, surv, upper, lower, firstx, tol) { qq <- findq(c(firstx,time), c(0, 1-surv), p, tol) # browser() if (missing(upper)) qq else rbind(qq, findq(c(firstx, time), c(0, 1-lower), p, tol), findq(c(firstx, time), c(0, 1-upper), p, tol)) } quantile.survfit <- function(x, probs=c(.25, .5, .75), conf.int=TRUE, tolerance= sqrt(.Machine$double.eps), ...) { if (!inherits(x, "survfit")) stop("Must be a survfit object") if (any(!is.numeric(probs)) || any(is.na(probs))) stop("invalid probability") if (any(probs <0 | probs >1)) stop("Invalid probability") if (is.null(x$lower)) conf.int <- FALSE nprob <- length(probs) pname <- format(probs*100) # What do we report for p=0? Use x$start.time if it exists, 0 otherwise xmin <- if (is.null(x$start.time)) 0 else x$start.time # There are 8 cases: strata yes/no # ncol(x$surv) =1 or >1 # conf.int = T/F if (is.null(x$strata)) { if (is.matrix(x$surv) && ncol(x$surv) >1) { qmat <- matrix(0., ncol=nprob, nrow=ncol(x$surv)) dimnames(qmat) <- list(dimnames(x$surv)[[2]], pname) if (conf.int) { qupper <- qlower <- qmat for (i in 1:ncol(x$surv)) { temp <- doquant(probs, x$time, x$surv[,i], x$upper[,i], x$lower[,i], xmin, tolerance) qmat[i,] <- temp[1,] qupper[i,] <- temp[3,] qlower[i,] <- temp[2,] } return(list(quantile=qmat, lower=qlower, upper=qupper)) } else { for (i in 1:ncol(x$surv)) qmat[i,] <- doquant(probs, x$time, x$surv[,i], firstx=xmin, tol=tolerance) return(qmat) } } else { # No strata and no matrix if (conf.int) { temp <- doquant(probs, x$time, x$surv, x$upper, x$lower, xmin, tolerance) dimnames(temp) <- list(NULL, pname) return(list(quantile=temp[1,], lower=temp[2,], upper=temp[3,])) } else { temp <- doquant(probs, x$time, x$surv, firstx=xmin, tol =tolerance) names(temp) <- pname return(temp) } } } else { nstrat <- length(x$strata) if (is.matrix(x$surv) && ncol(x$surv) >1) { # uncommon case, e.g., predicted survivals from a Cox model # return an array with strata as the first dimension, and # the probabilites as the third. qmat <- array(0., dim=c(nstrat, ncol(x$surv), nprob)) dimnames(qmat) <-list(names(x$strata), dimnames(x$surv)[[2]], pname) if (conf.int) { qupper <- qlower <- qmat for (strat in 1:nstrat) { z <- x[strat,] for (i in 1:ncol(z$surv)) { temp <- doquant(probs, z$time, z$surv[,i], z$upper[,i], z$lower[,i], xmin,tolerance) qmat[strat,i,] <- temp[1,] qupper[strat,i,] <- temp[3,] qlower[strat,i,] <- temp[2,] } } return(list(quantile=qmat, lower=qlower, upper=qupper)) } else { for (strat in 1:nstrat) { z <- x[strat] for (i in 1:ncol(z$surv)) qmat[strat,i,] <- doquant(probs, z$time, z$surv[,i], firstx=xmin, tol=tolerance) } return(qmat) } } else { # Only a strata, the most common case qmat <- matrix(0., nstrat, nprob) dimnames(qmat) <- list(names(x$strata), pname) if (conf.int) { qupper <- qlower <- qmat for (i in 1:nstrat) { z <- x[i] temp <- doquant(probs, z$time, z$surv, z$upper, z$lower, xmin, tolerance) qmat[i,] <- temp[1,] qupper[i,] <- temp[3,] qlower[i,] <- temp[2,] } return(list(quantile=qmat, lower=qlower, upper=qupper)) } else { for (i in 1:nstrat) { z <- x[i] qmat[i,] <- doquant(probs, z$time, z$surv, firstx=xmin, tol = tolerance) } return(qmat) } } } } # Why can't I just fudge the object and call quantile.survfit? Because # the code below uses subscripted objects, and the class of the chimeric # object doesn't work out for that operation. But more importantly, # I don't know how a quantile would be defined. # quantile.survfitms <- function(x, probs=c(.25, .5, .75), conf.int=TRUE, tolerance= sqrt(.Machine$double.eps), ...) { stop("quantiles are not a well defined quantity for multi-state models") } survival/R/ratetable.S0000644000175100001440000001144713016105374014442 0ustar hornikusers# # This source file has two distinct parts in it. The first is the # ratetable(), which is used inside pyears and survexp only to allow # users to match the names of variables in their data set to the names # of the dimensions in a ratetable. It returns a matrix with one # column for each argument; usually that argument will be a vector but # may also be a single constant. The result has a class "ratetable2", # whose only purpose is to allow na.action functions to work properly. # # The second part of the file are the methods for actual rate tables, like # the table of US survival rates by age and sex (survexp.us). Rate tables # have the "ratetable" class. However, since each one is rather unique, # there is no function to create a rate table. Each consists of a multi-way # array of event rates along with a set of attributes. # # The ideal for this function would be # ratetable <- function(...) data.frame(...) # Then missing, subsets, etc would all be fine, yet the variables would still # be special in the terms result so I could find them. But -- the only # multi-column objects that model.frame will accept are matrices. So I # make a data frame (both factors and numerics) that looks like a matrix. # ratetable <- function(...) { args <- list(...) nargs <- length(args) ll <- sapply(args, length) n <- max(ll) # We assume this is the dimension of the user's data frame levlist <- vector("list", nargs) isDate <- rep(FALSE, nargs) x <- matrix(0,n,nargs) dimnames(x) <- list(1:n, names(args)) for (i in 1:nargs) { if (ll[i] ==1) args[[i]] <- rep(args[[i]], n) else if (ll[i] != n) stop(paste("Aguments do not all have the same length (arg ", i, ")", sep='')) # In Splus cut and tcut produce class 'category' if (inherits(args[[i]], 'cateogory') || is.character(args[[i]])) args[[i]] <- as.factor(args[[i]]) if (is.factor(args[[i]])) { levlist[[i]] <- levels(args[[i]]) x[,i] <- as.numeric(args[[i]]) # the vector of levels } else { temp <- ratetableDate(args[[i]]) if (is.null(temp)) x[,i] <- as.numeric(args[[i]]) else { x[,i] <- temp isDate[i] <- TRUE } } } attr(x, "isDate") <- isDate attr(x, "levlist") <- levlist class(x) <- 'ratetable2' x } # The two functions below should only be called internally, when missing # values cause model.frame to drop some rows is.na.ratetable2 <- function(x) { attributes(x) <- list(dim=dim(x)) as.vector((1 * is.na(x)) %*% rep(1, ncol(x)) >0) } "[.ratetable2" <- function(x, rows, cols, drop=FALSE) { if (!missing(cols)) { stop("This should never be called!") } aa <- attributes(x) attributes(x) <- aa[c("dim", "dimnames")] y <- x[rows,,drop=FALSE] attr(y,'isDate') <- aa$isDate attr(y,'levlist') <- aa$levlist class(y) <- 'ratetable2' y } # # Functions to manipulate rate tables # "[.ratetable" <- function(x, ..., drop=TRUE) { aa <- attributes(x) attributes(x) <- aa[c("dim", "dimnames")] y <- NextMethod("[", drop=FALSE) newdim <- attr(y, 'dim') if (is.null(newdim)) return(y) #when the subscript was a single vector dropped <- (newdim==1) if (drop) change <- (newdim!=aa$dim & !dropped) else change <- (newdim!=aa$dim) if (any(change)) { #dims that got smaller, but not dropped newcut <- aa$cutpoints for (i in (1:length(change))[change]) if (!is.null(newcut[[i]])) newcut[[i]] <- (newcut[[i]])[match(dimnames(y)[[i]], aa$dimnames[[i]])] aa$cutpoints <- newcut } if (drop && any(dropped)){ if (all(dropped)) as.numeric(y) #single element else { #Note that we have to drop the summary function attributes(y) <- list( dim = dim(y)[!dropped], dimnames = dimnames(y)[!dropped], dimid = aa$dimid[!dropped], factor = aa$factor[!dropped], cutpoints =aa$cutpoints[!dropped], type = aa$type[!dropped]) class(y) <- 'ratetable' y } } else { aa$dim <- aa$dimnames <- NULL attributes(y) <- c(attributes(y), aa) y } } is.na.ratetable <- function(x) structure(is.na(as.vector(x)), dim=dim(x), dimnames=dimnames(x)) Math.ratetable <- function(x, ...) { attributes(x) <- attributes(x)[c("dim", "dimnames")] NextMethod(.Generic) } Ops.ratetable <- function(e1, e2) { #just treat it as an array if (nchar(.Method[1])) attributes(e1) <- attributes(e1)[c("dim","dimnames")] if (nchar(.Method[2])) attributes(e2) <- attributes(e2)[c("dim","dimnames")] NextMethod(.Generic) } as.matrix.ratetable <- function(x, ...) { attributes(x) <- attributes(x)[c("dim", "dimnames")] x } survival/R/cluster.S0000644000175100001440000000012011732700061014137 0ustar hornikusers# $Id: cluster.S 11166 2008-11-24 22:10:34Z therneau $ cluster <- function(x) x survival/R/aareg.taper.S0000644000175100001440000000223211732700061014655 0ustar hornikusers# SCCS $Id: aareg.taper.S 11166 2008-11-24 22:10:34Z therneau $ # # Do running averages of an information matrix # aareg.taper <- function(taper, imat, nevent) { dd <- dim(imat) if (length(taper)==0 || !is.numeric(taper) || any(taper <=0)) stop("Invalid taper vector") ntaper <- length(taper) ntime <- dd[3] if (ntaper > ntime) { taper <- taper[1:ntime] ntaper <- ntime } # # Turn imat into an array: 1 row per coef, one col per time # and then scale it by the number of events to get a variance # (coxph.detail returns imat = var(X) * nevents) # imat <- matrix(as.vector(imat), ncol=dd[3]) imat <- imat / rep(nevent, rep(dd[1]*dd[2], dd[3])) if (ntaper >1) { smoother <- matrix(0., ntime, ntime) tsum <- cumsum(rev(taper)) for (i in 1:ntaper) smoother[1:i, i] <- taper[seq(to=ntaper, length=i)]/tsum[i] if (ntaper < ntime) { for (i in (ntaper+1):ntime) smoother[seq(to=i, length=ntaper),i] <- taper/tsum[ntaper] } imat <- imat %*% smoother } array(imat, dim=dd) } survival/R/coxexact.fit.R0000644000175100001440000001024612504525636015101 0ustar hornikusers# This routine fits right censored data when the method is # "exact". The most common use for this option is matched # case-control data. coxexact.fit <- function(x, y, strata, offset, init, control, weights, method, rownames) { if (!is.matrix(x)) stop("Invalid formula for cox fitting function") if (!is.null(weights) && any(weights!=1)) stop("Case weights are not supported for the exact method") n <- nrow(x) nvar <- ncol(x) # The risk set addition in the C-code, which is the critically slow # part of the calculations, expects to have the data in sorted order: # (large to small times) within strata if (length(strata)==0) { sorted <- order(-y[,1]) newstrat <- as.integer(rep(0,n)) } else { sorted <- order(strata, -y[,1]) strata <- (as.numeric(strata))[sorted] newstrat <- as.integer(c(1, 1*(diff(strata)!=0))) } y <- y[sorted,] if (is.null(offset)) offset <- rep(0.,n) else offset <- offset[sorted] if (nvar==0) { # A special case: Null model. Trick the C code, which requires # at least one variable, by creating one and then doing 0 # iterations at beta=0 x <- matrix(1:n, ncol=1) init <- NULL maxiter <- 0 nullmodel <- TRUE nvar <- 1 } else { maxiter <- control$iter.max nullmodel <- FALSE } if (!is.null(init)) { if (length(init) != nvar) stop("Wrong length for inital values") } else init <- rep(0.,nvar) # Prescale the data set to improve numerical accuracy. # We will undo the scaling before finishing up. newx <- scale(x[sorted,]) # newx <- scale(x, scale=NULL) #debug rescale <- attr(newx, "scaled:scale") means <- attr(newx, "scaled:center") cfit <- .Call(Ccoxexact, as.integer(maxiter), as.double(y), # interger data? Just in case. newx, as.double(offset), as.integer(newstrat), as.double(init*rescale), as.double(control$eps), as.double(control$toler.chol) ) if (nullmodel) { score <- exp(offset[sorted]) cxres <- .C(Ccoxmart2, as.integer(n), as.double(y[,1]), as.integer(y[,2]), newstrat, score, rep(1.0, n), #weights resid=double(n)) resid <- double(n) resid[sorted] <- cxres$resid names(resid) <- rownames return( list(loglik = cfit$loglik[1], linear.predictors = offset, residuals = resid, method= c("coxph.null", "coxph"))) } loglik <- cfit$loglik[1:2] #these are packed into one vector sctest <- cfit$loglik[3] iter <- cfit$loglik[5] flag <- cfit$loglik[4] var <- matrix(cfit$imat,nvar,nvar) coef <- cfit$coef if (flag < nvar) which.sing <- diag(var)==0 else which.sing <- rep(FALSE,nvar) infs <- abs(cfit$u %*% var) if (control$iter.max >1) { if (flag == 1000) warning("Ran out of iterations and did not converge") else { infs <- ((infs > control$eps) & infs > control$toler.inf*abs(coef)) if (any(infs)) warning(paste("Loglik converged before variable ", paste((1:nvar)[infs],collapse=","), "; beta may be infinite. ")) } } names(coef) <- dimnames(x)[[2]] lp <- newx %*% coef + offset score <- as.double(exp(lp)) # Compute the residuals cxres <- .C(Ccoxmart2, as.integer(n), as.double(y[,1]), as.integer(y[,2]), newstrat, score, rep(1.0, n), #weights resid=double(n)) resid <- double(n) resid[sorted] <- cxres$resid names(resid) <- rownames coef[which.sing] <- NA lp.unsort <- double(n) lp.unsort[sorted] <- lp scmat <- diag(1/rescale, nvar,nvar) list(coefficients = coef/rescale, var = scmat %*% var %*% scmat, loglik = loglik, score = sctest, iter = iter, linear.predictors = lp.unsort, residuals = resid, means = means, method= 'coxph') } survival/R/anova.coxph.R0000644000175100001440000001107412714071414014717 0ustar hornikusers# The anova function for a coxph object anova.coxph <- function (object, ..., test = 'Chisq') { if (!inherits(object, "coxph")) stop ("argument must be a cox model") # All the ... args need to be coxph or coxme fits. If any of them # have a name attached, e.g., 'charlie=T' we assume a priori # that they are illegal # dotargs <- list(...) named <- if (is.null(names(dotargs))) rep(FALSE, length(dotargs)) else (names(dotargs) != "") if (any(named)) warning(paste("The following arguments to anova.coxph(..)", "are invalid and dropped:", paste(deparse(dotargs[named]), collapse = ", "))) dotargs <- dotargs[!named] if (length(dotargs) >0) { # Check that they are all cox or coxme models is.coxmodel <-unlist(lapply(dotargs, function(x) inherits(x, "coxph"))) is.coxme <- unlist(lapply(dotargs, function(x) inherits(x, "coxme"))) if (!all(is.coxmodel | is.coxme)) stop("All arguments must be Cox models") if (any(is.coxme)) { # We need the anova.coxmelist function from coxme # If coxme is not loaded the line below returns NULL temp <- getS3method("anova", "coxmelist", optional=TRUE) if (is.null(temp)) stop("a coxme model was found and library coxme is not loaded") else return(temp(c(list(object), dotargs), test = test)) } else return(anova.coxphlist(c(list(object), dotargs), test = test)) } # # The argument is a single Cox model # Show the nested list of models generated by this model. # By tradition the sequence is main effects (in the order found in # the model statement), then 2 way interactions, then 3, etc. # One does this by using the "assign" attribute of the model matrix. # (This does not work for penalized terms. if (length(object$rscore)>0) stop("Can't do anova tables with robust variances") has.strata <- !is.null(attr(terms(object), "specials")$strata) if (is.null(object[['y']]) || (has.strata && is.null(object$strata))) { # We need the model frame mf <- stats::model.frame(object) Y <- model.response(mf) X <- model.matrix(object, mf) if (has.strata) { stemp <- untangle.specials(terms(object), "strata") if (length(stemp$vars)==1) strata.keep <- mf[[stemp$vars]] else strata.keep <- strata(mf[,stemp$vars], shortlabel=TRUE) strats <- as.numeric(strata.keep) } } else { Y <- object[['y']] X <- model.matrix(object) if (has.strata) strats <- object$strata } assign <- attr(X, 'assign') alevels <- sort(unique(assign)) #if there are strata the sequence has holes nmodel <- length(alevels) df <- integer(nmodel+1) #this will hold the df vector loglik <- double(nmodel+1) #and the loglike vector df[nmodel+1] <- if (is.null(object$df)) sum(!is.na(object$coefficients)) else sum(object$df) loglik[nmodel+1] <- object$loglik[2] df[1] <- 0 loglik[1] <- object$loglik[1] # Now refit intermediate models for (i in seq.int(1, length.out =nmodel-1)){ if (length(object$offset)) { if (has.strata) tfit <- coxph(Y ~ X[,assign <= alevels[i]] + strata(strats) + offset(object$offset)) else tfit <- coxph(Y ~ X[, assign<= alevels[i]] + offet(object$offset)) } else { if (has.strata) tfit <- coxph(Y ~ X[,assign <= alevels[i]] + strata(strats)) else tfit <- coxph(Y ~ X[,assign <= alevels[i]]) } df[i+1] <- sum(!is.na(tfit$coefficients)) loglik[i+1] <- tfit$loglik[2] } table <- data.frame(loglik=loglik, Chisq=c(NA, 2*diff(loglik)), Df=c(NA, diff(df))) if (nmodel == 0) #failsafe for a NULL model table <- table[1, , drop = FALSE] if (length(test) >0 && test[1]=='Chisq') { table[['Pr(>|Chi|)']] <- 1- pchisq(table$Chisq, table$Df) } temp <- attr(terms(object), "term.labels") if (has.strata) temp <- temp[-stemp$terms] row.names(table) <- c('NULL', temp) title <- paste("Analysis of Deviance Table\n Cox model: response is ", deparse(object$terms[[2]]), "\nTerms added sequentially (first to last)\n", sep = "") structure(table, heading = title, class = c("anova", "data.frame")) } survival/R/lines.survexp.R0000644000175100001440000000015212264766610015324 0ustar hornikuserslines.survexp <- function(x, type="l", ...) { type <- type NextMethod("lines", type=type, ...) } survival/R/plot.survfit.R0000644000175100001440000007347013065013235015157 0ustar hornikusers# Automatically generated from the noweb directory plot.survfit<- function(x, conf.int, mark.time=FALSE, mark=3, col=1,lty=1, lwd=1, cex=1, log=FALSE, xscale=1, yscale=1, firstx=0, firsty=1, xmax, ymin=0, fun, xlab="", ylab="", xaxs='S', conf.times, conf.cap=.005, conf.offset=.012, ...) { dotnames <- names(list(...)) if (any(dotnames=='type')) stop("The graphical argument 'type' is not allowed") if (missing(mark.time) & !missing(mark)) mark.time <- TRUE if (inherits(x, "survfitms")) { x$surv <- 1- x$pstate if (is.matrix(x$surv)) { dimnames(x$surv) <- list(NULL, x$states) if (ncol(x$surv) > 1 && any(x$states == '')) { x$surv <- x$surv[, x$states != ''] if (is.matrix(x$p0)) x$p0 <- x$p0[, x$states != ''] else x$p0 <- x$p0[x$states != ''] } } if (!is.null(x$lower)) { x$lower <- 1- x$lower x$upper <- 1- x$upper } if (missing(fun)) fun <- "event" } if (missing(firsty) && !is.null(x$p0)) firsty <- 1-x$p0 if (is.logical(log)) { ylog <- log xlog <- FALSE if (ylog) logax <- 'y' else logax <- "" } else { ylog <- (log=='y' || log=='xy') xlog <- (log=='x' || log=='xy') logax <- log } if (!missing(fun)) { if (is.character(fun)) { if (fun=='log'|| fun=='logpct') ylog <- TRUE if (fun=='cloglog') { xlog <- TRUE if (ylog) logax <- 'xy' else logax <- 'x' } } } # The special x axis style only applies when firstx is not given if (missing(xaxs) && (firstx!=0 || !missing(fun) || (missing(fun) && inherits(x, "survfitms")))) xaxs <- par("xaxs") #use the default ssurv <- as.matrix(x$surv) stime <- x$time if( !is.null(x$upper)) { supper <- as.matrix(x$upper) slower <- as.matrix(x$lower) } else { conf.int <- FALSE supper <- NULL #marker for later code } # set up strata if (is.null(x$strata)) { nstrat <- 1 stemp <- rep(1, length(x$time)) # same length as stime } else { nstrat <- length(x$strata) stemp <- rep(1:nstrat, x$strata) # same length as stime } ncurve <- nstrat * ncol(ssurv) firsty <- matrix(firsty, nrow=nstrat, ncol=ncol(ssurv)) if (!missing(xmax) && any(x$time>xmax)) { # prune back the survival curves # I need to replace x's over the limit with xmax, and y's over the # limit with either the prior y value or firsty keepx <- keepy <- NULL # lines to keep tempn <- table(stemp) offset <- cumsum(c(0, tempn)) for (i in 1:nstrat) { ttime <-stime[stemp==i] if (all(ttime <= xmax)) { keepx <- c(keepx, 1:tempn[i] + offset[i]) keepy <- c(keepy, 1:tempn[i] + offset[i]) } else { bad <- min((1:tempn[i])[ttime>xmax]) if (bad==1) { #lost them all if (!is.na(firstx)) { # and we are plotting lines keepy <- c(keepy, 1+offset[i]) ssurv[1+offset[i],] <- firsty[i,] } } else keepy<- c(keepy, c(1:(bad-1), bad-1) + offset[i]) keepx <- c(keepx, (1:bad)+offset[i]) stime[bad+offset[i]] <- xmax x$n.event[bad+offset[i]] <- 1 #don't plot a tick mark } } # ok, now actually prune it stime <- stime[keepx] stemp <- stemp[keepx] x$n.event <- x$n.event[keepx] if (!is.null(x$n.censor)) x$n.censor <- x$n.censor[keepx] ssurv <- ssurv[keepy,,drop=FALSE] if (!is.null(supper)) { supper <- supper[keepy,,drop=FALSE] slower <- slower[keepy,,drop=FALSE] } } #stime <- stime/xscale #scaling is deferred until xmax processing is done if (!missing(fun)) { if (is.character(fun)) { tfun <- switch(fun, 'log' = function(x) x, 'event'=function(x) 1-x, 'cumhaz'=function(x) -log(x), 'cloglog'=function(x) log(-log(x)), 'pct' = function(x) x*100, 'logpct'= function(x) 100*x, #special case further below 'identity'= function(x) x, stop("Unrecognized function argument") ) } else if (is.function(fun)) tfun <- fun else stop("Invalid 'fun' argument") ssurv <- tfun(ssurv ) if (!is.null(supper)) { supper <- tfun(supper) slower <- tfun(slower) } firsty <- tfun(firsty) } if (missing(firstx)) { if (!is.null(x$start.time)) firstx <- x$start.time else { if (xlog) firstx <- min(stime[stime>0]) else firstx <- min(0, stime) } } # The default for plot and lines is to add confidence limits # if there is only one curve if (missing(conf.int) && missing(conf.times)) conf.int <- (ncurve==1) if (missing(conf.times)) conf.times <- NULL else { if (!is.numeric(conf.times)) stop('conf.times must be numeric') if (missing(conf.int)) conf.int <- TRUE } if (is.logical(conf.int)) plot.surv <- TRUE else { temp <- match.arg(conf.int, c("both", "only", "none")) if (is.na(temp)) stop("invalid value for conf.int") if (temp=="none") conf.int <- FALSE else conf.int <- TRUE if (temp=="only") plot.surv <- FALSE else plot.surv <- TRUE } # Marks are not placed on confidence bands mark <- rep(mark, length.out=ncurve) mcol <- rep(col, length.out=ncurve) if (is.numeric(mark.time)) mark.time <- sort(mark.time) # The actual number of curves is ncurve*3 if there are confidence bands, # unless conf.times has been given. Colors and line types in the latter # match the curves # If the number of line types is 1 and lty is an integer, then use lty # for the curve and lty+1 for the CI # If the length(lty) <= length(ncurve), use the same color for curve and CI # otherwise assume the user knows what they are about and has given a full # vector of line types. # Colors and line widths work like line types, excluding the +1 rule. if (conf.int & is.null(conf.times)) { if (length(lty)==1 && is.numeric(lty)) lty <- rep(c(lty, lty+1, lty+1), ncurve) else if (length(lty) <= ncurve) lty <- rep(rep(lty, each=3), length.out=(ncurve*3)) else lty <- rep(lty, length.out= ncurve*3) if (length(col) <= ncurve) col <- rep(rep(col, each=3), length.out=3*ncurve) else col <- rep(col, length.out=3*ncurve) if (length(lwd) <= ncurve) lwd <- rep(rep(lwd, each=3), length.out=3*ncurve) else lwd <- rep(lwd, length.out=3*ncurve) } else { col <- rep(col, length.out=ncurve) lty <- rep(lty, length.out=ncurve) lwd <- rep(lwd, length.out=ncurve) } #axis setting parmaters that depend on the fun argument if (!missing(fun)) { ymin <- tfun(ymin) #lines routine doesn't have it } # Do axis range computations if (xaxs=='S') { #special x- axis style for survival curves xaxs <- 'i' #what S thinks tempx <- max(stime) * 1.04 } else tempx <- max(stime) tempx <- c(firstx, tempx, firstx) if (ylog) { tempy <- range(ssurv[is.finite(ssurv)& ssurv>0]) if (tempy[2]==1) tempy[2] <- .99 if (any(ssurv==0)) { tempy[1] <- tempy[1]*.8 ssurv[ssurv==0] <- tempy[1] if (!is.null(supper)) { supper[supper==0] <- tempy[1] slower[slower==0] <- tempy[1] } } tempy <- c(tempy, firsty) } else tempy <- range(ssurv, firsty, finite=TRUE, na.rm=TRUE) if (missing(fun)) { tempx <- c(tempx, firstx) if (!ylog) tempy <- c(tempy, ymin) } # # Draw the basic box # plot(range(tempx, finite=TRUE, na.rm=TRUE)/xscale, range(tempy, finite=TRUE, na.rm=TRUE)*yscale, type='n', log=logax, xlab=xlab, ylab=ylab, xaxs=xaxs,...) if(yscale != 1) { if (ylog) par(usr =par("usr") -c(0, 0, log10(yscale), log10(yscale))) else par(usr =par("usr")/c(1, 1, yscale, yscale)) } if (xscale !=1) { if (xlog) par(usr =par("usr") -c(log10(xscale), log10(xscale), 0,0)) else par(usr =par("usr")*c(xscale, xscale, 1, 1)) } # Create a step function, removing redundancies that sometimes occur in # curves with lots of censoring. dostep <- function(x,y) { keep <- is.finite(x) & is.finite(y) if (!any(keep)) return() #all points were infinite or NA if (!all(keep)) { # these won't plot anyway, so simplify (CI values are often NA) x <- x[keep] y <- y[keep] } n <- length(x) if (n==1) list(x=x, y=y) else if (n==2) list(x=x[c(1,2,2)], y=y[c(1,1,2)]) else { # replace verbose horizonal sequences like # (1, .2), (1.4, .2), (1.8, .2), (2.3, .2), (2.9, .2), (3, .1) # with (1, .2), (.3, .2),(3, .1). # They are slow, and can smear the looks of the line type. temp <- rle(y)$lengths drops <- 1 + cumsum(temp[-length(temp)]) # points where the curve drops #create a step function if (n %in% drops) { #the last point is a drop xrep <- c(x[1], rep(x[drops], each=2)) yrep <- rep(y[c(1,drops)], c(rep(2, length(drops)), 1)) } else { xrep <- c(x[1], rep(x[drops], each=2), x[n]) yrep <- c(rep(y[c(1,drops)], each=2)) } list(x=xrep, y=yrep) } } drawmark <- function(x, y, mark.time, censor, cex, ...) { if (!is.numeric(mark.time)) { xx <- x[censor] yy <- y[censor] } else { #interpolate xx <- mark.time yy <- approx(x, y, xx, method="constant", f=0)$y } points(xx, yy, cex=cex, ...) } plot.surv <- TRUE type <- 's' c1 <- 1 # keeps track of the curve number c2 <- 1 # keeps track of the lty, col, etc xend <- yend <- double(ncurve) if (length(conf.offset) ==1) temp.offset <- (1:ncurve - (ncurve-1)/2)* conf.offset* diff(par("usr")[1:2]) else temp.offset <- rep(conf.offset, length=ncurve) * diff(par("usr")[1:2]) temp.cap <- conf.cap * diff(par("usr")[1:2]) for (j in 1:ncol(ssurv)) { for (i in unique(stemp)) { #for each strata who <- which(stemp==i) censor <- if (is.null(x$n.censor)) (x$n.event[who] ==0) else (x$n.event[who] ==0 & x$n.censor[who] >0) #censoring ties xx <- c(firstx, stime[who]) censor <- c(FALSE, censor) #no mark at firstx yy <- c(firsty[i,j], ssurv[who,j]) if (plot.surv) { if (type=='s') lines(dostep(xx, yy), lty=lty[c2], col=col[c2], lwd=lwd[c2]) else lines(xx, yy, type=type, lty=lty[c2], col=col[c2], lwd=lwd[c2]) if (is.numeric(mark.time) || mark.time) drawmark(xx, yy, mark.time, censor, pch=mark[c1], col=mcol[c1], cex=cex) } xend[c1] <- max(xx) yend[c1] <- yy[length(yy)] if (conf.int && !is.null(conf.times)) { # add vertical bars at the specified times x2 <- conf.times + temp.offset[c1] templow <- approx(xx, c(firsty[i,j], slower[who,j]), x2, method='constant', f=1)$y temphigh<- approx(xx, c(firsty[i,j], supper[who,j]), x2, method='constant', f=1)$y segments(x2, templow, x2, temphigh, lty=lty[c2], col=col[c2], lwd=lwd[c2]) if (conf.cap>0) { segments(x2-temp.cap, templow, x2+temp.cap, templow, lty=lty[c2], col=col[c2], lwd=lwd[c2] ) segments(x2-temp.cap, temphigh, x2+temp.cap, temphigh, lty=lty[c2], col=col[c2], lwd=lwd[c2]) } } c1 <- c1 +1 c2 <- c2 +1 if (conf.int && is.null(conf.times)) { if (type == 's') { lines(dostep(xx, c(firsty[i,j], slower[who,j])), lty=lty[c2], col=col[c2],lwd=lwd[c2]) c2 <- c2 +1 lines(dostep(xx, c(firsty[i,j], supper[who,j])), lty=lty[c2], col=col[c2], lwd= lwd[c2]) c2 <- c2 + 1 } else { lines(xx, c(firsty[i,j], slower[who,j]), lty=lty[c2], col=col[c2],lwd=lwd[c2], type=type) c2 <- c2 +1 lines(xx, c(firsty[i,j], supper[who,j]), lty=lty[c2], col=col[c2], lwd= lwd[c2], type= type) c2 <- c2 + 1 } } } } invisible(list(x=xend, y=yend)) } lines.survfit <- function(x, type='s', mark=3, col=1, lty=1, lwd=1, cex=1, mark.time=FALSE, xscale=1, firstx=0, firsty=1, xmax, fun, conf.int=FALSE, conf.times, conf.cap=.005, conf.offset=.012, ...) { xlog <- par("xlog") if (missing(mark.time) & !missing(mark)) mark.time <- TRUE if (inherits(x, "survfitms")) { x$surv <- 1- x$pstate if (is.matrix(x$surv)) { dimnames(x$surv) <- list(NULL, x$states) if (ncol(x$surv) > 1 && any(x$states == '')) { x$surv <- x$surv[, x$states != ''] if (is.matrix(x$p0)) x$p0 <- x$p0[, x$states != ''] else x$p0 <- x$p0[x$states != ''] } } if (!is.null(x$lower)) { x$lower <- 1- x$lower x$upper <- 1- x$upper } if (missing(fun)) fun <- "event" } if (missing(firsty) && !is.null(x$p0)) firsty <- 1-x$p0 ssurv <- as.matrix(x$surv) stime <- x$time if( !is.null(x$upper)) { supper <- as.matrix(x$upper) slower <- as.matrix(x$lower) } else { conf.int <- FALSE supper <- NULL #marker for later code } # set up strata if (is.null(x$strata)) { nstrat <- 1 stemp <- rep(1, length(x$time)) # same length as stime } else { nstrat <- length(x$strata) stemp <- rep(1:nstrat, x$strata) # same length as stime } ncurve <- nstrat * ncol(ssurv) firsty <- matrix(firsty, nrow=nstrat, ncol=ncol(ssurv)) if (!missing(xmax) && any(x$time>xmax)) { # prune back the survival curves # I need to replace x's over the limit with xmax, and y's over the # limit with either the prior y value or firsty keepx <- keepy <- NULL # lines to keep tempn <- table(stemp) offset <- cumsum(c(0, tempn)) for (i in 1:nstrat) { ttime <-stime[stemp==i] if (all(ttime <= xmax)) { keepx <- c(keepx, 1:tempn[i] + offset[i]) keepy <- c(keepy, 1:tempn[i] + offset[i]) } else { bad <- min((1:tempn[i])[ttime>xmax]) if (bad==1) { #lost them all if (!is.na(firstx)) { # and we are plotting lines keepy <- c(keepy, 1+offset[i]) ssurv[1+offset[i],] <- firsty[i,] } } else keepy<- c(keepy, c(1:(bad-1), bad-1) + offset[i]) keepx <- c(keepx, (1:bad)+offset[i]) stime[bad+offset[i]] <- xmax x$n.event[bad+offset[i]] <- 1 #don't plot a tick mark } } # ok, now actually prune it stime <- stime[keepx] stemp <- stemp[keepx] x$n.event <- x$n.event[keepx] if (!is.null(x$n.censor)) x$n.censor <- x$n.censor[keepx] ssurv <- ssurv[keepy,,drop=FALSE] if (!is.null(supper)) { supper <- supper[keepy,,drop=FALSE] slower <- slower[keepy,,drop=FALSE] } } #stime <- stime/xscale #scaling is deferred until xmax processing is done if (!missing(fun)) { if (is.character(fun)) { tfun <- switch(fun, 'log' = function(x) x, 'event'=function(x) 1-x, 'cumhaz'=function(x) -log(x), 'cloglog'=function(x) log(-log(x)), 'pct' = function(x) x*100, 'logpct'= function(x) 100*x, #special case further below 'identity'= function(x) x, stop("Unrecognized function argument") ) } else if (is.function(fun)) tfun <- fun else stop("Invalid 'fun' argument") ssurv <- tfun(ssurv ) if (!is.null(supper)) { supper <- tfun(supper) slower <- tfun(slower) } firsty <- tfun(firsty) } if (missing(firstx)) { if (!is.null(x$start.time)) firstx <- x$start.time else { if (xlog) firstx <- min(stime[stime>0]) else firstx <- min(0, stime) } } # The default for plot and lines is to add confidence limits # if there is only one curve if (missing(conf.int) && missing(conf.times)) conf.int <- (ncurve==1) if (missing(conf.times)) conf.times <- NULL else { if (!is.numeric(conf.times)) stop('conf.times must be numeric') if (missing(conf.int)) conf.int <- TRUE } if (is.logical(conf.int)) plot.surv <- TRUE else { temp <- match.arg(conf.int, c("both", "only", "none")) if (is.na(temp)) stop("invalid value for conf.int") if (temp=="none") conf.int <- FALSE else conf.int <- TRUE if (temp=="only") plot.surv <- FALSE else plot.surv <- TRUE } # Marks are not placed on confidence bands mark <- rep(mark, length.out=ncurve) mcol <- rep(col, length.out=ncurve) if (is.numeric(mark.time)) mark.time <- sort(mark.time) # The actual number of curves is ncurve*3 if there are confidence bands, # unless conf.times has been given. Colors and line types in the latter # match the curves # If the number of line types is 1 and lty is an integer, then use lty # for the curve and lty+1 for the CI # If the length(lty) <= length(ncurve), use the same color for curve and CI # otherwise assume the user knows what they are about and has given a full # vector of line types. # Colors and line widths work like line types, excluding the +1 rule. if (conf.int & is.null(conf.times)) { if (length(lty)==1 && is.numeric(lty)) lty <- rep(c(lty, lty+1, lty+1), ncurve) else if (length(lty) <= ncurve) lty <- rep(rep(lty, each=3), length.out=(ncurve*3)) else lty <- rep(lty, length.out= ncurve*3) if (length(col) <= ncurve) col <- rep(rep(col, each=3), length.out=3*ncurve) else col <- rep(col, length.out=3*ncurve) if (length(lwd) <= ncurve) lwd <- rep(rep(lwd, each=3), length.out=3*ncurve) else lwd <- rep(lwd, length.out=3*ncurve) } else { col <- rep(col, length.out=ncurve) lty <- rep(lty, length.out=ncurve) lwd <- rep(lwd, length.out=ncurve) } # Create a step function, removing redundancies that sometimes occur in # curves with lots of censoring. dostep <- function(x,y) { keep <- is.finite(x) & is.finite(y) if (!any(keep)) return() #all points were infinite or NA if (!all(keep)) { # these won't plot anyway, so simplify (CI values are often NA) x <- x[keep] y <- y[keep] } n <- length(x) if (n==1) list(x=x, y=y) else if (n==2) list(x=x[c(1,2,2)], y=y[c(1,1,2)]) else { # replace verbose horizonal sequences like # (1, .2), (1.4, .2), (1.8, .2), (2.3, .2), (2.9, .2), (3, .1) # with (1, .2), (.3, .2),(3, .1). # They are slow, and can smear the looks of the line type. temp <- rle(y)$lengths drops <- 1 + cumsum(temp[-length(temp)]) # points where the curve drops #create a step function if (n %in% drops) { #the last point is a drop xrep <- c(x[1], rep(x[drops], each=2)) yrep <- rep(y[c(1,drops)], c(rep(2, length(drops)), 1)) } else { xrep <- c(x[1], rep(x[drops], each=2), x[n]) yrep <- c(rep(y[c(1,drops)], each=2)) } list(x=xrep, y=yrep) } } drawmark <- function(x, y, mark.time, censor, cex, ...) { if (!is.numeric(mark.time)) { xx <- x[censor] yy <- y[censor] } else { #interpolate xx <- mark.time yy <- approx(x, y, xx, method="constant", f=0)$y } points(xx, yy, cex=cex, ...) } c1 <- 1 # keeps track of the curve number c2 <- 1 # keeps track of the lty, col, etc xend <- yend <- double(ncurve) if (length(conf.offset) ==1) temp.offset <- (1:ncurve - (ncurve-1)/2)* conf.offset* diff(par("usr")[1:2]) else temp.offset <- rep(conf.offset, length=ncurve) * diff(par("usr")[1:2]) temp.cap <- conf.cap * diff(par("usr")[1:2]) for (j in 1:ncol(ssurv)) { for (i in unique(stemp)) { #for each strata who <- which(stemp==i) censor <- if (is.null(x$n.censor)) (x$n.event[who] ==0) else (x$n.event[who] ==0 & x$n.censor[who] >0) #censoring ties xx <- c(firstx, stime[who]) censor <- c(FALSE, censor) #no mark at firstx yy <- c(firsty[i,j], ssurv[who,j]) if (plot.surv) { if (type=='s') lines(dostep(xx, yy), lty=lty[c2], col=col[c2], lwd=lwd[c2]) else lines(xx, yy, type=type, lty=lty[c2], col=col[c2], lwd=lwd[c2]) if (is.numeric(mark.time) || mark.time) drawmark(xx, yy, mark.time, censor, pch=mark[c1], col=mcol[c1], cex=cex) } xend[c1] <- max(xx) yend[c1] <- yy[length(yy)] if (conf.int && !is.null(conf.times)) { # add vertical bars at the specified times x2 <- conf.times + temp.offset[c1] templow <- approx(xx, c(firsty[i,j], slower[who,j]), x2, method='constant', f=1)$y temphigh<- approx(xx, c(firsty[i,j], supper[who,j]), x2, method='constant', f=1)$y segments(x2, templow, x2, temphigh, lty=lty[c2], col=col[c2], lwd=lwd[c2]) if (conf.cap>0) { segments(x2-temp.cap, templow, x2+temp.cap, templow, lty=lty[c2], col=col[c2], lwd=lwd[c2] ) segments(x2-temp.cap, temphigh, x2+temp.cap, temphigh, lty=lty[c2], col=col[c2], lwd=lwd[c2]) } } c1 <- c1 +1 c2 <- c2 +1 if (conf.int && is.null(conf.times)) { if (type == 's') { lines(dostep(xx, c(firsty[i,j], slower[who,j])), lty=lty[c2], col=col[c2],lwd=lwd[c2]) c2 <- c2 +1 lines(dostep(xx, c(firsty[i,j], supper[who,j])), lty=lty[c2], col=col[c2], lwd= lwd[c2]) c2 <- c2 + 1 } else { lines(xx, c(firsty[i,j], slower[who,j]), lty=lty[c2], col=col[c2],lwd=lwd[c2], type=type) c2 <- c2 +1 lines(xx, c(firsty[i,j], supper[who,j]), lty=lty[c2], col=col[c2], lwd= lwd[c2], type= type) c2 <- c2 + 1 } } } } invisible(list(x=xend, y=yend)) } points.survfit <- function(x, xscale, xmax, fun, censor=FALSE, col=1, pch, ...) { # this function is used rarely conf.int <- FALSE # never draw these with 'points' if (inherits(x, "survfitms")) { x$surv <- 1- x$pstate if (is.matrix(x$surv)) { dimnames(x$surv) <- list(NULL, x$states) if (ncol(x$surv) > 1 && any(x$states == '')) { x$surv <- x$surv[, x$states != ''] if (is.matrix(x$p0)) x$p0 <- x$p0[, x$states != ''] else x$p0 <- x$p0[x$states != ''] } } if (!is.null(x$lower)) { x$lower <- 1- x$lower x$upper <- 1- x$upper } if (missing(fun)) fun <- "event" } firstx <- firsty <- NA # part of the common args, but irrelevant for points ssurv <- as.matrix(x$surv) stime <- x$time if( !is.null(x$upper)) { supper <- as.matrix(x$upper) slower <- as.matrix(x$lower) } else { conf.int <- FALSE supper <- NULL #marker for later code } # set up strata if (is.null(x$strata)) { nstrat <- 1 stemp <- rep(1, length(x$time)) # same length as stime } else { nstrat <- length(x$strata) stemp <- rep(1:nstrat, x$strata) # same length as stime } ncurve <- nstrat * ncol(ssurv) firsty <- matrix(firsty, nrow=nstrat, ncol=ncol(ssurv)) if (!missing(xmax) && any(x$time>xmax)) { # prune back the survival curves # I need to replace x's over the limit with xmax, and y's over the # limit with either the prior y value or firsty keepx <- keepy <- NULL # lines to keep tempn <- table(stemp) offset <- cumsum(c(0, tempn)) for (i in 1:nstrat) { ttime <-stime[stemp==i] if (all(ttime <= xmax)) { keepx <- c(keepx, 1:tempn[i] + offset[i]) keepy <- c(keepy, 1:tempn[i] + offset[i]) } else { bad <- min((1:tempn[i])[ttime>xmax]) if (bad==1) { #lost them all if (!is.na(firstx)) { # and we are plotting lines keepy <- c(keepy, 1+offset[i]) ssurv[1+offset[i],] <- firsty[i,] } } else keepy<- c(keepy, c(1:(bad-1), bad-1) + offset[i]) keepx <- c(keepx, (1:bad)+offset[i]) stime[bad+offset[i]] <- xmax x$n.event[bad+offset[i]] <- 1 #don't plot a tick mark } } # ok, now actually prune it stime <- stime[keepx] stemp <- stemp[keepx] x$n.event <- x$n.event[keepx] if (!is.null(x$n.censor)) x$n.censor <- x$n.censor[keepx] ssurv <- ssurv[keepy,,drop=FALSE] if (!is.null(supper)) { supper <- supper[keepy,,drop=FALSE] slower <- slower[keepy,,drop=FALSE] } } #stime <- stime/xscale #scaling is deferred until xmax processing is done if (!missing(fun)) { if (is.character(fun)) { tfun <- switch(fun, 'log' = function(x) x, 'event'=function(x) 1-x, 'cumhaz'=function(x) -log(x), 'cloglog'=function(x) log(-log(x)), 'pct' = function(x) x*100, 'logpct'= function(x) 100*x, #special case further below 'identity'= function(x) x, stop("Unrecognized function argument") ) } else if (is.function(fun)) tfun <- fun else stop("Invalid 'fun' argument") ssurv <- tfun(ssurv ) if (!is.null(supper)) { supper <- tfun(supper) slower <- tfun(slower) } firsty <- tfun(firsty) } if (ncurve==1 || (length(col)==1 && missing(pch))) { if (censor) points(stime, ssurv, ...) else points(stime[x$n.event>0], ssurv[x$n.event>0], ...) } else { c2 <- 1 #cycles through the colors and characters col <- rep(col, length=ncurve) if (!missing(pch)) { if (length(pch)==1) pch2 <- rep(strsplit(pch, '')[[1]], length=ncurve) else pch2 <- rep(pch, length=ncurve) } for (j in 1:ncol(ssurv)) { for (i in unique(stemp)) { if (censor) who <- which(stemp==i) else who <- which(stemp==i & x$n.event >0) if (missing(pch)) points(stime[who], ssurv[who,j], col=col[c2], ...) else points(stime[who], ssurv[who,j], col=col[c2], pch=pch2[c2], ...) c2 <- c2+1 } } } } survival/R/survfitKM.S0000644000175100001440000002004612776723124014437 0ustar hornikusers# A version that does more work in S, less in C survfitKM <- function(x, y, casewt=rep(1,length(x)), type=c('kaplan-meier', 'fleming-harrington', 'fh2'), error=c('greenwood', "tsiatis"), se.fit=TRUE, conf.int= .95, conf.type=c('log', 'log-log', 'plain', 'none'), conf.lower=c('usual', 'peto', 'modified'), start.time, new.time) { type <- match.arg(type) method <- match(type, c("kaplan-meier", "fleming-harrington", "fh2")) error <- match.arg(error) error.int <- match(error, c("greenwood", "tsiatis")) conf.type <- match.arg(conf.type) conf.lower<- match.arg(conf.lower) if (is.logical(conf.int)) { # A common error is for users to use "conf.int = FALSE" # it's illegal, but allow it if (!conf.int) conf.type <- "none" conf.int <- .95 } if (!is.Surv(y)) stop("y must be a Surv object") if (!is.factor(x)) stop("x must be a factor") if (attr(y, 'type') != 'right' && attr(y, 'type') != 'counting') stop("Can only handle right censored or counting data") ny <- ncol(y) # Will be 2 for right censored, 3 for counting xlev <- levels(x) # Will supply names for the curves x <- as.numeric(x) # keep only the levels # Allow "new.time" as a synonym for start.time if (missing(start.time) && !missing(new.time)) start.time <- new.time if (!missing(start.time)) { n.all <- c(table(x)) # remember the original data size # remove any obs whose end time is <= start.time keep <- (y[,ny-1] >= start.time) if (all(keep==FALSE)) stop(paste("start.time =", start.time, "is greater than all time points.")) x <- x[keep] y <- y[keep,,drop=FALSE] #make sure y remains a matrix casewt <- casewt[keep] } n.used <- as.vector(table(x)) # This is for the printout nstrat <- length(n.used) # # Each of the necessary output objects is originally a list with one # element per strata. This doesn't use up extra S memory, the number # of curves is usually small enough that the "for" loop is no great # cost, and it's easier to see what's going on than C code. # If tapply gets fast again, this code will also be fast. # The remaining C-code is simple, but hard to do cleanly in S # Let nrisk=A and nevent=B. The terms in returned sum1 and sum2 are # If ndead= 0, sum1=sum2=1 (avoids a 0/0 in the S code) # If ndead= 1, sum1=1/A and sum2= 1/A*A # If ndead= 2, sum1= (1/2)[ 1/A + 1/(A- B/2)] # sum2= (1/2)[ 1/A^2 + (1/(A-B/2))^2] # If ndead =3, sum1 = (1/3)[1/A + 1/(A-B/3) + 1/(A -2B/3)] # If ndead =4, sum1 = (1/4)[1/A + 1/(A-B/4) + 1/(A -2B/4) + 1/(A-3B/4)] # and etc. time <- vector('list', nstrat) n.risk <- vector('list', nstrat) surv <- vector('list', nstrat) n.cens <- vector('list', nstrat) n.event<- vector('list', nstrat) strata <- integer(nstrat) if (se.fit) varhaz <- vector('list', nstrat) if (ny==3) n.enter <- vector('list', nstrat) uniquex <- sort(unique(x)) for (i in 1:nstrat) { who <- (x== uniquex[i]) if (ny==2) { # the "factor" + levels ensures 2 columns in temp even if all # are dead or all are alive temp <- tapply(casewt[who], list(factor(y[who,1]), factor(y[who,2], levels=0:1)), sum) temp <- ifelse(is.na(temp), 0, temp) time[[i]] <- sort(unique(y[who,1])) # old version of line above ntemp <- (dim(temp))[1] nevent <- as.vector(temp[,2]) ncens <- as.vector(temp[,1]) nrisk <- rev(cumsum(rev(temp %*% c(1,1)))) ndead <- as.vector(table(y[who,1], factor(y[who,2], levels=0:1)) [,2]) } else { # The counting process case # We have to be a bit more clever here -- if I did a table of the # start times and a separate one of the stop times, they wouldn't # necessarily match. So do it all at once with a fake 'status' # variable which is ==2 for start times and = status for stop # Also, the number of rows in output (ntemp) may be bigger than # the number of rows of input (n). n <- sum(who) temp <- factor(c(rep(2,n),y[who,3]), levels=0:3) temp <- tapply(rep(casewt[who],2), list(factor(y[who,1:2]), temp), sum) temp <- ifelse(is.na(temp), 0, temp) time[[i]] <- as.numeric(dimnames(temp)[[1]]) ntemp <- (dim(temp))[1] nevent <- as.vector(temp[,2]) ncens <- as.vector(temp[,1]) nenter <- as.vector(temp[,3]) nrisk <- cumsum(nenter - (nevent + ncens)) nrisk <- c(0, nrisk[-ntemp]) #risk counts change at time t+0 n.enter[[i]] <- nenter # again, a fake status to make sure that all the times appear ndead <- as.vector(table(y[who,1:2], factor(c(rep(0,n),y[who,3]), levels=0:2))[,2]) } strata[i] <- ntemp trisk <- ifelse(nrisk==0, 1, nrisk) #avoid 0/0 cases if (method==1) surv[[i]] <- cumprod((trisk-nevent)/trisk) if (method==2) { hazard <- nevent/trisk #Nelson's hazard estimate surv[[i]] <- exp(- cumsum(hazard)) } if (method==3) { tsum <- .C(Csurvfit4, as.integer(length(ncens)), as.integer(ndead), sum1 = as.double(nrisk), sum2 = as.double(nevent)) hazard <- nevent *tsum$sum1 surv[[i]] <- exp(-cumsum(hazard)) } if (se.fit) { if (error.int==1) # Greenwood varhaz[[i]] <- cumsum(nevent/(trisk*(trisk-nevent))) else { if (method <3) varhaz[[i]] <- cumsum(nevent/(trisk^2)) else varhaz[[i]] <- cumsum(nevent* tsum$sum2) } } n.event[[i]] <- nevent n.cens[[i]] <- ncens n.risk[[i]] <- nrisk } if (ny==2) { temp <- list(n=n.used, time = unlist(time), n.risk = unlist(n.risk), n.event= unlist(n.event), n.censor = unlist(n.cens), surv = unlist(surv), type='right') } else { temp <- list(n=n.used, time = unlist(time), n.risk = unlist(n.risk), n.event= unlist(n.event), n.censor = unlist(n.cens), n.enter = unlist(n.enter), surv = unlist(surv), type='counting') } if (nstrat >1) { names(strata) <- xlev[sort(unique(x))] temp$strata <- strata } if (!missing(start.time)) { temp$start.time <- start.time # user defined time to start temp$n.all <- n.all } if (se.fit) { std.err <- sqrt(unlist(varhaz)) temp$std.err <- std.err # # n.lag = the # at risk the last time there was an event (or # the first time of a strata) # events <- temp$n.event >0 if (nstrat==1) events[1] <- TRUE else events[1 + cumsum(c(0, strata[-nstrat]))] <- TRUE zz <- 1:length(events) n.lag <- rep(temp$n.risk[events], diff(c(zz[events], 1+max(zz)))) std.low <- switch(conf.lower, 'usual' = std.err, 'peto' = sqrt((1-temp$surv)/ temp$n.risk), 'modified' = std.err * sqrt(n.lag/temp$n.risk)) zval <- qnorm(1- (1-conf.int)/2, 0,1) if (conf.type=='plain') { temp1 <- temp$surv + zval* std.err * temp$surv temp2 <- temp$surv - zval* std.low * temp$surv temp <- c(temp, list(upper=pmin(temp1,1), lower=pmax(temp2,0), conf.type='plain', conf.int=conf.int)) } if (conf.type=='log') { #avoid some "log(0)" messages xx <- ifelse(temp$surv==0,1,temp$surv) temp1 <- ifelse(temp$surv==0, NA, exp(log(xx) + zval* std.err)) temp2 <- ifelse(temp$surv==0, NA, exp(log(xx) - zval* std.low)) temp <- c(temp, list(upper=pmin(temp1,1), lower=temp2, conf.type='log', conf.int=conf.int)) } if (conf.type=='log-log') { who <- (temp$surv==0 | temp$surv==1) #special cases temp3 <- ifelse(temp$surv==0, NA, 1) xx <- ifelse(who, .1,temp$surv) #avoid some "log(0)" messages temp1 <- exp(-exp(log(-log(xx)) + zval*std.err/log(xx))) temp1 <- ifelse(who, temp3, temp1) temp2 <- exp(-exp(log(-log(xx)) - zval*std.low/log(xx))) temp2 <- ifelse(who, temp3, temp2) temp <- c(temp, list(upper=temp1, lower=temp2, conf.type='log-log', conf.int=conf.int)) } } temp } survival/R/survConcordance.R0000644000175100001440000000441313065013242015623 0ustar hornikusers# Automatically generated from the noweb directory survConcordance <- function(formula, data, weights, subset, na.action) { Call <- match.call() # save a copy of of the call, as documentation m <- match.call(expand.dots=FALSE) m[[1L]] <- quote(stats::model.frame) m$formula <- if(missing(data)) terms(formula, "strata") else terms(formula, "strata", data=data) m <- eval(m, sys.parent()) Terms <- attr(m, 'terms') Y <- model.extract(m, "response") if (!inherits(Y, "Surv")) { if (is.numeric(Y) && is.vector(Y)) Y <- Surv(Y) else stop("left hand side of the formula must be a numeric vector or a surival") } n <- nrow(Y) wt <- model.extract(m, 'weights') offset<- attr(Terms, "offset") if (length(offset)>0) stop("Offset terms not allowed") stemp <- untangle.specials(Terms, 'strata') if (length(stemp$vars)) { if (length(stemp$vars)==1) strat <- m[[stemp$vars]] else strat <- strata(m[,stemp$vars], shortlabel=TRUE) Terms <- Terms[-stemp$terms] } else strat <- NULL x <- model.matrix(Terms, m)[,-1, drop=FALSE] #remove the intercept if (ncol(x) > 1) stop("Only one predictor variable allowed") count <- survConcordance.fit(Y, x, strat, wt) if (is.null(strat)) { concordance <- (count[1] + count[3]/2)/sum(count[1:3]) std.err <- count[5]/(2* sum(count[1:3])) } else { temp <- colSums(count) concordance <- (temp[1] + temp[3]/2)/ sum(temp[1:3]) std.err <- temp[5]/(2*sum(temp[1:3])) } fit <- list(concordance= concordance, stats=count, n=n, std.err=std.err, call=Call) na.action <- attr(m, "na.action") if (length(na.action)) fit$na.action <- na.action oldClass(fit) <- 'survConcordance' fit } print.survConcordance <- function(x, ...) { if(!is.null(cl <- x$call)) { cat("Call:\n") dput(cl) cat("\n") } omit <- x$na.action if(length(omit)) cat(" n=", x$n, " (", naprint(omit), ")\n", sep = "") else cat(" n=", x$n, "\n") cat("Concordance= ", format(x$concordance), " se= ", format(x$std.err), '\n', sep='') print(x$stats) invisible(x) } survival/R/frailty.controlaic.S0000644000175100001440000000354212470201064016276 0ustar hornikusers# $Id: frailty.controlaic.S 11166 2008-11-24 22:10:34Z therneau $ # Control function to minimize the AIC # the optional paramater "caic" chooses corrected aic (default=FALSE) # n is the "effective" sample size # frailty.controlaic <- function(parms, iter, old, n, df, loglik) { if (iter==0) { # initial call if (is.null(parms$init)) theta <-0.005 else theta <- parms$init[1] return(list(theta=theta, done=FALSE)) } # by default, do the corrected AIC if (length(parms$caic)) correct <- parms$caic else correct <- FALSE if (n < df+2) dfc <- (df -n) + (df+1)*df/2 -1 #avoid pathology else dfc <- -1 + (df+1)/(1- ((df+2)/n)) if (iter==1) { # Second guess in series history <- c(theta=old$theta, loglik=loglik, df=df, aic=loglik-df, aicc=loglik - dfc) if (length(parms$init) <2) theta <-1 else theta <- parms$init[2] temp <- list(theta=theta, done=FALSE, history=history) return(temp) } history <- rbind(old$history,c(old$theta, loglik, df, loglik-df, loglik -dfc)) if (iter==2) { #Third guess theta <- mean(history[,1]) return(list(theta=theta, done=FALSE, history=history)) } # # Ok, now we're ready to actually use prior data # Now, history has iter rows, each row contains the # value of theta, the Cox PL, the df, aic, and corrected aic if (correct) aic <- history[,5] #use corrected aic for convergence else aic <- history[,4] done <- (abs(1- aic[iter]/aic[iter-1]) < parms$eps) x <- history[,1] if (x[iter]== max(aic) && x[iter]==max(x)) newtheta <- 2* max(x) else newtheta <- frailty.brent(x, aic, lower=parms$lower, upper=parms$upper) if (length(parms$trace) && parms$trace) { print(history) cat(" new theta=", format(newtheta), "\n\n") } list(theta=newtheta, done=done, history=history) } survival/R/strata.S0000644000175100001440000000450012465203762013774 0ustar hornikusers# Create a strata variable, possibly from many objects # strata <- function(..., na.group=FALSE, shortlabel, sep=', ') { # First, grab a copy of the call, which will be used to manufacture # labels for unlabeled arguments # Then get the arguments as a list words <- as.character((match.call())[-1]) allf <- list(...) # If there is only one argument, and it itself is a list, use # it instead if(length(allf) == 1 && is.list(ttt <- unclass(allf[[1]]))) allf <- ttt nterms <- length(allf) # Keep the names of named args as their label, what was typed otherwise if (is.null(names(allf))) { argname <- words[1:nterms] if (missing(shortlabel)) shortlabel <- all(sapply(allf, function(x) is.character(x) | inherits(x, 'factor'))) } else { argname <- ifelse(names(allf) == '', words[1:nterms], names(allf)) if (missing(shortlabel)) shortlabel <- FALSE } # If the arguments are not all the same length, stop now # Mostly this is to stop calls with an improper object arglength <- sapply(allf, length) if (any(arglength != arglength[1])) stop("all arguments must be the same length") if (!all(sapply(allf, is.atomic))) stop("all arguments must be vectors") # Process the first argument what <- allf[[1]] if(is.null(levels(what))) what <- factor(what) levs <- unclass(what) - 1 wlab <- levels(what) if (na.group && any(is.na(what))){ # add "NA" as a level levs[is.na(levs)] <- length(wlab) wlab <- c(wlab, "NA") } if (shortlabel) labs <- wlab else labs <- paste(argname[1], wlab, sep='=') # Now march through the other variables, if any for (i in (1:nterms)[-1]) { what <- allf[[i]] if(is.null(levels(what))) what <- factor(what) wlab <- levels(what) wlev <- unclass(what) - 1 if (na.group && any(is.na(wlev))){ wlev[is.na(wlev)] <- length(wlab) wlab <- c(wlab, "NA") } if (!shortlabel) wlab <- format(paste(argname[i], wlab, sep='=')) levs <- wlev + levs*(length(wlab)) labs <- paste(rep(labs, rep(length(wlab), length(labs))), rep(wlab, length(labs)), sep=sep) } levs <- levs + 1 ulevs <- sort(unique(levs[!is.na(levs)])) levs <- match(levs, ulevs) labs <- labs[ulevs] factor(levs, labels=labs) } survival/R/survfit.R0000644000175100001440000001751013065013245014174 0ustar hornikusers# Automatically generated from the noweb directory survfit <- function(formula, ...) { UseMethod("survfit", formula) } dim.survfit <- function(x) { if (is.null(x$strata)) { if (is.matrix(x$surv)) c(1L, ncol(x$surv)) else 1L } else { nr <- length(x$strata) if (is.matrix(x$surv)) c(nr, ncol(x$surv)) else nr } } "[.survfit" <- function(x, ..., drop=TRUE) { nmatch <- function(indx, target) { # This function lets R worry about character, negative, or logical subscripts # It always returns a set of positive integer indices temp <- 1:length(target) names(temp) <- target temp[indx] } if (missing(..1)) i<- NULL else i <- ..1 if (missing(..2)) j<- NULL else j <- ..2 if (is.null(i) && is.null(j)) return (x) #no subscripts present! if (!is.matrix(x$surv) && !is.null(j)) stop("survfit object does not have 2 dimensions") if (is.null(x$strata)) { if (is.matrix(x$surv)) { if (is.null(j) && !is.null(i)) j <- i #special case noted above x$surv <- x$surv[,j,drop=drop] if (!is.null(x$std.err)) x$std.err <- x$std.err[,j,drop=drop] if (!is.null(x$upper)) x$upper <- x$upper[,j,drop=drop] if (!is.null(x$lower)) x$lower <- x$lower[,j,drop=drop] if (!is.null(x$cumhaz)) x$cumhaz <- x$cumhaz[,j,drop=drop] } else warning("survfit object has only a single survival curve") } else { if (is.null(i)) keep <- seq(along.with=x$time) else { indx <- nmatch(i, names(x$strata)) #strata to keep if (any(is.na(indx))) stop(paste("strata", paste(i[is.na(indx)], collapse=' '), 'not matched')) # Now, indx may not be in order: some can use curve[3:2] to reorder # The list/unlist construct will reorder the data temp <- rep(1:length(x$strata), x$strata) keep <- unlist(lapply(indx, function(x) which(temp==x))) if (length(indx) <=1 && drop) x$strata <- NULL else x$strata <- x$strata[i] x$n <- x$n[indx] x$time <- x$time[keep] x$n.risk <- x$n.risk[keep] x$n.event <- x$n.event[keep] x$n.censor<- x$n.censor[keep] if (!is.null(x$n.enter)) x$n.enter <- x$n.enter[keep] } if (is.matrix(x$surv)) { # If the curve has been selected by strata and keep has only # one row, we don't want to lose the second subscript too if (!is.null(i) && (is.null(j) ||length(j) >1)) drop <- FALSE if (is.null(j)) { x$surv <- x$surv[keep,,drop=drop] if (!is.null(x$std.err)) x$std.err <- x$std.err[keep,,drop=drop] if (!is.null(x$upper)) x$upper <-x$upper[keep,,drop=drop] if (!is.null(x$lower)) x$lower <-x$lower[keep,,drop=drop] if (!is.null(x$cumhaz)) x$cumhaz <-x$cumhaz[keep,,drop=drop] } else { x$surv <- x$surv[keep,j, drop=drop] if (!is.null(x$std.err)) x$std.err <- x$std.err[keep,j, drop=drop] if (!is.null(x$upper)) x$upper <- x$upper[keep,j, drop=drop] if (!is.null(x$lower)) x$lower <- x$lower[keep,j, drop=drop] if (!is.null(x$cumhaz)) x$cumhaz <- x$cumhaz[keep,j, drop=drop] } } else { x$surv <- x$surv[keep] if (!is.null(x$std.err)) x$std.err <- x$std.err[keep] if (!is.null(x$upper)) x$upper <- x$upper[keep] if (!is.null(x$lower)) x$lower <- x$lower[keep] if (!is.null(x$cumhaz)) x$cumhaz <- x$cumhaz[keep] } } x } survfit.formula <- function(formula, data, weights, subset, na.action, etype, id, istate, timefix=TRUE, ...) { Call <- match.call() Call[[1]] <- as.name('survfit') #make nicer printout for the user # create a copy of the call that has only the arguments we want, # and use it to call model.frame() indx <- match(c('formula', 'data', 'weights', 'subset','na.action', 'istate', 'id', "etype"), names(Call), nomatch=0) #It's very hard to get the next error message other than malice # eg survfit(wt=Surv(time, status) ~1) if (indx[1]==0) stop("a formula argument is required") temp <- Call[c(1, indx)] temp[[1L]] <- quote(stats::model.frame) m <- eval.parent(temp) Terms <- terms(formula, c("strata", "cluster")) ord <- attr(Terms, 'order') if (length(ord) & any(ord !=1)) stop("Interaction terms are not valid for this function") n <- nrow(m) Y <- model.extract(m, 'response') if (!is.Surv(Y)) stop("Response must be a survival object") casewt <- model.extract(m, "weights") if (is.null(casewt)) casewt <- rep(1,n) if (!is.null(attr(Terms, 'offset'))) warning("Offset term ignored") id <- model.extract(m, 'id') istate <- model.extract(m,"istate") temp <- untangle.specials(Terms, "cluster") if (length(temp$vars)>0) { if (length(temp$vars) > 1) stop("can not have two cluster terms") if (!is.null(id)) stop("can not have both a cluster term and an id variable") id <- m[[temp$vars]] Terms <- Terms[-temp$terms] } ll <- attr(Terms, 'term.labels') if (length(ll) == 0) X <- factor(rep(1,n)) # ~1 on the right else X <- strata(m[ll]) if (!is.Surv(Y)) stop("y must be a Surv object") # Backwards support for the now-depreciated etype argument etype <- model.extract(m, "etype") if (!is.null(etype)) { if (attr(Y, "type") == "mcounting" || attr(Y, "type") == "mright") stop("cannot use both the etype argument and mstate survival type") if (length(istate)) stop("cannot use both the etype and istate arguments") status <- Y[,ncol(Y)] etype <- as.factor(etype) temp <- table(etype, status==0) if (all(rowSums(temp==0) ==1)) { # The user had a unique level of etype for the censors newlev <- levels(etype)[order(-temp[,2])] #censors first } else newlev <- c(" ", levels(etype)[temp[,1] >0]) status <- factor(ifelse(status==0,0, as.numeric(etype)), labels=newlev) if (attr(Y, 'type') == "right") Y <- Surv(Y[,1], status, type="mstate") else if (attr(Y, "type") == "counting") Y <- Surv(Y[,1], Y[,2], status, type="mstate") else stop("etype argument incompatable with survival type") } # Deal with the near-ties problem if (!is.logical(timefix) || length(timefix) > 1) stop("invalid value for timefix option") if (timefix) newY <- aeqSurv(Y) # Call the appropriate helper function if (attr(Y, 'type') == 'left' || attr(Y, 'type') == 'interval') temp <- survfitTurnbull(X, newY, casewt, ...) else if (attr(Y, 'type') == "right" || attr(Y, 'type')== "counting") temp <- survfitKM(X, newY, casewt, ...) else if (attr(Y, 'type') == "mright" || attr(Y, "type")== "mcounting") temp <- survfitCI(X, newY, weights=casewt, id=id, istate=istate, ...) else { # This should never happen stop("unrecognized survival type") } if (is.null(temp$states)) class(temp) <- 'survfit' else class(temp) <- c("survfitms", "survfit") if (!is.null(attr(m, 'na.action'))) temp$na.action <- attr(m, 'na.action') temp$call <- Call temp } survfit.Surv <- function(formula, ...) stop("the survfit function requires a formula as its first argument") survival/R/predict.survreg.penal.S0000644000175100001440000000063211732700061016712 0ustar hornikusers# $Id: predict.survreg.penal.S 11166 2008-11-24 22:10:34Z therneau $ # # This routine just stops disastrous arithmetic for models with sparse # terms. A placeholder until the proper sparse terms actions are inserted. # predict.survreg.penal <- function(object, ...) { pterms <- object$pterms if (any(pterms==2)) stop("Predictions not available for sparse models") NextMethod('predict') } survival/R/coxph.getdata.S0000644000175100001440000000321012676277403015233 0ustar hornikusers# # Reconstruct the Cox model data. This is done in so many routines # that I extracted it out. # Newer routines use model.matrix.coxph and model.frame.coxph methods. # # The "stratax" name is to avoid conflicts with the strata() function, but # still allow users to type "strata" as an arg. # coxph.getdata <- function(fit, y=TRUE, x=TRUE, stratax=TRUE, offset=FALSE) { ty <- fit[['y']] #avoid grabbing this by accident due to partial matching tx <- fit[['x']] # for x, fit$x will get fit$xlevels --> not good strat <- fit$strata Terms <- fit$terms if (is.null(attr(Terms, 'offset'))) offset <- FALSE if (offset) x<- TRUE if (!inherits(Terms, 'terms')) stop("invalid terms component of fit") strats <- attr(Terms, "specials")$strata if (length(strats)==0) stratax <- FALSE if ( (y && is.null(ty)) || (x && is.null(tx)) || (stratax && is.null(strat)) || offset) { # get the model frame m <- stats::model.frame(fit) # Pull things out if (y && is.null(ty)) ty <- model.extract(m, 'response') if (offset) toff <- model.extract(m, 'offset') # strata was saved in the fit if and only if x was if ((x || stratax) && is.null(tx)) { if (stratax) { temp <- untangle.specials(Terms, 'strata', 1) strat <- strata(m[temp$vars], shortlabel=T) } if (x) tx <- model.matrix(fit, data=m) } } else if (offset) toff <- fit$linear.predictors -(c(tx %*% fit$coef) - sum(fit$means*fit$coef)) temp <- list() if (y) temp$y <- ty if (x) temp$x <- tx if (stratax) temp$strata <- strat if (offset) temp$offset <- toff temp } survival/R/basehaz.R0000644000175100001440000000167112466715763014132 0ustar hornikusers# # This function is simply an alias for "survfit". In the Cox model # case users often look for the words "baseline hazard" # basehaz <- function (fit, centered = TRUE) { if (!inherits(fit, "coxph")) stop("must be a coxph object") sfit <- survfit(fit, se.fit=FALSE) if (!centered) { # The right thing to do here is to call survfit with a vector of # all zeros for the "subject to predict". But if there is a factor # in the model, there may be no subject at all who will give all # zeros, so we post process instead zcoef <- ifelse(is.na(coef(fit)), 0, coef(fit)) offset <- sum(fit$means * zcoef) chaz <- sfit$cumhaz * exp(-offset) } else chaz <- sfit$cumhaz new <- data.frame(hazard=chaz, time=sfit$time) strata <- sfit$strata if (!is.null(strata)) new$strata <- factor(rep(names(strata), strata), levels = names(strata)) new } survival/R/frailty.controlgauss.S0000644000175100001440000000556312470201064016671 0ustar hornikusers# $Id: frailty.controlgauss.S 11166 2008-11-24 22:10:34Z therneau $ # # The control function for REML on a gaussian # frailty.controlgauss <- function(opt, iter, old, fcoef, trH, loglik){ if (iter==0) { # initial call # Because of how the iteration works, 0 is not a useful trial value if (!is.null(opt$theta)) theta <- opt$theta #fixed theta case else { if (is.null(opt$init)) theta <- 1 else theta <- opt$init[1] } list(theta=theta) } else { if (is.null(opt$trace)) trace <-FALSE else trace <- opt$trace nfrail <- length(fcoef) fsum <- sum(fcoef^2) theta <- old$theta resid <- fsum/(nfrail - trH/theta) - theta # save history of the iteration, and get the next theta if (iter==1) { history <- c(theta=theta, resid=resid, fsum=fsum, trace=trH) if (is.null(opt$init )) { if (resid>0) theta <- theta*3 else theta <- theta/3 } else theta <- opt$init[2] list(theta=theta, done=FALSE, history=history) } else { history <- rbind(old$history, as.vector(c(theta, resid, fsum, trH))) if (iter ==2) { if (all(history[,2] > 0)) theta <- history[2,1]*2 else if (all(history[,2] <0)) theta <- history[2,1]/2 else theta <- mean(history[1:2,1]) if (trace) { print(history) cat(" new theta=", theta, "\n\n") } list(theta=theta, done=FALSE, history=history) } else { done <- (abs(history[iter,2]) < opt$eps) ord <- order(history[,1]) tempy <- history[ord,2] #x & y from left to right tempx <- history[ord,1] # make sure we have one positve and one negative y value # y must be positive near 0, and negative for large x if (all(tempy>0)) newtheta <- 2*max(tempx) else if (all(tempy<0)) newtheta <- .5 * min(tempx) else{ #find the latest point, and one on each side of 0 b1 <- (1:iter)[ord==iter] if (b1==1) b1 <-2 else if (b1==iter) b1 <- iter-1 # Brent's formula, straight from Numerical Recipies # Why, you may ask, don't we use the uniroot() function # which is built into S, and implements Brent's method? # Because all we want is the next guess for x. The interal # loop of coxph is calling us, not the other way around. R <- tempy[b1]/ tempy[b1+1] S <- tempy[b1]/ tempy[b1-1] U <- R/S P <- S* (U*(R-U)*(tempx[b1+1]-tempx[b1]) - (1-R)*(tempx[b1]-tempx[b1-1])) Q <- (U-1)*(R-1)*(S-1) newtheta <- tempx[b1] + P/Q # if the new guess is outside the brackets, do a binomial # search step if (newtheta > tempx[b1+1]) newtheta <- mean(tempx[b1+0:1]) if( newtheta < tempx[b1-1]) newtheta <- mean(tempx[b1-0:1]) } if (trace) { print(history) cat(" new theta=", format(newtheta), "\n\n") } list(theta=newtheta, done=done, history=history) } } } } survival/R/print.survreg.penal.S0000644000175100001440000000715412423461670016432 0ustar hornikusersprint.survreg.penal <- function(x, terms=FALSE, maxlabel=25, digits=max(options()$digits - 4, 3), ...) { if (!inherits(x, 'survreg.penal')) stop("Invalid object") if (!is.null(x$call)) { cat("Call:\n") dput(x$call) cat("\n") } if (!is.null(x$fail)) { cat(" Survreg failed.", x$fail, "\n") return() } savedig <- options(digits = digits) on.exit(options(savedig)) coef <- x$coefficients if (length(coef)==0) stop("Penalized fits must have an intercept!") # # Map terms to special print functions, and the list of iteration histories # pterms <- x$pterms nterms <- length(pterms) npenal <- sum(pterms>0) print.map <- rep(0,nterms) if (!is.null(x$printfun)) { temp <- unlist(lapply(x$printfun, is.null)) #which ones are missing print.map[pterms>0] <- (1:npenal) * (!temp) } # Tedious, but build up the coef matrix a term at a time print1 <- NULL pname1 <- NULL if (is.null(x$assign2)) alist <- x$assign else alist <- x$assign2 print2 <- NULL for (i in 1:nterms) { kk <- alist[[i]] if (print.map[i] >0) { j <- print.map[i] if (pterms[i]==2) temp <- (x$printfun[[j]])(x$frail, x$fvar, ,x$df[i], x$history[[j]]) else temp <- (x$printfun[[j]])(coef[kk], x$var[kk,kk], x$var2[kk,kk], x$df[i], x$history[[j]]) print1 <- rbind(print1, temp$coef) if (is.matrix(temp$coef)) { xx <- dimnames(temp$coef)[[1]] if (is.null(xx)) xx <- rep(names(pterms)[i], nrow(temp$coef)) else xx <- paste(names(pterms)[i], xx, sep=', ') pname1 <- c(pname1, xx) } else pname1 <- c(pname1, names(pterms)[i]) print2 <- c(print2, temp$history) } else if (terms && length(kk)>1) { pname1 <- c(pname1, names(pterms)[i]) temp <- coxph.wtest(x$var[kk,kk], coef[kk])$test print1 <- rbind(print1, c(NA, NA, NA, temp, x$df[i], 1-pchisq(temp, 1))) } else { pname1 <- c(pname1, names(coef)[kk]) tempe<- (diag(x$var))[kk] temp <- coef[kk]^2/ tempe print1 <- rbind(print1, cbind(coef[kk], sqrt(tempe), sqrt((diag(x$var2))[kk]), temp, 1, 1-pchisq(temp, 1))) } } # Format out the NA's temp <- cbind(format(print1[,1]), format(print1[,2]), format(print1[,3]), format(round(print1[,4], 2)), format(round(print1[,5], 2)), format(signif(print1[,6], 2))) temp <- ifelse(is.na(print1), "", temp) dimnames(temp) <- list(substring(pname1,1, maxlabel), c("coef","se(coef)", "se2", "Chisq","DF","p")) print(temp, quote=FALSE) # # Write out the remaider of the info # if (nrow(x$var)==length(coef)) cat("\nScale fixed at",format(x$scale),"\n") else if (length(x$scale)==1) cat ("\nScale=", format(x$scale), "\n") else { cat("\nScale:\n") print(x$scale, ...) } cat("\nIterations:", x$iter[1], "outer,", x$iter[2], "Newton-Raphson\n") if (length(print2)) { # cat("Penalized terms:\n") for (i in 1:length(print2)) cat(" ", print2[i], "\n") } logtest <- -2 * (x$loglik[1] - x$loglik[2]) df <- sum(x$df) - x$idf # cat("\n") cat("Degrees of freedom for terms=", format(round(x$df,1)), "\n") # cat("Loglik (initial,final) = ", format(round(x$loglik,2)), # " Penalty = ", format(x$penalty), "\n") cat("Likelihood ratio test=", format(round(logtest, 2)), " on ", round(df,1), " df,", " p=", format(1 - pchisq(logtest, df)), sep="") n <- length(x$linear.predictors) omit <- x$na.action if (length(omit)) cat("\n n=", n, " (", naprint(omit), ")\n", sep="") else cat(" n=", n, "\n") invisible() } survival/R/survreg.fit.S0000644000175100001440000001766313016105374014763 0ustar hornikusers# # Do the actual fit of a survreg model. This routine is for the case # of no penalized terms (splines, etc). # survreg.fit<- function(x, y, weights, offset, init, controlvals, dist, scale=0, nstrat=1, strata, parms=NULL, assign) { iter.max <- controlvals$iter.max eps <- controlvals$rel.tolerance toler.chol <- controlvals$toler.chol if (!is.matrix(x)) stop("Invalid X matrix ") n <- nrow(x) nvar <- ncol(x) ny <- ncol(y) if (is.null(offset)) offset <- rep(0,n) if (missing(weights)|| is.null(weights)) weights<- rep(1.0,n) else if (any(weights<=0)) stop("Invalid weights, must be >0") if (scale <0) stop("Invalid scale") if (scale >0 && nstrat >1) stop("Cannot have both a fixed scale and strata") if (nstrat>1 && (missing(strata) || length(strata)!= n)) stop("Invalid strata variable") if (nstrat==1) strata <- rep(1,n) if (scale >0) nstrat2 <- 0 # number of variances to estimate else nstrat2 <- nstrat if (is.character(dist)) { sd <- survreg.distributions[[dist]] if (is.null(sd)) stop ("Unrecognized distribution") } else sd <- dist if (!is.function(sd$density)) stop("Missing density function in the definition of the distribution") dnum <- match(sd$name, c("Extreme value", "Logistic", "Gaussian")) if (is.na(dnum)) { # We need to set up a callback routine # This returns the 5 number distribution summary (see the density # functions in survreg.distributions). Interval censored obs require # 2 evals and all others 1, so the call to the routine will have n2 # values. dnum <- 4 # flag for the C routine n2 <- n + sum(y[,ny]==3) # not needed, keep for documentation # # Create an expression that will be evaluated by the C-code, # but with knowledge of some current variables # In the R doc, this would be "body(function(z) {" # in Splus (Chambers book): "functionBody(function(z)" # same action, different name. Luckily 'quote' exists in both. # We make very sure the result is the right type and length here # rather than in the C code, for simplicity. f.expr <- quote({ if (length(parms)) temp <- sd$density(z, parms) else temp <- sd$density(z) if (!is.matrix(temp) || any(dim(temp) != c(n2,5)) || !is.numeric(temp)) stop("Density function returned an invalid matrix") as.vector(as.double(temp)) }) # create an isolated sandbox (frame or environment) in which # we can do the evaluation without endangering local objects # but still with knowlege of sd, parms, and n2 rho <- new.env() #inherits necessary objects } else { f.expr <- 1 #dummy values for the .Call rho <- 1 } # This is a subset of residuals.survreg: define the first and second # derivatives at z=0 for the 4 censoring types # Used below for starting estimates derfun <- function(y, eta, sigma, density, parms) { ny <- ncol(y) status <- y[,ny] z <- (y[,1] - eta)/sigma dmat <- density(z,parms) dtemp<- dmat[,3] * dmat[,4] #f' if (any(status==3)) { z2 <- (y[,2] - eta)/sigma dmat2 <- density(z2, parms) } else { dmat2 <- matrix(0,1,5) #dummy values z2 <- 0 } tdenom <- ((status==0) * dmat[,2]) + ((status==1) * 1 ) + ((status==2) * dmat[,1]) + ((status==3) * ifelse(z>0, dmat[,2]-dmat2[,2], dmat2[,1] - dmat[,1])) tdenom <- 1/(tdenom* sigma) dg <- -tdenom *(((status==0) * (0-dmat[,3])) + ((status==1) * dmat[,4]) + ((status==2) * dmat[,3]) + ((status==3) * (dmat2[,3]- dmat[,3]))) ddg <- (tdenom/sigma)*(((status==0) * (0- dtemp)) + ((status==1) * dmat[,5]) + ((status==2) * dtemp) + ((status==3) * (dmat2[,3]*dmat2[,4] - dtemp))) list(dg = dg, ddg = ddg - dg^2) } # # A good initial value of the scale turns out to be critical for successful # iteration, in a surprisingly large number of data sets. # The best way we've found to get one is to fit a model with only the # mean and the scale. We don't need to do this in 3 situations: # 1. The only covariate is a mean (this step is then just a duplicate # of the main fit). # 2. There are no scale parameters to estimate # 3. The user gave initial estimates for the scale # However, for 2 and 3 we still want the loglik for a mean only model # as a part of the returned object. # nvar2 <- nvar + nstrat2 meanonly <- (nvar==1 && all(x==1)) if (!meanonly) { yy <- ifelse(y[,ny]!=3, y[,1], (y[,1]+y[,2])/2 ) coef <- sd$init(yy, weights, parms) #starting estimate for this model #init returns \sigma^2, I need log(sigma) # We sometimes get into trouble with a small estimate of sigma, # (the surface isn't SPD), but never with a large one. Double it. if (scale >0) vars <- log(scale) else vars <- log(4*coef[2])/2 # log(2*sqrt(variance)) = log(4*var)/2 coef <- c(coef[1], rep(vars, nstrat)) # get a better initial value for the mean using the "glim" trick deriv <- derfun(y, yy, exp(vars), sd$density, parms) wt <- -1*deriv$ddg*weights coef[1] <- sum(weights*deriv$dg + wt*(yy -offset)) / sum(wt) # Now the fit proper (intercept only) fit0 <- .Call(Csurvreg6, iter = as.integer(20), nvar = as.integer(1), as.double(y), as.integer(ny), x = as.double(rep(1.0, n)), as.double(weights), as.double(offset), coef= as.double(coef), as.integer(nstrat2), as.integer(strata), as.double(eps), as.double(toler.chol), as.integer(dnum), f.expr, rho) } # # Fit the model with all covariates # if (is.numeric(init)) { if (length(init) == nvar && (nvar2 > nvar)) { # Add on the variance estimates from above init <- c(init, fit0$coef[-1]) } if (length(init) != nvar2) stop("Wrong length for initial parameters") if (scale >0) init <- c(init, log(scale)) } else { # Do the 'glim' method of finding an initial value of coef if (meanonly) { yy <- ifelse(y[,ny]!=3, y[,1], (y[,1]+y[,2])/2 ) coef <- sd$init(yy, weights, parms) if (scale >0) vars <- rep(log(scale), nstrat) else vars <- rep(log(4*coef[2])/2, nstrat) } else vars <- fit0$coef[-1] eta <- yy - offset #what would be true for a 'perfect' model deriv <- derfun(y, yy, exp(vars[strata]), sd$density, parms) wt <- -1*deriv$ddg*weights coef <- coxph.wtest(t(x)%*% (wt*x), c((wt*eta + weights*deriv$dg)%*% x), toler.chol=toler.chol)$solve init <- c(coef, vars) } # Now for the fit in earnest fit <- .Call(Csurvreg6, iter = as.integer(iter.max), as.integer(nvar), as.double(y), as.integer(ny), as.double(x), as.double(weights), as.double(offset), as.double(init), as.integer(nstrat2), as.integer(strata), as.double(eps), as.double(toler.chol), as.integer(dnum), f.expr, rho) if (iter.max >1 && fit$flag > nvar2) { warning("Ran out of iterations and did not converge") } cname <- dimnames(x)[[2]] if (is.null(cname)) cname <- paste("x", 1:ncol(x)) if (scale==0) cname <- c(cname, rep("Log(scale)", nstrat)) if (scale>0) fit$coef <- fit$coef[1:nvar2] names(fit$coef) <- cname if (meanonly) { coef0 <- fit$coef loglik <- rep(fit$loglik,2) } else { coef0 <- fit0$coef names(coef0) <- c("Intercept", rep("Log(scale)", nstrat)) loglik <- c(fit0$loglik, fit$loglik) } temp <- list(coefficients = fit$coef, icoef = coef0, var = matrix(fit$var, nvar2, dimnames=list(cname, cname)), loglik = loglik, iter = fit$iter, linear.predictors = c(x %*% fit$coef[1:nvar] + offset), df= length(fit$coef), score = fit$u ) temp } survival/R/survreg.distributions.S0000644000175100001440000001045712377203072017100 0ustar hornikusers# # Create the survreg.distributions object # survreg.distributions <- list( 'extreme' = list( name = "Extreme value", variance = function(parm) pi^2/6, init = function(x, weights, ...) { mean <- sum(x*weights)/ sum(weights) var <- sum(weights*(x-mean)^2)/ sum(weights) c(mean + .572, var/1.64) }, deviance= function(y, scale, parms) { status <- y[,ncol(y)] width <- ifelse(status==3,(y[,2] - y[,1])/scale, 1) temp <- width/(exp(width)-1) # the definition of "center" is discussed in the parametric # section of the survival document center <- ifelse(status==3, y[,1] - log(temp), y[,1]) temp3 <- (-temp) + log(1- exp(-exp(width))) loglik <- ifelse(status==1, -(1+log(scale)), ifelse(status==3, temp3, 0)) list(center=center, loglik=loglik) }, density = function(x,parms) { w <- exp(x) ww <- exp(-w) cbind(1-ww, ww, w*ww, (1-w), w*(w-3) +1) }, quantile = function(p,parms) log(-log(1-p)) ), logistic = list( name = "Logistic", variance = function(parm) pi^2/3, init = function(x, weights, ...) { mean <- sum(x*weights)/ sum(weights) var <- sum(weights*(x-mean)^2)/ sum(weights) c(mean, var/3.2) }, deviance= function(y, scale, parms) { status <- y[,ncol(y)] width <- ifelse(status==3,(y[,2] - y[,1])/scale, 0) # for the symmetric distributions "center" is obvious center <- ifelse(status==3, rowMeans(y), y[,1]) temp2 <- ifelse(status==3, exp(width/2), 2) #avoid a log(0) message temp3 <- log((temp2-1)/(temp2+1)) loglik <- ifelse(status==1, -log(4*scale), ifelse(status==3, temp3, 0)) list(center=center, loglik=loglik) }, density = function(x, parms) { w <- exp(x) cbind(w/(1+w), 1/(1+w), w/(1+w)^2, (1-w)/(1+w), (w*(w-4) +1)/(1+w)^2) }, quantile = function(p, parms) log(p/(1-p)) ), gaussian = list( name = "Gaussian", variance = function(parm) 1, init = function(x, weights, ...) { mean <- sum(x*weights)/ sum(weights) var <- sum(weights*(x-mean)^2)/ sum(weights) c(mean, var) }, deviance= function(y, scale, parms) { status <- y[,ncol(y)] width <- ifelse(status==3,(y[,2] - y[,1])/scale, 0) center <- ifelse(status==3, rowMeans(y), y[,1]) temp2 <- log(1 - 2*pnorm(width/2)) loglik <- ifelse(status==1, -log(sqrt(2*pi)*scale), ifelse(status==3, temp2, 0)) list(center=center, loglik=loglik) }, density = function(x, parms) { cbind(pnorm(x), pnorm(-x), dnorm(x), -x, x^2-1) }, quantile = function(p, parms) qnorm(p) ), weibull = list( name = "Weibull", dist = 'extreme', trans = function(y) log(y), dtrans= function(y) 1/y , itrans= function(x) exp(x) ), exponential = list( name = "Exponential", dist = 'extreme', trans = function(y) log(y), dtrans= function(y) 1/y, scale =1, itrans= function(x) exp(x) ), rayleigh = list( name = "Rayleigh", dist = 'extreme', trans = function(y) log(y), dtrans= function(y) 1/y, itrans= function(x) exp(x), scale =0.5 ), loggaussian = list( name = "Log Normal", dist = 'gaussian', trans = function(y) log(y), itrans= function(x) exp(x), dtrans= function(y) 1/y ), lognormal = list( name = "Log Normal", dist = 'gaussian', trans = function(y) log(y), itrans= function(x) exp(x), dtrans= function(y) 1/y ), loglogistic = list( name = "Log logistic", dist = 'logistic', trans = function(y) log(y), dtrans= function(y) 1/y , itrans= function(x) exp(x) ), t = list( name = "Student-t", variance = function(df) df/(df-2), parms = c(df=4), init = function(x, weights, df) { if (df <=2) stop ("Degrees of freedom must be >=3") mean <- sum(x*weights)/ sum(weights) var <- sum(weights*(x-mean)^2)/ sum(weights) c(mean, var*(df-2)/df) }, deviance= function(y, scale, parms) { status <- y[,ncol(y)] width <- ifelse(status==3,(y[,2] - y[,1])/scale, 0) center <- ifelse(status==3, rowMeans(y), y[,1]) temp2 <- log(1 - 2*pt(width/2, df=parms)) loglik <- ifelse(status==1, -log(dt(0, df=parms)*scale), ifelse(status==3, temp2, 0)) list(center=center, loglik=loglik) }, density = function(x, df) { cbind(pt(x, df), pt(-x, df), dt(x,df), -(df+1)*x/(df+x^2), (df+1)*(x^2 *(df+3)/(df+x^2) - 1)/(df +x^2)) }, quantile = function(p, df) qt(p, df) ) ) survival/R/summary.aareg.S0000644000175100001440000001023613016105374015245 0ustar hornikusers# The summary routine for aareg models. # A lot of the work below relates to one particular issue: the coeffients # of an aareg model often get "wild" near the end (at the largest times). # So, a common case is to # fit the model (very slow) # look at the printout -- Hmmm x1 is significant, x2 not, ...., why? # look at plot(fit) and # oh my gosh, I should have cut the time scale off at 520 days # # This routine allows one to do that. If maxtime is given, the overall # test statistic is re-computed. One consequence is that lots of the # intermediate material from the fit had to be included in the aareg # object. # The "variance" based weighting for a test is not allowed, because it would # have meant an awful lot more stuff to pass, lots more work, for a test # that is rarely used. # summary.aareg <- function(object, maxtime, test=c('aalen', 'nrisk'), scale=1,...) { if (!inherits(object, 'aareg')) stop ("Must be an aareg object") if (missing(test)) test <- object$test test <- match.arg(test) if (!missing(maxtime)) ntime <- sum(object$time <= maxtime) else ntime <- nrow(object$coefficient) times <- object$time[1:ntime] if (test=='aalen') { twt <- (as.matrix(object$tweight))[1:ntime,] scale <- apply(twt, 2, sum)/scale } else { twt <- object$nrisk[1:ntime] scale <- ntime/scale } # Compute a "slope" for each line, using appropriate weighting # Since this is a single variable model, no intercept, I # don't need to call lm.wfit! tx <- as.matrix(twt * object$coefficient[1:ntime,]) ctx <- apply(tx, 2, cumsum) if (is.matrix(twt) && ncol(twt) >1) tempwt <- apply(twt*times^2, 2, sum) else tempwt <- sum(twt*times^2) if (ncol(ctx) >1) slope<- apply(ctx* times, 2, sum)/ tempwt else slope <- sum(ctx*times) / tempwt if (!missing(maxtime) || object$test != test) { # Compute the test statistic test.stat <- apply(tx, 2, sum) #sum of tested coefficients test.var <- t(tx) %*% tx #std Poisson, ind coefficients variance if (!is.null(object$dfbeta)) { dd <- dim(object$dfbeta) indx <- match(unique(times), object$times) influence <- matrix(0, dd[1], dd[2]) for (i in 1:length(indx)) { if (test=='aalen') influence <- influence + object$dfbeta[,,i] %*% diag(twt[indx[i],]) else influence <- influence + object$dfbeta[,,i]* object$nrisk[indx[i]] } if (!is.null(object$cluster)) influence <- rowsum(influence, cluster) test.var2 <- t(influence) %*% influence } else test.var2 <- NULL } else { #use the value that was passed in test.stat <- object$test.statistic test.var <- object$test.var test.var2 <- object$test.var2 #NULL if dfbeta option was false } # create the matrix for printing out # The chisquare test does not include the intercept se1 <- sqrt(diag(test.var)) if (is.null(test.var2)) { mat <- cbind(slope, test.stat/scale, se1/scale, test.stat/se1, 2*pnorm(-abs(test.stat/se1))) dimnames(mat) <- list((dimnames(object$coefficient)[[2]]), c("slope", "coef", "se(coef)", "z", "p")) chi <- test.stat[-1] %*% solve(test.var[-1,-1],test.stat[-1]) } else { se2 <- sqrt(diag(test.var2)) mat <- cbind(slope, test.stat/scale, se1/scale, se2/scale, test.stat/se2, 2*pnorm(-abs(test.stat/se2))) dimnames(mat) <- list((dimnames(object$coefficient)[[2]]), c("slope", "coef", "se(coef)", "robust se", "z", "p")) chi <- test.stat[-1] %*% solve(test.var2[-1,-1], test.stat[-1]) } temp <- list(table=mat, test=test, test.statistic=test.stat, test.var=test.var, test.var2=test.var2, chisq=chi, n = c(object$n[1], length(unique(times)), object$n[3])) class(temp) <- 'summary.aareg' temp } print.summary.aareg <- function(x, ...) { print(signif(x$table,3)) chi <- x$chisq df <- length(x$test.statistic) -1 cat("\nChisq=", format(round(chi,2)), " on ", df, " df, p=", signif(1- pchisq(chi, df),2), "; test weights=", x$test, "\n", sep='') invisible(x$table) } survival/R/predict.coxph.penal.S0000644000175100001440000000701212470201064016334 0ustar hornikusers# $Id: predict.coxph.penal.S 11516 2012-04-24 12:49:14Z therneau $ predict.coxph.penal <- function(object, newdata, type=c("lp", "risk", "expected", "terms"), se.fit=FALSE, terms=names(object$assign), collapse, safe=FALSE, ...) { type <- match.arg(type) n <- object$n pterms <- object$pterms # If there are no sparse terms if (!any(pterms==2) || (missing(newdata) && se.fit==FALSE && type!='terms')) NextMethod('predict',object,...) else { # treat the sparse term as an offset term # It gets picked up in the linear predictor, so all I need to # do is "X" it out of the model so that it doesn't get picked up # as a part of the X matrix and etc. # I know that the sparse term is a single column BTW # termname <- names(object$pterms) sparsename <- termname[object$pterms==2] nvar <- length(termname) na.action <- object$na.action object$na.action <- NULL if (missing(newdata) && (se.fit || type=='terms')) { # I need the X matrix x <- object[['x']] # object$x might grab object$xlevels if (is.null(x)) { temp <- coxph.getdata(object, y=TRUE, x=TRUE, stratax=TRUE) if (is.null(object$y)) object$y <- temp$y if (is.null(object$strata)) object$strata <- temp$strata x <- temp$x } xvar <- match(sparsename, dimnames(x)[[2]]) indx <- as.numeric(as.factor(x[,xvar])) object$x <- x[, -xvar, drop=FALSE] } if (nvar==1) { # Only the sparse term! if (!missing(newdata)) { n <- nrow(as.data.frame(newdata)) pred <- rep(0,n) } se <- sqrt(object$fvar[indx]) pred <- object$linear.predictor if (type=='risk') pred <- exp(pred) if (type=='expected') { pred <- object$y[,ncol(object$y)] -object$residuals se.fit=FALSE } } else { # temporarily remove the sparse term, call NextMethod, # and then put it back oldTerms <- object$terms temp <- attr(object$terms, 'term.labels') object$terms <- object$terms[-match(sparsename, temp)] pred <- NextMethod('predict',object,terms=terms,...) object$terms<- oldTerms if (se.fit) { se <- pred$se.fit pred <- pred$fit } if (type=='terms' && missing(newdata)) { # In this case (only) I add the sparse term back in spterm <- object$frail[indx] spstd <- sqrt(object$fvar[indx]) if (nvar==2) { if (xvar==2) { pred <- cbind(pred, spterm) if (se.fit) se <- cbind(se, spstd) } else { pred <- cbind(spterm, pred) if (se.fit) se <- cbind(spstd, se) } } else { first <- if (xvar==1) 0 else 1:(xvar-1) secnd <- if (xvar==nvar) 0 else (xvar+1):nvar pred <- cbind(pred[,first], spterm, pred[,secnd]) if (se.fit) se <- cbind(se[,first], spstd, se[,secnd]) } dimnames(pred) <- list(dimnames(x)[[1]], termname) if (se.fit) dimnames(se) <- dimnames(pred) } } #Expand out the missing values in the result # But only if operating on the original dataset if (missing(newdata) && !is.null(na.action)) { pred <- naresid(na.action, pred) if (is.matrix(pred)) n <- nrow(pred) else n <- length(pred) if(se.fit) se <- naresid(na.action, se) } # Collapse over subjects, if requested if (!missing(collapse)) { if (length(collapse) != n) stop("Collapse vector is the wrong length") pred <- drop(rowsum(pred, collapse)) if (se.fit) se <- sqrt(drop(rowsum(se^2, collapse))) } if (se.fit) list(fit=pred, se.fit=se) else pred } } survival/R/frailty.gamma.S0000644000175100001440000001145313016105374015227 0ustar hornikusers# # Defining function for gamma frailty fits # frailty.gamma <- function(x, sparse=(nclass >5), theta, df, eps= 1e-5, method=c("em", "aic", "df", "fixed"), ...) { nclass <- length(unique(x[!is.na(x)])) if (sparse) x <-as.numeric(factor(x)) #drop extra levels if a factor else{ x <- factor(x) attr(x,'contrasts') <- contr.treatment(nclass, contrasts=FALSE) } class(x) <- c("coxph.penalty",class(x)) # Check for consistency of the arguments if (missing(method)) { if (!missing(theta)) { method <- 'fixed' if (!missing(df)) stop("Cannot give both a df and theta argument") } else if (!missing(df)) method <- 'df' } method <- match.arg(method) if (method=='df' && missing(df)) stop("Method = df but no df argument") if (method=='fixed' && missing(theta)) stop("Method= fixed but no theta argument") if (method!='df' && !missing(df)) stop("Method is not df, but have a df argument") if (method !='fixed' && !missing(theta)) stop("Method is not 'fixed', but have a theta argument") pfun<- function(coef, theta, ndeath){ if (theta==0) list(recenter=0, penalty=0, flag=TRUE) else { recenter <- log(mean(exp(coef))) coef <- coef - recenter nu <- 1/theta list(recenter=recenter, first= (exp(coef) -1) * nu, second= exp(coef) * nu, penalty= -sum(coef)*nu, # The exp part sums to a constant flag=FALSE) } } printfun <- function(coef, var, var2, df, history) { if (!is.null(history$history)) theta <- history$history[nrow(history$history),1] else theta <- history$theta clog <- history$c.loglik if (is.matrix(var)) test <- coxph.wtest(var, coef)$test else test <- sum(coef^2/var) df2 <- max(df, .5) # Stop silly p-values list(coef=c(NA, NA, NA, test, df, 1-pchisq(test, df2)), history=paste("Variance of random effect=", format(theta), " I-likelihood =", format(round(clog,1), digits=10))) } # The final coxph object will contain a copy of printfun. Stop it from # also containing huge unnecessary variables, e.g. 'x', known at this # point in time. Not an issue for pfun, which does not get saved. # Setting to globalenv() will not suffice since coxph.wtest is not visible # outside the survival library's name space. temp <- new.env(parent=globalenv()) assign("cox.zph", cox.zph, envir=temp) #make a private copy environment(printfun) <- temp if (method=='fixed') { temp <- list(pfun=pfun, printfun=printfun, diag =TRUE, sparse= sparse, cargs = c("x", "status", "loglik"), cfun = frailty.controlgam, cparm= list(theta=theta, ...)) } else if (method=='em'){ temp <- list(pfun=pfun, printfun=printfun, diag =TRUE, sparse= sparse, cargs = c("x", "status", "loglik"), cfun = frailty.controlgam, cparm= c(list(eps=eps), ...)) } else if (method=='aic') { temp <- list(pfun=pfun, printfun=printfun, diag =TRUE, sparse= sparse, cargs = c("x", "status", "loglik", "neff","df", "plik"), cparm=list(eps=eps, lower=0, init=c(.1, 1), ...), cfun =function(opt, iter, old, group, status, loglik,...){ temp <- frailty.controlaic(opt, iter, old, ...) if (iter >0) { #compute correction to the loglik if (old$theta==0) correct <- 0 else { if (is.matrix(group)) group <-c(group %*% 1:ncol(group)) d <- tapply(status,group,sum) correct <- frailty.gammacon(d, 1/old$theta) } temp$c.loglik <- loglik + correct } temp }) } else { #df method # The initial guess is based on the observation that theta=1 often # gives about df= (#groups)/3 if (missing(eps)) eps <- .1 temp <- list(pfun=pfun, printfun=printfun, diag =TRUE, sparse= sparse, cargs= c('df', "x", "status", "loglik"), cparm=list(df=df, thetas=0, dfs=0, eps=eps, guess=3*df/length(unclass(x)), ...), cfun =function(opt, iter, old, df, group, status, loglik){ temp <- frailty.controldf(opt, iter, old, df) if (iter >0) { #compute correction to the loglik if (old$theta==0) correct <- 0 else { if (is.matrix(group)) group <-c(group %*% 1:ncol(group)) d <- tapply(status,group,sum) correct <- frailty.gammacon(d, 1/old$theta) } temp$c.loglik <- loglik + correct } temp }) } # If not sparse, give shorter names to the coefficients, so that any # printout of them is readable. if (!sparse) { vname <- paste("gamma", levels(x), sep=':') temp <- c(temp, list(varname=vname)) } attributes(x) <- c(attributes(x), temp) x } survival/R/survConcordance.fit.R0000644000175100001440000000567013065013243016413 0ustar hornikusers# Automatically generated from the noweb directory survConcordance.fit <- function(y, x, strata, weight) { # The coxph program may occassionally fail, and this will kill the C # routine below if (any(is.na(x)) || any(is.na(y))) return(NULL) btree <- function(n) { ranks <- rep(0L, n) #will be overwritten yet.to.do <- 1:n depth <- floor(logb(n,2)) start <- as.integer(2^depth) lastrow.length <- 1+n-start indx <- seq(1L, by=2L, length= lastrow.length) ranks[yet.to.do[indx]] <- start + 0:(length(indx)-1L) yet.to.do <- yet.to.do[-indx] while (start >1) { start <- as.integer(start/2) indx <- seq(1L, by=2L, length=start) ranks[yet.to.do[indx]] <- start + 0:(start-1L) yet.to.do <- yet.to.do[-indx] } ranks } docount <- function(stime, risk, wts) { if (attr(stime, 'type') == 'right') { ord <- order(stime[,1], -stime[,2]) ux <- sort(unique(risk)) n2 <- length(ux) index <- btree(n2)[match(risk[ord], ux)] - 1L .Call(Cconcordance1, stime[ord,], as.double(wts[ord]), as.integer(index), as.integer(length(ux))) } else if (attr(stime, 'type') == "counting") { sort.stop <- order(-stime[,2], stime[,3]) sort.start <- order(-stime[,1]) ux <- sort(unique(risk)) n2 <- length(ux) index <- btree(n2)[match(risk, ux)] - 1L .Call(Cconcordance2, stime, as.double(wts), as.integer(index), as.integer(length(ux)), as.integer(sort.stop-1L), as.integer(sort.start-1L)) } else stop("Invalid survival type for concordance") } if (missing(weight) || length(weight)==0) weight <- rep(1.0, length(x)) storage.mode(y) <- "double" if (missing(strata) || length(strata)==0) { count <- docount(y, x, weight) if (count[1]==0 && count[2]==0) count[5]<-0 else count[5] <- 2*sqrt(count[5]) names(count) <- c("concordant", "discordant", "tied.risk", "tied.time", "std(c-d)") } else { strata <- as.factor(strata) ustrat <- levels(strata)[table(strata) >0] #some strata may have 0 obs count <- matrix(0., nrow=length(ustrat), ncol=5) for (i in 1:length(ustrat)) { keep <- which(strata == ustrat[i]) count[i,] <- docount(y[keep,,drop=F], x[keep], weight[keep]) } count[,5] <- 2*sqrt(ifelse(count[,1]+count[,2]==0, 0, count[,5])) dimnames(count) <- list(ustrat, c("concordant", "discordant", "tied.risk", "tied.time", "std(c-d)")) } count } survival/R/print.survdiff.S0000644000175100001440000000236211732700061015453 0ustar hornikusers# $Date: 2006-08-28 14:31:20 $ $Id: print.survdiff.S 11166 2008-11-24 22:10:34Z therneau $ print.survdiff <- function(x, digits = max(options()$digits - 4, 3), ...) { saveopt <-options(digits=digits) on.exit(options(saveopt)) if (!inherits(x, 'survdiff')) stop("Object is not the result of survdiff") if (!is.null(cl<- x$call)) { cat("Call:\n") dput(cl) cat("\n") } omit <- x$na.action if (length(omit)) cat("n=", sum(x$n), ", ", naprint(omit), ".\n\n", sep='') if (length(x$n)==1) { z <- sign(x$exp - x$obs) * sqrt(x$chisq) temp <- c(x$obs, x$exp, z, signif(1-pchisq(x$chisq, 1),digits)) names(temp) <- c("Observed", "Expected", "Z", "p") print(temp) } else { if (is.matrix(x$obs)){ otmp <- apply(x$obs,1,sum) etmp <- apply(x$exp,1,sum) } else { otmp <- x$obs etmp <- x$exp } df <- (sum(1*(etmp>0))) -1 temp <- cbind(x$n, otmp, etmp, ((otmp-etmp)^2)/ etmp, ((otmp-etmp)^2)/ diag(x$var)) dimnames(temp) <- list(names(x$n), c("N", "Observed", "Expected", "(O-E)^2/E", "(O-E)^2/V")) print(temp) cat("\n Chisq=", format(round(x$chisq,1)), " on", df, "degrees of freedom, p=", format(signif(1-pchisq(x$chisq, df),digits)), "\n") } invisible(x) } survival/R/lines.survfit.coxph.S0000644000175100001440000000042012703163037016421 0ustar hornikusers# $Id: lines.survfit.coxph.S 11166 2008-11-24 22:10:34Z therneau $ lines.survfit.coxph <- function(x, mark.time=FALSE, ...) { if (is.logical(mark.time) & mark.time) stop("Invalid value for mark.time") invisible(NextMethod('lines', mark.time=mark.time)) } survival/R/coxph.R0000644000175100001440000003627113065013232013614 0ustar hornikusers# Automatically generated from the noweb directory #tt <- function(x) x coxph <- function(formula, data, weights, subset, na.action, init, control, ties= c("efron", "breslow", "exact"), singular.ok =TRUE, robust=FALSE, model=FALSE, x=FALSE, y=TRUE, tt, method=ties, ...) { ties <- match.arg(ties) Call <- match.call() ## We want to pass any ... args to coxph.control, but not pass things ## like "dats=mydata" where someone just made a typo. The use of ... ## is simply to allow things like "eps=1e6" with easier typing extraArgs <- list(...) if (length(extraArgs)) { controlargs <- names(formals(coxph.control)) #legal arg names indx <- pmatch(names(extraArgs), controlargs, nomatch=0L) if (any(indx==0L)) stop(gettextf("Argument %s not matched", names(extraArgs)[indx==0L]), domain = NA) } if (missing(control)) control <- coxph.control(...) # create a call to model.frame() that contains the formula (required) # and any other of the relevant optional arguments # then evaluate it in the proper frame indx <- match(c("formula", "data", "weights", "subset", "na.action"), names(Call), nomatch=0) if (indx[1] ==0) stop("A formula argument is required") temp <- Call[c(1,indx)] # only keep the arguments we wanted temp[[1L]] <- quote(stats::model.frame) # change the function called special <- c("strata", "cluster", "tt") temp$formula <- if(missing(data)) terms(formula, special) else terms(formula, special, data=data) # Make "tt" visible for coxph formulas, without making it visible elsewhere if (!is.null(attr(temp$formula, "specials")$tt)) { coxenv <- new.env(parent= environment(formula)) assign("tt", function(x) x, env=coxenv) environment(temp$formula) <- coxenv } mf <- eval(temp, parent.frame()) if (nrow(mf) ==0) stop("No (non-missing) observations") Terms <- terms(mf) Y <- model.extract(mf, "response") if (!inherits(Y, "Surv")) stop("Response must be a survival object") type <- attr(Y, "type") if (type!='right' && type!='counting') stop(paste("Cox model doesn't support \"", type, "\" survival data", sep='')) data.n <- nrow(Y) #remember this before any time transforms if (control$timefix) Y <- aeqSurv(Y) if (length(attr(Terms, 'variables')) > 2) { # a ~1 formula has length 2 ytemp <- terms.inner(formula[1:2]) xtemp <- terms.inner(formula[-2]) if (any(!is.na(match(xtemp, ytemp)))) warning("a variable appears on both the left and right sides of the formula") } # The time transform will expand the data frame mf. To do this # it needs Y and the strata. Everything else (cluster, offset, weights) # should be extracted after the transform # strats <- attr(Terms, "specials")$strata if (length(strats)) { stemp <- untangle.specials(Terms, 'strata', 1) if (length(stemp$vars)==1) strata.keep <- mf[[stemp$vars]] else strata.keep <- strata(mf[,stemp$vars], shortlabel=TRUE) strats <- as.numeric(strata.keep) } timetrans <- attr(Terms, "specials")$tt if (missing(tt)) tt <- NULL if (length(timetrans)) { timetrans <- untangle.specials(Terms, 'tt') ntrans <- length(timetrans$terms) if (is.null(tt)) { tt <- function(x, time, riskset, weights){ #default to O'Brien's logit rank obrien <- function(x) { r <- rank(x) (r-.5)/(.5+length(r)-r) } unlist(tapply(x, riskset, obrien)) } } if (is.function(tt)) tt <- list(tt) #single function becomes a list if (is.list(tt)) { if (any(!sapply(tt, is.function))) stop("The tt argument must contain function or list of functions") if (length(tt) != ntrans) { if (length(tt) ==1) { temp <- vector("list", ntrans) for (i in 1:ntrans) temp[[i]] <- tt[[1]] tt <- temp } else stop("Wrong length for tt argument") } } else stop("The tt argument must contain a function or list of functions") if (ncol(Y)==2) { if (length(strats)==0) { sorted <- order(-Y[,1], Y[,2]) newstrat <- rep.int(0L, nrow(Y)) newstrat[1] <- 1L } else { sorted <- order(strats, -Y[,1], Y[,2]) #newstrat marks the first obs of each strata newstrat <- as.integer(c(1, 1*(diff(strats[sorted])!=0))) } if (storage.mode(Y) != "double") storage.mode(Y) <- "double" counts <- .Call(Ccoxcount1, Y[sorted,], as.integer(newstrat)) tindex <- sorted[counts$index] } else { if (length(strats)==0) { sort.end <- order(-Y[,2], Y[,3]) sort.start<- order(-Y[,1]) newstrat <- c(1L, rep(0, nrow(Y) -1)) } else { sort.end <- order(strats, -Y[,2], Y[,3]) sort.start<- order(strats, -Y[,1]) newstrat <- c(1L, as.integer(diff(strats[sort.end])!=0)) } if (storage.mode(Y) != "double") storage.mode(Y) <- "double" counts <- .Call(Ccoxcount2, Y, as.integer(sort.start -1L), as.integer(sort.end -1L), as.integer(newstrat)) tindex <- counts$index } Y <- Surv(rep(counts$time, counts$nrisk), counts$status) type <- 'right' # new Y is right censored, even if the old was (start, stop] mf <- mf[tindex,] strats <- rep(1:length(counts$nrisk), counts$nrisk) weights <- model.weights(mf) if (!is.null(weights) && any(!is.finite(weights))) stop("weights must be finite") tcall <- attr(Terms, 'variables')[timetrans$terms+2] pvars <- attr(Terms, 'predvars') pmethod <- sub("makepredictcall.", "", as.vector(methods("makepredictcall"))) for (i in 1:ntrans) { newtt <- (tt[[i]])(mf[[timetrans$var[i]]], Y[,1], strats, weights) mf[[timetrans$var[i]]] <- newtt nclass <- class(newtt) if (any(nclass %in% pmethod)) { # It has a makepredictcall method dummy <- as.call(list(as.name(class(newtt)[1]), tcall[[i]][[2]])) ptemp <- makepredictcall(newtt, dummy) pvars[[timetrans$terms[i]+2]] <- ptemp } } attr(Terms, "predvars") <- pvars } cluster<- attr(Terms, "specials")$cluster if (length(cluster)) { robust <- TRUE #flag to later compute a robust variance tempc <- untangle.specials(Terms, 'cluster', 1:10) ord <- attr(Terms, 'order')[tempc$terms] if (any(ord>1)) stop ("Cluster can not be used in an interaction") cluster <- strata(mf[,tempc$vars], shortlabel=TRUE) #allow multiples dropterms <- tempc$terms #we won't want this in the X matrix # Save away xlevels after removing cluster (we don't want to save upteen # levels of that variable, which we will never need). xlevels <- .getXlevels(Terms[-tempc$terms], mf) } else { dropterms <- NULL if (missing(robust)) robust <- FALSE xlevels <- .getXlevels(Terms, mf) } contrast.arg <- NULL #due to shared code with model.matrix.coxph attr(Terms, "intercept") <- 1 adrop <- 0 #levels of "assign" to be dropped; 0= intercept stemp <- untangle.specials(Terms, 'strata', 1) if (length(stemp$vars) > 0) { #if there is a strata statement hasinteractions <- FALSE for (i in stemp$vars) { #multiple strata terms are allowed # The factors attr has one row for each variable in the frame, one # col for each term in the model. Pick rows for each strata # var, and find if it participates in any interactions. if (any(attr(Terms, 'order')[attr(Terms, "factors")[i,] >0] >1)) hasinteractions <- TRUE } if (!hasinteractions) dropterms <- c(dropterms, stemp$terms) else adrop <- c(0, match(stemp$var, colnames(attr(Terms, 'factors')))) } if (length(dropterms)) { temppred <- attr(terms, "predvars") Terms2 <- Terms[ -dropterms] if (!is.null(temppred)) { # subscripting a Terms object currently drops predvars, in error attr(Terms2, "predvars") <- temppred[-(1+dropterms)] # "Call" object } X <- model.matrix(Terms2, mf, constrasts=contrast.arg) # we want to number the terms wrt the original model matrix # Do not forget the intercept, which will be a zero renumber <- match(colnames(attr(Terms2, "factors")), colnames(attr(Terms, "factors"))) attr(X, "assign") <- c(0, renumber)[1+attr(X, "assign")] } else X <- model.matrix(Terms, mf, contrasts=contrast.arg) # drop the intercept after the fact, and also drop strata if necessary Xatt <- attributes(X) xdrop <- Xatt$assign %in% adrop #columns to drop (always the intercept) X <- X[, !xdrop, drop=FALSE] attr(X, "assign") <- Xatt$assign[!xdrop] #if (any(adrop>0)) attr(X, "contrasts") <- Xatt$contrasts[-adrop] #else attr(X, "contrasts") <- Xatt$contrasts attr(X, "contrasts") <- Xatt$contrasts offset <- model.offset(mf) if (is.null(offset) | all(offset==0)) offset <- rep(0., nrow(mf)) else if (any(!is.finite(offset))) stop("offsets must be finite") weights <- model.weights(mf) if (!is.null(weights) && any(!is.finite(weights))) stop("weights must be finite") assign <- attrassign(X, Terms) contr.save <- attr(X, "contrasts") if (missing(init)) init <- NULL else { if (length(init) != ncol(X)) stop("wrong length for init argument") temp <- X %*% init - sum(colMeans(X) * init) if (any(temp < .Machine$double.min.exp | temp > .Machine$double.max.exp)) stop("initial values lead to overflow or underflow of the exp function") } pterms <- sapply(mf, inherits, 'coxph.penalty') if (any(pterms)) { pattr <- lapply(mf[pterms], attributes) pname <- names(pterms)[pterms] # # Check the order of any penalty terms ord <- attr(Terms, "order")[match(pname, attr(Terms, 'term.labels'))] if (any(ord>1)) stop ('Penalty terms cannot be in an interaction') pcols <- assign[match(pname, names(assign))] fit <- coxpenal.fit(X, Y, strats, offset, init=init, control, weights=weights, method=method, row.names(mf), pcols, pattr, assign) } else { if( method=="breslow" || method =="efron") { if (type== 'right') fitter <- get("coxph.fit") else fitter <- get("agreg.fit") } else if (method=='exact') { if (type== "right") fitter <- get("coxexact.fit") else fitter <- get("agexact.fit") } else stop(paste ("Unknown method", method)) fit <- fitter(X, Y, strats, offset, init, control, weights=weights, method=method, row.names(mf)) } if (is.character(fit)) { fit <- list(fail=fit) class(fit) <- 'coxph' } else { if (!is.null(fit$coefficients) && any(is.na(fit$coefficients))) { vars <- (1:length(fit$coefficients))[is.na(fit$coefficients)] msg <-paste("X matrix deemed to be singular; variable", paste(vars, collapse=" ")) if (singular.ok) warning(msg) else stop(msg) } fit$n <- data.n fit$nevent <- sum(Y[,ncol(Y)]) fit$terms <- Terms fit$assign <- assign class(fit) <- fit$method if (robust) { fit$naive.var <- fit$var fit$method <- method # a little sneaky here: by calling resid before adding the # na.action method, I avoid having missings re-inserted # I also make sure that it doesn't have to reconstruct X and Y fit2 <- c(fit, list(x=X, y=Y, weights=weights)) if (length(strats)) fit2$strata <- strats if (length(cluster)) { temp <- residuals.coxph(fit2, type='dfbeta', collapse=cluster, weighted=TRUE) # get score for null model if (is.null(init)) fit2$linear.predictors <- 0*fit$linear.predictors else fit2$linear.predictors <- c(X %*% init) temp0 <- residuals.coxph(fit2, type='score', collapse=cluster, weighted=TRUE) } else { temp <- residuals.coxph(fit2, type='dfbeta', weighted=TRUE) fit2$linear.predictors <- 0*fit$linear.predictors temp0 <- residuals.coxph(fit2, type='score', weighted=TRUE) } fit$var <- t(temp) %*% temp u <- apply(as.matrix(temp0), 2, sum) fit$rscore <- coxph.wtest(t(temp0)%*%temp0, u, control$toler.chol)$test } #Wald test if (length(fit$coefficients) && is.null(fit$wald.test)) { #not for intercept only models, or if test is already done nabeta <- !is.na(fit$coefficients) # The init vector might be longer than the betas, for a sparse term if (is.null(init)) temp <- fit$coefficients[nabeta] else temp <- (fit$coefficients - init[1:length(fit$coefficients)])[nabeta] fit$wald.test <- coxph.wtest(fit$var[nabeta,nabeta], temp, control$toler.chol)$test } na.action <- attr(mf, "na.action") if (length(na.action)) fit$na.action <- na.action if (model) { if (length(timetrans)) { # Fix up the model frame -- still in the thinking stage mf[[".surv."]] <- Y mf[[".strata."]] <- strats stop("Time transform + model frame: code incomplete") } fit$model <- mf } if (x) { fit$x <- X if (length(strats)) { if (length(timetrans)) fit$strata <- strats else fit$strata <- strata.keep } } if (y) fit$y <- Y } if (!is.null(weights) && any(weights!=1)) fit$weights <- weights names(fit$means) <- names(fit$coefficients) fit$formula <- formula(Terms) if (length(xlevels) >0) fit$xlevels <- xlevels fit$contrasts <- contr.save if (any(offset !=0)) fit$offset <- offset fit$call <- Call fit$method <- method fit } survival/R/agexact.fit.S0000644000175100001440000000545212113164602014667 0ustar hornikusers agexact.fit <- function(x, y, strata, offset, init, control, weights, method, rownames) { if (!is.matrix(x)) stop("Invalid formula for cox fitting function") if (!is.null(weights) && any(weights!=1)) stop("Case weights are not supported for the exact method") n <- nrow(x) nvar <- ncol(x) if (ncol(y)==3) { start <- y[,1] stopp <- y[,2] event <- y[,3] } else { start <- rep(0,n) stopp <- y[,1] event <- y[,2] } # Sort the data (or rather, get a list of sorted indices) if (length(strata)==0) { sorted <- order(stopp, -event) newstrat <- as.integer(rep(0,n)) } else { sorted <- order(strata, stopp, -event) strata <- (as.numeric(strata))[sorted] newstrat <- as.integer(c(1*(diff(strata)!=0), 1)) } if (is.null(offset)) offset <- rep(0,n) sstart <- as.double(start[sorted]) sstop <- as.double(stopp[sorted]) sstat <- as.integer(event[sorted]) if (is.null(nvar)) { # A special case: Null model. Not worth coding up stop("Cannot handle a null model + exact calculation (yet)") } if (!is.null(init)) { if (length(init) != nvar) stop("Wrong length for inital values") } else init <- rep(0,nvar) agfit <- .C(Cagexact, iter= as.integer(control$iter.max), as.integer(n), as.integer(nvar), sstart, sstop, sstat, x= x[sorted,], as.double(offset[sorted]), newstrat, means = double(nvar), coef= as.double(init), u = double(nvar), imat= double(nvar*nvar), loglik=double(2), flag=integer(1), double(2*nvar*nvar +nvar*4 + n), integer(2*n), as.double(control$eps), as.double(control$toler.chol), sctest=double(1)) var <- matrix(agfit$imat,nvar,nvar) coef <- agfit$coef if (agfit$flag < nvar) which.sing <- diag(var)==0 else which.sing <- rep(FALSE,nvar) infs <- abs(agfit$u %*% var) if (control$iter.max >1) { if (agfit$flag == 1000) warning("Ran out of iterations and did not converge") else { infs <- ((infs > control$eps) & infs > control$toler.inf*abs(coef)) if (any(infs)) warning(paste("Loglik converged before variable ", paste((1:nvar)[infs],collapse=","), "; beta may be infinite. ")) } } names(coef) <- dimnames(x)[[2]] lp <- x %*% coef + offset - sum(coef *agfit$means) score <- as.double(exp(lp[sorted])) agres <- .C(Cagmart, as.integer(n), as.integer(0), sstart, sstop, sstat, score, rep(1.0, n), newstrat, resid=double(n)) resid <- double(n) resid[sorted] <- agres$resid names(resid) <- rownames coef[which.sing] <- NA list(coefficients = coef, var = var, loglik = agfit$loglik, score = agfit$sctest, iter = agfit$iter, linear.predictors = lp, residuals = resid, means = agfit$means, method= 'coxph') } survival/R/print.summary.survexp.R0000644000175100001440000000311012423461152017025 0ustar hornikusersprint.summary.survexp <- function(x, digits = max(options()$digits - 4, 3), ...) { savedig <- options(digits=digits) on.exit(options(savedig)) if (!is.null(cl<- x$call)) { cat("Call: ") dput(cl) cat("\n") } omit <- x$na.action if (length(omit)) cat(naprint(omit), "\n") mat <- cbind(x$time, x$n.risk, x$surv) if (is.matrix(x$n.risk)) cnames <- c("time", paste("nrisk", 1:ncol(x$n.risk), sep='')) else cnames <- c("time", "n.risk") if (is.matrix(x$surv)) ncurve <- ncol(x$surv) else ncurve <- 1 if (ncurve==1) { #only 1 curve cnames <- c(cnames, "survival") # if (!is.null(x$std.err)) { # if (is.null(x$lower)) { # mat <- cbind(mat, x$std.err) # cnames <- c(cnames, "std.err") # } # else { # mat <- cbind(mat, x$std.err, x$lower, x$upper) # cnames <- c(cnames, 'std.err', # paste("lower ", x$conf.int*100, "% CI", sep=''), # paste("upper ", x$conf.int*100, "% CI", sep='')) # } # } } else cnames <- c(cnames, paste("survival", seq(ncurve), sep='')) if (!is.matrix(mat)) mat <- matrix(mat, nrow=1) if (!is.null(mat)) { dimnames(mat) <- list(rep("", nrow(mat)), cnames) if (is.null(x$strata)) print(mat) else { #print it out one strata at a time strata <- x$strata for (i in levels(strata)) { who <- (strata==i) cat(" ", i, "\n") print(mat[who,]) cat("\n") } } } else stop("There are no observations to print.") invisible(x) } survival/R/summary.survexp.R0000644000175100001440000001232212205423426015677 0ustar hornikusers# # Almost identical to summary.survfit. The big differences # are no calls to the survmean function (irrelevant), and # there is no censoring, extend, or rmean argument. # And there is never an se, upper or lower component. # Because survexp objects do not contain n.event or n.censor, # subsetting is easier. summary.survexp <- function(object, times, scale=1, ...) { fit <- object if (!inherits(fit, 'survexp')) stop("Invalid data") # The fit$surv object is sometimes a vector and sometimes a matrix. # Make a copy of it that is always a matrix, to simplify the number of # cases for our subscripting work below. At the end of the routine # we'll turn it back into a vector if needed. Similar treatment is # given to the n.risk argument. surv <- as.matrix(fit$surv) n.risk <- as.matrix(fit$n.risk) if (is.null(fit$strata)) { nstrat <- 1 stemp <- rep(1, nrow(surv)) strata.names <- "" } else { nstrat <- length(fit$strata) stemp <- rep(1:nstrat, fit$strata) strata.names <- names(fit$strata) } # if (is.null(fit$std.err)) std.err <- NULL # else std.err <- fit$std.err * surv # if (!is.null(fit$lower)) { # lower <- as.matrix(fit$lower) # upper <- as.matrix(fit$upper) # } if (missing(times)) { times <- fit$time strata <- factor(stemp, labels=strata.names) } else { #this case is harder, since it involves "in between" points times <- sort(times) #just in case the user didn't # The basic idea is to process the curves one at a time, # adding the results for that curve onto a list, so the # survival surv[[1], surv[[2]], etc. # For the survival, stderr, and confidence limits it suffices # to create a single list 'indx1' containing a subscripting vector indx1 <- indx2 <- newtimes <- vector('list', nstrat) n <- length(stemp) for (i in 1:nstrat) { who <- (1:n)[stemp==i] # the rows of the object for this strata stime <- fit$time[who] # First, toss any printing times that are outside our range mintime <- min(stime, 0) ptimes <- times[times >= mintime] maxtime <- max(stime) ptimes <- ptimes[ptimes <= maxtime] newtimes[[i]] <- ptimes # If we tack a -1 onto the front of the vector of survival # times, then indx1 is the subscript for that vector # corresponding to the list of "ptimes". If the input # data had stime=c(10,20) and ptimes was c(5,10,15,20), # the result would be 1,2,2,3. # For n.risk we want a slightly different index: 2,2,3,3. # "In between" times point to the next higher index for n.risk, # but the next lower one for survival. (Survival drops at time t, # the n.risk immediately afterwords at time t+0: you were at # risk just before you die, but not a moment after). The # extra point needs to be added at the end. # ntime <- length(stime) #number of points temp1 <- approx(c(mintime-1, stime), 0:ntime, xout=ptimes, method='constant', f=0, rule=2)$y indx1[[i]] <- ifelse(temp1==0, 1, 1+ who[pmax(1,temp1)]) # Why not just "who[temp1]" instead of who[pmax(1,temp1)] in the # line just above? When temp1 has zeros, the first expression # gives a vector that is shorter than temp1, and the ifelse # doesn't work right due to mismatched lengths. # Compute the number at risk. If stime = 1,10, 20 and ptime=3,10, # 12, then temp1 = 2,2,3: the nrisk looking ahead # approx() doesn't work if stime is of length 1 if (ntime ==1) temp1 <- rep(1, length(ptimes)) else temp1 <- approx(stime, 1:ntime, xout=ptimes, method='constant', f=1, rule=2)$y indx2[[i]] <- ifelse(ptimes>max(stime), length(n.risk), who[temp1]) } # Now create the output list times <- unlist(newtimes) n.risk <- unlist(n.risk) indx1 <- unlist(indx1) surv <- (rbind(1.,surv))[indx1,,drop=FALSE] n.risk <- n.risk[unlist(indx2),, drop=FALSE] # if (!is.null(std.err)) std.err <- rbind(0.,std.err)[indx1,,drop=FALSE] # if (!is.null(fit$lower)) { # lower <- rbind(1.,lower)[indx1,,drop=FALSE] # upper <- rbind(1.,upper)[indx1,,drop=FALSE] # } if (!is.null(fit$strata)) { scount <- unlist(lapply(newtimes, length)) strata <- factor(rep(1:nstrat, scount), labels=names(fit$strata)) } } # # Final part of the routine: paste the material together into # the correct output structure # temp <- list(time=times/scale, n.risk=n.risk, surv=surv) if (ncol(surv)==1) { # Make surve & etc vectors again temp$surv <- drop(temp$surv) temp$n.risk <- drop(temp$n.risk) # if (!is.null(std.err)) temp$std.err <- drop(std.err) # if (!is.null(fit$lower)) { # temp$lower <- drop(lower) # temp$upper <- drop(upper) # } } # else { # if (!is.null(std.err)) temp$std.err <- std.err # if (!is.null(fit$lower)) { # temp$lower <- lower # temp$upper <- upper # } # } if (!is.null(fit$strata)) { temp$strata <- strata } temp$method <- fit$method temp$call <- fit$call if (!is.null(fit$na.action)) temp$na.action <- fit$na.action class(temp) <- "summary.survexp" temp } survival/R/survfitcoxph.fit.R0000644000175100001440000001720513065013250016014 0ustar hornikusers# Automatically generated from the noweb directory survfitcoxph.fit <- function(y, x, wt, x2, risk, newrisk, strata, se.fit, survtype, vartype, varmat, id, y2, strata2, unlist=TRUE) { if (is.factor(strata)) ustrata <- levels(strata) else ustrata <- sort(unique(strata)) nstrata <- length(ustrata) survlist <- vector('list', nstrata) names(survlist) <- ustrata for (i in 1:nstrata) { indx <- which(strata== ustrata[i]) survlist[[i]] <- agsurv(y[indx,,drop=F], x[indx,,drop=F], wt[indx], risk[indx], survtype, vartype) } expand <- function(fit, x2, varmat, se.fit) { if (survtype==1) surv <- cumprod(fit$surv) else surv <- exp(-fit$cumhaz) if (is.matrix(x2) && nrow(x2) >1) { #more than 1 row in newdata fit$surv <- outer(surv, newrisk, '^') dimnames(fit$surv) <- list(NULL, row.names(x2)) if (se.fit) { varh <- matrix(0., nrow=length(fit$varhaz), ncol=nrow(x2)) for (i in 1:nrow(x2)) { dt <- outer(fit$cumhaz, x2[i,], '*') - fit$xbar varh[,i] <- (cumsum(fit$varhaz) + rowSums((dt %*% varmat)* dt))* newrisk[i]^2 } fit$std.err <- sqrt(varh) } fit$cumhaz <- outer(fit$cumhaz, newrisk, '*') } else { fit$surv <- surv^newrisk if (se.fit) { dt <- outer(fit$cumhaz, c(x2)) - fit$xbar varh <- (cumsum(fit$varhaz) + rowSums((dt %*% varmat)* dt)) * newrisk^2 fit$std.err <- sqrt(varh) } fit$cumhaz <- fit$cumhaz * newrisk } fit } if (missing(id) || is.null(id)) result <- lapply(survlist, expand, x2, varmat, se.fit) else { onecurve <- function(slist, x2, y2, strata2, newrisk, se.fit) { ntarget <- nrow(x2) #number of different time intervals surv <- vector('list', ntarget) n.event <- n.risk <- n.censor <- varh1 <- varh2 <- time <- surv hazard <- vector('list', ntarget) stemp <- as.integer(strata2) timeforward <- 0 for (i in 1:ntarget) { slist <- survlist[[stemp[i]]] indx <- which(slist$time > y2[i,1] & slist$time <= y2[i,2]) if (length(indx)==0) { timeforward <- timeforward + y2[i,2] - y2[i,1] # No deaths or censors in user interval. Possible # user error, but not uncommon at the tail of the curve. } else { time[[i]] <- diff(c(y2[i,1], slist$time[indx])) #time increments time[[i]][1] <- time[[i]][1] + timeforward timeforward <- y2[i,2] - max(slist$time[indx]) hazard[[i]] <- slist$hazard[indx]*newrisk[i] if (survtype==1) surv[[i]] <- slist$surv[indx]^newrisk[i] n.event[[i]] <- slist$n.event[indx] n.risk[[i]] <- slist$n.risk[indx] n.censor[[i]]<- slist$n.censor[indx] dt <- outer(slist$cumhaz[indx], x2[i,]) - slist$xbar[indx,,drop=F] varh1[[i]] <- slist$varhaz[indx] *newrisk[i]^2 varh2[[i]] <- rowSums((dt %*% varmat)* dt) * newrisk[i]^2 } } cumhaz <- cumsum(unlist(hazard)) if (survtype==1) surv <- cumprod(unlist(surv)) #increments (K-M) else surv <- exp(-cumhaz) if (se.fit) list(n=as.vector(table(strata)[stemp[1]]), time=cumsum(unlist(time)), n.risk = unlist(n.risk), n.event= unlist(n.event), n.censor= unlist(n.censor), surv = surv, cumhaz= cumhaz, std.err = sqrt(cumsum(unlist(varh1)) + unlist(varh2))) else list(n=as.vector(table(strata)[stemp[1]]), time=cumsum(unlist(time)), n.risk = unlist(n.risk), n.event= unlist(n.event), n.censor= unlist(n.censor), surv = surv, cumhaz= cumhaz) } if (all(id ==id[1])) { result <- list(onecurve(survlist, x2, y2, strata2, newrisk, se.fit)) } else { uid <- unique(id) result <- vector('list', length=length(uid)) for (i in 1:length(uid)) { indx <- which(id==uid[i]) result[[i]] <- onecurve(survlist, x2[indx,,drop=FALSE], y2[indx,,drop=FALSE], strata2[indx], newrisk[indx], se.fit) } names(result) <- uid } } if (unlist) { if (length(result)==1) { # the no strata case if (se.fit) result[[1]][c("n", "time", "n.risk", "n.event", "n.censor", "surv", "cumhaz", "std.err")] else result[[1]][c("n", "time", "n.risk", "n.event", "n.censor", "surv", "cumhaz")] } else { temp <-list(n = unlist(lapply(result, function(x) x$n), use.names=FALSE), time= unlist(lapply(result, function(x) x$time), use.names=FALSE), n.risk= unlist(lapply(result, function(x) x$n.risk), use.names=FALSE), n.event= unlist(lapply(result, function(x) x$n.event), use.names=FALSE), n.censor=unlist(lapply(result, function(x) x$n.censor), use.names=FALSE), strata = sapply(result, function(x) length(x$time))) names(temp$strata) <- names(result) if ((missing(id) || is.null(id)) && nrow(x2)>1) { temp$surv <- t(matrix(unlist(lapply(result, function(x) t(x$surv)), use.names=FALSE), nrow= nrow(x2))) dimnames(temp$surv) <- list(NULL, row.names(x2)) temp$cumhaz <- t(matrix(unlist(lapply(result, function(x) t(x$cumhaz)), use.names=FALSE), nrow= nrow(x2))) if (se.fit) temp$std.err <- t(matrix(unlist(lapply(result, function(x) t(x$std.err)), use.names=FALSE), nrow= nrow(x2))) } else { temp$surv <- unlist(lapply(result, function(x) x$surv), use.names=FALSE) temp$cumhaz <- unlist(lapply(result, function(x) x$cumhaz), use.names=FALSE) if (se.fit) temp$std.err <- unlist(lapply(result, function(x) x$std.err), use.names=FALSE) } temp } } else { names(result) <- ustrata result } } survival/R/frailty.S0000644000175100001440000000075211732700061014143 0ustar hornikusers# $Id: frailty.S 11166 2008-11-24 22:10:34Z therneau $ # # Parent function for frailty, calls the actuall working functions # frailty <- function(x, distribution = 'gamma', ...) { dlist <- c("gamma", "gaussian", "t") i <- pmatch(distribution, dlist) if (!is.na(i)) distribution <- dlist[i] temp <- paste("frailty", distribution, sep='.') if (!exists(temp)) stop(paste("Function '", temp, "' not found", sep="")) (get(temp))(x, ...) } survival/R/logLik.coxph.R0000644000175100001440000000152212617221626015035 0ustar hornikusers# # The AIC function depends on a logLik method # logLik.coxph <- function(object, ...) { out <- object$loglik[2] if (!is.null(object$df)) attr(out, "df") <- object$df[2] else attr(out, 'df') <- sum(!is.na(coefficients(object))) attr(out, "nobs") <- object$nevent class(out) <- 'logLik' out } # Cox models with no covariates logLik.coxph.null <- function(object, ...) { out <- object$loglik[1] attr(out, "df") <- 0 attr(out, "nobs") <- object$nevent class(out) <- "loglik" out } logLik.survreg <- function(object, ...) { out <- object$loglik[2] dd <- diag(object$var) if (!is.null(object$df)) attr(out, "df") <- sum(object$df) else attr(out, 'df') <- sum(!is.na(dd) & dd > 0) # attr(out, "nobs") <- sum(object$df) + object$df.residual class(out) <- 'logLik' out } survival/R/lines.aareg.S0000644000175100001440000000440011732700061014653 0ustar hornikusers# $Id: lines.aareg.S 11166 2008-11-24 22:10:34Z therneau $ lines.aareg <- function(x, se=FALSE, maxtime, type='s', ...) { if (!inherits(x, 'aareg')) stop ("Must be an aareg object") if (missing(maxtime)) keep <- 1:length(x$time) else keep <- 1:sum(x$time <= maxtime) if (is.matrix(x$coefficient) && ncol(x$coefficient)>1) { yy <- apply(x$coefficient[keep,], 2,cumsum) yy <- rbind(0,yy) # make the plot start at 0,0 if (se) { if (!is.null(x$dfbeta)) { # There was a cluster term, so use the robust variance # dfbeta will be of dimension (n, nvar, n-unique-times) # The first variance increment is apply(dfbeta[,,1]^2,2,sum) # second is apply(dfbeta[,,2]^2,2,sum) # ... , apply(dfbeta[,,ndeath]..... # By being sneaky, it can be done quickly dd <- dim(x$dfbeta) keep2 <- 1:length(unique(x$time[keep])) temp <- matrix(x$dfbeta[,,keep2], nrow=dd[1]) se.increment <- matrix(apply(temp^2, 2, sum), nrow=dd[2]) se.yy <- sqrt(apply(t(se.increment), 2, cumsum)) } else se.yy <- sqrt(apply(x$coefficient[keep,]^2, 2,cumsum)) se.yy <- rbind(0, se.yy) } ncurve <- ncol(yy) } else { # this is the branch most often called, when someone has done # plot(fit[3]), so that only 1 coefficient remains yy <- cumsum(c(0, x$coefficient[keep])) if (se) { if (!is.null(x$dfbeta)) { dd <- dim(x$dfbeta) keep2 <- 1:length(unique(x$time[keep])) temp <- matrix(x$dfbeta[,,keep2], nrow=dd[1]) se.yy <- sqrt(cumsum(c(0, apply(temp^2, 2, sum)))) } else se.yy <- sqrt(cumsum(c(0, x$coefficient[keep]^2))) } ncurve <- 1 } xx <- c(0, x$time[keep]) # There may be multiplicities in x$times. Only plot the last of # each of them indx <- 1 + length(xx) - rev(match(unique(rev(xx)), rev(xx))) xx <- xx[indx] yy <- as.matrix(yy)[indx,] if (se) { if (is.null(x$dfbeta)) se.yy<- as.matrix(se.yy)[indx,] yy <- cbind(yy, yy + 1.96*se.yy, yy - 1.96*se.yy) if (ncurve >1) { for (i in 1:ncurve) { j <- c(i, i+ncurve, i+2*ncurve) matlines(xx, yy[,j], type=type, ..., col=1, lty=c(1,2,2)) } } else matlines(xx, yy, type=type, ..., col=1, lty=c(1,2,2),) } else { matlines(xx, yy, type=type, ..., xlab='Time') } } survival/R/print.summary.survfitms.S0000644000175100001440000000416313003732027017362 0ustar hornikusersprint.summary.survfitms <- function(x, digits = max(options()$digits - 4, 3), ...) { savedig <- options(digits=digits) on.exit(options(savedig)) if (!is.null(cl<- x$call)) { cat("Call: ") dput(cl) cat("\n") } tsum <- function(x) { if (is.matrix(x)) rowSums(x) else x } omit <- x$na.action if (length(omit)) cat(naprint(omit), "\n") if (x$type == 'mright' || is.null(x$n.enter)) { mat <- cbind(x$time, tsum(x$n.risk), tsum(x$n.event), x$pstate) cnames <- c("time", "n.risk", "n.event") } else if (x$type == 'mcounting') { mat <- cbind(x$time, tsum(x$n.risk), tsum(x$n.event), x$pstate,) cnames <- c("time", "n.risk", "n.event") } if (is.matrix(x$pstate)) ncurve <- ncol(x$pstate) else ncurve <- 1 if (ncurve==1) { #only 1 curve cnames <- c(cnames, "P") if (!is.null(x$std.err)) { if (is.null(x$lower)) { mat <- cbind(mat, x$std.err) cnames <- c(cnames, "std.err") } else { mat <- cbind(mat, x$std.err, x$lower, x$upper) cnames <- c(cnames, 'std.err', paste("lower ", x$conf.int*100, "% CI", sep=''), paste("upper ", x$conf.int*100, "% CI", sep='')) } } } else cnames <- c(cnames, paste0("P(", x$states[1:ncurve], ")")) if (!is.null(x$start.time)) { mat.keep <- mat[,1] >= x$start.time mat <- mat[mat.keep,,drop=FALSE] if (is.null(dim(mat))) stop(paste("No information available using start.time =", x$start.time, ".")) } if (!is.matrix(mat)) mat <- matrix(mat, nrow=1) if (!is.null(mat)) { dimnames(mat) <- list(rep("", nrow(mat)), cnames) if (is.null(x$strata)) print(mat) else { #print it out one strata at a time strata <- x$strata if (!is.null(x$start.time)) strata <- strata[mat.keep] for (i in levels(strata)) { who <- (strata==i) cat(" ", i, "\n") print(mat[who,]) cat("\n") } } } else stop("There are no events to print. Please use the option ", "censored=TRUE with the summary function to see the censored ", "observations.") invisible(x) } survival/R/aareg.S0000644000175100001440000003432713016105374013560 0ustar hornikusers# Aalen's additive regression model # Originally, this tried to call coxph with certain options. # But we found the passing ... to a model method just doesn't work (for # optional things like weights). So the first portion of this is # essentially coxph, to set up for coxph.detail. # For distribution, the "variance" test is omitted. Not all aspects are # yet supported by the downstream printing. # aareg <- function(formula, data, weights, subset, na.action, qrtol=1e-7, nmin, dfbeta=FALSE, taper=1, test = c('aalen', 'variance', 'nrisk'), model=FALSE, x=FALSE, y=FALSE) { call <- match.call() m <- match.call(expand.dots=FALSE) temp <- c("", "formula", "data", "weights", "subset", "na.action") m <- m[ match(temp, names(m), nomatch=0)] special <- c("strata", "cluster") Terms <- if(missing(data)) terms(formula, special) else terms(formula, special, data=data) m$formula <- Terms m[[1L]] <- quote(stats::model.frame) m <- eval(m, sys.parent()) test <- match.arg(test) #check for legal argument # Now grab the terms that we need Y <- model.extract(m, "response") if (!inherits(Y, "Surv")) stop("Response must be a survival object") offset<- attr(Terms, "offset") tt <- length(offset) offset <- if(tt == 0) rep(0, nrow(Y)) else if(tt == 1) m[[offset]] else { #multiple offset terms! add them ff <- m[[offset[1]]] for(i in 2:tt) ff <- ff + m[[offset[i]]] ff } # Create an X matrix, to feed to the coxdetail routine. attr(Terms,"intercept")<- 1 # force no intercept strats <- attr(Terms, "specials")$strata cluster<- attr(Terms, "specials")$cluster dropx <- NULL if (length(cluster)) { dfbeta <- TRUE tempc <- untangle.specials(Terms, 'cluster', 1:10) ord <- attr(Terms, 'order')[tempc$terms] if (any(ord>1)) stop ("Cluster can not be used in an interaction") cluster <- strata(m[,tempc$vars], shortlabel=TRUE) #allow multiples cluster <- as.numeric(cluster) #labels don't matter, and processing # is a bit faster without them dropx <- tempc$terms } else cluster <- 1:nrow(m) # Adding strata, when there is a coefficent per death, is identical # to doing a totally separate fit per group. # Using "factor(group)" to get multiple baselines is likely what the # user wants. However, because we have not processed the strata # statement (taken it out of X, and created the 'newstrat' of coxph) # it will act just like a factor. # I've changed my mind multiple times on commenting out the line below. # Computationally identical to factor() -- is an error message or not # an error message the greater source of confusion to a user? if (length(strats)) { stop("Strata terms not allowed") } if (length(dropx)) X <- model.matrix(Terms[-dropx], m)[,-1,drop=FALSE] else X <- model.matrix(Terms, m)[,-1,drop=FALSE] nvar <- ncol(X) nused<- nrow(X) weights <- model.extract(m, 'weights') if (length(weights)==0) weights <- rep(1.0, nused) type <- attr(Y, "type") if (type!='right' && type!='counting') stop(paste("Aalen model doesn't support \"", type, "\" survival data", sep='')) # Get the peices that I need from the coxdetail routine # 1. It expects a "counting process" type of Y if (ncol(Y)==2) { mintime <- min(Y[,1]) if (mintime < 0) Y <- cbind( 2*mintime -1, Y) else Y <- cbind(-1,Y) } # Because there are no strata, the number of unique death times is the # number that will be in the output structures times <- as.vector(Y[,2]) # toss the labels away status<- as.vector(Y[,3]) ndeath <- length(unique(times[status==1])) # Sort everything ord <- order(times, -status) times <- times[ord] status <- status[ord] weights <- weights[ord] if (x) saveX <- X X <- X[ord,,drop=FALSE] storage.mode(Y) <- 'double' ff <- .C(Ccoxdetail, as.integer(nused), as.integer(nvar), ndeath= as.integer(ndeath), y = Y[ord,], as.double(X), index = as.integer(rep(0,nused)), event2 = rep(1.0, nused), weights = as.double(weights), means= c(0., double(ndeath*nvar-1)), u = double(ndeath*nvar), i = double(ndeath*nvar*nvar), rmat = integer(ndeath*nused), nrisk2 = double(ndeath), double(nvar*(3 + 2*nvar)) ) # riskmat is an nused by ndeath 0/1 matrix showing who is present riskmat <- matrix(ff$rmat, nused, ndeath) # Note that imat, as returned by coxdetail, is Var(X) * nevents. dt <- list(means= (matrix(ff$means,ndeath, nvar)), var = aareg.taper(taper, array(ff$i, c(nvar, nvar, ndeath)), ff$event2[1:ndeath]), time = times[ff$index[1:ndeath]], nrisk= ff$nrisk2, #weighted # at risk nevent=ff$event2[1:ndeath]) #weighted number of events # Set the number of deaths that will be used in the analysis # This may be smaller than the curren "ndeath", due to small nrisk # The number of times may even be smaller, if imat is singular at that # time point. if (missing(nmin)) nmin <- 3*nvar if (nvar==1) ndeath <- sum(dt$nrisk>= nmin & c(dt$var)>0) else { ndeath <- sum(dt$nrisk >= nmin) if (ndeath >0) { while (1) { #we expect very few iterations of this loop qri <- qr(dt$var[,,ndeath], tol=qrtol) if (qri$rank >= nvar) break #not singular ndeath <- ndeath -1 } } } if (ndeath<=1) stop("The threshold 'nmin' is too high, no model can be fit") # This matches the death times in the data set to the # sorted list of unique death times. "0" = not a death index <- match(times, dt$time[1:ndeath], nomatch=0) * status deaths <- (status==1 & index >0) dindex <- index[deaths] #for each death, a pointer into dt objects nevent <- length(dindex) #total number of events (ndeath = #unique times) if (length(cluster)) ncluster <- length(unique(cluster)) else ncluster <- nused if (dfbeta) { dmat <- array(0.0, dim=c(ncluster, nvar+1, ndeath)) # the resid marix has a row for each death, and nused cols # each row has a "1" in it at the position of the death # the yhat part is subtracted later resid <- rep(0., nevent*nused) resid[nevent*((1:nused)[deaths]-1) + 1:nevent] <- 1.0 resid <- matrix(resid, ncol=nused) } # Coefficient is the step in Aalen's plots # If we keep one row of "coefficent" per death, then Aalen's # variance is coef *% t(coef), treating coef as a col vector. # If we kept one row per death, then the ndeath nvar by nvar variance # matrices would need to be kept too. So keep 1 row per event. # Things like plot will end up accumlating. # There is no such cheat for dfbeta: it is kept as "# unique deaths" # p by p matrices. # if (nvar==1) { # special case of only 1 covariate means <- dt$means[dindex] nrisk <- dt$nrisk[dindex] xx <- (X[deaths] - means) * weights[deaths] v.inverse <- 1/dt$var[dindex] #for all time points twt <- nrisk* 1/cbind(1+ means^2*v.inverse, v.inverse) coefficient <- v.inverse * xx / nrisk # Note that ybar is always w_i/nrisk, since we are doing the # regressions one event at a time. b0 <- weights[deaths]/nrisk - means*coefficient if (dfbeta) { # We first create the nused * #events matrix, and then # collapse it to be ncluster by n-unique-death-times xx <- c(X) * riskmat[,dindex] # X repeated in each col, if at risk predicted <- coefficient * t(xx) + b0*t(riskmat[,dindex]) resid <- resid - predicted #nused cols, nvevent rows temp1 <- (resid * (t(xx) -means)/(nrisk*dt$var[dindex])) * rep(weights, rep(nevent, nused)) # temp1[i,j] is the change in alpha at time i for subject j # the "intercept dfbeta" is resid*wt/sum(wt) - xbar*temp1 temp0 <- resid * outer(1/nrisk, weights) - temp1 * means # get the matrix, nused by 2, which is the influence of each # subject on the test statistic. # This is a bit easier before collapsing if (test=='nrisk') { test.dfbeta <- cbind(apply(temp0*nrisk, 2, sum), apply(temp1*nrisk, 2, sum)) } else { test.dfbeta <- cbind(apply(temp0*twt[,1], 2, sum), apply(temp1*twt[,2], 2, sum)) } # Now collapse dfbeta, first on the deaths, and then on the cluster if (nevent > ndeath) { temp1 <- rowsum(temp1, times[deaths], reorder=FALSE) temp0 <- rowsum(temp0, times[deaths], reorder=FALSE) } dmat[,1,] <- rowsum(t(temp0), cluster[ord], reorder= FALSE) dmat[,2,] <- rowsum(t(temp1), cluster[ord], reorder =FALSE) } # Compute the test statistic, including the intercept term # (Much of the code above was a litte easier to write without # the intercept term in thec coef matrix, that below is easier # with it in). coefficient <- cbind(b0,coefficient) if (test=='nrisk') { temp <- coefficient*nrisk test.statistic <- apply(temp,2,sum) test.var <- matrix(0.,2,2) diag(test.var) <- apply(temp^2, 2, sum) test.var[1,2] <- test.var[2,1] <- sum(temp[,1]*temp[,2]) } else { # full V^{-1} and diag(V){-1} variance (Aalen) are the same temp <- coefficient* twt test.statistic <- apply(temp,2,sum) test.var <- matrix(0.,2,2) diag(test.var) <- apply(temp^2, 2, sum) test.var[1,2] <- test.var[2,1] <- sum(temp[,1]*temp[,2]) } } else { # 2 or more covariates coefficient <- matrix(0,nevent, nvar) twt <- matrix(0, nevent, nvar+1) means <- dt$means[dindex,] # vector of means, at each deatj nrisk <- dt$nrisk[dindex] dindex2 <- (1:nused)[deaths] # row number of each death ybar <- weights[deaths]/nrisk test.var <- matrix(0.0, nvar, nvar) if (dfbeta) test.dfbeta <- matrix(0., nused, nvar+1) for (i in 1:nevent) { who <- riskmat[,dindex[i]] # 0/1 vector of who is at risk wt <- weights* who xx <- who* (X- rep(means[i,], rep(nused, nvar))) # (X-Xbar) # solve, and check for singularity # Note that the increment to imat, as returned by # the coxph.detail function, is Var(X) * #events # and qri is intended to be the qr of V-inverse if (i==1 || dindex[i] != dindex[i-1]) { #don't redo qr for ties qri <- qr(dt$var[,,dindex[i]], tol=qrtol) vmat <- qr.coef(qri, diag(nvar)) twt[i,] <- nrisk[i] /c(1+ means[i,] %*% vmat %*% means[i,], diag(vmat)) } else twt[i,] <- twt[i-1,] j <- dindex2[i] coefficient[i,] <-qr.coef(qri, wt[j]*xx[j,]) / nrisk[i] if (test=='variance') { temp <- wt[j]*xx[j,] test.var <- test.var + outer(temp,temp) } if (dfbeta) { resid[i, ] <- resid[i,]- c(ybar[i] + xx %*% c(coefficient[i,])) temp1 <- t(qr.coef(qri, t(resid[i,]* wt *xx)))/ nrisk[i] temp0 <- resid[i,]*wt/nrisk[i] - temp1%*% means[i,] if (test=='aalen') test.dfbeta <- test.dfbeta + cbind(temp0, temp1) %*% diag(twt[i,]) else if (test=='nrisk') test.dfbeta <- test.dfbeta + cbind(temp0, temp1)* nrisk[i] else { test.dfbeta[,-1] <- test.dfbeta[,-1] + resid[i,]* wt *xx # There really isn't a definition for what weight to # put on the intercept in the "variance" weighting # (and who really cares about "testing the intercept" # anyway). So use the twt one test.dfbeta[,1] <- test.dfbeta[,1] + temp0*twt[i,1] } dmat[,-1,dindex[i]] <- dmat[,-1, dindex[i]] + rowsum(temp1, cluster[ord], reorder=FALSE) dmat[,1, dindex[i]] <- dmat[,1,dindex[i]] + rowsum(temp0, cluster[ord], reorder=FALSE) } } temp <- apply(means*coefficient, 1, sum) # xbar * coef at time t b0 <- weights[deaths]/nrisk - temp coefficient <- cbind(b0,coefficient) # Note - the intercept is a part of the test statistic, even # though it will always be ignored in the overall chisquare test if (test=='aalen') { temp <- twt* coefficient test.statistic <- colSums(temp) test.var <- t(temp) %*% temp } else if (test=='nrisk') { temp <- coefficient * nrisk test.statistic <- colSums(temp) test.var <- t(temp) %*% temp } else { xx <- weights[deaths]*(X[deaths,] - means[dindex,]) test.statistic <- apply(xx, 2, sum) } } if (dfbeta) { # The model variance is sum( term[i]^2), i ranging over times, # and each term an n by p matrix (one row per person) # The dfbeta one is essentially [sum(term[i])]^2 # the test.dfbeta matrix contains this sum over death times temp <- rowsum(test.dfbeta, cluster, reorder=FALSE) test.var2 <- t(temp) %*% temp } dimnames(coefficient) <- list(times[deaths], c("Intercept", dimnames(X)[[2]])) names(test.statistic) <- c("Intercept", dimnames(X)[[2]]) dimnames(twt) <- NULL ans <- list(n= c(nused, ndeath, length(dt$time)), times=times[deaths], nrisk=dt$nrisk[dindex], coefficient=coefficient, test.statistic=test.statistic, test.var=test.var, test=test, tweight = twt, call=call) if (dfbeta) { ans$dfbeta <- dmat ans$test.var2 <- test.var2 } if (any(weights!=1)) ans$weights <- weights # if (ncluster < nused) ans$cluster <- as.numeric(cluster) na.action <- attr(m, "na.action") if (length(na.action)) ans$na.action <- na.action if (model) ans$model <- m else { if (x) ans$x <- saveX if (y) ans$y <- Y } class(ans) <- 'aareg' ans } "[.aareg" <- function(x, ..., drop=FALSE) { if (!inherits(x, 'aareg')) stop ("Must be an aareg object") i <- ..1 if (is.matrix(x$coefficient)) { x$coefficient <- x$coefficient[,i, drop=drop] x$tweight <- x$tweight[,i,drop=drop] } else stop("Subsripting impossible, coefficient component not a matrix") if (!is.null(x$dfbeta)){ x$dfbeta <- x$dfbeta[,i,,drop=drop] x$test.var2 <- x$test.var2[i,i,drop=drop] } x$test.statistic <- x$test.statistic[i, drop=drop] x$test.var <- x$test.var[i,i,drop=drop] x } survival/R/cch.R0000644000175100001440000003463713060076567013253 0ustar hornikusers### Suite of programs for case-cohort analysis ### Main program cch <- function(formula, data=sys.parent(), subcoh, id, stratum=NULL, cohort.size, method=c("Prentice", "SelfPrentice", "LinYing","I.Borgan","II.Borgan"), robust=FALSE){ call <- match.call() if (is.data.frame(data)){ if (inherits(id,"formula")) id<- stats::model.frame(id,data,na.action=na.fail)[,1] if (inherits(subcoh,"formula")) subcoh<- stats::model.frame(subcoh,data,na.action=na.fail)[,1] if (inherits(stratum,"formula")) stratum<- stats::model.frame(stratum,data,na.action=na.fail)[,1] } ## Check id, subcoh and cohort.size variables if(length(id)!=length(unique(id))) stop("Multiple records per id not allowed") if (is.logical(subcoh)) subcoh <- as.numeric(subcoh) tt <- table(subcoh) if(min(charmatch(names(tt), c("0","1"), 0))==0) stop("Permissible values for subcohort indicator are 0/1 or TRUE/FALSE") if(length(id)>sum(cohort.size)) stop("Number of records greater than cohort size") nn <- cohort.size method<-match.arg(method) stratified<-method %in% c("I.Borgan","II.Borgan") if (!is.null(stratum)) stratum<-factor(stratum) if (stratified){ if (robust) warning("`robust' not implemented for stratified analysis.") if (is.null(stratum)) stop("method (",method,") requires 'stratum'") if (length(cohort.size)!=length(levels(stratum))) stop("cohort.size and stratum do not match") if (!(all(levels(stratum) %in% names(cohort.size)))) warning("stratum levels and names(cohort.size) do not agree") subcohort.sizes<-table(stratum) } else if(!stratified) { if (!(method =="LinYing") && robust) warning("`robust' ignored for method (",method,")") if (!is.null(stratum)) warning("'stratum' ignored for method (",method,")") if (length(cohort.size)!=1) stop("cohort size must be a scalar for unstratified analysis") subcohort.sizes<-length(id) } if (any(subcohort.sizes>cohort.size)) stop("Population smaller than sample in some strata") ## Evaluate model formula m <- match.call(expand.dots=FALSE) m$method <- m$cohort.size <- m$id <- m$subcoh <- m$stratum <-m$robust<- NULL m[[1L]] <- quote(stats::model.frame) m <- eval(m,sys.parent()) Terms <- attr(m,"terms") Y <- model.extract(m, "response") if(!inherits(Y, "Surv")) stop("Response must be a survival object") type <- attr(Y, "type") itype<-charmatch(type,c("right","counting"),nomatch=0) cens<-switch(itype+1, stop(paste("Cox model doesn't support \"", type, "\" survival data", sep = "")), Y[,2], Y[,3]) if (any(!subcoh & !cens)) stop(sum(!subcoh & !cens),"censored observations not in subcohort") cc<-cens+1-subcoh texit<-switch(itype+1, stop(), Y[,1], Y[,2]) tenter<-switch(itype+1, stop(), rep(0,length(texit)), Y[,1]) X <- model.matrix(Terms, m) X <- X[,2:ncol(X)] fitter <- get(method) # The artificial offset is 1/2 the minimal distance between events # If there is only one unique event time then any offset is ok if (ncol(Y)==3) dtime <- unique(Y[cens==1,2]) else dtime <- unique(Y[cens==1, 1]) if (length(dtime) > 1) delta <- min(diff(sort(dtime))) /2 else delta <- 1 if (stratified) out<-fitter(tenter=tenter, texit=texit, cc=cc, id=id, X=X, stratum=as.numeric(stratum), stratum.sizes=cohort.size, delta) else out<-fitter(tenter=tenter, texit=texit, cc=cc, id=id, X=X, ntot=nn, robust=robust, delta) out$method <- method names(out$coefficients) <- dimnames(X)[[2]] if(!is.null(out$var)) dimnames(out$var) <- list(dimnames(X)[[2]], dimnames(X)[[2]]) if(!is.null(out$naive.var)) dimnames(out$naive.var) <- list(dimnames(X)[[2]], dimnames(X)[[2]]) out$call <- call out$cohort.size <- cohort.size out$stratified<-stratified if (stratified){ out$stratum<-stratum out$subcohort.size <-subcohort.sizes } else { out$subcohort.size <- tt[2] } class(out) <- "cch" out } ### Subprograms Prentice <- function(tenter, texit, cc, id, X, ntot,robust, delta){ cens <- as.numeric(cc>0) # Censorship indicators subcoh <- as.numeric(cc<2) # Subcohort indicators ## Calculate Prentice estimate ent2 <- tenter ent2[cc==2] <- texit[cc==2]- delta fit1 <- coxph(Surv(ent2,texit,cens)~X, x=TRUE, timefix=FALSE) ## Calculate Prentice estimate and variance nd <- sum(cens) # Number of failures nc <- sum(subcoh) # Number in subcohort ncd <- sum(cc==1) #Number of failures in subcohort X <- as.matrix(X) aent <- c(tenter[cc>0],tenter[cc<2]) aexit <- c(texit[cc>0],texit[cc<2]) aX <- rbind(as.matrix(X[cc>0,]),as.matrix(X[cc<2,])) aid <- c(id[cc>0],id[cc<2]) dum <- rep(-100,nd) dum <- c(dum,rep(0,nc)) gp <- rep(1,nd) gp <- c(gp,rep(0,nc)) fit <- coxph(Surv(aent,aexit,gp)~aX+offset(dum)+cluster(aid), x=TRUE, iter.max=35,init=fit1$coefficients, timefix=FALSE) db <- resid(fit,type="dfbeta") db <- as.matrix(db) db <- db[gp==0,] fit$phase2var<-(1-(nc/ntot))*t(db)%*%(db) fit$naive.var <- fit$naive.var+fit$phase2var fit$var<-fit$naive.var fit$coefficients <- fit$coef <- fit1$coefficients fit } SelfPrentice <- function(tenter, texit, cc, id, X, ntot,robust, delta){ cens <- as.numeric(cc>0) # Censorship indicators subcoh <- as.numeric(cc<2) # Subcohort indicators ## Calculate Self-Prentice estimate and variance nd <- sum(cens) # Number of failures nc <- sum(subcoh) # Number in subcohort ncd <- sum(cc==1) #Number of failures in subcohort X <- as.matrix(X) aent <- c(tenter[cc>0],tenter[cc<2]) aexit <- c(texit[cc>0],texit[cc<2]) aX <- rbind(as.matrix(X[cc>0,]),as.matrix(X[cc<2,])) aid <- c(id[cc>0],id[cc<2]) dum <- rep(-100,nd) dum <- c(dum,rep(0,nc)) gp <- rep(1,nd) gp <- c(gp,rep(0,nc)) fit <- coxph(Surv(aent,aexit,gp)~aX+offset(dum)+cluster(aid), x=TRUE, timefix=FALSE) db <- resid(fit,type="dfbeta") db <- as.matrix(db) db <- db[gp==0,,drop=FALSE] fit$phase2var<-(1-(nc/ntot))*t(db)%*%(db) fit$naive.var <- fit$naive.var+fit$phase2var fit$var<-fit$naive.var fit } LinYing <- function(tenter, texit, cc, id, X, ntot,robust, delta){ cens <- as.numeric(cc>0) # Censorship indicators subcoh <- as.numeric(cc<2) # Subcohort indicators nd <- sum(cens) # Number of failures nc <- sum(subcoh) # Number in subcohort ncd <- sum(cc==1) #Number of failures in subcohort ## Calculate Lin-Ying estimate and variance offs <- rep((ntot-nd)/(nc-ncd),length(texit)) offs[cc>0] <- 1 loffs <- log(offs) fit <- coxph(Surv(tenter, texit, cens)~X+offset(loffs)+cluster(id), x=TRUE, timefix=FALSE) db <- resid(fit,type="dfbeta") db <- as.matrix(db) db0 <- db[cens==0,,drop=FALSE] dbm <- apply(db0,2,mean) db0 <- sweep(db0,2,dbm) fit$phase2var<-(1-(nc-ncd)/(ntot-nd))*crossprod(db0) fit$naive.var <- fit$naive.var+fit$phase2var if (robust) fit$var<- crossprod(db,db/offs)+fit$phase2var else fit$var<-fit$naive.var fit } I.Borgan <- function(tenter, texit, cc, id, X, stratum, stratum.sizes, delta){ nobs <- length(texit) idx <- 1:length(nobs) jj <- max(stratum) nn <- stratum.sizes ## Cohort stratum sizes n <- table(stratum) ## Sample stratum sizes d <- table(stratum[cc>0]) ## Failures in each stratum tt <- table(cc,stratum) cens <- as.numeric(cc>0) ## Failure indicators subcoh <- as.numeric(cc<2) ## Subcohort indicators nd <- sum(cens) ## Number of failures nc <- sum(subcoh) ## Number in subcohort ncd <- sum(as.numeric(cc==1)) #Number of failures in subcohort m0 <- tt[1,] ## Subcohort stratum sizes (noncases only) if (ncd>0) m <- m0+tt[2,] else m <- m0 #Subcohort stratum sizes X <- as.matrix(X) kk <- ncol(X) ## Number of variables wt <- as.vector(nn/m) ## Weights for Estimator I stratum <- c(stratum[cc>0],stratum[cc<2]) w <- wt[stratum] ent <- c(tenter[cc > 0], tenter[cc < 2]) exit <- c(texit[cc > 0], texit[cc < 2]) X <- rbind(as.matrix(X[cc > 0, ]), as.matrix(X[cc < 2, ])) id <- c(id[cc > 0], id[cc < 2]) dum <- rep(-100, nd) dum <- c(dum, rep(0, nc)) gp <- rep(1, nd) gp <- c(gp, rep(0, nc)) w[gp==1] <- 1 fit <- coxph(Surv(ent,exit,gp)~X+offset(dum)+cluster(id), weights=w, x=T, iter.max=25, timefix=FALSE) score <- resid(fit, type = "score", weighted=F) sc <- resid(fit, type="score", collapse=id, weighted=T) score <- as.matrix(score) score <- score[gp == 0,,drop=F] st <- stratum[gp==0] sto <- st %o% rep(1,kk) Index <- col(score) tscore <- tapply(score,list(sto,Index),mean) pscore <- tapply(score,list(sto,Index)) score <- score-tscore[pscore] delta <- matrix(0,kk,kk) opt <- NULL for (j in 1:jj) { temp <- t(score[st==j,])%*%score[st==j,]/(m[j]-1) delta <- matrix(delta+(wt[j]-1)*nn[j]*temp,kk,kk) if(is.null(opt)) opt <- nn[j]*sqrt(diag(fit$naive.var %*% temp %*% fit$naive.var)) else opt <- rbind(opt,nn[j]*sqrt(diag(fit$naive.var %*% temp %*% fit$naive.var))) } z <- apply(opt,2,sum) fit$opt <- sweep(opt,2,z,FUN="/") fit$phase2var<-fit$naive.var%*%delta%*%fit$naive.var fit$naive.var <- fit$naive.var+fit$phase2var fit$var<-fit$naive.var fit$delta <- delta fit$sc <- sc fit } II.Borgan <- function(tenter, texit, cc, id, X, stratum, stratum.sizes, delta){ jj <- max(stratum) nn <- stratum.sizes ## Cohort stratum sizes n <- table(stratum) ## Sample stratum sizes d <- table(stratum[cc>0]) ## Failures in each stratum tt <- table(cc,stratum) cens <- as.numeric(cc>0) ## Failure indicators subcoh <- as.numeric(cc<2) ## Subcohort indicators nd <- sum(cens) ## Number of failures nc <- sum(subcoh) ## Number in subcohort ncd <- sum(as.numeric(cc==1)) #Number of failures in subcohort m0 <- tt[1,] ## Subcohort stratum sizes (controls only) if (ncd>0) m <- m0+tt[2,] else m <- m0 #Subcohort stratum sizes X <- as.matrix(X) kk <- ncol(X) ## Number of variables nn0 <- nn-as.vector(d) #Noncases in cohort wt <- as.vector(nn0/m0) w <- wt[stratum] w[cens==1] <- 1 fit <- coxph(Surv(tenter,texit,cens)~X+cluster(id), weights=w, x=T, iter.max=25, timefix=FALSE) ## Borgan Estimate II score <- resid(fit, type = "score", weighted=F) sc <- resid(fit,type="score", collapse=id, weighted=T) score <- as.matrix(score) score <- score[cens == 0,,drop=F] ## Scores for controls st <- stratum[cens==0] ## Stratum indicators for controls sto <- st %o% rep(1,kk) Index <- col(score) tscore <- tapply(score,list(sto,Index),mean) ## Within stratum control score means pscore <- tapply(score,list(sto,Index)) score <- score-tscore[pscore] ## Subtract off within stratum score means delta <- matrix(0,kk,kk) opt <- NULL for (j in 1:jj) { temp <- t(score[st==j,])%*%score[st==j,]/(m0[j]-1) ## Borgan equation (19) delta <- delta+(wt[j]-1)*nn0[j]*temp ## Borgan equation (17) if(is.null(opt)) opt <- nn0[j]*sqrt(diag(fit$naive.var %*% temp %*% fit$naive.var)) else opt <- rbind(opt,nn0[j]*sqrt(diag(fit$naive.var %*% temp %*% fit$naive.var))) } z <- apply(opt,2,sum) fit$opt <- sweep(opt,2,z,FUN="/") fit$phase2var<-fit$naive.var %*% delta %*% fit$naive.var fit$naive.var <- fit$naive.var+fit$phase2var fit$var<-fit$naive.var fit$delta <- delta fit$sc <- sc fit } ## Methods vcov.cch<-function(object,...) object$var "print.cch"<- function(x,...) { ## produces summary from an x of the class "cch" call<-x$call coef <- coef(x) method <- x$method se <- sqrt(diag(vcov(x))) Z<- abs(coef/se) p<- pnorm(Z) cohort.size<-x$cohort.size subcohort.size<-x$subcohort.size coefficients <- matrix(0, nrow = length(coef), ncol = 4) dimnames(coefficients) <- list(names(coef), c("Value", "SE", "Z", "p")) coefficients[, 1] <- coef coefficients[, 2] <- se coefficients[, 3] <- Z coefficients[, 4] <- 2*(1-p) if (x$stratified){ cat("Exposure-stratified case-cohort analysis,", x$method, "method.\n") m<-rbind(subcohort=x$subcohort.size, cohort=x$cohort.size) print(m,quote=FALSE) } else{ cat("Case-cohort analysis,") cat("x$method,", x$method,"\n with subcohort of", x$subcohort.size,"from cohort of", x$cohort.size,"\n\n") } cat("Call: "); print(x$call) cat("\nCoefficients:\n") print(coefficients) invisible(x) } "summary.cch"<-function(object,...) { ## produces summary from an object of the class "cch" call<-object$call coef <- coef(object) method <- object$method se <- sqrt(diag(vcov(object))) Z<- abs(coef/se) p<- pnorm(Z) cohort.size<-object$cohort.size subcohort.size<-object$subcohort.size coefficients <- matrix(0, nrow = length(coef), ncol = 4) dimnames(coefficients) <- list(names(coef), c("Value", "SE", "Z", "p")) coefficients[, 1] <- coef coefficients[, 2] <- se coefficients[, 3] <- Z coefficients[, 4] <- 2*(1-p) structure(list(call=call, method=method, cohort.size=cohort.size, subcohort.size=subcohort.size, coefficients = coefficients, stratified=object$stratified), class = "summary.cch") } print.summary.cch <- function(x,digits=3,...){ if (x$stratified){ cat("Exposure-stratified case-cohort analysis,", x$method, "method.\n") m<-rbind(subcohort=x$subcohort.size, cohort=x$cohort.size) print(m,quote=FALSE) } else{ cat("Case-cohort analysis,") cat("x$method,", x$method,"\n with subcohort of", x$subcohort.size,"from cohort of", x$cohort.size,"\n\n") } cat("Call: "); print(x$call) cat("\nCoefficients:\n") output<-cbind(Coef=x$coefficients[,1],HR=exp(x$coefficients[,1]), "(95%"=exp(x$coefficients[,1]-1.96*x$coefficients[,2]), "CI)"=exp(x$coefficients[,1]+1.96*x$coefficients[,2]), "p"=x$coefficients[,4] ) print(round(output,3)) invisible(x) } survival/R/print.pyears.R0000644000175100001440000003723013065013240015124 0ustar hornikusers# Automatically generated from the noweb directory print.pyears <- function(x, ...) { if (!is.null(cl<- x$call)) { cat("Call:\n") dput(cl) cat("\n") } if (is.null(x$data)) { if (!is.null(x$event)) cat("Total number of events:", format(sum(x$event)), "\n") cat ( "Total number of person-years tabulated:", format(sum(x$pyears)), "\nTotal number of person-years off table:", format(x$offtable), "\n") } else { if (!is.null(x$data$event)) cat("Total number of events:", format(sum(x$data$event)), "\n") cat ( "Total number of person-years tabulated:", format(sum(x$data$pyears)), "\nTotal number of person-years off table:", format(x$offtable), "\n") } if (!is.null(x$summary)) { cat("Matches to the chosen rate table:\n ", x$summary) } cat("Observations in the data set:", x$observations, "\n") if (!is.null(x$na.action)) cat(" (", naprint(x$na.action), ")\n", sep='') cat("\n") invisible(x) } summary.pyears <- function(object, header=TRUE, call=header, n= TRUE, event=TRUE, pyears=TRUE, expected = TRUE, rate = FALSE, rr = expected, ci.r = FALSE, ci.rr = FALSE, totals=FALSE, legend=TRUE, vline = FALSE, vertical = TRUE, nastring=".", conf.level=0.95, scale= 1, ...) { # Usual checks if (!inherits(object, "pyears")) stop("input must be a pyears object") temp <- c(is.logical(header), is.logical(call), is.logical(n), is.logical(event) , is.logical(pyears), is.logical(expected), is.logical(rate), is.logical(ci.r), is.logical(rr), is.logical(ci.rr), is.logical(vline), is.logical(vertical), is.logical(legend), is.logical(totals)) tname <- c("header", "call", "n", "event", "pyears", "expected", "rate", "ci.r", "rr", "ci.rr", "vline", "vertical", "legend", "totals") if (any(!temp) || length(temp) != 14 || any(is.na(temp))) { stop("the ", paste(tname[!temp], collapse=", "), "argument(s) must be single logical values") } if (!is.numeric(conf.level) || conf.level <=0 || conf.level >=1 | length(conf.level) > 1 || is.na(conf.level) > 1) stop("conf.level must be a single numeric between 0 and 1") if (is.na(scale) || !is.numeric(scale) || length(scale) !=1 || scale <=0) stop("scale must be a value > 0") vname <- attr(terms(object), "term.labels") #variable names if (!is.null(object$data)) { # Extra work: restore the tables which had been unpacked into a df # All of the categories are factors in this case tdata <- object$data[vname] # the conditioning variables dname <- lapply(tdata, function(x) { if (is.factor(x)) levels(x) else sort(unique(x))}) # dimnames dd <- sapply(dname, length) # dim of arrays index <- tapply(tdata[,1], tdata) restore <- c('n', 'event', 'pyears', 'expected') #do these, if present restore <- restore[restore %in% names(object$data)] new <- lapply(object$data[restore], function(x) { temp <- array(0L, dim=dd, dimnames=dname) temp[index] <- x temp} ) object <- c(object, new) } if (is.null(object$expected)) { expected <- FALSE rr <- FALSE ci.rr <- FALSE } if (is.null(object$event)) { event <- FALSE rate <- FALSE ci.r <- FALSE rr <- FALSE ci.rr <- FALSE } # print out the front matter if (call && !is.null(object$call)) { cat("Call: ") dput(object$call) cat("\n") } if (header) { cat("number of observations =", object$observations) if (length(object$omit)) cat(" (", naprint(object$omit), ")\n", sep="") else cat("\n") if (object$offtable > 0) cat(" Total time lost (off table)", format(object$offtable), "\n") cat("\n") } # Add in totals if requested if (totals) { # if the pyear object was based on any time dependent cuts, then # the "n" component cannot be totaled up. tcut <- if (is.null(object$tcut)) TRUE else object$tcut object$n <- pytot(object$n, na=tcut) object$pyears <- pytot(object$pyears) if (event) object$event <- pytot(object$event) if (expected) object$expected <- pytot(object$expected) } dd <- dim(object$n) vname <- attr(terms(object), "term.labels") #variable names # Put the elements to be printed onto a list pname <- (tname[3:6])[c(n, event, pyears, expected)] plist <- object[pname] if (rate) { pname <- c(pname, "rate") plist$r <- scale* object$event/object$pyears } if (ci.r) { pname <- c(pname, "ci.r") plist$ci.r <- cipoisson(object$event, object$pyears, p=conf.level) *scale } if (rr) { pname <- c(pname, "rr") plist$rr <- object$event/object$expected } if (ci.rr) { pname <- c(pname, "ci.rr") plist$ci.rr <- cipoisson(object$event, object$expected, p=conf.level) } rname <- c(n = "N", event="Events", pyears= "Time", expected= "Expected events", rate = "Event rate", ci.r = "CI (rate)", rr= "Obs/Exp", ci.rr= "CI (O/E)") rname <- rname[pname] if (length(dd) ==1) { # 1 dimensional table cname <- names(object$n) #category names if (vertical) { # The person-years objects list across the top, categories up and down # This makes columns line up in a standard "R" way # The first column label is the variable name, content is the categories plist <- lapply(plist, pformat, nastring, ...) # make it character pcol <- sapply(plist, function(x) nchar(x[1])) #width of each one colwidth <- pmax(pcol, nchar(rname)) +2 for (i in 1:length(plist)) plist[[i]] <- strpad(plist[[i]], colwidth[i]) colwidth <- c(max(nchar(vname), nchar(cname)) +2, colwidth) leftcol <- list(strpad(cname, colwidth[1])) header <- strpad(c(vname, rname), colwidth) } else { # in this case each column will have different types of objects in it # alignment is the nuisance newmat <- pybox(plist, length(plist[[1]]), nastring, ...) colwidth <- pmax(nchar(cname), apply(nchar(newmat), 1, max)) +2 # turn the list sideways plist <- split(newmat, row(newmat)) for (i in 1:length(plist)) plist[[i]] <- strpad(plist[[i]], colwidth[i]) colwidth <- c(max(nchar(vname), nchar(rname)) +2, colwidth) leftcol <- list(strpad(rname, colwidth[1])) header <- strpad(c(vname, cname), colwidth) } # Now print it if (vline) { # use a pipe table cat(paste(header, collapse = "|"), "\n") cat(paste(strpad("-", colwidth, "-"), collapse="|"), "\n") temp <- do.call("paste", c(leftcol, plist, list(sep ="|"))) cat(temp, sep= '\n') } else { cat(paste(header, collapse = " "), "\n") cat(paste(strpad("-", colwidth, "-"), collapse=" "), "\n") temp <- do.call("paste", c(leftcol, plist, list(sep =" "))) cat(temp, sep='\n') } } else { # more than 1 dimension if (header) { # the header is itself a table width <- max(nchar(rname)) if (vline) { cat('+', strpad('-', width, '-'), "+\n", sep="") cat(paste0('|',strpad(rname, width), '|'), sep='\n') cat('+', strpad('-', width, '-'), "+\n\n", sep="") } else { cat(strpad('-', width, '-'), "\n") cat(strpad(rname, width), sep='\n') cat(strpad('-', width, '-'), "\n\n") } } tname <- vname[1:2] #names for the row and col rowname <- dimnames(object$n)[[1]] colname <- dimnames(object$n)[[2]] if (length(dd) > 2) newmat <- pybox(plist, c(dd[1],dd[2], prod(dd[-(1:2)])), nastring, ...) else newmat <- pybox(plist, dd, nastring, ...) if (length(dd) > 2) { newmat <- pybox(plist, c(dd[1],dd[2], prod(dd[-(1:2)])), nastring, ...) outer.label <- do.call("expand.grid", dimnames(object$n)[-(1:2)]) temp <- names(outer.label) for (i in 1:nrow(outer.label)) { # first the caption, then data cat(paste(":", paste(temp, outer.label[i,], sep="=")), '\n') pyshow(newmat[,,i,], tname, rowname, colname, vline) } } else { newmat <- pybox(plist, dd, nastring, ...) pyshow(newmat, tname, rowname, colname, vline) } } invisible(object) } strpad <- function(x, width, pad=' ') { # x = the string(s) to be padded out # width = width of desired string. nc <- nchar(x) added <- width - nc left <- pmax(0, floor(added/2)) # can't add negative space right <- pmax(0, width - (nc + left)) # right will be >= left if (all(right <=0)) { if (length(x) >= length(width)) x # nothing needs to be done else rep(x, length=length(width)) } else { # Each pad could be a different length. # Make a long string from which we can take a portion longpad <- paste(rep(pad, max(right)), collapse='') paste0(substring(longpad, 1, left), x, substring(longpad,1, right)) } } pformat <- function(x, nastring, ...) { # This is only called for single index tables, in vertical mode # Any matrix will be a confidence interval if (is.matrix(x)) ret <- paste(ifelse(is.na(x[,1]), nastring, format(x[,1], ...)), "-", ifelse(is.na(x[,2]), nastring, format(x[,2], ...))) else ret <- ifelse(is.na(x), nastring, format(x, ...)) } pybox <- function(plist, dd, nastring, ...) { ci <- (substring(names(plist), 1,3) == "ci.") # the CI components int <- sapply(plist, function(x) all(x == floor(x) | is.na(x))) int <- (!ci & int) real<- (!ci & !int) nc <- prod(dd) final <- matrix("", nrow=nc, ncol=length(ci)) if (any(int)) { # integers if (any(sapply(plist[int], length) != nc)) stop("programming length error, notify package author") temp <- unlist(plist[int]) final[,int] <- ifelse(is.na(temp), nastring, format(temp)) } if (any(real)) { # floating point if (any(sapply(plist[real], length) != nc)) stop("programming length error, notify package author") temp <- unlist(plist[real]) final[,real] <- ifelse(is.na(temp), nastring, format(temp, ...)) } if (any(ci)) { if (any(sapply(plist[ci], length) != nc*2)) stop("programming length error, notify package author") temp <- unlist(plist[ci]) temp <- array(ifelse(is.na(temp), nastring, format(temp, ...)), dim=c(nc, 2, sum(ci))) final[,ci] <- paste(temp[,1,], temp[,2,], sep='-') } array(final, dim=c(dd, length(ci))) } pyshow <- function(dmat, labels, rowname, colname, vline) { # Every column is the same width, except the first colwidth <- c(max(nchar(rowname), nchar(labels[1])), rep(max(nchar(dmat[1,1,]), nchar(colname)), length(colname))) colwidth[2] <- max(colwidth[2], nchar(labels[2])) ncol <- length(colwidth) dd <- dim(dmat) # vector of length 3, third dim is the statistics rline <- ceiling(dd[3]/2) #which line to put the row label on. if (vline) { # use a grid table cat("+", paste(strpad('-', colwidth, pad='-'), collapse='+'), "+\n", sep='') temp <- rep(' ', ncol); temp[2] <- labels[2] cat("|", paste(strpad(temp, colwidth), collapse="|"), "|\n", sep='') cat("|", paste(strpad(c(labels[1], colname), colwidth), collapse="|"), "|\n", sep='') cat("+", paste(strpad('=', colwidth, pad='='), collapse="+"), "+\n", sep='') for (i in 1:dd[1]) { for (j in 1:dd[3]) { #one printout line per stat if (j==rline) temp <- c(rowname[i], dmat[i,,j]) else temp <- c("", dmat[i,,j]) cat("|", paste(strpad(temp, colwidth), collapse='|'), "|\n", sep='') } cat("+", paste(strpad('-', colwidth, '-'), collapse='+'), "+\n", sep='') } } else { # use a multiline table cat(paste(strpad('-', colwidth, '-'), collapse='-'), "\n") temp <- rep(' ', ncol); temp[2] <- labels[2] cat(paste(strpad(temp, colwidth), collapse=" "), "\n") cat(paste(strpad(c(labels[1], colname), colwidth), collapse=" "), "\n") cat(paste(strpad('-', colwidth, pad='-'), collapse=" "), "\n") for (i in 1:dd[1]) { for (j in 1:dd[3]) { #one printout line per stat if (j==rline) temp <- c(rowname[i], dmat[i,,j]) else temp <- c("", dmat[i,,j]) cat(paste(strpad(temp, colwidth), collapse=' '), "\n") } if (i< dd[1]) cat(" \n") #blank line } cat(paste(strpad('-', colwidth, '-'), collapse='-'), "\n") } } pytot <- function(x, na=FALSE) { dd <- dim(x) if (length(dd) ==1) { if (na) array(c(x, NA), dim= length(x) +1, dimnames=list(c(dimnames(x)[[1]], "Total"))) else array(c(x, sum(x)), dim= length(x) +1, dimnames=list(c(dimnames(x)[[1]], "Total"))) } else if (length(dd) ==2) { if (na) new <- rbind(cbind(x, NA), NA) else { new <- rbind(x, colSums(x)) new <- cbind(new, rowSums(new)) } array(new, dim=dim(x) + c(1,1), dimnames=list(c(dimnames(x)[[1]], "Total"), c(dimnames(x)[[2]], "Total"))) } else { # The general case index <- 1:length(dd) if (na) sum1 <- sum2 <- sum3 <- NA else { sum1 <- apply(x, index[-1], sum) # row sums sum2 <- apply(x, index[-2], sum) # col sums sum3 <- apply(x, index[-(1:2)], sum) # total sums } # create a new matrix and then fill it in d2 <- dd d2[1:2] <- dd[1:2] +1 dname <- dimnames(x) dname[[1]] <- c(dname[[1]], "Total") dname[[2]] <- c(dname[[2]], "Total") new <- array(x[1], dim=d2, dimnames=dname) # say dim(x) =(5,8,4); we want new[6,-9,] <- sum1; new[-6,9,] <- sum2 # and new[6,9,] <- sum3 # if dim is longer, we need to add more commas commas <- rep(',', length(dd) -2) eval(parse(text=paste("new[1:dd[1], 1:dd[2]", commas, "] <- x"))) eval(parse(text=paste("new[ d2[1],-d2[2]", commas, "] <- sum1"))) eval(parse(text=paste("new[-d2[1], d2[2]", commas, "] <- sum2"))) eval(parse(text=paste("new[ d2[1], d2[2]", commas, "] <- sum3"))) new } } survival/R/frailty.controldf.S0000644000175100001440000000602711732700061016135 0ustar hornikusers# $Id: frailty.controldf.S 11373 2009-10-28 17:12:59Z therneau $ # A function to calibrate the df # very empirical # Find the closest 3 points that span the target value # We know the function is monotone, so fit the function # dy = a * (dx)^p to the 3 points, where dx and dy are the distance # from the leftmost of the three points. # This method can fail near a boundary, so use step halving if things don't # go well # On input, parms$df = target degrees of freedom # parms$dfs, parms$thetas = known values (usually 0,0) # parms$guess = first guess # frailty.controldf <- function(parms, iter, old, df) { if (iter==0) { theta <- parms$guess return(list(theta=theta, done=FALSE, history=cbind(thetas=parms$thetas, dfs=parms$dfs))) } eps <- parms$eps if (length(eps)==0) eps <- .1 thetas <- c(old$history[,1], old$theta) dfs <- c(old$history[,2], df) nx <- length(thetas) if (nx==2) { #linear guess based on first two # but try extra hard to bracket the root theta <- thetas[1] + (thetas[2]-thetas[1])*(parms$df - dfs[1])/ (dfs[2] - dfs[1]) if (parms$df > df) theta <- theta * 1.5 return(list(theta=theta, done=FALSE, history=cbind(thetas=thetas, dfs=dfs), half=0)) } else{ # Now, thetas= our guesses at theta # dfs = the degrees of freedom for each guess done <- (iter>1 && (abs(dfs[nx]-parms$df) < eps)) # look for a new minimum x <- thetas y <- dfs target <- parms$df # How am I doing if ( abs( (y[nx]-target)/(y[nx-1]-target)) > .6) doing.well <- FALSE else doing.well <- TRUE ord <- order(x) if ((x[1]-x[2])*(y[1]-y[2]) >0) y <- y[ord] #monotone up else { #monotone down y <- -1* y[ord] target <- -target } x <- x[ord] if (all(y>target)) b1 <- 1 #points 1:3 are the closest then else if (all(y1 && ((target -y[b1]) < (y[b1+1] -target)))) b1 <- b1-1 } #now have the best 3 points # fit them with a power curve anchored at the leftmost one b2 <- b1 + 1:2 xx <- log(x[b2] - x[b1]) yy <- log(y[b2] - y[b1]) power <- diff(yy)/diff(xx) a <- yy[1] - power*xx[1] newx <- (log(target -y[b1]) - a)/power if (length(parms$trace) && parms$trace){ print(cbind(thetas=thetas, dfs=dfs)) cat(" new theta=" , format(x[b1] + exp(newx)), "\n\n") } list(theta=x[b1] + exp(newx), done=done, history=cbind(thetas=thetas, dfs=dfs), half=0) } } survival/R/agreg.fit.R0000644000175100001440000001075513065013230014336 0ustar hornikusers# Automatically generated from the noweb directory agreg.fit <- function(x, y, strata, offset, init, control, weights, method, rownames) { n <- nrow(y) nvar <- ncol(x) event <- y[,3] if (all(event==0)) stop("Can't fit a Cox model with 0 failures") # Sort the data (or rather, get a list of sorted indices) # For both stop and start times, the indices go from last to first if (length(strata)==0) { sort.end <- order(-y[,2]) -1L #indices start at 0 for C code sort.start<- order(-y[,1]) -1L newstrat <- n } else { sort.end <- order(strata, -y[,2]) -1L sort.start<- order(strata, -y[,1]) -1L newstrat <- cumsum(table(strata)) } if (missing(offset) || is.null(offset)) offset <- rep(0.0, n) if (missing(weights)|| is.null(weights))weights<- rep(1.0, n) else if (any(weights<=0)) stop("Invalid weights, must be >0") else weights <- as.vector(weights) if (is.null(nvar) || nvar==0) { # A special case: Null model. Just return obvious stuff # To keep the C code to a small set, we call the usual routines, but # with a dummy X matrix and 0 iterations nvar <- 1 x <- matrix(as.double(1:n), ncol=1) #keep the .C call happy maxiter <- 0 nullmodel <- TRUE if (length(init) !=0) stop("Wrong length for inital values") init <- 0.0 #dummy value to keep a .C call happy (doesn't like 0 length) } else { nullmodel <- FALSE maxiter <- control$iter.max if (is.null(init)) init <- rep(0., nvar) if (length(init) != nvar) stop("Wrong length for inital values") } # the returned value of agfit$coef starts as a copy of init, so make sure # is is a vector and not a matrix; as.double suffices. # Solidify the storage mode of other arguments storage.mode(y) <- storage.mode(x) <- "double" storage.mode(offset) <- storage.mode(weights) <- "double" storage.mode(newstrat) <- "integer" agfit <- .Call(Cagfit4, y, x, newstrat, weights, offset, as.double(init), sort.start, sort.end, as.integer(method=="efron"), as.integer(maxiter), as.double(control$eps), as.double(control$toler.chol), as.integer(1)) # internally rescale var <- matrix(agfit$imat,nvar,nvar) coef <- agfit$coef if (agfit$flag[1] < nvar) which.sing <- diag(var)==0 else which.sing <- rep(FALSE,nvar) if (maxiter >1) { infs <- abs(agfit$u %*% var) if (any(!is.finite(coef)) || any(!is.finite(var))) stop("routine failed due to numeric overflow.", "This should never happen. Please contact the author.") if (agfit$iter > maxiter) warning("Ran out of iterations and did not converge") else { infs <- ((infs > control$eps) & infs > control$toler.inf*abs(coef)) if (any(infs)) warning(paste("Loglik converged before variable ", paste((1:nvar)[infs],collapse=","), "; beta may be infinite. ")) } } lp <- as.vector(x %*% coef + offset - sum(coef * colMeans(x))) score <- as.double(exp(lp)) resid <- .Call(Cagmart3, y, score, weights, newstrat, cbind(sort.end, sort.start), as.integer(method=='efron')) names(resid) <- rownames if (nullmodel) { list(loglik=agfit$loglik[2], linear.predictors = offset, residuals = resid, method= c("coxph.null", 'coxph') ) } else { names(coef) <- dimnames(x)[[2]] if (maxiter > 0) coef[which.sing] <- NA # always leave iter=0 alone flag <- agfit$flag names(flag) <- c("rank", "rescale", "step halving") concordance <- survConcordance.fit(y, lp, strata, weights) list(coefficients = coef, var = var, loglik = agfit$loglik, score = agfit$sctest, iter = agfit$iter, linear.predictors = as.vector(lp), residuals = resid, means = colMeans(x), concordance = concordance, first = agfit$u, info = flag, method= 'coxph') } } survival/R/print.summary.survreg.S0000644000175100001440000000320712470201064017012 0ustar hornikusers# $Id: print.summary.survreg.S 11166 2008-11-24 22:10:34Z therneau $ print.summary.survreg <- function(x, digits = max(options()$digits - 4, 3), ...) { correl <- x$correlation if(is.null(digits)) digits <- options()$digits cat("\nCall:\n") dput(x$call) print(x$table, digits = digits) if (nrow(x$var)==length(x$coefficients)) cat("\nScale fixed at",format(x$scale, digits=digits),"\n") else if (length(x$scale)==1) cat ("\nScale=", format(x$scale, digits=digits), "\n") else { cat("\nScale:\n") print(x$scale, digits=digits, ...) } cat("\n", x$parms, "\n", sep='') df <- sum(x$df) - x$idf # The sum is for penalized models cat("Loglik(model)=", format(round(x$loglik[2],1)), " Loglik(intercept only)=", format(round(x$loglik[1],1))) if (df > 0) cat("\n\tChisq=", format(round(x$chi,2)), "on", round(df,1), "degrees of freedom, p=", format(signif(1-pchisq(x$chi, df),2)), "\n") else cat("\n") if (x$robust) cat("(Loglikelihood assumes independent observations)\n") cat("Number of Newton-Raphson Iterations:", format(trunc(x$iter)), "\n") omit <- x$na.action if (length(omit)) cat("n=", x$n, " (", naprint(omit), ")\n", sep="") else cat("n=", x$n, "\n") if(!is.null(correl)) { p <- dim(correl)[2] if(p > 1) { cat("\nCorrelation of Coefficients:\n") ll <- lower.tri(correl) correl[ll] <- format(round(correl[ll], digits=digits)) correl[!ll] <- "" print(correl[-1, - p, drop = FALSE], quote = FALSE) } } cat("\n") invisible(NULL) } survival/R/coxpenal.df.S0000644000175100001440000000610411732700061014667 0ustar hornikusers# $Id: coxpenal.df.S 11166 2008-11-24 22:10:34Z therneau $ # # degrees of freedom computation, based on Bob Gray's paper # # hmat = right hand slice of cholesky of H # hinv = right hand slice of cholesky of H-inverse # fdiag= diagonal of D-inverse # assign.list: terms information # ptype= 1 or 3 if a sparse term exists, 2 or 3 if a non-sparse exists # nvar = # of non-sparse terms # pen1 = the penalty matrix (diagonal thereof) for the sparse terms # pen2 = the penalty matrix for the non-sparse terms # sparse = indicates which term is the sparse one coxpenal.df <- function(hmat, hinv, fdiag, assign.list, ptype, nvar, pen1, pen2, sparse) { if (ptype ==1 & nvar==0) { #only sparse terms hdiag <- 1/fdiag list(fvar2=(hdiag-pen1)*fdiag^2, df=sum((hdiag-pen1)*fdiag), fvar = fdiag, trH=sum(fdiag)) } else if (ptype==2) { # only dense ones hmat.full <- t(hmat) %*% (ifelse(fdiag==0, 0,1/fdiag)* hmat) hinv.full <- hinv %*% (fdiag* t(hinv)) if (length(pen2)==length(hmat.full)) imat <- hmat.full - pen2 else imat <- hmat.full - diag(pen2) var <- hinv.full %*% imat %*% hinv.full if (length(assign.list)==1) list(var2=var, df=sum(imat * hinv.full), trH=sum(diag(hinv.full)), var=hinv.full) else { df <- trH <- NULL d2 <- diag(hinv.full) for (i in assign.list) { temp <- coxph.wtest(hinv.full[i,i], var[i,i])$solve if (is.matrix(temp)) df <- c(df, sum(diag(temp))) else df <- c(df, sum(temp)) trH<- c(trH, sum(d2[i])) } list(var2=var, df=df, trH=trH, var = hinv.full) } } else { # sparse terms + other vars nf <- length(fdiag) - nvar nr1 <- 1:nf nr2 <- (nf+1):(nf+nvar) d1 <- fdiag[nr1] d2 <- fdiag[nr2] temp <- t(hinv[nr1,]) temp2<- t(hinv[nr2,,drop=FALSE]) A.diag <- d1 + c(rep(1,nvar) %*% (temp^2*d2)) B <- hinv[nr1,] %*% (d2 * temp2) C <- hinv[nr2,] %*% (d2 * temp2) #see notation in paper var2 <- C - t(B) %*% (pen1 * B) if (ptype==3) { #additional work when we have penalties on both the sparse term # and on non-sparse terms hmat.22 <- t(hmat) %*%(ifelse(fdiag==0, 0,1/fdiag)* hmat) temp <- C - coxph.wtest(hmat.22, diag(nvar))$solve if (nvar==1) { var2 <- var2 - C*pen2*C # C will be 1 by 1 temp2 <- c(temp*pen2) } else if (length(pen2) == nvar) { var2 <- var2 - C %*% (pen2 * C) #diagonal penalty temp2 <- sum(diag(temp) * pen2) } else { var2 <- var2 - C %*% matrix(pen2,nvar) %*% C temp2 <- sum(diag(temp * pen2)) } } else temp2 <- 0 #temp2 contains trace[B'A^{-1}B P2], this line: P2=0 df <- trH <- NULL cdiag <- diag(C) for (i in 1:length(assign.list)) { if (sparse==i){ df <- c(df, nf - (sum(A.diag * pen1) + temp2)) trH <- c(trH, sum(A.diag)) } else { j <- assign.list[[i]] temp <- coxph.wtest(C[j,j], var2[j,j])$solve if (is.matrix(temp)) df <- c(df, sum(diag(temp))) else df <- c(df, sum(temp)) trH <- c(trH, sum(cdiag[j])) } } list(var=C, df=df, trH=trH, fvar=A.diag, var2=var2) } } survival/R/firstlib.R0000644000175100001440000000011612675234657014324 0ustar hornikusers.onUnload <- function(libpath) library.dynam.unload("survival", libpath) survival/R/survfitTurnbull.S0000644000175100001440000002471313064773235015743 0ustar hornikusers# Compute the K-M for left/right/interval censored data via Turnbull's # slow EM calculation # x is a factor giving the groups, y is a survival object survfitTurnbull <- function(x, y, casewt, type=c('kaplan-meier', 'fleming-harrington', 'fh2'), error=c('greenwood', "tsiatis"), se.fit=TRUE, conf.int= .95, conf.type=c('log', 'log-log', 'plain', 'none'), conf.lower=c('usual', 'peto', 'modified'), start.time) { type <- match.arg(type) error <- match.arg(error) conf.type <- match.arg(conf.type) conf.lower<- match.arg(conf.lower) if (is.logical(conf.int)) { # A common error is for users to use "conf.int = FALSE" # it's illegal, but allow it if (!conf.int) conf.type <- "none" conf.int <- .95 } if (!is.Surv(y)) stop("y must be a Surv object") if (!is.factor(x)) stop("x must be a factor") xlev <- levels(x) # Will supply names for the curves x <- as.numeric(x) # keep only the levels if (!missing(start.time)) { # The user has requested that survival be "survival given that they # made it to start.time". We do this by just tossing those who # are known to end before start.time. Now if one of the times were # interval censored (15,42) and start.time were 20, perhaps it should # be modified too, but we don't. I really don't know what the # correct action would be, actually. # ny <- ncol(y) # remove any obs whose end time is <= start.time keep <- (y[,ny-1] >= start.time) if (all(keep==FALSE)) stop(paste("start.time =", start.time, "is greater than all time points.")) x <- x[keep] y <- y[keep,,drop=FALSE] #make sure y remains a matrix casewt <- casewt[keep] } n.used <- as.vector(table(x)) # This is for the printout nstrat <- length(n.used) # Make sure that the time variable is not "counting" type, # and convert "left" to "interval" style. stype <- attr(y, 'type') if (stype=='counting') stop("survfitTurnbull not appropriate for counting process data") if (stype=='interval') status <- y[,3] if (stype=='left') status <- ifelse(y[,2]==0,2,1) if (stype=='right')status <- y[,2] # If any exact times were represented as interval censored, e.g. (x,x) # as the interval for some x, change the code to "uncensored". if (any(status==3)) { who <- (status==3 & y[,1]==y[,2]) status[who] <- 1 } # the code below actually does the estimate, one curve at a time doit <- function(y,status, wt, ...) { n <- length(status) # Find all of the jump points for the KM in the data set, which are # the exact times, plus any right-followed-by-left pairs. # For this computation, an interval censored observation is considered # to be of the form (a,b], left censored is (-infinity,b] and right # censored is (a, infinity). If there are two interval censored # obs of (10,20] and (20,40], we do NOT want to create a jtimes entry # at 20. # # The algorithm puts a [ at t for each exact, a ( at t for each right # censored, a ] at t for each left censored, and ( and ] at t1/t2 # for each interval censor. In ties, order the parens as [, ], (. # Then find pairs of left-followed-immediately-by-right. The stat2 # variable is 0= [ at t, 1= ] at t, 2= ( at t. # The variables time2, stat2 are never needed after jtimes has # been created. if (any(status==3)) { #interval censored stat2 <- c(c(2,0,1,2)[status+1], rep(1, sum(status==3))) time2 <- c(y[,1], y[status==3,2]) } else { stat2 <- c(2,0,1)[status+1] time2 <- y[,1] } ord <- order(time2, stat2) time2 <- time2[ord] stat2 <- stat2[ord] n2 <- length(time2) pairs <- (stat2[-n2]!=1 & stat2[-1]==1) jtimes <- c(time2[stat2==0], .5*(time2[-n2] + time2[-1])[pairs]) # # If any of the left censored times are < min(jtime), then treat # them as though they were exact (for now). The formal MLE # algebra puts all their mass at an arbitray point between the # smallest of such times and -infinity. # mintime <- min(jtimes) who <- (status==2 & y[,1] < mintime) if (any(who)) { status[who] <- 1 jtimes <- c(y[who,1], jtimes) } # The KM is computed on a fake data set with njump points # standing in for the left and interval censored observations # So tempy contains the exact and right censored y data, followed # by the fakes jtimes <- sort(unique(jtimes)) njump <- length(jtimes) nreal <- sum(status<2) tempx <- factor(rep(1, njump + nreal)) #dummy x var for survfit.km tempy <- Surv(c(y[status<2, 1], jtimes), c(status[status<2], rep(1, njump))) # wtmat marks, for each left/interval obs, which jump points are in it # A column is a "fake" time point, a row is an observation # For a left censored obs, we assume that the true event time is # <= the time recorded, and for an interval one that (a, b] contains # the true event time. This is motivated by data that would come # from repeated visits, and agrees with Turnbull's paper. # If all status <=1, this is the unusual case of left censoring before # some minimal time, in which case I can skip this step. There are # no interval censored or left censored be "split". if (any(status>1)) { temp <- matrix(jtimes, nrow=sum(status>1), ncol=njump, byrow=TRUE) indx <- (1:n)[status>1] #the subjects of interest temp1 <- (temp <= y[indx,1]) # logical matrix for the left censored if (any(status>2)) #interval censored temp2 <- (temp > y[indx,1] & temp <= y[indx,2]) else temp2 <- FALSE & temp1 temp3 <- rep(status[indx]==2, njump) wtmat <- matrix(as.numeric((temp3&temp1) | (!temp3 & temp2)), ncol=njump) lwt <- wt[indx] # the input vector of case weights, for these } else { wtmat <- matrix(rep(1, length(jtimes)), nrow=1) lwt <- 1 } eps <- 1 # The initial "starter" KM is proportional to the number of intervals # that overlap each time point temp <- apply(wtmat, 2, sum) tfit <- list(time=jtimes, surv= 1- cumsum(temp)/sum(temp)) old <- tfit$surv iter <- 0 aitken1 <- jump1 <- 0 #dummy values for lagging while (eps > .00005) { iter <- iter +1 # partition each left/interval person out over the jumps jumps <- -diff(c(1, tfit$surv[match(jtimes, tfit$time)])) #KM jumps if (TRUE) { # add Aitken acceleration to speed things up # Given 3 points on a sequence, it guesses ahead. So we use # a set of 3 to guess ahead, generate 3 more regular EM, # guess ahead, 3 regular EM, etc. # Actually, we go every 5th below instead of every 3rd, to # give the EM a chance to restabilize the relative # sizes of elements of "jump". We also only allow it to # stop when comparing two "real EM" iterations. aitken2 <- aitken1 aitken1 <- jumps - jump1 jsave <- jumps if (iter%%5 ==0) { oldlik <- sum(log(wtmat %*% jumps)) jumps <- jump2 - (aitken2)^2/(aitken1 - aitken2) bad <- (jumps<=0 | jumps >=1 | is.na(jumps)) jumps[bad] <- jsave[bad] #failsafe newlik <- sum(log(wtmat %*% jumps)) if (newlik < oldlik) jumps <- jsave # aitkin didn't work! } jump2 <- jump1 # jumps, lagged by 2 iterations jump1 <- jsave # jumps, lagged by 1 iteration } wt2 <- wtmat %*% diag(jumps, length(jumps)) wt2 <- (lwt/(apply(wt2,1,sum))) * wt2 wt2 <- apply(wt2, 2, sum) tfit <- survfitKM(tempx, tempy, casewt=c(wt[status<2], wt2), ...) if (FALSE) { # these lines are in for debugging: change the above to # " if (TRUE)" to turn on the printing cat("\n Iteration = ", iter, "\n") cat("survival=", format(round(tfit$surv[tfit$n.event>0],3)), "\n") cat(" weights=", format(round(wt2,3)), "\n") } stemp <- tfit$surv[match(jtimes, tfit$time)] if (iter%%5<2) eps <- 1 #only check eps for a pair of EM iters else eps <- max(abs(old-stemp)) old <- stemp } # # Now, fix up the "cheating" I did for any left censoreds which were # less than the smallest jump time who <- (tfit$time < mintime & tfit$n.event >0) if (any(who)) { indx <- match(mintime, tfit$time) # first "real" time # tfit$surv[who] <- tfit$surv[indx] tfit$n.event[who] <- 0 # if (!is.null(tfit$std.err)) { # tfit$std.err[who] <- tfit$std.err[indx] # tfit$lower[who] <- tfit$lower[indx] # tfit$upper[who] <- tfit$upper[indx] # } } tfit } # # Now to work, one curve at a time # time <- vector('list', nstrat) n.risk <- vector('list', nstrat) surv <- vector('list', nstrat) n.cens <- vector('list', nstrat) n.event<- vector('list', nstrat) uniquex <- sort(unique(x)) for (i in 1:nstrat) { who <- (x== uniquex[i]) tfit <- doit(y[who,,drop=FALSE], status[who], casewt[who]) time[[i]] <- tfit$time n.risk[[i]] <- tfit$n.risk surv[[i]] <- tfit$surv n.cens[[i]] <- tfit$n.cens n.event[[i]]<- tfit$n.event if (i==1) { if (!is.null(tfit$std.err)) { std.err <- vector('list', nstrat) conf.lower <- vector('list', nstrat) conf.upper <- vector('list', nstrat) se.fit <- TRUE } else se.fit <- FALSE } if (se.fit) { std.err[[i]] <- tfit$std.err conf.lower[[i]] <- tfit$lower conf.upper[[i]] <- tfit$upper } } temp <- list(n=n.used, time = unlist(time), n.risk = unlist(n.risk), n.event= unlist(n.event), n.censor = unlist(n.cens), surv = unlist(surv), type='right') if (nstrat >1) { strata <- unlist(lapply(time, length)) names(strata) <- xlev[sort(unique(x))] temp$strata <- strata } if (se.fit) { temp$std.err <- unlist(std.err) temp$lower <- unlist(conf.lower) temp$upper <- unlist(conf.upper) temp$conf.type <- tfit$conf.type temp$conf.int <- tfit$conf.int } temp } survival/R/survdiff.fit.S0000644000175100001440000000257512675234730015123 0ustar hornikuserssurvdiff.fit <- function(y, x, strat, rho=0) { # # This routine is almost always called from survdiff # If called directly, remember that it does no error checking # n <- length(x) if (ncol(y) !=2) stop ("Invalid y matrix") if (nrow(y) !=n | length(x) !=n) stop("Data length mismatch") ngroup <- length(unique(x)) if (ngroup <2) stop ("There is only 1 group") if (inherits(x, "factor")) x <- as.numeric(x) else x <- match(x, unique(x)) if (missing(strat)) strat <- rep(1,n) else strat <- as.numeric(as.factor(strat)) nstrat <- length(unique(strat)) if (length(strat) !=n) stop("Data length mismatch") ord <- order(strat, y[,1], -y[,2]) strat2 <- c(1*(diff(strat[ord])!=0), 1) xx <- .C(Csurvdiff2, as.integer(n), as.integer(ngroup), as.integer(nstrat), as.double(rho), as.double(y[ord,1]), as.integer(y[ord,2]), as.integer(x[ord]), as.integer(strat2), observed = double(ngroup*nstrat), expected = double(ngroup*nstrat), var.e = double(ngroup * ngroup), double(ngroup), double(n)) if (nstrat==1) list(expected = xx$expected, observed = xx$observed, var = matrix(xx$var.e, ngroup, ngroup)) else list(expected = matrix(xx$expected, ngroup), observed = matrix(xx$observed, ngroup), var = matrix(xx$var.e, ngroup, ngroup)) } survival/R/print.summary.coxph.penal.S0000644000175100001440000000445612423460706017553 0ustar hornikusersprint.summary.coxph.penal <- function(x, digits = max(options()$digits - 3, 3), signif.stars = getOption("show.signif.stars"), ...) { if (!is.null(x$call)) { cat("Call:\n") dput(x$call) cat("\n") } if (!is.null(x$fail)) { cat(" Coxreg failed.", x$fail, "\n") return() } savedig <- options(digits = digits) on.exit(options(savedig)) omit <- x$na.action cat(" n=", x$n) if (!is.null(x$nevent)) cat(", number of events=", x$nevent, "\n") else cat("\n") if (length(omit)) cat(" (", naprint(omit), ")\n\n", sep="") else cat("\n") # Format out the NA in the coef matrix print1 <- x$coefficients temp <- cbind(format(print1[,1]), format(print1[,2]), format(print1[,3]), format(round(print1[,4], 2)), format(round(print1[,5], 2)), format(signif(print1[,6], 2))) temp <- ifelse(is.na(print1), "", temp) dimnames(temp) <- dimnames(print1) print(temp, quote=FALSE) if(length(x$conf.int) >0 ) { cat("\n") print(x$conf.int) } logtest <- -2 * (x$loglik[1] - x$loglik[2]) sctest <- x$score cat("\nIterations:", x$iter[1], "outer,", x$iter[2], "Newton-Raphson\n") if (length(x$print2)) { for (i in 1:length(x$print2)) cat(" ", x$print2[i], "\n") } if (is.null(x$df)) df <- sum(!is.na(coef)) else df <- round(sum(x$df),2) cat("Degrees of freedom for terms=", format(round(x$df,1)), "\n") if (!is.null(x$concordance)) { cat("Concordance=", format(round(x$concordance[1],3)), " (se =", format(round(x$concordance[2], 3)),")\n") } cat("Likelihood ratio test= ", format(round(logtest, 2)), " on ", df, " df,", " p=", format(1 - pchisq(logtest, df)), "\n", sep = "") if (!is.null(x$wald.test)) cat("Wald test = ", format(round(x$wald.test, 2)), " on ", df, " df, p=", format(1 - pchisq(x$wald.test, df)), sep = "") if (!is.null(x$score)) cat("\nScore (logrank) test = ", format(round(sctest, 2)), " on ", df, " df,", " p=", format(1 - pchisq(sctest, df)), sep ="") if (is.null(x$rscore)) cat("\n") else cat(", Robust = ", format(round(x$rscore, 2)), " p=", format(1 - pchisq(x$rscore, df)), "\n", sep="") invisible() } survival/R/print.summary.survfit.S0000644000175100001440000000405212757355022017032 0ustar hornikusersprint.summary.survfit <- function(x, digits = max(options()$digits - 4, 3), ...) { savedig <- options(digits=digits) on.exit(options(savedig)) if (!is.null(cl<- x$call)) { cat("Call: ") dput(cl) cat("\n") } omit <- x$na.action if (length(omit)) cat(naprint(omit), "\n") if (x$type == 'right' || is.null(x$n.enter)) { mat <- cbind(x$time, x$n.risk, x$n.event, x$surv) cnames <- c("time", "n.risk", "n.event") } else if (x$type == 'counting') { mat <- cbind(x$time, x$n.risk, x$n.event, x$n.censor, x$surv) cnames <- c("time", "n.risk", "n.event", "censored") } if (is.matrix(x$surv)) ncurve <- ncol(x$surv) else ncurve <- 1 if (ncurve==1) { #only 1 curve cnames <- c(cnames, "survival") if (!is.null(x$std.err)) { if (is.null(x$lower)) { mat <- cbind(mat, x$std.err) cnames <- c(cnames, "std.err") } else { mat <- cbind(mat, x$std.err, x$lower, x$upper) cnames <- c(cnames, 'std.err', paste("lower ", x$conf.int*100, "% CI", sep=''), paste("upper ", x$conf.int*100, "% CI", sep='')) } } } else cnames <- c(cnames, paste("survival", seq(ncurve), sep='')) if (!is.null(x$start.time)) { mat.keep <- mat[,1] >= x$start.time mat <- mat[mat.keep,,drop=FALSE] if (is.null(dim(mat))) stop(paste("No information available using start.time =", x$start.time, ".")) } if (!is.matrix(mat)) mat <- matrix(mat, nrow=1) if (!is.null(mat)) { dimnames(mat) <- list(rep("", nrow(mat)), cnames) if (is.null(x$strata)) print(mat) else { #print it out one strata at a time strata <- x$strata if (!is.null(x$start.time)) strata <- strata[mat.keep] for (i in levels(strata)) { who <- (strata==i) cat(" ", i, "\n") print(mat[who,]) cat("\n") } } } else stop("There are no events to print. Please use the option ", "censored=TRUE with the summary function to see the censored ", "observations.") invisible(x) } survival/R/dsurvreg.S0000644000175100001440000000305012160146613014327 0ustar hornikusers# The density, quantile, and CDF functions for those distributions # supported by survreg # dsurvreg <- function(x, mean, scale=1, distribution='weibull', parms) { dist <- survreg.distributions[[casefold(distribution)]] if (is.null(dist)) stop("Distribution not found") if (!is.null(dist$trans)) { dx <- dist$dtrans(x) x <- dist$trans(x) x <- (x-mean)/scale dist <- survreg.distributions[[dist$dist]] y <- dist$density(x, parms)[,3] y *dx / scale } else { x <- (x-mean)/scale y <- dist$density(x, parms)[,3] y/ scale } } psurvreg <- function(q, mean, scale=1, distribution='weibull', parms) { dist <- survreg.distributions[[casefold(distribution)]] if (is.null(dist)) stop("Distribution not found") if (!is.null(dist$trans)) { q <- dist$trans(q) q <- (q-mean)/scale dist <- survreg.distributions[[dist$dist]] dist$density(q, parms)[,1] } else { q <- (q-mean)/scale dist$density(q, parms)[,1] } } qsurvreg <- function(p, mean, scale=1, distribution='weibull', parms) { dist <- survreg.distributions[[casefold(distribution)]] if (is.null(dist)) stop("Distribution not found") if (!is.null(dist$trans)) { d2 <- survreg.distributions[[dist$dist]] x <- d2$quantile(p, parms) dist$itrans(x*scale + mean) } else { x <- dist$quantile(p, parms) x*scale + mean } } rsurvreg <- function(n, mean, scale=1, distribution='weibull', parms) { if (missing(parms)) qsurvreg(runif(n), mean, scale, distribution) else qsurvreg(runif(n), mean, scale, distribution, parms) } survival/R/anova.coxphlist.S0000644000175100001440000000426313016105374015615 0ustar hornikusers# This is usually called from anova.coxph, not a user # It's first argument must be a list of coxph models anova.coxphlist <- function (object, test = 'Chisq' ,...) { if (!is.list(object)) stop("First argument must be a list") if (!all(unlist(lapply(object, function(x) inherits(x, 'coxph'))))) stop("Argument must be a list of coxph models") if (any(sapply(object, function(x) !is.null(x$naive.var)))) stop("Can't do anova tables with robust variances") responses <- as.character(unlist(lapply(object, function(x) deparse(formula(x)[[2]])))) sameresp <- (responses == responses[1]) if (!all(sameresp)) { object <- object[sameresp] warning(paste("Models with response", deparse(responses[!sameresp]), "removed because response differs from", "model 1")) } ns <- sapply(object, function(x) length(x$residuals)) if (any(ns != ns[1])) stop("models were not all fitted to the same size of dataset") nmodels <- length(object) if (nmodels == 1) # only one model remains return(anova.coxph(object[[1]], test = test)) # The model ~1 only has one loglik value, hence the rev(x)[1], not x[2] loglik <- unlist(lapply(object, function(x) rev(x$loglik)[1])) df <- unlist(lapply(object, function(x) if (!is.null(x$df)) sum(x$df) else if (is.null(coef(x))) 0 else sum(!is.na(coef(x))))) table <- data.frame(loglik, Chisq= c(NA, abs(2*diff(loglik))), Df= abs(c(NA, diff(df)))) tfun <- function(x) paste(as.character(delete.response(terms(formula(x)))), collapse=' ') variables <- lapply(object, tfun) dimnames(table) <- list(1:nmodels, c("loglik", "Chisq", "Df")) title <- paste("Analysis of Deviance Table\n Cox model: response is ", responses[1]) topnote <- paste(" Model ", format(1:nmodels), ": ", variables, sep = "", collapse = "\n") if (!is.null(test)) { table[['P(>|Chi|)']] <- 1-pchisq(table$Chisq, table$Df) } structure(table, heading = c(title, topnote), class = c("anova", "data.frame")) } survival/R/survfit.coxph.R0000644000175100001440000004032513065013247015316 0ustar hornikusers# Automatically generated from the noweb directory survfit.coxph <- function(formula, newdata, se.fit=TRUE, conf.int=.95, individual=FALSE, type, vartype, conf.type=c("log", "log-log", "plain", "none"), censor=TRUE, id, start.time, na.action=na.pass, ...) { Call <- match.call() Call[[1]] <- as.name("survfit") #nicer output for the user object <- formula #'formula' because it has to match survfit if (!is.null(attr(object$terms, "specials")$tt)) stop("The survfit function can not yet process coxph models with a tt term") if (missing(type)) { # Use the appropriate one from the model temp1 <- c("exact", "breslow", "efron") survtype <- match(object$method, temp1) } else { temp1 <- c("kalbfleisch-prentice", "aalen", "efron", "kaplan-meier", "breslow", "fleming-harrington", "greenwood", "tsiatis", "exact") survtype <- match(match.arg(type, temp1), temp1) survtype <- c(1,2,3,1,2,3,2,2,1)[survtype] } if (missing(vartype)) { vartype <- survtype } else { temp2 <- c("greenwood", "aalen", "efron", "tsiatis") vartype <- match(match.arg(vartype, temp2), temp2) if (vartype==4) vartype<- 2 } if (!se.fit) conf.type <- "none" else conf.type <- match.arg(conf.type) tfac <- attr(terms(object), 'factors') temp <- attr(terms(object), 'specials')$strata has.strata <- !is.null(temp) if (has.strata) { # Toss out strata terms in tfac before doing the test 1 line below, as # strata end up in the model with age:strat(grp) terms or *strata() terms # (There might be more than one strata term) for (i in temp) tfac <- tfac[,tfac[i,] ==0] # toss out strata terms } if (any(tfac >1)) stop("not able to create a curve for models that contain an interaction without the lower order effect") if (is.null(object$y) || is.null(object[['x']]) || !is.null(object$call$weights) || (has.strata && is.null(object$strata)) || !is.null(attr(object$terms, 'offset'))) { mf <- stats::model.frame(object) } else mf <- NULL #useful for if statements later if (is.null(mf)) y <- object[['y']] else { y <- model.response(mf) y2 <- object[['y']] # Avoid issues with roundoff. The data set may have been saved and # then read back in, for instance if (!is.null(y2)) { if (ncol(y2) != ncol(y) || length(y2) != length(y)) stop("Could not reconstruct the y vector") if (FALSE) { # removed in 2.40-1. With the addition of aeqSurv # other packages were being flagged due to tiny discrpancies if (ncol(y2) != ncol(y) || length(y2) != length(y) || !(isTRUE(all.equal(y[,1], y2[,1]))) || !(isTRUE(all.equal(y[,2], y2[,2]))) || (ncol(y)==3 && any(y[,3] != y2[,3]))) stop("Could not reconstruct the y vector") } } } if (is.null(object[['x']])) x <- model.matrix.coxph(object, data=mf) else x <- object[['x']] missid <- missing(id) # I need this later, and setting id below makes # "missing(id)" always false if (!missid) individual <- TRUE else if (missid && individual) id <- rep(0,nrow(y)) #dummy value else id <- NULL if (!missing(start.time)) { if (!is.numeric(start.time) || length(start.time) > 1) stop("start.time must be a single numeric value") # Start the curves after start.time # To do so, remove any rows of the data with an endpoint before that # time. if (ncol(y)==3) { keep <- y[,2] > start.time y[keep,1] <- pmax(y[keep,1], start.time) } else keep <- y[,1] > start.time if (!any(y[keep, ncol(y)]==1)) stop("start.time argument has removed all endpoints") y <- y[keep,,drop=FALSE] x <- x[keep,,drop=FALSE] if (length(id) >0 ) id <- id[keep] n <- nrow(y) } else { n <- nrow(y) if (n != object$n[1] || nrow(x) !=n) stop("Failed to reconstruct the original data set") } if (is.null(mf)) wt <- rep(1., n) else { wt <- model.weights(mf) if (is.null(wt)) wt <- rep(1.0, n) } type <- attr(y, 'type') if (type != 'right' && type != 'counting') stop("Cannot handle \"", type, "\" type survival data") if (individual && missing(newdata)) { stop("the id and/or individual options only make sense with new data") } if (individual && type!= 'counting') stop("The individual option is only valid for start-stop data") if (is.null(mf)) offset <- 0 else { offset <- model.offset(mf) if (is.null(offset)) offset <- 0 } Terms <- object$terms if (!has.strata) strata <- rep(0L,n) else { stangle <- untangle.specials(Terms, 'strata') # used multiple times strata <- object$strata #try this first if (is.null(strata)){ if (length(stangle$vars) ==1) strata <- mf[[stangle$vars]] else strata <- strata(mf[, stangle$vars], shortlabel=TRUE) } if (!missing(start.time)) strata <- strata[keep] } if (has.strata) { temp <- attr(Terms, "specials")$strata factors <- attr(Terms, "factors")[temp,] strata.interaction <- any(t(factors)*attr(Terms, "order") >1) } if (is.null(x) || ncol(x)==0) { # a model with ~1 on the right hand side # Give it a dummy x so the rest of the code goes through # (This case is really rare) x <- matrix(0., nrow=n) coef <- 0.0 varmat <- matrix(0.0,1,1) risk <- rep(exp(offset- mean(offset)), length=n) } else { varmat <- object$var coef <- ifelse(is.na(object$coefficients), 0, object$coefficients) xcenter <- object$means if (is.null(object$frail)) { x <- scale(x, center=xcenter, scale=FALSE) risk <- c(exp(x%*% coef + offset - mean(offset))) } else { keep <- !grepl("frailty(", dimnames(x)[[2]], fixed=TRUE) x <- x[,keep, drop=F] # varmat <- varmat[keep,keep] #coxph already has trimmed it risk <- exp(object$linear.predictor) x <- scale(x, center=xcenter, scale=FALSE) } } subterms <- function(tt, i) { dataClasses <- attr(tt, "dataClasses") predvars <- attr(tt, "predvars") oldnames <- dimnames(attr(tt, 'factors'))[[1]] tt <- tt[i] index <- match(dimnames(attr(tt, 'factors'))[[1]], oldnames) if (length(index) >0) { if (!is.null(predvars)) attr(tt, "predvars") <- predvars[c(1, index+1)] if (!is.null(dataClasses)) attr(tt, "dataClasses") <- dataClasses[index] } tt } temp <- untangle.specials(Terms, 'cluster') if (length(temp$terms)) Terms <- subterms(Terms, -temp$terms) if (missing(newdata)) { mf2 <- as.list(object$means) #create a dummy newdata names(mf2) <- names(object$coefficients) mf2 <- as.data.frame(mf2) found.strata <- FALSE } else { if (!is.null(object$frail)) stop("Newdata cannot be used when a model has frailty terms") Terms2 <- Terms if (!individual) Terms2 <- delete.response(Terms) if (is.vector(newdata, "numeric")) { if (individual) stop("newdata must be a data frame") if (is.null(names(newdata))) { stop("Newdata argument must be a data frame") } newdata <- data.frame(as.list(newdata)) } if (missid) { if (has.strata && !strata.interaction) { found.strata <- TRUE tempenv <- new.env(, parent=emptyenv()) assign("strata", function(..., na.group, shortlabel, sep) list(...), envir=tempenv) assign("list", list, envir=tempenv) for (svar in stangle$vars) { temp <- try(eval(parse(text=svar), newdata, tempenv), silent=TRUE) if (!is.list(temp) || any(unlist(lapply(temp, class))== "function")) found.strata <- FALSE } if (found.strata) mf2 <- stats::model.frame(Terms2, data=newdata, na.action=na.action, xlev=object$xlevels) else { Terms2 <- subterms(Terms2, -attr(Terms2, 'specials')$strata) if (!is.null(object$xlevels)) { myxlev <- object$xlevels[match(attr(Terms2, "term.labels"), names(object$xlevels), nomatch=0)] if (length(myxlev)==0) myxlev <- NULL } else myxlev <- NULL mf2 <- stats::model.frame(Terms2, data=newdata, na.action=na.action, xlev=myxlev) } } else { mf2 <- stats::model.frame(Terms2, data=newdata, na.action=na.action, xlev=object$xlevels) found.strata <- has.strata #would have failed otherwise } } else { tcall <- Call[c(1, match(c('id', "na.action"), names(Call), nomatch=0))] tcall$data <- newdata tcall$formula <- Terms2 tcall$xlev <- object$xlevels tcall[[1L]] <- quote(stats::model.frame) mf2 <- eval(tcall) found.strata <- has.strata # would have failed otherwise } } if (has.strata && found.strata) { #pull them off temp <- untangle.specials(Terms2, 'strata') strata2 <- strata(mf2[temp$vars], shortlabel=TRUE) strata2 <- factor(strata2, levels=levels(strata)) if (any(is.na(strata2))) stop("New data set has strata levels not found in the original") # An expression like age:strata(sex) will have temp$vars= "strata(sex)" # and temp$terms = integer(0). This does not work as a subscript if (length(temp$terms) >0) Terms2 <- Terms2[-temp$terms] } else strata2 <- factor(rep(0, nrow(mf2))) if (individual) { if (missing(newdata)) stop("The newdata argument must be present when individual=TRUE") if (!missid) { #grab the id variable id <- model.extract(mf2, "id") if (is.null(id)) stop("id=NULL is an invalid argument") } else id <- rep(1, nrow(mf2)) x2 <- model.matrix(Terms2, mf2)[,-1, drop=FALSE] #no intercept if (length(x2)==0) stop("Individual survival but no variables") x2 <- scale(x2, center=xcenter, scale=FALSE) offset2 <- model.offset(mf2) if (length(offset2) >0) offset2 <- offset2 - mean(offset) else offset2 <- 0 y2 <- model.extract(mf2, 'response') if (attr(y2,'type') != type) stop("Survival type of newdata does not match the fitted model") if (attr(y2, "type") != "counting") stop("Individual=TRUE is only valid for counting process data") y2 <- y2[,1:2, drop=F] #throw away status, it's never used newrisk <- exp(c(x2 %*% coef) + offset2) result <- survfitcoxph.fit(y, x, wt, x2, risk, newrisk, strata, se.fit, survtype, vartype, varmat, id, y2, strata2) } else { if (missing(newdata)) { if (has.strata && strata.interaction) stop ("Models with strata by covariate interaction terms require newdata") x2 <- matrix(0.0, nrow=1, ncol=ncol(x)) offset2 <- 0 } else { offset2 <- model.offset(mf2) if (length(offset2) >0) offset2 <- offset2 - mean(offset) else offset2 <- 0 x2 <- model.matrix(Terms2, mf2)[,-1, drop=FALSE] #no intercept x2 <- scale(x2, center=xcenter, scale=FALSE) } newrisk <- exp(c(x2 %*% coef) + offset2) result <- survfitcoxph.fit(y, x, wt, x2, risk, newrisk, strata, se.fit, survtype, vartype, varmat) if (has.strata && found.strata) { if (is.matrix(result$surv)) { nr <- nrow(result$surv) #a vector if newdata had only 1 row indx1 <- split(1:nr, rep(1:length(result$strata), result$strata)) rows <- indx1[as.numeric(strata2)] #the rows for each curve indx2 <- unlist(rows) #index for time, n.risk, n.event, n.censor indx3 <- as.integer(strata2) #index for n and strata for(i in 2:length(rows)) rows[[i]] <- rows[[i]]+ (i-1)*nr #linear subscript indx4 <- unlist(rows) #index for surv and std.err temp <- result$strata[indx3] names(temp) <- row.names(mf2) new <- list(n = result$n[indx3], time= result$time[indx2], n.risk= result$n.risk[indx2], n.event=result$n.event[indx2], n.censor=result$n.censor[indx2], strata = temp, surv= result$surv[indx4], cumhaz = result$cumhaz[indx4]) if (se.fit) new$std.err <- result$std.err[indx4] result <- new } } } if (!censor) { kfun <- function(x, keep){ if (is.matrix(x)) x[keep,,drop=F] else if (length(x)==length(keep)) x[keep] else x} keep <- (result$n.event > 0) if (!is.null(result$strata)) { temp <- factor(rep(names(result$strata), result$strata), levels=names(result$strata)) result$strata <- c(table(temp[keep])) } result <- lapply(result, kfun, keep) } if (se.fit) { zval <- qnorm(1- (1-conf.int)/2, 0,1) if (conf.type=='plain') { temp1 <- result$surv + zval* result$std.err * result$surv temp2 <- result$surv - zval* result$std.err * result$surv result <- c(result, list(upper=pmin(temp1,1), lower=pmax(temp2,0), conf.type='plain', conf.int=conf.int)) } if (conf.type=='log') { xx <- ifelse(result$surv==0,1,result$surv) #avoid some "log(0)" messages temp1 <- ifelse(result$surv==0, 0*result$std.err, exp(log(xx) + zval* result$std.err)) temp2 <- ifelse(result$surv==0, 0*result$std.err, exp(log(xx) - zval* result$std.err)) result <- c(result, list(upper=pmin(temp1,1), lower=temp2, conf.type='log', conf.int=conf.int)) } if (conf.type=='log-log') { who <- (result$surv==0 | result$surv==1) #special cases xx <- ifelse(who, .1,result$surv) #avoid some "log(0)" messages temp1 <- exp(-exp(log(-log(xx)) + zval*result$std.err/log(xx))) temp1 <- ifelse(who, result$surv + 0*result$std.err, temp1) temp2 <- exp(-exp(log(-log(xx)) - zval*result$std.err/log(xx))) temp2 <- ifelse(who, result$surv + 0*result$std.err, temp2) result <- c(result, list(upper=temp1, lower=temp2, conf.type='log-log', conf.int=conf.int)) } } if (!missing(start.time)) result$start.time <- start.time result$call <- Call # The "type" component is in the middle -- match history indx <- match('surv', names(result)) result <- c(result[1:indx], type=attr(y, 'type'), result[-(1:indx)]) class(result) <- c('survfit.cox', 'survfit') result } survival/R/frailty.gammacon.S0000644000175100001440000000136712470201064015726 0ustar hornikusers# $Id: frailty.gammacon.S 11166 2008-11-24 22:10:34Z therneau $ # Correct the loglik for a gamma frailty # Term2 is the hard one, discussed in section 3.5 of the report # The penalty function only adds \vu \sum(w_j) to the CoxPL, so this # does a bit more than equation 15. # frailty.gammacon <- function(d, nu) { maxd <- max(d) if (nu > 1e7*maxd) term1 <- sum(d*d)/nu #second order Taylor series else term1 <- sum(d + nu*log(nu/(nu+d))) #easy part tbl <- table(factor(d[d>0], levels=1:maxd)) ctbl<- rev(cumsum(rev(tbl))) dlev<- 1:maxd term2.numerator <- nu + rep(dlev-1, ctbl) term2.denom <- nu + rep(dlev, tbl*dlev) term2 <- sum(log(term2.numerator/term2.denom)) term1 + term2 } survival/R/xtras.R0000644000175100001440000000332512653737062013646 0ustar hornikusersvcov.coxph<-function (object, ...) { rval<-object$var dimnames(rval)<-list(names(coef(object)),names(coef(object))) rval } vcov.survreg<-function (object, ...) { object$var } # The extractAIC methods for coxph and survreg objects are defined # in the stats package. Don't reprise them here. extractAIC.coxph.penal<- function(fit,scale,k=2,...){ edf<-sum(fit$df) loglik <- fit$loglik[length(fit$loglik)] c(edf, -2 * loglik + k * edf) } labels.survreg <- function(object, ...) attr(object,"term.labels") rep.Surv <- function(x, ...) { indx <- rep(1:nrow(x), ...) x[indx,] } # This function is just like all.vars -- except that it does not recur # on the $ sign, it follows both arguments of +, * and - in order to # track formulas, all arguments of Surv, and only the first of things # like ns(). And - it works only on formulas. # This is used to generate a warning in coxph if the same variable is used # on both sides, so perfection is not required of the function. terms.inner <- function(x) { if (inherits(x, "formula")) { if (length(x) ==3) c(terms.inner(x[[2]]), terms.inner(x[[3]])) else terms.inner(x[[2]]) } else if (class(x)== "call" && (x[[1]] != as.name("$") && x[[1]] != as.name("["))) { if (x[[1]] == '+' || x[[1]]== '*' || x[[1]] == '-') { # terms in a model equation, unary minus only has one argument if (length(x)==3) c(terms.inner(x[[2]]), terms.inner(x[[3]])) else terms.inner(x[[2]]) } else if (x[[1]] == as.name("Surv")) unlist(lapply(x[-1], terms.inner)) else terms.inner(x[[2]]) } else(deparse(x)) } survival/R/print.cox.zph.S0000644000175100001440000000026211732700061015211 0ustar hornikusers# $Id: print.cox.zph.S 11166 2008-11-24 22:10:34Z therneau $ print.cox.zph <- function(x, digits = max(options()$digits - 4, 3),...) invisible(print(x$table, digits=digits)) survival/R/labels.survreg.S0000644000175100001440000000021211732700061015416 0ustar hornikusers# $Id: labels.survreg.S 11166 2008-11-24 22:10:34Z therneau $ labels.survreg <- function(object, ...) attr(object$terms, "term.labels") survival/R/coxpenal.fit.R0000644000175100001440000004664712470400252015076 0ustar hornikusers# # General penalized likelihood # coxpenal.fit <- function(x, y, strata, offset, init, control, weights, method, rownames, pcols, pattr, assign) { eps <- control$eps n <- nrow(y) if (is.matrix(x)) nvar <- ncol(x) else if (length(x)==0) stop("Must have an X variable") else nvar <-1 if (missing(offset) || is.null(offset)) offset <- rep(0,n) if (missing(weights)|| is.null(weights))weights<- rep(1,n) else { if (any(weights<=0)) stop("Invalid weights, must be >0") } # Get the list of sort indices, but don't sort the data itself if (ncol(y) ==3) { if (length(strata) ==0) { sorted <- cbind(order(-y[,2], y[,3]), order(-y[,1])) -1L newstrat <- as.integer(n) } else { sorted <- cbind(order(strata, -y[,2], y[,3]), order(strata, -y[,1])) -1L newstrat <- as.integer(cumsum(table(strata))) } status <- y[,3] andersen <- TRUE } else { if (length(strata) ==0) { sorted <- order(-y[,1], y[,2]) -1L newstrat <- as.integer(n) } else { sorted <- order(strata, -y[,1], y[,2]) -1L newstrat <- as.integer(cumsum(table(strata))) } status <- y[,2] andersen <- FALSE } n.eff <- sum(y[,ncol(y)]) #effective n for a Cox model is #events # # are there any sparse frailty terms? # npenal <- length(pattr) if (npenal == 0 || length(pcols) != npenal) stop("Invalid pcols or pattr arg") sparse <- sapply(pattr, function(x) !is.null(x$sparse) && x$sparse) if (sum(sparse) >1) stop("Only one sparse penalty term allowed") # # Create a marking vector for the terms, the same length as assign # with pterms == 0=ordinary term, 1=penalized, 2=sparse, # pindex = length of pcols = position in pterms # # Make sure that pcols is a strict subset of assign, so that the # df computation (and printing) can unambiguously decide which cols of # X are penalized and which are not when doing "terms" like actions. # To make some downstream things easier, order pcols and pattr to be # in the same relative order as the terms in 'assign' # ## can't compute assign attribute in R without terms ## if (missing(assign)) assign <- attr(x, 'assign')[-1] ##Remove 'intercept' pterms <- rep(0, length(assign)) names(pterms) <- names(assign) pindex <- rep(0, npenal) for (i in 1:npenal) { temp <- unlist(lapply(assign, function(x,y) (length(x) == length(y) && all(x==y)), pcols[[i]])) if (sparse[i]) pterms[temp] <- 2 else pterms[temp] <- 1 pindex[i] <- (seq(along.with=temp))[temp] } if ((sum(pterms==2) != sum(sparse)) || (sum(pterms>0) != npenal)) stop("pcols and assign arguments disagree") if (any(pindex != sort(pindex))) { temp <- order(pindex) pindex <- pindex[temp] pcols <- pcols[temp] pattr <- pattr[temp] } # ptype= 1 or 3 if a sparse term exists, 2 or 3 if a non-sparse exists ptype <- any(sparse) + 2*(any(!sparse)) ## Make sure these get defined f.expr1<-function(coef) NULL f.expr2<-function(coef) NULL if (any(sparse)) { sparse.attr <- (pattr[sparse])[[1]] #can't use [[sparse]] directly # if 'sparse' is a T/F vector fcol <- unlist(pcols[sparse]) if (length(fcol) > 1) stop("Sparse term must be single column") # Remove the sparse term from the X matrix xx <- x[, -fcol, drop=FALSE] for (i in 1:length(assign)){ j <- assign[[i]] if (j[1] > fcol) assign[[i]] <- j-1 } for (i in 1:npenal) { j <- pcols[[i]] if (j[1] > fcol) pcols[[i]] <- j-1 } frailx <- x[, fcol] frailx <- match(frailx, sort(unique(frailx))) nfrail <- max(frailx) nvar <- nvar - 1 #Set up the callback for the sparse frailty term pfun1 <- sparse.attr$pfun ### In R we use a function and eval() it, not an expression f.expr1 <- function(coef){ coxlist1$coef <- coef if (is.null(extra1)) temp <- pfun1(coef, theta1, n.eff) else temp <- pfun1(coef, theta1, n.eff, extra1) if (!is.null(temp$recenter)) coxlist1$coef <- coxlist1$coef - as.double(temp$recenter) if (!temp$flag) { coxlist1$first <- -as.double(temp$first) coxlist1$second <- as.double(temp$second) } coxlist1$penalty <- -as.double(temp$penalty) coxlist1$flag <- as.logical(temp$flag) if (any(sapply(coxlist1, length) != c(rep(nfrail,3), 1, 1))) stop("Incorrect length in coxlist1") coxlist1 } if (!is.null(getOption("survdebug"))) debug(f.expr1) coxlist1 <- list(coef=double(nfrail), first=double(nfrail), second=double(nfrail), penalty=0.0, flag=FALSE) ## we pass f.expr1 in as an argument in R ##.C("init_coxcall1", as.integer(sys.nframe()), expr1) } else { xx <- x frailx <- 0 nfrail <- 0 } # Now the non-sparse penalties if (sum(!sparse) >0) { full.imat <- !all(unlist(lapply(pattr, function(x) x$diag))) ipenal <- (1:length(pattr))[!sparse] #index for non-sparse terms f.expr2 <- function(coef){ coxlist2$coef<-coef ## pentot <- 0 for (i in ipenal) { pen.col <- pcols[[i]] coef <- coxlist2$coef[pen.col] if (is.null(extralist[[i]])) temp <- ((pattr[[i]])$pfun)(coef, thetalist[[i]],n.eff) else temp <- ((pattr[[i]])$pfun)(coef, thetalist[[i]], n.eff,extralist[[i]]) if (!is.null(temp$recenter)) coxlist2$coef[pen.col] <- coxlist2$coef[pen.col]- temp$recenter if (temp$flag) coxlist2$flag[pen.col] <- TRUE else { coxlist2$flag[pen.col] <- FALSE coxlist2$first[pen.col] <- -temp$first if (full.imat) { tmat <- matrix(coxlist2$second, nvar, nvar) tmat[pen.col,pen.col] <- temp$second coxlist2$second <- c(tmat) } else coxlist2$second[pen.col] <- temp$second } pentot <- pentot - temp$penalty } coxlist2$penalty <- as.double(pentot) if (any(sapply(coxlist2, length) != length2)) stop("Length error in coxlist2") coxlist2 } if (!is.null(getOption("survdebug"))) debug(f.expr2) if (full.imat) { coxlist2 <- list(coef=double(nvar), first=double(nvar), second= double(nvar*nvar), penalty=0.0, flag=rep(FALSE,nvar)) length2 <- c(nvar, nvar, nvar*nvar, 1, nvar) } else { coxlist2 <- list(coef=double(nvar), first=double(nvar), second=double(nvar), penalty= 0.0, flag=rep(FALSE,nvar)) length2 <- c(nvar, nvar, nvar, 1, nvar) } ## in R, f.expr2 is passed as an argument later ##.C("init_coxcall2", as.integer(sys.nframe()), expr2) } else full.imat <- FALSE # # Set up initial values for the coefficients # If there are no sparse terms, finit is set to a vector of length 1 # rather than length 0, just to stop some "zero length" errors for # later statements where fcoef is saved (but not used) # if (nfrail >0) finit <- rep(0,nfrail) else finit <- 0 if (!missing(init) && !is.null(init)) { if (length(init) != nvar) { if (length(init) == (nvar+nfrail)) { finit <- init[-(1:nvar)] init <- init[1:nvar] } else stop("Wrong length for inital values") } } else init <- double(nvar) # # "Unpack" the passed in paramter list, # and make the initial call to each of the external routines # cfun <- lapply(pattr, function(x) x$cfun) parmlist <- lapply(pattr, function(x,eps) c(x$cparm, eps2=eps), sqrt(eps)) extralist<- lapply(pattr, function(x) x$pparm) iterlist <- vector('list', length(cfun)) thetalist <- vector('list', length(cfun)) printfun <- lapply(pattr, function(x) x$printfun) for (i in 1:length(cfun)) { temp <- (cfun[[i]])(parmlist[[i]], iter=0) if (sparse[i]) { theta1 <- temp$theta extra1 <- extralist[[i]] } thetalist[[i]] <- temp$theta iterlist[[i]] <- temp } # # Manufacture the list of calls to cfun, with appropriate arguments # ## Amazingly, all this works in R, so I don't need to understand it. ## temp1 <- c('x', 'coef', 'plik', 'loglik', 'status', 'neff', 'df', 'trH') temp2 <- c('frailx', 'coxfit$fcoef', 'loglik1', 'coxfit$loglik', 'status', 'n.eff') temp3 <- c('xx[,pen.col]', 'coxfit$coef[pen.col]','loglik1', 'coxfit$loglik', 'status', 'n.eff') calls <- vector('expression', length(cfun)) cargs <- lapply(pattr, function(x) x$cargs) for (i in 1:length(cfun)) { tempchar <- paste("(cfun[[", i, "]])(parmlist[[", i, "]], iter,", "iterlist[[", i, "]]") temp2b <- c(temp2, paste('pdf[', i, ']'), paste('trH[', i, ']')) temp3b <- c(temp3, paste('pdf[', i, ']'), paste('trH[', i, ']')) if (length(cargs[[i]])==0) calls[i] <- parse(text=paste(tempchar, ")")) else { temp <- match(cargs[[i]], temp1) if (any(is.na(temp))) stop(paste((cargs[[i]])[is.na(temp)], "not matched")) if (sparse[i]) temp4 <- paste(temp2b[temp], collapse=',') else temp4 <- paste(temp3b[temp], collapse=',') calls[i] <- parse(text=paste(paste(tempchar,temp4,sep=','),')')) } } need.df <- any(!is.na(match(c('df', 'trH'), unlist(cargs))))#do any use df? # # Last of the setup: create the vector of variable names # varnames <- dimnames(xx)[[2]] for (i in 1:length(cfun)) { if (!is.null(pattr[[i]]$varname)) varnames[pcols[[i]]] <- pattr[[i]]$varname } ## need the current environment for callbacks rho<-environment() # # Have C store the data, and get the loglik for beta=initial, frailty=0 # storage.mode(y) <- storage.mode(weights) <- "double" storage.mode(xx) <- storage.mode(offset) <- "double" if (andersen) coxfit <- .C(Cagfit5a, as.integer(n), as.integer(nvar), y, xx , offset, weights, newstrat, sorted, means= double(nvar), coef= as.double(init), u = double(nvar), loglik=double(1), as.integer(method=='efron'), as.integer(ptype), as.integer(full.imat), as.integer(nfrail), as.integer(frailx), #R callback additions f.expr1,f.expr2,rho) else coxfit <- .C(Ccoxfit5a, as.integer(n), as.integer(nvar), y, xx, offset, weights, newstrat, sorted, means= double(nvar), coef= as.double(init), u = double(nvar), loglik=double(1), as.integer(method=='efron'), as.integer(ptype), as.integer(full.imat), as.integer(nfrail), as.integer(frailx), f.expr1,f.expr2,rho) loglik0 <- coxfit$loglik means <- coxfit$means # # Now for the actual fit # iter2 <- 0 iterfail <- NULL thetasave <- unlist(thetalist) for (outer in 1:control$outer.max) { if (andersen) coxfit <- .C(Cagfit5b, iter=as.integer(control$iter.max), as.integer(n), as.integer(nvar), as.integer(newstrat), coef = as.double(init), u = double(nvar+nfrail), hmat = double(nvar*(nvar+nfrail)), hinv = double(nvar*(nvar+nfrail)), loglik = double(1), flag = integer(1), as.double(control$eps), as.double(control$toler.chol), as.integer(method=='efron'), as.integer(nfrail), fcoef = as.double(finit), fdiag = double(nfrail+nvar), f.expr1,f.expr2,rho) else coxfit <- .C(Ccoxfit5b, iter=as.integer(control$iter.max), as.integer(n), as.integer(nvar), as.integer(newstrat), coef = as.double(init), u = double(nvar+nfrail), hmat = double(nvar*(nvar+nfrail)), hinv = double(nvar*(nvar+nfrail)), loglik = double(1), flag = integer(1), as.double(control$eps), as.double(control$toler.chol), as.integer(method=='efron'), as.integer(nfrail), fcoef = as.double(finit), fdiag = double(nfrail+nvar), f.expr1,f.expr2,rho) iter <- outer iter2 <- iter2 + coxfit$iter if (coxfit$iter >=control$iter.max) iterfail <- c(iterfail, iter) # If any penalties were infinite, the C code has made fdiag=1 out # of self-preservation (0 divides). But such coefs are guarranteed # zero so the variance should be too.) temp <- rep(FALSE, nvar+nfrail) if (nfrail>0) temp[1:nfrail] <- coxlist1$flag if (ptype >1) temp[nfrail+ 1:nvar] <- coxlist2$flag fdiag <- ifelse(temp, 0, coxfit$fdiag) if (need.df) { #get the penalty portion of the second derive matrix if (nfrail>0) temp1 <- coxlist1$second else temp1 <- 0 if (ptype>1) temp2 <- coxlist2$second else temp2 <- 0 dftemp <-coxpenal.df(matrix(coxfit$hmat, ncol=nvar), matrix(coxfit$hinv, ncol=nvar), fdiag, assign, ptype, nvar, temp1, temp2, pindex[sparse]) df <- dftemp$df var <- dftemp$var var2 <- dftemp$var2 pdf <- df[pterms>0] # df's for penalized terms trH <- dftemp$trH[pterms>0] # trace H } if (nfrail >0) penalty <- -coxlist1$penalty else penalty <- 0 if (ptype >1) penalty <- penalty - coxlist2$penalty loglik1 <- coxfit$loglik + penalty #C code returns PL - penalty if (iter==1) penalty0 <- penalty # # Call the control function(s) # done <- TRUE for (i in 1:length(cfun)) { pen.col <- pcols[[i]] temp <- eval(calls[i]) if (sparse[i]) theta1 <- temp$theta thetalist[[i]] <- temp$theta iterlist[[i]] <- temp done <- done & temp$done } if (done) break # # Choose starting estimates for the next iteration # if (iter==1) { init <- coefsave <- coxfit$coef finit <- fsave <- coxfit$fcoef thetasave <- cbind(thetasave, unlist(thetalist)) } else { # the "as.vector" removes names, dodging a bug in Splus5.1 temp <- as.vector(unlist(thetalist)) coefsave <- cbind(coefsave, coxfit$coef) fsave <- cbind(fsave, coxfit$fcoef) # temp = next guess for theta # *save = prior thetas and the resultant fits # choose as initial values the result for the closest old theta howclose <- apply((thetasave-temp)^2,2, sum) which <- min((1:iter)[howclose==min(howclose)]) if (nvar>0) init <- coefsave[,which] if (nfrail>0) finit<- fsave[,which] thetasave <- cbind(thetasave, temp) } } if (nfrail >0) { lp <- offset + coxfit$fcoef[frailx] if (nvar >0) #sparse frailties and covariates lp <- lp + x[,-fcol,drop=FALSE] %*%coxfit$coef - sum(means*coxfit$coef) } else lp <- offset + as.vector(x%*%coxfit$coef) - sum(means*coxfit$coef) # release the memory if (andersen) { .C(Cagfit5c, as.integer(nvar)) #release the memory resid <- .Call(Cagmart3, y, exp(lp), weights, newstrat, sorted, as.integer(method=='efron')) } else { expect <- .C(Ccoxfit5c, as.integer(n), as.integer(nvar), as.integer(newstrat), as.integer(method=='efron'), expect= double(n))$expect resid <- status - expect } names(resid) <- rownames if (!need.df) { #didn't need it iteration by iteration, but do it now #get the penalty portion of the second derive matrix if (nfrail>0) temp1 <- coxlist1$second else temp1 <- 0 if (ptype>1) temp2 <- coxlist2$second else temp2 <- 0 dftemp <-coxpenal.df(matrix(coxfit$hmat,ncol=nvar), matrix(coxfit$hinv,ncol=nvar), fdiag, assign, ptype, nvar, temp1, temp2, pindex[sparse]) df <- dftemp$df trH <- dftemp$trH var <- dftemp$var var2 <- dftemp$var2 } if (control$iter.max >1 && length(iterfail)>0) warning(paste("Inner loop failed to coverge for iterations", paste(iterfail, collapse=' '))) which.sing <- (fdiag[nfrail + 1:nvar] ==0) coef <- coxfit$coef names(coef) <- varnames coef[which.sing] <- NA names(iterlist) <- names(pterms[pterms>0]) if (nfrail >0) { if (nvar >0) { #sparse frailties and covariates list(coefficients = coef, var = var, var2 = var2, loglik = c(loglik0, loglik1), iter = c(iter, iter2), linear.predictors = as.vector(lp), residuals = resid, means = means, concordance= survConcordance.fit(y, lp, strata, weights), method= c('coxph.penal', 'coxph'), frail = coxfit$fcoef, fvar = dftemp$fvar, df = df, df2=dftemp$df2, penalty= c(penalty0, penalty), pterms = pterms, assign2=assign, history= iterlist, coxlist1=coxlist1, printfun=printfun) } else { #sparse frailties only list( loglik = c(loglik0, loglik1), iter = c(iter, iter2), linear.predictors = as.vector(lp), residuals = resid, means = means, concordance= survConcordance.fit(y, lp, strata, weights), method= c('coxph.penal', 'coxph'), frail = coxfit$fcoef, fvar = dftemp$fvar, df = df, df2=dftemp$df2, penalty = c(penalty0, penalty), pterms = pterms, assign2=assign, history= iterlist, printfun=printfun) } } else { #no sparse terms list(coefficients = coef, var = var, var2 = var2, loglik = c(loglik0, loglik1), iter = c(iter, iter2), linear.predictors = lp, residuals = resid, means = means, concordance= survConcordance.fit(y, lp, strata, weights), method= c('coxph.penal', 'coxph'), df = df, df2=dftemp$df2, penalty= c(penalty0, penalty), pterms = pterms, assign2=assign, history= iterlist, coxlist2=coxlist2, printfun= printfun) } } survival/R/anova.coxph.penal.R0000644000175100001440000001164112676277124016032 0ustar hornikusers# The first section of this is identical to anova.coxph anova.coxph.penal <- function (object, ..., test = 'Chisq') { if (!inherits(object, "coxph")) stop ("argument must be a cox model") # All the ... args need to be coxph or coxme fits. If any of them # have a name attached, e.g., 'charlie=T' we assume a priori # that they are illegal # dotargs <- list(...) named <- if (is.null(names(dotargs))) rep(FALSE, length(dotargs)) else (names(dotargs) != "") if (any(named)) warning(paste("The following arguments to anova.coxph(..)", "are invalid and dropped:", paste(deparse(dotargs[named]), collapse = ", "))) dotargs <- dotargs[!named] if (length(dotargs) >0) { # Check that they are all cox or coxme models is.coxmodel <-unlist(lapply(dotargs, function(x) inherits(x, "coxph"))) is.coxme <- unlist(lapply(dotargs, function(x) inherits(x, "coxme"))) if (!all(is.coxmodel | is.coxme)) stop("All arguments must be Cox models") if (any(is.coxme)) { # We need the anova.coxmelist function from coxme # If coxme is not loaded the line below returns NULL temp <- getS3method("anova", "coxmelist", optional=TRUE) if (is.null(temp)) stop("a coxme model was found and library coxme is not loaded") else return(temp(c(list(object), dotargs), test = test)) } else return(anova.coxphlist(c(list(object), dotargs), test = test)) } # # The argument is a single Cox model # Show the nested list of models generated by this model. # By tradition the sequence is main effects (in the order found in # the model statement), then 2 way interactions, then 3, etc. # One does this by using the "assign" attribute of the model matrix. # This does not work for penalized terms, however, so we use a mixed # strategy. The penalized terms do not participate in interactions # (which are the terms for which assign is really handy). Use # the model frame for the penalized terms, and assign for all the # others. if (length(object$rscore)>0) stop("Can't do anova tables with robust variances") has.strata <- !is.null(attr(terms(object), "specials")$strata) # The following line causes pspline terms to be re-evaluated correctly # The predvars attr for them does not retrieve the correct penalty attr(object$terms, "predvars") <- NULL mf <- stats::model.frame(object) # we must have the model frame Y <- model.response(mf) X <- model.matrix(object, mf) assign <- attr(X, 'assign') if (has.strata) { stemp <- untangle.specials(terms(object), "strata") if (length(stemp$vars)==1) strata.keep <- mf[[stemp$vars]] else strata.keep <- strata(mf[,stemp$vars], shortlabel=TRUE) strats <- as.numeric(strata.keep) } pname <- names(object$pterms)[object$pterms >0] pindex <- match(pname, attr(terms(object), "term.labels")) alevels <- sort(unique(assign)) #if there are strata the sequence has holes nmodel <- length(alevels) df <- integer(nmodel+1) #this will hold the df vector loglik <- double(nmodel+1) #and the loglike vector df[nmodel+1] <- if (is.null(object$df)) sum(!is.na(object$coefficients)) else sum(object$df) loglik[nmodel+1] <- object$loglik[2] df[1] <- 0 loglik[1] <- object$loglik[1] # Now refit intermediate models assign2 <- assign[!(assign %in% pindex)] pform <- paste("mf[['", pname, "']]", sep='') for (i in seq.int(1, length.out=nmodel-1)){ j <- assign2[assign2 <= alevels[i]] if (length(j)) form <- "Y ~ X[,j]" else form <- "Y ~" form <- paste(c(form, pform[pindex <= i]), collapse=" +") if (length(object$offset)) form <- paste(form, " + offset(object$offset") if (has.strata) form <- paste(form, " + strata(strats)") tfit <- coxph(as.formula(form)) df[i+1] <- if (!is.null(tfit$df)) sum(tfit$df) else sum(!is.na(tfit$coefficients)) loglik[i+1] <- tfit$loglik[2] } table <- data.frame(loglik=loglik, Chisq=c(NA, 2*diff(loglik)), Df=c(NA, diff(df))) if (nmodel == 0) #failsafe for a NULL model table <- table[1, , drop = FALSE] if (length(test) >0 && test[1]=='Chisq') { table[['Pr(>|Chi|)']] <- 1- pchisq(table$Chisq, table$Df) } row.names(table) <- c('NULL', attr(terms(object), "term.labels")) title <- paste("Analysis of Deviance Table\n Cox model: response is ", deparse(object$terms[[2]]), "\nTerms added sequentially (first to last)\n", sep = "") structure(table, heading = title, class = c("anova", "data.frame")) } survival/R/aeqSurv.R0000644000175100001440000000241613026501446014121 0ustar hornikusers# # Create time values such that tiny differences are treated as a tie # The decision and tolerance are the same as all.equal # aeqSurv <- function(x, tolerance = sqrt(.Machine$double.eps)) { if (!missing(tolerance)) { if (!is.numeric(tolerance) || length(tolerance)!=1 || !is.finite(tolerance)) stop("invalid value for tolerance") if (tolerance <=0) return(x) # do nothing } if (!is.Surv(x)) stop("argument is not a Surv object") y <- sort(unique(c(x[, -ncol(x)]))) y <- y[is.finite(y)] #someone may hand us an INF dy <- diff(y) tied <- ((dy <=tolerance) |( (dy/ mean(abs(y)) <=tolerance))) if (!any(tied)) return(x) # all values are unique cuts <- y[c(TRUE, !tied)] if (ncol(x) ==2) { # simple survival z <- findInterval(x[,1], cuts) z <- cbind(cuts[z], as.integer(x[,2])) } else { z <- matrix(findInterval(x[,1:2], cuts), ncol=2) # We may have created zero length intervals zeros <- which(z[,1] == z[,2]) if (length(zeros)>0 && any(x[zeros,1] != x[zeros,2])) stop("aeqSurv exception, an interval has effective length 0") z <- cbind(matrix(cuts[z], ncol=2), as.integer(x[,3])) } attributes(z) <- attributes(x) z } survival/R/residuals.coxph.penal.S0000644000175100001440000000236111755254054016713 0ustar hornikusers# $Id: residuals.coxph.penal.S 11516 2012-04-24 12:49:14Z therneau $ residuals.coxph.penal <- function(object, type=c("martingale", "deviance", "score", "schoenfeld", "dfbeta", "dfbetas", "scaledsch","partial"), collapse=FALSE, weighted=FALSE, ...) { type <- match.arg(type) # Are there any sparse terms, and if so do I need the X matrix? if (any(object$pterms==2) && !(type=='martingale' || type=='deviance')){ # treat the sparse term as an offset term # It gets picked up in the linear predictor, so all I need to # do is "X" it out of the model so that it doesn't get picked up # as a part of the X matrix and etc. # I know that the sparse term is a single column BTW # sparsename <- (names(object$pterms))[object$pterms==2] x <- object[['x']] #don't accidentally get object$xlevels if (is.null(x)) { temp <- coxph.getdata(object, y=TRUE, x=TRUE, stratax=TRUE) if (is.null(object$y)) object$y <- temp$y if (is.null(object$strata)) object$strata <- temp$strata x <- temp$x } object$x <- x[, -match(sparsename, dimnames(x)[[2]]), drop=FALSE] temp <- attr(object$terms, 'term.labels') object$terms <- object$terms[-match(sparsename, temp)] } NextMethod('residuals') } survival/R/attrassign.R0000644000175100001440000000252412257335007014655 0ustar hornikusers# $Id$ # When X is a model matrix, Splus and R have a different format # for the "assign" attribute # For instance # survreg(Surv(time, status) ~ age + sex + factor(ph.ecog), lung) # R gives the compact form, a vector (0, 1, 2, 3, 3, 3); which can be # read as "the first column of the X matrix (intercept) goes with none of # the terms', 'the second column goes with term 1', etc. # Splus gives a list # $(Intercept) 1 # $age 2 # $sex 3 # $factor(ph.ecog) 4 5 6 # # This function creates the Splus style of output from the R style. Several # of the routines in the package use this, as it is somewhat easier (more # transparent) to work with. # attrassign<-function (object, ...) UseMethod("attrassign") attrassign.lm<-function(object, ...){ attrassign(model.matrix(object), terms(object))} attrassign.default<-function(object, tt, ...){ if (!inherits(tt,"terms")) stop("need terms object") aa<-attr(object,"assign") if (is.null(aa)) stop("argument is not really a model matrix") ll<-attr(tt,"term.labels") temp <- c("(Intercept)", ll)[aa+1] #vector of term names # Don't put them in alphabetical order, retain the order we inherited split(seq(along=temp), factor(temp, levels=unique(temp))) } survival/vignettes/0000755000175100001440000000000013070714004014147 5ustar hornikuserssurvival/vignettes/adjcurve.Rnw0000644000175100001440000014734513017617770016475 0ustar hornikusers\documentclass{article}[11pt] \usepackage{Sweave} \usepackage{amsmath} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} \SweaveOpts{keep.source=TRUE, fig=FALSE} % Ross Ihaka suggestions \DefineVerbatimEnvironment{Sinput}{Verbatim} {xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} \SweaveOpts{prefix.string=adjcurve,width=6,height=4} \setkeys{Gin}{width=\textwidth} %\VignetteIndexEntry{Adjusted Survival Curves} <>= options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text require(survival, quietly=TRUE) fdata <- flchain[flchain$futime > 7,] fdata$age2 <- cut(fdata$age, c(0,54, 59,64, 69,74,79, 89, 110), labels = c(paste(c(50,55,60,65,70,75,80), c(54,59,64,69,74,79,89), sep='-'), "90+")) @ \title{Adjusted Survival Curves} \author{Terry M Therneau, Cynthia S Crowson, Elizabeth J Atkinson} \date{Jan 2015} \newcommand{\myfig}[1]{\includegraphics[height=!, width=\textwidth] {adjcurve-#1.pdf}} \begin{document} \maketitle \section{Introduction} Suppose we want to investigate to what extent some factor influences survival, as an example we might compare the experience of diabetic patients who are using metformin versus those on injected insulin as their primary treatment modality. There is some evidence that metformin has a positive influence, particularly in cancers, but the ascertainment is confounded by the fact that it is a first line therapy: the patients on metformin will on average be younger and have had a diabetes diagnosis for a shorter amount of time than those using insulin. ``Young people live longer'' is not a particularly novel observation. The ideal way to test this is with a controlled clinical trial. This is of course not always possible, and assessments using available data that includes and adjusts for such confounders is also needed. There is extensive literature --- and debate --- on this topic in the areas of modeling and testing. The subtopic of how to create honest survival curve estimates in the presence of confounders is less well known, and is the focus of this note. Assume that we have an effect of interest, treatment say, and a set of possible confounding variables. Creation a pair of adjusted survival curves has two parts: definition of a reference population for the confounders, and then the computation of estimated curves for that population. There are important choices in both steps. The first, definition of a target, is often not explicitly stated but can be critical. If an outcome differs with age, myocardial infarction say, and two treatments also had age dependent efficacy, then the comparison will depend greatly on whether we are talking about a population of young, middle aged, or older subjects. The computational step has two main approaches. The first, sometimes known as \emph{marginal} analysis, first reweights the data such that each subgroup's weighted distribution matches that of our population target. An immediate consequence is that all subgroups will be balanced with respect to the confounding variables. We can then proceed with a simple analysis of survival using the reformulated data, ignoring the confounders. The second approach seeks to understand and model the effect of each confounder, with this we can then correct for them. From a comprehensive overall model we can obtain predicted survival curves for any configuration of variables, and from these get predicted overall curves for the reference population. This is often called the \emph{conditional} approach since we are using conditional survival curves given covariates $x$. A third but more minor choice is division of the covariates $x$ into effects of interest vs. confounders. For instance, we might want to see separate curves for two treatments, each adjusted for age and sex. The reference population will describe the age and sex distribution. For simplicity we will use $x$ to describe all the confounding variables and use $c$ for the control variable(s), e.g. treatment. The set $c$ might be empty, producing a single overall curve, but this is the uncommon case. As shown below, our two methods differ essentially in the \emph{order} in which the two necessary operations are done, balancing and survival curve creation. \begin{center} \begin{tabular}{rccc} Marginal: & balance data on $x$ & $\longrightarrow$ & form survival curves for each $c$\\ Conditional: & predicted curves for $\{x,c\}$ subset & $\longrightarrow$ & average the predictions for each $c$ \end{tabular} \end{center} We can think of them as ``balance and then model'' versus ``model then balance''. An analysis might use a combinations of these, of course, balancing on some factors and modeling others. All analyses are marginal analyses with respect to important predictors that are unknown to us, although in that case we have no assurance of balance on those factors. \begin{figure}[tb] \myfig{flc1} \caption{Survival of \Sexpr{nrow(flchain)} residents of Olmsted County, broken into three cohorts based on FLC value.} \label{flc1} \end{figure} \section{Free Light Chain} Our example data set for this comparison uses a particular assay of plasma immunoglobulins and is based on work of Dr Angela Dispenzieri and her colleagues at the Mayo Clinic \cite{Dispenzieri12}. In brief: plasma cells (PC) are responsible for the production of immunoglobulins, but PC comprise only a small portion ($<1$\%) of the total blood and marrow hematapoetic cell population in normal patients. The normal human repertoire is estimated to contain over $10^{8}$ unique immunoglobulins, conferring a broad range of immune protection. In multiple myeloma, the most common form of plasma cell malignancy, almost all of the circulating antigen will be identical, the product of a single malignant clone. An electrophoresis examination of circulating immunoglobulins will exhibit a ``spike'' corresponding to this unique molecule. This anomaly is used both as a diagnostic method and in monitoring the course of the disease under treatment. The presence of a similar, albeit much smaller, spike in normal patients has been a long term research interest of the Mayo Clinic hematology research group \cite{Kyle93}. In 1995 Dr Robert Kyle undertook a population based study of this, and collected serum samples on 19,261 of the 24,539 residents of Olmsted County, Minnesota, aged 50 years or more \cite{Kyle06}. In 2010 Dr. Angela Dispenzieri assayed a sub fraction of the immunoglobulins, the free light chain (FLC), on 15,748 of these subjects who had sufficient remaining sera from the original sample collection. All studies took place under the oversight of the appropriate Institutional Review Boards, which ensure rigorous safety and ethical standards in research. A subset of the Dispenzieri study is available in the survival package as data set \texttt{flchain}. Because the original study assayed nearly the entire population, there is concern that some portions of the anonymized data could be linked to actual subjects by a diligent searcher, and so only a subset of the study has been made available as a measure to strengthen anonymity. It was randomly selected from the whole within sex and age group strata so as to preserve the age/sex structure. The data set contains 3 subjects whose blood sample was obtained on the day of their death. It is rather odd to think of a sample obtained on the final day as ``predicting'' death, or indeed for any results obtained during a patient's final mortality cascade. There are also a few patients with no follow-up beyond the clinic visit at which the assay occurred. We have chosen in this analysis to exclude the handful of subjects with less than 7 days of follow-up, leaving \Sexpr{nrow(fdata)} observations. \begin{table} \centering \begin{tabular}{l|cccc} & 50--59 & 60--69 & 70--79 & 80+ \\ \hline <>= group3 <- factor(1+ 1*(fdata$flc.grp >7) + 1*(fdata$flc.grp >9), levels=1:3, labels=c("FLC < 3.38", "3.38 - 4.71", "FLC > 4.71")) age1 <- cut(fdata$age, c(49,59,69,79, 110)) levels(age1) <- c(paste(c(50,60,70), c(59,69,79), sep='-'), '80+') temp1 <- table(group3, age1) temp2 <- round(100* temp1/rowSums(temp1)) pfun <- function(x,y) { paste(ifelse(x<1000, "\\phantom{0}", ""), x, " (", ifelse(y<10, "\\phantom{0}", ""), y, ") ", sep="") } cat(paste(c("FLC $<$ 3.38", pfun(temp1[1,], temp2[1,])), collapse=" & "), "\\\\\n") cat(paste(c("FLC 3.38--4.71", pfun(temp1[2,], temp2[2,])), collapse=" & "), "\\\\\n") cat(paste(c("FLC $>$ 4.71", pfun(temp1[3,], temp2[3,])), collapse=" & "), "\n") @ \end{tabular} \caption{Comparison of the age distributions (percents) for each of the three groups.} \label{tflc1} \end{table} Figure \ref{flc1} shows the survival curves for three subgroups of the patients: those whose total free light chain (FLC) is in the upper 10\% of all values found in the full study, those in the 70--89th percentile, and the remainder. There is a clear survival effect. Average free light chain amounts rise with age, however, at least in part because it is eliminated through the kidneys and renal function declines with age. Table \ref{tflc1} shows the age distribution for each of the three groups. In the highest decile of FLC (group 3) over half the subjects are age 70 or older compared to only 23\% in those below the 70th percentile. How much of the survival difference is truly associated with FLC and how much is simply an artifact of age? (The cut points are arbitrary, but we have chosen to mimic the original study and retain them. Division into three groups is a convenient number to illustrate the methods in this vignette, but we do not make any claim that such a categorization is optimal or even sensible statistical practice.) The R code for figure 1 is shown below. <>= fdata <- flchain[flchain$futime >=7,] fdata$age2 <- cut(fdata$age, c(0,54, 59,64, 69,74,79, 89, 110), labels = c(paste(c(50,55,60,65,70,75,80), c(54,59,64,69,74,79,89), sep='-'), "90+")) fdata$group <- factor(1+ 1*(fdata$flc.grp >7) + 1*(fdata$flc.grp >9), levels=1:3, labels=c("FLC < 3.38", "3.38 - 4.71", "FLC > 4.71")) sfit1 <- survfit(Surv(futime, death) ~ group, fdata) plot(sfit1, mark.time=F, col=c(1,2,4), lty=1, lwd=2, xscale=365.25, xlab="Years from Sample", ylab="Survival") text(c(11.1, 10.5, 7.5)*365.25, c(.88, .57, .4), c("FLC < 3.38", "3.38 - 4.71", "FLC > 4.71"), col=c(1,2,4)) @ \section{Reference populations} There are a few populations that are commonly used as the reference group. \begin{enumerate} \item Empirical. The overall distribution of confounders $x$ in the data set as a whole. For this study we would use the observed age/sex distribution, ignoring FLC group. This is also called the ``sample'' or ``data'' distribution. \item External reference. The distribution from some external study or standard. \item Internal reference. A particular subset of the data is chosen as the reference, and other subsets are then aligned with it. \end{enumerate} Method 2 is common in epidemiology, using a reference population based on a large external population such as the age/sex distribution of the 2000 United States census. Method 3 most often arises in the case-control setting, where one group is small and precious (a rare disease say) and the other group (the controls) from which we can sample is much larger. In each case the final result of the computation can be thought of as the expected answer we ``would obtain'' in a study that was perfectly balanced with respect to the list of confounders $x$. Population 1 is the most frequent. \section{Marginal approach} \begin{table} \centering \begin{tabular}{crrrrrrrr} \multicolumn{3}{c}{Females} \\ & \multicolumn{8}{c}{Age} \\ FLC group & 50--54& 55--59& 60--64 & 65--69 & 70--74 & 75--79 & 80--89& 90+ \\ \hline <>= tab1 <- with(fdata, table(group, age2, sex)) cat("Low&", paste(tab1[1,,1], collapse=" &"), "\\\\\n") cat("Med&", paste(tab1[2,,1], collapse=" &"), "\\\\\n") cat("High&", paste(tab1[3,,1], collapse=" &"), "\\\\\n") @ \\ \multicolumn{3}{c}{Males} \\ % & 50--54& 55--59& 60--64 & 65--69 & 70--74 & 75--79 & 80--89& 90+ \\ \hline <>= cat("Low&", paste(tab1[1,,2], collapse=" &"), "\\\\\n") cat("Med&", paste(tab1[2,,2], collapse=" &"), "\\\\\n") cat("High&", paste(tab1[3,,2], collapse=" &"), "\n") @ \end{tabular} \caption{Detailed age and sex distribution for the study population} \label{tab2} \end{table} \subsection{Selection} One approach for balancing is to select a subset of the data such that its distribution matches the referent for each level of $c$, i.e., for each curve that we wish to obtain. As an example we take a case-control like approach to the FLC data, with FLC high as the ``cases'' since it is the smallest group. Table \ref{tab2} shows a detailed distribution of the data with respect to age and sex. The balanced subset has all \Sexpr{tab1[3,1,1]} females aged 50--54 from the high FLC group, a random sample of \Sexpr{tab1[3,1,1]} out of the \Sexpr{tab1[1,1,1]} females in the age 50--54 low FLC group, and \Sexpr{tab1[3,1,1]} out of \Sexpr{tab1[2,1,1]} for the middle FLC. Continue this for all age/sex subsets. We cannot \emph{quite} compute a true case-control estimate for this data since there are not enough ``controls'' in the female 90+ category to be able to select one unique control for each case, and likewise in the male 80-89 and 90+ age groups. To get around this we will sample with replacement in these strata. \begin{figure}[tb] \myfig{flc2} \caption{Survival curves from a case-control sample are shown as solid lines, dashed lines are curves for the unweighted data set (as found in figure \ref{flc1}).} \label{flc2} \end{figure} <>= temp <- with(fdata, table(group, age2, sex)) dd <- dim(temp) # Select subjects set.seed(1978) select <- array(vector('list', length=prod(dd)), dim=dd) for (j in 1:dd[2]) { for (k in 1:dd[3]) { n <- temp[3,j,k] # how many to select for (i in 1:2) { indx <- which(as.numeric(fdata$group)==i & as.numeric(fdata$age2) ==j & as.numeric(fdata$sex) ==k) select[i,j,k] <- list(sample(indx, n, replace=(n> temp[i,j,k]))) } indx <- which(as.numeric(fdata$group)==3 & as.numeric(fdata$age2) ==j & as.numeric(fdata$sex) ==k) select[3,j,k] <- list(indx) #keep all the group 3 = high } } data2 <- fdata[unlist(select),] sfit2 <- survfit(Surv(futime, death) ~ group, data2) plot(sfit2,col=c(1,2,4), lty=1, lwd=2, xscale=365.25, xlab="Years from Sample", ylab="Survival") lines(sfit1, col=c(1,2,4), lty=2, lwd=1, xscale=365.25) legend(730, .4, levels(fdata$group), lty=1, col=c(1,2,4), bty='n', lwd=2) @ %\begin{table}[tb] \centering % \begin{tabular}{ccccccc} % &\multicolumn{2}{c}{FLC low} & \multicolumn{2}{c}{FLC med}& % \multicolumn{2}{c}{FLC high} \\ % & Total & Subset & Total & Subset & Total & Subset \\ \hline %<>= %tab3 <- with(fdata, table(age2, group)) %tab3 <- round(100*scale(tab3, center=F, scale=colSums(tab3))) %tab4 <- with(data2, table(age2, group)) %tab4 <- round(100*scale(tab4, center=F, scale=colSums(tab4))) %tab5 <- cbind(tab3[,1], tab4[,1], tab3[,2], tab4[,2], tab3[,3], tab4[,3]) %pfun <- function(x) paste(ifelse(x<10, paste("\\phantom{0}", x), x), % collapse=" &") %dtemp <- dimnames(tab5)[[1]] %for (j in 1:7) % cat(dtemp[j], " &", pfun(tab5[j,]), "\\\\\n") %cat(dtemp[8], " & ", pfun(tab5[8,]), "\n") %@ %\end{tabular} %\caption{Age distributions (\%) of the original data set along with that of % the subset, for the three FLC groups.} %\label{tflc2} %\end{table} The survival curves for the subset data are shown in figure \ref{flc2}. The curve for the high risk group is unchanged, since by definition all of those subjects were retained. We see that adjustment for age and sex has reduced the apparent survival difference between the groups by about half, but a clinically important effect for high FLC values remains. The curve for group 1 has moved more than that for group 2 since the age/sex adjustment is more severe for that group. <>= # I can't seem to put this all into an Sexpr z1 <- with(fdata,table(age, sex, group)) z2<- apply(z1, 1:2, min) ztemp <- 3*sum(z2) z1b <- with(fdata, table(age>64, sex, group)) ztemp2 <- sum(apply(z1b, 1:2, min)) @ In actual practice, case-control designs arise when matching and selection can occur \emph{before} data collection, leading to a substantial decrease in the amount of data that needs to be gathered and a consequent cost or time savings. When a data set is already in hand it has two major disadvantages. The first is that the approach wastes data; throwing away information in order to achieve balance is always a bad idea. Second is that though it returns an unbiased comparison, the result is for a very odd reference population. One advantage of matched subsets is that standard variance calculations for the curves are correct; the values provided by the usual Kaplan-Meier program need no further processing. We can also use the usual statistical tests to check for differences between the curves. <<>>= survdiff(Surv(futime, death) ~ group, data=data2) @ \subsection{Reweighting} \label{sect:logistic} A more natural way to adjust the data distribution is by weighting. Let $\pi(a,s)$, $a$ = age group, $s$ = sex be a target population age/sex distribution for our graph, and $p(a,s,i)$ the observed probability of each age/sex/group combination in the data. Both $\pi$ and $p$ sum to 1. Then if each observation in the data set is given a case weight of \begin{equation} w_{asi} = \frac{\pi(a,s)}{p(a,s,i)} \label{wt1} \end{equation} the weighted age/sex distribution for each of the groups will equal the target distribution $\pi$. An obvious advantage of this approach is that the resulting curves represent a tangible and well defined group. As an example, we will first adjust our curves to match the age/sex distribution of the 2000 US population, a common reference target in epidemiology studies. The \texttt{uspop2} data set is found in later releases of the survival package in R. It is an array of counts with dimensions of age, sex, and calendar year. We only want ages of 50 and over, and the population data set has collapsed ages of 100 and over into a single category. We create a table \texttt{tab100} of observed age/sex counts within group for our own data, using the same upper age threshold. New weights are the values $\pi/p$ = \texttt{pi.us/tab100}. <<>>= refpop <- uspop2[as.character(50:100),c("female", "male"), "2000"] pi.us <- refpop/sum(refpop) age100 <- factor(ifelse(fdata$age >100, 100, fdata$age), levels=50:100) tab100 <- with(fdata, table(age100, sex, group))/ nrow(fdata) us.wt <- rep(pi.us, 3)/ tab100 #new weights by age,sex, group range(us.wt) @ There are infinite weights! This is because the US population has coverage at all ages, but our data set does not have representatives in every age/sex/FLC group combination; there are for instance no 95 year old males in in the data set. Let us repeat the process, collapsing the US population from single years into the 8 age groups used previously in table \ref{tab2}. Merging the per age/sex/group weights found in the 3-dimensional array \texttt{us.wt} into the data set as per-subject weights uses matrix subscripts, a useful but less known feature of R. <<>>= temp <- as.numeric(cut(50:100, c(49, 54, 59, 64, 69, 74, 79, 89, 110)+.5)) pi.us<- tapply(refpop, list(temp[row(refpop)], col(refpop)), sum)/sum(refpop) tab2 <- with(fdata, table(age2, sex, group))/ nrow(fdata) us.wt <- rep(pi.us, 3)/ tab2 range(us.wt) index <- with(fdata, cbind(as.numeric(age2), as.numeric(sex), as.numeric(group))) fdata$uswt <- us.wt[index] sfit3a <-survfit(Surv(futime, death) ~ group, data=fdata, weight=uswt) @ \begin{figure}[tb] \myfig{flc3a} \caption{Population totals for the US reference (red) and for the observed data set (black).} \label{flc3a} \end{figure} A more common choice is to use the overall age/sex distribution of the sample itself as our target distribution $\pi$, i.e., the empirical distribution. Since FLC data set is population based and has excellent coverage of the county, this will not differ greatly from the US population in this case, as is displayed in figure \ref{flc3a}. <>= tab1 <- with(fdata, table(age2, sex))/ nrow(fdata) matplot(1:8, cbind(pi.us, tab1), pch="fmfm", col=c(2,2,1,1), xlab="Age group", ylab="Fraction of population", xaxt='n') axis(1, 1:8, levels(fdata$age2)) tab2 <- with(fdata, table(age2, sex, group))/nrow(fdata) tab3 <- with(fdata, table(group)) / nrow(fdata) rwt <- rep(tab1,3)/tab2 fdata$rwt <- rwt[index] # add per subject weights to the data set sfit3 <- survfit(Surv(futime, death) ~ group, data=fdata, weight=rwt) temp <- rwt[,1,] #show female data temp <- temp %*% diag(1/apply(temp,2,min)) round(temp, 1) #show female data @ \begin{figure}[tb] \myfig{flc3} \caption{Survival curves for the three groups using reweighted data are shown with solid lines, the original unweighted analysis as dashed lines. The heavier solid line adjusts to the Olmsted population and the lighter one to the US population.} \label{flc3} \end{figure} <>= plot(sfit3, mark.time=F, col=c(1,2,4), lty=1, lwd=2, xscale=365.25, xlab="Years from Sample", ylab="Survival") lines(sfit3a, mark.time=F, col=c(1,2,4), lty=1, lwd=1, xscale=365.25) lines(sfit1, mark.time=F, col=c(1,2,4), lty=2, lwd=1, xscale=365.25) legend(730, .4, levels(fdata$group), lty=1, col=c(1,2,4), bty='n', lwd=2) @ The calculation of weights is shown above, and finishes with a table of the weights for the females. The table was scaled so as to have a minimum weight of 1 in each column for simpler reading. We see that for the low FLC group there are larger weights for the older ages, whereas the high FLC group requires substantial weights for the youngest ages in order to achieve balance. The resulting survival curve is shown in figure \ref{flc3}. The distance between the adjusted curves is similar to the results from subset selection, which is as expected since both approaches are correcting for the same bias, but results are now for an overall population distribution that matches Olmsted County. The curves estimate what the results would have looked like, had each of the FLC groups contained the full distribution of ages. Estimation based on reweighted data is a common theme in survey sampling. Correct standard errors for the curves are readily computed using methods from that literature, and are available in some software packages. In R the \texttt{svykm} routine in the \texttt{survey} package handles both this simple case and more complex sampling schemes. Tests of the curves can be done using a weighted Cox model; the robust variance produced by \texttt{coxph} is identical to the standard Horvitz-Thompsen variance estimate used in survey sampling \cite{Binder92}. The robust score test from \texttt{coxph} corresponds to a log-rank test corrected for weighting. (In the example below the svykm function is only run if the survey package is already loaded, as the variance calculation is very slow for this large data set.) <<>>= id <- 1:nrow(fdata) cfit <- coxph(Surv(futime, death) ~ group + cluster(id), data=fdata, weight=rwt) summary(cfit)$robscore if (exists("svykm")) { #true if the survey package is loaded sdes <- svydesign(id = ~0, weights=~rwt, data=fdata) dfit <- svykm(Surv(futime, death) ~ group, design=sdes, se=TRUE) } @ Note: including the \texttt{cluster} term in the coxph call causes it to treat the weights as resampling values and thus use the proper survey sampling style variance. The default without that term would be to treat the case weights as replication counts. This same alternate variance estimate is also called for when there are correlated observations; many users will be more familiar with the cluster statement in that context. \paragraph{Inverse probability weighting} Notice that when using the overall population as the target distribution $\pi$ we can use Bayes rule to rewrite the weights as \begin{align*} \frac{1}{w_{asi}} &= \frac{{\rm Pr}({\rm age}=a, {\rm sex} =s, {\rm group}=i)} {{\rm Pr}({\rm age}=a, {\rm sex} =s)} \\ &= {\rm Pr}({\rm group}=i | {\rm age}=a, {\rm sex} =s) \end{align*} This last is precisely the probability estimated by a logistic regression model, leading to \emph{inverse probability weighting} as an alternate label for this approach. We can reproduce the weights calculated just above with three logistic regression models. <>= options(na.action="na.exclude") gg <- as.numeric(fdata$group) lfit1 <- glm(I(gg==1) ~ factor(age2) * sex, data=fdata, family="binomial") lfit2 <- glm(I(gg==2) ~ factor(age2) * sex, data=fdata, family="binomial") lfit3 <- glm(I(gg==3) ~ factor(age2) * sex, data=fdata, family="binomial") temp <- ifelse(gg==1, predict(lfit1, type='response'), ifelse(gg==2, predict(lfit2, type='response'), predict(lfit3, type='response'))) all.equal(1/temp, fdata$rwt) @ If there were only 2 groups then only a single regression model is needed since P(group 2) = 1 - P(group 1). Note the setting of na.action, which causes the predicted vector to have the same length as the original data even when there are missing values. This simplifies merging the derived weights with the original data set. An advantage of the regression framework is that one can easily accommodate more variables by using a model with additive terms and only a few selected interactions, and the model can contain continuous as well as categorical predictors. The disadvantage is that such models are often used without the necessary work to check their validity. For instance models with \texttt{age + sex} could have been used above. This makes the assumption that the odds of being a member of group 1 is linear in age and with the same slope for males and females; ditto for the models for group 2 and group 3. How well does this work? Since the goal of reweighting is to standardize the ages, a reasonable check is to compute and plot the reweighted age distribution for each flc group. \begin{figure}[tb] \myfig{flc4} \caption{The re-weighted age distribution using logistic regression with continuous age, for females, FLC groups 1--3. The target distribution is shown as a ``+''. The original unadjusted distribution is shown as dashed lines.} \label{flc4} \end{figure} Figure \ref{flc4} shows the result. The reweighted age distribution is not perfectly balanced, i.e., the `1', `2' and `3' symbols do no exactly overlay one another, but in this case the simple linear model has done an excellent job. We emphasize that whenever the reweighting is based on a simplified model then such a check is obligatory. It is quite common that a simple model is not sufficient and the resulting weight adjustment is inadequate. Like a duct tape auto repair, proceeding forward as though the underlying problem has been addressed is then most unwise. <>= lfit1b <-glm(I(gg==1) ~ age + sex, data=fdata, family="binomial") lfit2b <- glm(I(gg==2) ~ age +sex, data=fdata, family="binomial") lfit3b <- glm(I(gg==3) ~ age + sex, data=fdata, family="binomial") # weights for each group using simple logistic twt <- ifelse(gg==1, 1/predict(lfit1b, type="response"), ifelse(gg==2, 1/predict(lfit2b, type="response"), 1/predict(lfit3b, type="response"))) tdata <- data.frame(fdata, lwt=twt) #grouped plot for the females temp <- tdata[tdata$sex=='F',] temp$gg <- as.numeric(temp$group) c1 <- with(temp[temp$gg==1,], tapply(lwt, age2, sum)) c2 <- with(temp[temp$gg==2,], tapply(lwt, age2, sum)) c3 <- with(temp[temp$gg==3,], tapply(lwt, age2, sum)) xtemp <- outer(1:8, c(-.1, 0, .1), "+") #avoid overplotting ytemp <- 100* cbind(c1/sum(c1), c2/sum(c2), c3/sum(c3)) matplot(xtemp, ytemp, col=c(1,2,4), xlab="Age group", ylab="Weighted frequency (%)", xaxt='n') ztab <- table(fdata$age2) points(1:8, 100*ztab/sum(ztab), pch='+', cex=1.5, lty=2) # Add the unadjusted temp <- tab2[,1,] temp <- scale(temp, center=F, scale=colSums(temp)) matlines(1:8, 100*temp, pch='o', col=c(1,2,4), lty=2) axis(1, 1:8, levels(fdata$age2)) @ \paragraph{Rescaled weights} As the weights were defined in equation \ref{wt1}, the sum of weights for each of the groups is \Sexpr{nrow(fdata)}, the number of observations in the data set. Since the number of subjects in group 3 is one seventh of that in group 1, the average weight in group 3 is much larger. An alternative is to define weights in terms of the \emph{within} group distribution rather than the overall distribution, leading to the rescaled weights $w^*$ \begin{align} w^* &= \frac{\pi(a,s)}{p(a,s|i)} \label{wt2} \\ &= \frac{{\rm P}({\rm group}=i)} {{\rm P}({\rm group}=i | {\rm age}=a, {\rm sex}=s)} \label{wt2b} \end{align} Each group's weights are rescaled by the overall prevalence of the group. In its simplest form, the weights in each group are scaled to add up to the number of subjects in the group. <<>>= # compute new weights wtscale <- table(fdata$group)/ tapply(fdata$rwt, fdata$group, sum) wt2 <- c(fdata$rwt * wtscale[fdata$group]) c("rescaled cv"= sd(wt2)/mean(wt2), "rwt cv"=sd(fdata$rwt)/mean(fdata$rwt)) cfit2a <- coxph(Surv(futime, death) ~ group + cluster(id), data=fdata, weight= rwt) cfit2b <- coxph(Surv(futime, death) ~ group + cluster(id), data=fdata, weight=wt2) round(c(cfit2a$rscore, cfit2b$rscore),1) @ The rescaling results in weights that are much less variable across groups. This operation has no impact on the individual survival curves or their standard errors, since within group we have multiplied all weights by a constant. When comparing curves across groups, however, the rescaled weights reduce the standard error of the test statistic. This results in increased power for the robust score test, although in this particular data set the improvement is not very large. \section{Conditional method} In the marginal approach we first balance the data set and then compute results on the adjusted data. In the conditional approach we first compute a predicted survival curve for each subject that accounts for flc group, age and sex, and then take a weighted average of the curves to get an overall estimate for each flc group. For both methods a central consideration is the population of interest, which drives the weights. Modeling has not removed the question of \emph{who} these curves should represent, it has simply changed the order of operation between the weighting step and the survival curves step. \subsection{Stratification} Our first approach is to subset the data into homogeneous age/sex strata, compute survival curves within each strata, and then combine results. We will use the same age/sex combinations as before. The interpretation of these groups is different, however. In the marginal approach it was important to find age/sex groups for which the probability of membership within each FLC group was constant within the strata (independent of age and sex, within strata), in this case it is important that the survival for each FLC group is constant in each age/sex stratum. Homogeneity of membership within each stratum and homogeneity of survival within each stratum may lead to different partitions for some data sets. Computing curves for all the combinations is easy. <>= allfit <- survfit(Surv(futime, death) ~ group + age2 + sex, fdata) temp <- summary(allfit)$table temp[1:6, c(1,4)] #abbrev printout to fit page @ The resultant survival object has 48 curves: 8 age groups * 2 sexes * 3 FLC groups. To get a single curve for the first FLC group we need to take a weighted average over the 16 age/sex combinations that apply to that group, and similarly for the second and third FLC subset. Combining the curves is a bit of a nuisance computationally because each of them is reported on a different set of time points. A solution is to use the \texttt{summary} function for survfit objects along with the \texttt{times} argument of that function. This feature was originally designed to allow printout of curves at selected time points (6 months, 1 year, \ldots), but can also be used to select a common set of time points for averaging. We will arbitrarily use 4 per year, which is sufficient to create a visually smooth plot over the time span of interest. By default \texttt{summary} does not return data for times beyond the end of a curve, i.e., when there are no subjects left at risk; the \texttt{extend} argument causes a full set of times to always be reported. As seen in the printout above, the computed curves are in sex within age within group order. The overall curve is a weighted average chosen to match the original age/sex distribution of the population. <>= xtime <- seq(0, 14, length=57)*365.25 #four points/year for 14 years smat <- matrix(0, nrow=57, ncol=3) # survival curves serr <- smat #matrix of standard errors pi <- with(fdata, table(age2, sex))/nrow(fdata) #overall dist for (i in 1:3) { temp <- allfit[1:16 + (i-1)*16] #curves for group i for (j in 1:16) { stemp <- summary(temp[j], times=xtime, extend=T) smat[,i] <- smat[,i] + pi[j]*stemp$surv serr[,i] <- serr[,i] + pi[i]*stemp$std.err^2 } } serr <- sqrt(serr) plot(sfit1, lty=2, col=c(1,2,4), xscale=365.25, xlab="Years from sample", ylab="Survival") matlines(xtime, smat, type='l', lwd=2, col=c(1,2,4),lty=1) @ \begin{figure}[tb] \myfig{flc5} \caption{Estimated curves from a stratified model, along with those from the uncorrected fit as dashed lines.} \label{flc5} \end{figure} Figure \ref{flc5} shows the resulting averaged curves. Overlaid are the curves for the unadjusted model. Very careful comparison of these curves with the weighted estimate shows that they have almost identical spread, with just a tiny amount of downward shift. There are two major disadvantages to the stratified curves. The first is that when the original data set is small or the number of confounders is large, it is not always feasible to stratify into a large enough set of groups that each will be homogeneous. The second is a technical aspect of the standard error estimate. Since the curves are formed from disjoint sets of observations they are independent and the variance of the weighted average is then a weighted sum of variances. However, when a Kaplan-Meier curve drops to zero the usual standard error estimate at that point involves 0/0 and becomes undefined, leading to the NaN (not a number) value in R. Thus the overall standard error becomes undefined if any of the component curves falls to zero. In the above example this happens at about the half way point of the graph. (Other software packages carry forward the se value from the last no-zero point on the curve, but the statistical validity of this is uncertain.) To test for overall difference between the curves we can use a stratified test statistic, which is a sum of the test statistics computed within each subgroup. The most common choice is the stratified log-rank statistic which is shown below. The score test from a stratified Cox model would give the same result. <<>>= survdiff(Surv(futime, death) ~ group + strata(age2, sex), fdata) @ \subsection{Modeling} The other approach for conditional estimation is to model the risks due to the confounders. Though we have left it till last, this is usually the first (and most often the only) approach used by most data analysts. Let's start with the very simplest method: a stratified Cox model. <>= cfit4a <- coxph(Surv(futime, death) ~ age + sex + strata(group), data=fdata) surv4a <- survfit(cfit4a) plot(surv4a, col=c(1,2,4), mark.time=F, xscale=365.25, xlab="Years post sample", ylab="Survival") @ This is a very fast and easy way to produce a set of curves, but it has three problems. First is the assumption that this simple model adequately accounts for the effects of age and sex on survival. That is, it assumes that the effect of age on mortality is linear, the sex difference is constant across all ages, and that the coefficients for both are identical for the three FLC groups. The second problem with this approach is that it produces the predicted curve for a single hypothetical subject of age \Sexpr{round(cfit4a[['means']][1], 1)} years and sex \Sexpr{round(cfit4a[['means']][2],2)}, the means of the covariates, under each of the 3 FLC scenarios. However, we are interested in the adjusted survival of a \emph{cohort} of subjects in each range of FLC, and the survival of an ``average'' subject is not the average survival of a cohort. The third and most serious issue is that it is not clear exactly what these ``adjusted'' curves represent --- exactly who \emph{is} this subject with a sex of \Sexpr{round(cfit4a[['means']][2],2)}? Multiple authors have commented on this problem, see Thomsen et al \cite{Thomsen91}, Nieto and Coresh \cite{Nieto96} or chapter 10 of Therneau and Grambsh \cite{Therneau00} for examples. Even worse is a Cox model that treated the FLC group as a covariate, since that will impose an additional constraint of proportional hazards across the 3 FLC groups. \begin{figure} \myfig{flc6} \caption{Curves for the three groups, adjusted for age and sex via a risk model. Dotted lines show the curves from marginal adjustment. Solid curves are for the simple risk model \texttt{cfit4a}.} \label{flc6} \end{figure} We can address this last problem problem by doing a proper average. A Cox model fit can produce the predicted curves for any age/sex combination. The key idea is to produce a predicted survival curve for every subject of some hypothetical population, and then take the average of these curves. The most straightforward approach is to retrieve the predicted individual curves for all \Sexpr{nrow(fdata)} subjects in the data set, assuming each of the three FLC strata one by one, and take a simple average for each strata. For this particular data set that is a bit slow since it involves \Sexpr{nrow(fdata)} curves. However there are only 98 unique age/sex pairs in the data, it is sufficient to obtain the 98 * 3 FLC groups unique curves and take a weighted average. We will make use of the survexp function, which is designed for just this purpose. Start by creating a data set which has one row for each age/sex combination along with its count. Then replicate it into 3 copies, assigning one copy to each of the three FLC strata. <>= tab4a <- with(fdata, table(age, sex)) uage <- as.numeric(dimnames(tab4a)[[1]]) tdata <- data.frame(age = uage[row(tab4a)], sex = c("F","M")[col(tab4a)], count= c(tab4a)) tdata3 <- tdata[rep(1:nrow(tdata), 3),] #three copies tdata3$group <- factor(rep(1:3, each=nrow(tdata)), labels=levels(fdata$group)) sfit4a <- survexp(~group, data=tdata3, weight = count, ratetable=cfit4a) plot(sfit4a, mark.time=F, col=c(1,2,4), lty=1, lwd=2, xscale=365.25, xlab="Years from Sample", ylab="Survival") lines(sfit3, mark.time=F, col=c(1,2,4), lty=2, lwd=1, xscale=365.25) legend(730,.4, c("FLC low", "FLC med", "FLC high"), lty=1, col=c(1,2,4), bty='n', lwd=2) @ Figure \ref{flc6} shows the result. Comparing this to the prior 3 adjustments shown in figures \ref{flc3}, \ref{flc4}, and \ref{flc5} we see that this result is different. Why? Part of the reason is due to the fact that $E[f(X)] \ne f(E[X])$ for any non-linear operation $f$, so that averages of survival curves and survival curves of averages will never be exactly the same. This may explain the small difference between the stratified and the marginal approaches of figures \ref{flc3} and \ref{flc5}, which were based on the same subsets. The Cox based result is systematically higher than the stratified one, however, so something more is indicated. Aside: An alternate computational approach is to create the individual survival curves using the \texttt{survfit} function and then take averages. <<>>= tfit <- survfit(cfit4a, newdata=tdata, se.fit=FALSE) curves <- vector('list', 3) twt <- c(tab4a)/sum(tab4a) for (i in 1:3) { temp <- tfit[i,] curves[[i]] <- list(time=temp$time, surv= c(temp$surv %*% twt)) } @ The above code is a bit sneaky. I know that the result from the survfit function contains a matrix \texttt{tfit\$surv} of 104 columns, one for each row in the tdata data frame, each column containing the curves for the three strata one after the other. Sub setting \texttt{tfit} results in the matrix for a single flc group. Outside of R an approach like the above may be needed, however. \begin{figure} \myfig{flc6b} \caption{Left panel: comparison of Cox model based adjustment (solid) with the curves based on marginal adjustment (dashed). The Cox model curves without (black) and with (red) an age*sex interaction term overlay. Right panel: plot of the predicted relative risks from a Cox model \texttt{crate} versus population values from the Minnesota rate table.} \label{flc6b} \end{figure} So why are the modeling results so different than either reweighting or stratification? Suspicion first falls on the use of a simple linear model for age and sex, so start by fitting a slightly more refined model that allows for a different slope for the two sexes, but is still linear in age. In this particular data set an external check on the fit is also available via the Minnesota death rate tables, which are included with the survival package as \texttt{survexp.mn}. This is an array that contains daily death rates by age, sex, and calendar year. <>= par(mfrow=c(1,2)) cfit4b <- coxph(Surv(futime, death) ~ age*sex + strata(group), fdata) sfit4b <- survexp(~group, data=tdata3, ratetable=cfit4b, weights=count) plot(sfit4b, fun='event', xscale=365.25, xlab="Years from sample", ylab="Deaths") lines(sfit3, mark.time=FALSE, fun='event', xscale=365.25, lty=2) lines(sfit4a, fun='event', xscale=365.25, col=2) temp <- median(fdata$sample.yr) mrate <- survexp.mn[as.character(uage),, as.character(temp)] crate <- predict(cfit4b, newdata=tdata, reference='sample', type='lp') crate <- matrix(crate, ncol=2)[,2:1] # mrate has males then females, match it # crate contains estimated log(hazards) relative to a baseline, # and mrate absolute hazards, make both relative to a 70 year old for (i in 1:2) { mrate[,i] <- log(mrate[,i]/ mrate[21,2]) crate[,i] <- crate[,i] - crate[21,2] } matplot(mrate, crate, col=2:1, type='l') abline(0, 1, lty=2, col=4) @ The resulting curves are shown in the left panel of figure \ref{flc6b} and reveal that addition of an interaction term did not change the predictions, and that the Cox model result for the highest risk group is distinctly different predicted survival for the highest FLC group is distinctly different when using model based prediction. The right hand panel of the figure shows that though there are slight differences with the Minnesota values, linearity of the age effect is very well supported. So where exactly does the model go wrong? Since this is such a large data set we have the luxury of looking at subsets. This would be a very large number of curves to plot --- age by sex by FLC = 48 --- so an overlay of the observed and expected curves by group would be too confusing. Instead we will summarize each of the groups according to their observed and predicted number of events. <>= obs <- with(fdata, tapply(death, list(age2, sex, group), sum)) pred<- with(fdata, tapply(predict(cfit4b, type='expected'), list(age2, sex, group), sum)) excess <- matrix(obs/pred, nrow=8) #collapse 3 way array to 2 dimnames(excess) <- list(dimnames(obs)[[1]], c("low F", "low M", "med F", "med M", "high F", "high M")) round(excess, 1) @ The excess risks, defined as the observed/expected number of deaths, are mostly modest ranging from .8 to 1.2. The primary exception exception is the high FLC group for ages 50--59 which has values of 1.6 to 2.5; the Cox model fit has greatly overestimated the survival for the age 50--54 and 55--59 groups. Since this is also the age category with the highest count in the data set, this overestimation will have a large impact on the overall curve for high FLC subset, which is exactly where the the deviation in figure \ref{flc6b} is observed to lie. There is also mild evidence for a linear trend in age for the low FLC females, in the other direction. Altogether this suggests that the model might need to have a different age coefficient for each of the three FLC groups. <<>>= cfit5a <- coxph(Surv(futime, death) ~ strata(group):age +sex, fdata) cfit5b <- coxph(Surv(futime, death) ~ strata(group):(age +sex), fdata) cfit5c <- coxph(Surv(futime, death) ~ strata(group):(age *sex), fdata) options(show.signif.stars=FALSE) # see footnote anova(cfit4a, cfit5a, cfit5b, cfit5c) temp <- coef(cfit5a) names(temp) <- c("sex", "ageL", "ageM", "ageH") round(temp,3) @ The model with separate age coefficients for each FLC group gives a major improvement in goodness of fit, but adding separate sex coefficients per group or further interactions does not add importantly beyond that. \footnote{There are certain TV shows that make one dumber just by watching them; adding stars to the output has the same effect on statisticians.} \begin{figure} \myfig{flc7} \caption{Adjusted survival for the 3 FLC groups based on the improved Cox model fit. Dashed lines show the predictions from the marginal model.} \label{flc7} \end{figure} A recheck of the observed/expected values now shows a much more random pattern, though some excess remains in the upper right corner. The updated survival curves are shown in figure \ref{flc7} and now are in closer concordance with the marginal fit. <>= pred5a <- with(fdata, tapply(predict(cfit5a, type='expected'), list(age2, sex, group), sum)) excess5a <- matrix(obs/pred5a, nrow=8, dimnames=dimnames(excess)) round(excess5a, 1) sfit5 <- survexp(~group, data=tdata3, ratetable=cfit5a, weights=count) plot(sfit3, fun='event', xscale=365.25, mark.time=FALSE, lty=2, col=c(1,2,4), xlab="Years from sample", ylab="Deaths") lines(sfit5, fun='event', xscale=365.25, col=c(1,2,4)) @ One problem with the model based estimate is that standard errors for the curves are complex. Standard errors of the individual curves for each age/sex/FLC combination are a standard output of the survfit function, but the collection of curves is correlated since they all depend on a common estimate of the model's coefficient vector $\beta$. Curves with disparate ages are anti-correlated (an increase in the age coefficient of the model would raise one and lower the other) whereas those for close ages are positively correlated. A proper variance for the unweighted average has been derived by Gail and Byar \cite{Gail86}, but this has not been implemented in any of the standard packages, nor extended to the weighted case. A bootstrap estimate would appear to be the most feasible. \section{Conclusions} When two populations need to be adjusted and one is much larger than the other, the balanced subset method has been popular. It is most often seen in the context of a case-control study, with cases as the rarer group and a set of matched controls selected from the larger one. This method has the advantage that the usual standard error estimates from a standard package are appropriate, so no further work is required. However, in the general situation it leads to a correct answer but for the wrong problem, i.e., not for a population in which we are interested. The population reweighted estimate is flexible, has a readily available variance in some statistical packages (but not all), and the result is directly interpretable. It is the method we recommend in general. The approach can be extended to a large number of balancing factors by using a regression model to derive the weights. Exploration and checking of said model for adequacy is an important step in this case. The biggest downside to the method arises when there is a subset which is rare in the data sample but frequent in the adjusting population. In this case subjects in that subset will be assigned large weights, and the resulting curves will have high variance. The stratified method is closely related to reweighting (not shown). It does not do well if the sample size is small, however. Risk set modeling is a very flexible method, but is also the one where it is easiest to go wrong by using an inadequate model, and variance estimation is also difficult. To the extent that the fitted model is relevant, it allows for interpolation and extrapolation to a reference population with a different distribution of covariates than the one in the training data. It may be applicable in cases such as rare subsets where population reweighting is problematic, with the understanding that one is depending heavily on extrapolation in this case, which is always dangerous. \section{A note on type 3 tests} One particular software package (not R) and its proponents are very fond of something called ``type 3'' tests. Said tests are closely tied to a particular reference population: \begin{itemize} \item For all continuous covariates in the model, the empirical distribution is used as the reference. \item For all categorical adjusters, a uniform distribution over the categories is used. \end{itemize} Figure \ref{flc8} shows the fit from such a model. Not surprisingly, the predicted death rate is very high: 1/4 of our population is over 80 years old! The authors do not find such a prediction particularly useful since we don't ever expect to see a population like this (it's sort of like planning for the zombie apocalypse), but for those enamored of type 3 tests this shows how to create the corresponding curves. <>= # there is a spurious warning from the model below: R creates 3 unneeded # columns in the X matrix cfit6 <- coxph(Surv(futime, death) ~ strata(group):age2 + sex, fdata) saspop <- with(fdata, expand.grid(age2= levels(age2), sex= levels(sex), group = levels(group))) sfit6 <- survexp(~group, data=saspop, ratetable=cfit6) plot(sfit6, fun='event', xscale=365.25, mark.time=FALSE, lty=1, col=c(1,2,4), xlab="Years from sample", ylab="Deaths") lines(sfit5, fun='event', xscale=365.25, lty=2, col=c(1,2,4)) @ \begin{figure} \myfig{flc8} \caption{Adjusted survival for the 3 FLC groups based on a fit with categorical age, and predicting for a uniform age/sex population. 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These functions are used in the document, but not discussed until the end crisk <- function(what, horizontal = TRUE, ...) { nstate <- length(what) connect <- matrix(0, nstate, nstate, dimnames=list(what, what)) connect[1,-1] <- 1 # an arrow from state 1 to each of the others if (horizontal) statefig(c(1, nstate-1), connect, ...) else statefig(matrix(c(1, nstate-1), ncol=1), connect, ...) } state3 <- function(what, horizontal=TRUE, ...) { if (length(what) != 3) stop("Should be 3 states") connect <- matrix(c(0,0,0, 1,0,0, 1,1,0), 3,3, dimnames=list(what, what)) if (horizontal) statefig(1:2, connect, ...) else statefig(matrix(1:2, ncol=1), connect, ...) } state4 <- function() { sname <- c("Entry", "CR", "Transplant", "Transplant") layout <- cbind(c(1/2, 3/4, 1/4, 3/4), c(5/6, 1/2, 1/2, 1/6)) connect <- matrix(0,4,4, dimnames=list(sname, sname)) connect[1, 2:3] <- 1 connect[2,4] <- 1 statefig(layout, connect) } state5 <- function(what, ...) { sname <- c("Entry", "CR", "Tx", "Rel", "Death") connect <- matrix(0, 5, 5, dimnames=list(sname, sname)) connect[1, -1] <- c(1,1,1, 1.4) connect[2, 3:5] <- c(1, 1.4, 1) connect[3, c(2,4,5)] <- 1 connect[4, c(3,5)] <- 1 statefig(matrix(c(1,3,1)), connect, cex=.8,...) } @ \maketitle \section{Multi-state curves} Consider the simple \code{survfit} call <>= curves <- survfit(Surv(time, status) ~ group, data=mydata) @ In the classic case \code{status} is either a logical or 0/1 numeric variable that represents censoring (0 or false) or an event (1 or true), and the result is a survival curve for each group. If \code{status} is a factor, however, the result is a multi-state estimate. In this case the first level of \code{status} is used to code censoring while the remaining ones are possible states. Here is a simple competing risks example where the three endpoints are labeled as a, b and c. <>= set.seed(1952) crdata <- data.frame(time=1:11, endpoint=factor(c(1,1,2,0,1,1,3,0,2,3,0), labels=c("censor", "a", "b", "c"))) tfit <- survfit(Surv(time, endpoint) ~ 1, data=crdata) dim(tfit) summary(tfit) @ The resulting object \code{tfit} contains an estimate of $P$(state), the probability of being in each state. $P$ is a matrix with one row for each time and one column for each of the four states a--c and the "no event as of yet" state; we will often refer to the latter as the entry state. By definition each row of $P$ sums to 1. The plot of the fit will have 3 curves, by default the curve for an unnamed state is not displayed. (Since they sum to 1 one of the 4 curves is redundant, and the entry state is normally the least interesting of the set.) <>= plot(tfit, col=1:3, lwd=2, ylab="Probability in state") @ The resulting \code{survfms} object appears as a matrix and can be subscripted as such, with a column for each state and rows for each group that was created by any variables on the right hand side of the formula. This makes it simple to display a subset of the curves using plot or lines commands. The unnamed state in the above fit, for instance, can be displayed with \code{plot(tfit[,4])}. The curves are computed using the Aalen-Johansen estimator. The Kaplan-Meier estimate and the cumulative incidence estimate (for competing risks) are each a special case of the AJ estimate. It is more general that that, however; a given subject can have multiple transitions from state to state, including transitions to a state that was visited earlier. In this case the dataset structure is similar to that for time varying covariates in a Cox model: the time variable will be intervals $(t_1, t_2]$ which are open on the left and closed on the right, and the status variable contains the state that was entered at time $t_2$, and a subject will have multiple lines of data. There are a few restrictions. \begin{itemize} \item An identifier variable is required which indicates which rows of the data frame belong to each subject. If the \code{id} argument is missing the code assumes that each row of data is a separate subject, which leads to a nonsense estimate when there are actually multiple rows for each. \item Subjects do not have to enter at time 0 or all at the same time, but each must traverse a connected segment of time. Disjoint intervals such as the pair $(0,5]$, $(8, 10]$ are illegal. \item A subject cannot change groups. Any covariates on the right hand side of the formula must remain constant within subject. (This function is not a way to creat supposed `time-dependent' survival curves.) \item Subjects may have case weights, and these weights may change over time for a subject. \end{itemize} By default every subject is assumed to start in an unnamed common entry state. The \code{istate} argument can instead be used to designate an entry state for each subject; like variables in the formula it is searched for in the \code{data} argument. The distribution of states at the first event time is treated as the initial distribution of states; like ordinary survival an observation which is censored before the first event time has no impact on the results. The extended example below is intended to give more information about the routines. \section{Data set} The \code{myeloid} data set contains simulated data which mimics that from a trial in subjects with acute myeloid leukemia. In this comparison of two conditioning regimens the canonical path for a subject is initial therapy $\rightarrow$ complete response (CR) $\rightarrow$ hematologic stem cell transplant (HSCT) $\rightarrow$ sustained remission, followed by relapse or death. <>= myeloid[1:5,] @ The first few rows of data are shown above. The data set contains the follow-up time and status at last follow-up for each subject, along with the time to transplant (txtime), complete response (crtime) or relapse after CR (rltime). Subject 1 did not receive a transplant, as shown by the NA value, and subject 2 did not achieve CR. \begin{figure} \myfig{sfit0} \caption{Overall survival curves for the two treatments.} \label{sfit0} \end{figure} Overall survival curves for the data are shown in figure \ref{sfit0}. The difference between the treatment arms A and B is substantial. A goal of this analysis is to better understand this difference. Here is the code to generate the simple survival curves: <>= sfit0 <- survfit(Surv(futime, death) ~ trt, myeloid) plot(sfit0, xscale=365.25, xaxs='r', col=1:2, lwd=2, xlab="Years post enrollment", ylab="Survival") legend(20, .4, c("Arm A", "Arm B"), col=1:2, lwd=2, bty='n') @ \section{Competing risks} A first step towards deeper analysis is to look at intermediate states one at a time, e.g., how many subjects ever achieve a CR or ever receive a transplant. Create a working data set that contains variables for simple 2-state competing risks for the pairs CR/death and transplant/death. For competing risks each subject has a single row of data, so this data set simply adds two new variables and redefines two others. At the same time we will convert from days to months. This is the natural time scale for our plots, and forestalls adding the \code{xscale} argument to every plot call. <>= data1 <- myeloid data1$crstat <- factor(with(data1, ifelse(is.na(crtime), death, 2)), labels=c("censor", "death", "CR")) data1$crtime <- with(data1, ifelse(crstat=="CR", crtime, futime)) data1$txstat <- factor(with(data1, ifelse(is.na(txtime), death, 2)), labels=c("censor", "death", "transplant")) data1$txtime <- with(data1, ifelse(txstat=="transplant", txtime, futime)) for (i in c("futime", "crtime", "txtime", "rltime")) data1[[i]] <- data1[[i]] * 12/365.25 #rescale to months @ \begin{figure} \myfig{curve1} \caption{Overall survival curves: time to death, to transplant (Tx), and to complete response (CR). Each shows the estimated fraction of subjects who have ever reached the given state. The vertical line at 2 months is for reference. The curves were limited to the first 48 months to more clearly show early events. The right hand panel shows the state-space model for each pair of curves.} \label{curve1} \end{figure} This data set is the basis for our first set of curves, which are shown in figure \ref{curve1}. The plot overlays three separate \code{survfit} calls: standard survival until death, complete response with death as a competing risk, and transplant with death as a competing risk. For each fit we have shown one selected state: the fraction who have died, fraction ever in CR, and fraction ever to receive transplant, respectively. Most of the CR events happen before 2 months (the green vertical line) and nearly all the additional CRs conferred by treatment B occur between months 2 and 8. Most transplants happen after 2 months, which is consistent with the clinical guide of transplant after CR. The survival advantage for treatment B begins between 4 and 5 months, which argues that it could be at least partially a consequence of the additional CR events. The code to draw figure \ref{curve1} is below. It can be separated into 5 parts: \begin{enumerate} \item Fits for the 3 endpoints are simple and found in the first 3 lines. The \code{crstat} and \code{txstat} variables are factors, which causes a multi-state curve to be generated. \item The \code{layout} and \code{par} commands are used to create a multi-part plot with curves on the left and state space diagrams on the right, and to reduce the amount of white space between them. \item Draw a subset of the curves via subscripting. A multi-state survfit object appears as a matrix of curves, with one row for each group (treatment) and one column for each state. The CR state is the second column in \code{sfit2}, for instance. The CR fit was drawn first simply because it has the greatest y-axis range, then the other curves added using the lines command. \item Decoration of the plots. This includes the line types, colors, legend, choice of x-axis labels, etc. \item Add the state space diagrams. The functions for this are described in the last section of the vignette. \end{enumerate} <>= sfit1 <- survfit(Surv(futime, death) ~ trt, data1) #survival sfit2 <- survfit(Surv(crtime, crstat) ~ trt, data1) # CR sfit3 <- survfit(Surv(txtime, txstat) ~ trt, data1) layout(matrix(c(1,1,1,2,3,4), 3,2), widths=2:1) oldpar <- par(mar=c(5.1, 4.1, 1.1, .1)) plot(sfit2[,2], mark.time=FALSE, fun='event', xmax=48, lty=3, lwd=2, col=1:2, xaxt='n', xlab="Months post enrollment", ylab="Events") lines(sfit1, mark.time=FALSE, xmax=48, fun='event', col=1:2, lwd=2) lines(sfit3[,2], mark.time=FALSE, xmax=48, fun='event', col=1:2, lty=2, lwd=2) xtime <- c(0, 6, 12, 24, 36, 48) axis(1, xtime, xtime) #marks every year rather than 10 months temp <- outer(c("A", "B"), c("death", "transplant", "CR"), paste) temp[7] <- "" legend(25, .3, temp[c(1,2,7,3,4,7,5,6,7)], lty=c(1,1,1, 2,2,2 ,3,3,3), col=c(1,2,0), bty='n', lwd=2) abline(v=2, lty=2, col=3) # add the state space diagrams par(mar=c(4,.1,1,1)) crisk(c("Entry","Death", "CR"), alty=3) crisk(c("Entry","Death", "Tx"), alty=2) crisk(c("Entry","Death")) par(oldpar) @ The association between a particular curve and its corresponding state space diagram is critical. As we will see below, many different models are possible and it is easy to get confused. Attachment of a diagram directly to each curve, as was done above, will not necessarily be day-to-day practice, but the state space should always be foremost. If nothing else, draw it on a scrap of paper and tape it to the side of the terminal when creating a data set and plots. \begin{figure} \myfig{badfit} \caption{Correct (solid) and invalid (dashed) estimates of the number of subjects transplanted.} \label{badfit} \end{figure} Figure \ref{badfit} shows the transplant curves overlaid with the naive KM that censors subjects at death. There is no difference in the initial portion as no deaths have yet intervened, but the final portion overstates the transplant outcome by more than 10\%. \begin{enumerate} \item The key problem with the naive estimate is that subjects who die can never have a transplant. The result of censoring them is an estimate of the ``fraction who would be transplanted, if death before transplant were abolished''. This is not a real world quantity. \item In order to estimate this fictional quantity one needs to assume that death is uninformative with respect to future disease progression. The early deaths in months 0--2, before transplant begins, are however a very different class of patient. Non-informative censoring is untenable. \end{enumerate} We are left with an unreliable estimate of an uninteresting quantity. Mislabeling any true state as censoring is always a mistake, one that will not be repeated here. Here is the code for figure \ref{badfit}. The use of a logical (true/false) as the status variable in the \code{Surv} call leads to ordinary survival calculations. <>= badfit <- survfit(Surv(txtime, txstat=="transplant") ~ trt, data1) layout(matrix(c(1,1,1,2,3,4), 3,2), widths=2:1) oldpar <- par(mar=c(5.1, 4.1, 1.1, .1)) plot(badfit, fun="event", xmax=48, xaxt='n', col=1:2, lty=2, lwd=2, xlab="Months from enrollment", ylab="P(state)") axis(1, xtime, xtime) lines(sfit3[,2], fun='event', xmax=48, col=1:2, lwd=2) legend(24, .3, c("Arm A", "Arm B"), lty=1, lwd=2, col=1:2, bty='n', cex=1.2) par(mar=c(4,.1,1,1)) crisk(c("Entry", "transplant"), alty=2, cex=1.2) crisk(c("Entry","transplant", "Death"), cex=1.2) par(oldpar) @ \section{Multi-state models} The multi-state models are based on a second data set which looks very much like the (start, stop] data sets that are used for time dependent covariates. Consider subject 5 who experienced CR on day 56, relapse on day 112 and death on day 200. In the expanded data set this subject will have 3 lines, one for each of the intervals (0,56], (56, 112] and (112, 200]. The first interval ends with CR and the second with relapse. What if someone has two endpoints on the same day? Creation of a zero length interval will lead to a justifiable complaint from the programs; subjects are not allowed to do instantaneous transitions. For each such observation a decision needs to be made, preferably based on rational scientific argument rather than statistical or programming convenience. It turns out that we do have one such case in the myeloid data: one subject who was declared to be a CR on the day of their transplant. Since complete response will occur before its clinical detection I decided to make the tied CR one day earlier. This issue didn't come up in creating \code{data1} only because it dealt with the pairs CR:death and transplant:death, and neither of these has a tie. We create the data set using the \code{tmerge} function in R, code is shown below. (Because such start-stop data sets are commonly used for Cox models with time-dependent covariates, this is a familiar task to many users and they will have developed their own favorite work flow; tmerge is a useful but not essential tool.) The tmerge function uses a baseline data set, in this case the variables from the starting data that are constant over time, and then adds rows to it. Each \code{event} and \code{tdc} statement sequentially adds either an endpoint or time-dependent covariate as new rows to the data, in much the same way that one would insert new folders into the proper position in a file drawer. Each addition will split a subject's time interval as necessary. <<>= temp <- myeloid id <- which(temp$crtime == temp$txtime) # the one special person temp$crtime[id] <- temp$crtime[id] -1 # move their CR back by 1 day data2 <- tmerge(myeloid[, c('id', 'trt')], temp, id=id, death=event(futime, death), transplant = event(txtime), response = event(crtime), relapse = event(rltime), priortx = tdc(txtime), priorcr = tdc(crtime)) attr(data2, "tcount") data2$event <- with(data2, factor(death + 2*response + 3*transplant + 4*relapse, 0:4, labels=c("censor", "death", "CR", "transplant", "relapse"))) data2[1:10,c(1:4, 11, 9, 10)] @ The tmerge call starts by adding death/censoring time, which appears in the `trailing' column of the tcount table since it defines the right endpoint for each subject, and thus by definition occurs at the trailing end of their interval. Then transplant is added which has 363 within and 1 trailing: there is one subject whose transplant date is also their last follow-up date. Response and relapse times all fall within a prior interval. Looking above at the first 4 subjects in \code{data2}, the fourth follows the canonical path of CR followed by transplant. Subject 1 relapses after CR, without transplant, and subject 2 has transplant without a CR. A critical step in any multi-state model is to print out some portion of the created data set and \emph{read} it. This data set is key, and any errors will invalidate all the analysis which follows. This step has been abbreviated for the vignette; inspection of only the first 4 subjects is a very small sample. Rescale the data set from days to months and look at three more summaries. <>= for (i in c("tstart", "tstop")) data2[[i]] <- data2[[i]] *12/365.25 #scale to months ctab <- table(table(data2$id)) ctab with(data2, table( table(id, event))) etab <- table(data2$event, useNA="ifany") etab @ In the final result there are \Sexpr{ctab[1]} subjects with only a single row of data, \Sexpr{ctab[2]} with 2 rows, etc. The table of \code{id} by \code{event} contains only 0 and 1 as values, i.e., no one has two events of the same type, which is correct for this data set. Overall \Sexpr{etab['CR']} of the \Sexpr{nrow(myeloid)} subjects experience a CR at some point in the study. \begin{figure} \myfig{cr2} \caption{Models for `ever in CR' and `currently in CR'; the only difference is an additional transition. Both models ignore transplant.} \label{cr2} \end{figure} Complete response is a goal of the initial therapy; figure \ref{cr2} looks more closely at this. As was noted before arm B has an increased number of late responses. The duration of response is also increased: the solid curves show the number of subjects still in response, and we see that they spread farther apart than the dotted ``ever in response'' curves. The figure shows only the first eight months in order to better visualize the details, but continuing the curves out to 48 months reveals a similar pattern. Here is the code to create the figure. <>= crstat <- data2$event crstat[crstat=="transplant"] <- "censor" # ignore transplants crsurv <- survfit(Surv(tstart, tstop, crstat) ~ trt, data= data2, id=id, influence=TRUE) layout(matrix(c(1,1,2,3), 2,2), widths=2:1) oldpar <- par(mar=c(5.1, 4.1, 1.1, .1)) plot(sfit2[,2], lty=3, lwd=2, col=1:2, xmax=12, xlab="Months", ylab="CR") lines(crsurv[,2], lty=1, lwd=2, col=1:2, xmax=12) par(mar=c(4, .1, 1, 1)) crisk( c("Entry","CR", "Death"), alty=3) state3(c("Entry", "CR", "Death/Relapse")) par(oldpar) @ Rather than create a new data set, the above code modifies the event variable so as to ignore transitions to the transplant state. They become a non-event, in the same way that extra lines with a status of zero are used to create time-dependent covariates for a Cox model fit. The \code{survfit} call above included the \code{influence=TRUE} argument, which causes the influence array to be calculated and returned. It contains, for each subject, that subject's influence on the time by state matrix of results and allows for calculation of the standard error of the restricted mean. We will return to this in a later section. <>= print(crsurv, rmean=48, digits=2) @ <>= temp <- summary(crsurv, rmean=48)$table delta <- round(temp[4,3] - temp[3,3], 2) @ @ The restricted mean time in the CR state is extended by \Sexpr{round(temp[4,3], 1)} - \Sexpr{round(temp[3,3], 1)} = \Sexpr{delta} months. A question which immediately gets asked is whether this difference is ``significant'', to which there are two answers. The first and more important is to ask whether 5 months is an important gain from either a clinical or patient perspective. The overall restricted mean survival for the study is approximately 30 of the first 48 months post entry (use print(sfit1, rmean=48)); on this backdrop an extra 5 months in CR might or might not be an meaningful advantage from a patient's point of view. The less important answer is to test whether the apparent gain is sufficiently rare from a mathematical point of view, i.e., ``statistical'' significance. The standard errors of the two values are \Sexpr{round(temp[3,4],1)} and \Sexpr{round(temp[4,4],1)}, and since they are based on disjoint subjects the values are independent, leading to a standard error for the difference of $\sqrt{1.1^2 + 1.2^2} = 1.6$. The difference is over 3 standard errors. \begin{figure} \myfig{txsurv} \caption{Transplant status of the subjects, broken down by whether it occurred before or after CR.} \label{txsurv} \end{figure} In summary \begin{itemize} \item Arm B adds late complete responses (about 4\%); there are 212/310 in arm B vs. 244/338 in arm B. \item The difference in 4 year survival is about 6\%. \item There is approximately 2 months longer average duration of CR (of 48). \end{itemize} CR $\rightarrow$ transplant is the target treatment path for a patient; given the improvements listed above why does figure \ref{curve1} show no change in the number transplanted? Figure \ref{txsurv} shows the transplants broken down by whether this happened before or after complete response. Most of the non-CR transplants happen by 10 months. One possible explanation is that once it is apparent to the patient/physician pair that CR is not going to occur, they proceed forward with other treatment options. The extra CR events on arm B, which occur between 2 and 8 months, lead to a consequent increase in transplant as well, but at a later time of 12--24 months: for a subject in CR we can perhaps afford to defer the transplant date. Computation is again based on a manipulation of the event variable: in this case dividing the transplant state into two sub-states based on the presence of a prior CR. The code makes use of the time-dependent covariate \code{priorcr}. (Because of scheduling constraints within a hospital it is unlikely that a CR that is within a few days prior to transplant could have effected the decision to schedule a transplant, however. An alternate breakdown that might be useful would be ``transplant without CR or within 7 days after CR'' versus those that are more than a week later. There are many sensible questions that can be asked.) <>= event2 <- with(data2, ifelse(event=="transplant" & priorcr==1, 6, as.numeric(event))) event2 <- factor(event2, 1:6, c(levels(data2$event), "tx after CR")) txsurv <- survfit(Surv(tstart, tstop, event2) ~ trt, data2, id=id, subset=(priortx ==0)) layout(matrix(c(1,1,1,2,2,0),3,2), widths=2:1) oldpar <- par(mar=c(5.1, 4.1, 1,.1)) plot(txsurv[,c(3,5)], col=1:2, lty=c(1,1,2,2), lwd=2, xmax=48, xaxt='n', xlab="Months", ylab="Transplanted") axis(1, xtime, xtime) legend(15, .13, c("A, transplant without CR", "B, transplant without CR", "A, transplant after CR", "B, transplant after CR"), col=1:2, lty=c(1,1,2,2), lwd=2, bty='n') state4() # add the state figure par(oldpar) @ \begin{figure} \myfig{sfit4} \caption{The full multi-state curves for the two treatment arms.} \label{sfit4} \end{figure} Figure \ref{sfit4} shows the full set of state occupancy probabilities for the cohort over the first 4 years. At each point in time the curves estimate the fraction of subjects currently in that state. The total who are in the transplant state peaks at about 9 months and then decreases as subjects relapse or die; the curve rises whenever someone receives a transplant and goes down whenever someone leaves the state. At 36 months treatment arm B (dashed) has a lower fraction who have died, the survivors are about evenly split between those who have received a transplant and those whose last state is a complete response (only a few of the latter are post transplant). The fraction currently in relapse -- a transient state -- is about 5\% for each arm. The figure omits the curve for ``still in the entry state''. The reason is that at any point in time the sum of the 5 possible states is 1 --- everyone has to be somewhere. Thus one of the curves is redundant, and the fraction still in the entry state is the least interesting of them. (A multi-state \code{survfit} call that does not include the \code{istate} argument will assume that everyone starts in an unnamed entry state. The default plot behavior is to omit the curves for any unnamed states.) <>= sfit4 <- survfit(Surv(tstart, tstop, event) ~ trt, data2, id=id) sfit4$transitions layout(matrix(1:2,1,2), widths=2:1) oldpar <- par(mar=c(5.1, 4.1, 1,.1)) plot(sfit4, col=rep(1:4,each=2), lwd=2, lty=1:2, xmax=48, xaxt='n', xlab="Months", ylab="Current state") axis(1, xtime, xtime) text(c(40, 40, 40, 40), c(.51, .13, .32, .01), c("Death", "CR", "Transplant", "Recurrence"), col=1:4) par(mar=c(5.1, .1, 1, .1)) state5() par(oldpar) @ The transitions table above shows \Sexpr{sfit4$transitions[5,1]} %$ direct transitions from entry to death, i.e., subjects who die without experiencing any of the other intermediate points, \Sexpr{sfit4$transitions[2,3]} who go from CR to transplant (as expected), \Sexpr{sfit4$transitions[3,2]} who go from transplant to CR, etc. %$ No one was observed to go from relapse to CR in the data set, this serves as a data check since it should not be possible per the data entry plan. \section{Influence matrix} For one of the curves above we returned the influence array. For each value in the matrix $P$ = probability in state and each subject $i$ in the data set, this contains the effect of that subject on each value in $P$. Formally, \begin{equation*} I_{ij}(t) = \left . \frac{\partial p_j(t)}{\partial w_i} \right|_w \end{equation*} where $I_{ij}(t)$ is the influence of subject $i$ on $p_j(t)$, and $p_j(t)$ is the estimated probability for state $j$ at time $t$. This is known as the infinitesimal jackknife (among other labels). <>= crsurv <- survfit(Surv(tstart, tstop, crstat) ~ trt, data= data2, id=id, influence=TRUE) curveA <- crsurv[1,] # select treatment A dim(curveA$pstate) # P matrix for treatement A dim(curveA$influence) # influence matrix for treatment A table(data1$trt) curveA$p0 # state distribution at time 0 @ For treatment arm A there are \Sexpr{table(data1$trt)[1]} subjects and \Sexpr{dim(curveA$pstate)[1]} time points in the $P$ matrix. The influence array has subject as the first dimension, and for each subject it has an image of the $P$ matrix containing that subject's influence on each value in $P$, i.e., \code{influence[1,,]} is the influence of subject 1 on $P$. The influence has one extra row, however; the first row for each subjects is the influence of that subject on $p_0$, the initial state probabilities. For this data set everyone starts in the entry state, $p_0$ will always be (0, 0, 0, 1), and so this first influence row will be zero; this does not hold if not all subjects start in the same state. As an exercise we will calculate the mean time in state out to 48 weeks. This is the area under the individual curves from time 0 to 48. Since the curves are step functions this is simple sum of rectangles, treating any intervals after 48 months as having 0 width. <>= t48 <- pmin(48, curveA$time) delta <- diff(c(0, t48, 48)) # width of intervals rfun <- function(pmat, delta) colSums(pmat * delta) #area under the curve rmean <- rfun(rbind(curveA$p0, curveA$pstate), delta) round(rmean, 2) # Apply the same calculation to each subject's influence slice inf <- apply(curveA$influence, 1, rfun, delta=delta) # inf is now a 5 state by 310 subject matrix, containing the IJ estimates # on the AUC or mean time. The sum of squares is a variance. se.rmean <- sqrt(rowSums(inf^2)) round(se.rmean, 2) @ In general, let $U_i$ be the influence of subject $i$. For some function $f(P)$ of the prevalence matrix, the influence of subject $i$ will be $\delta_i = f(P + U_i) - f(P)$ and the infinitesimal jackknife estimate of variance will be $\sum_i \delta^2$. For the simple case of adding up rectangles $f(P +U_i) - f(P) = f(U_i)$ leading to particularly simple code, but this will not always be the case. \section{State space figures} The state space figures in this document were drawn with a simple utility function \code{statefig}. It has two primary arguments along with standard graphical options of color, line type, etc. \begin{enumerate} \item A layout vector or matrix. A vector with values of (1, 3, 1) for instance will allocate one state, then a column with 3 states, then one more state, proceeding from left to right. A matrix with a single row will do the same, whereas a matrix with one column will proceed from top to bottom. \item A $k$ by $k$ connection matrix $C$ where $k$ is the number of states. If $C_{ij} \ne 0$ then an arrow is drawn from state $i$ to state $j$. The row or column names of the matrix are used to label the states. The lines connecting the states can be straight or curved, see the help file for the function for an example. \end{enumerate} The first few state space diagrams were competing risk models, which use the following derived function. It accepts a vector of state names, where the first name is the starting state and the remainder are the possible outcomes. <>= crisk <- function(what, horizontal = TRUE, ...) { nstate <- length(what) connect <- matrix(0, nstate, nstate, dimnames=list(what, what)) connect[1,-1] <- 1 # an arrow from state 1 to each of the others if (horizontal) statefig(c(1, nstate-1), connect, ...) else statefig(matrix(c(1, nstate-1), ncol=1), connect, ...) } @ This next function draws a variation of the illness-death model. It has an initial state, an absorbing state (normally death), and an optional intermediate state. <>= state3 <- function(what, horizontal=TRUE, ...) { if (length(what) != 3) stop("Should be 3 states") connect <- matrix(c(0,0,0, 1,0,0, 1,1,0), 3,3, dimnames=list(what, what)) if (horizontal) statefig(1:2, connect, ...) else statefig(matrix(1:2, ncol=1), connect, ...) } @ The most complex of the state space figures has all 5 states. <>= state5 <- function(what, ...) { sname <- c("Entry", "CR", "Tx", "Rel", "Death") connect <- matrix(0, 5, 5, dimnames=list(sname, sname)) connect[1, -1] <- c(1,1,1, 1.4) connect[2, 3:5] <- c(1, 1.4, 1) connect[3, c(2,4,5)] <- 1 connect[4, c(3,5)] <- 1 statefig(matrix(c(1,3,1)), connect, cex=.8, ...) } @ For figure \ref{txsurv} I want a third row with a single state, but don't want that state centered. For this I need to create my own (x,y) coordinate list as the layout parameter. Coordinates must be between 0 and 1. <>= state4 <- function() { sname <- c("Entry", "CR", "Transplant", "Transplant") layout <- cbind(x =c(1/2, 3/4, 1/4, 3/4), y =c(5/6, 1/2, 1/2, 1/6)) connect <- matrix(0,4,4, dimnames=list(sname, sname)) connect[1, 2:3] <- 1 connect[2,4] <- 1 statefig(layout, connect) } @ The statefig function was written to do ``good enough'' state space figures quickly and easily, in the hope that users will find it simple enough that diagrams are drawn early and often. Other packages such as diagram, DiagrammeR, or dagR are far more flexible and can create more nuanced and well decorated results. \section{Conclusion} With a data set such as this we can fit many different multi-state models. These fits are easy to do, and can give substantial further insight into a data set. \end{document} survival/vignettes/.install_extras0000644000175100001440000000001012472644117017207 0ustar hornikusersfigures survival/vignettes/compete.Rnw0000644000175100001440000014726013055122145016307 0ustar hornikusers\documentclass{article}[11pt] \usepackage{Sweave} \usepackage{amsmath} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} %\VignetteIndexEntry{Multi-state models and competing risks} \SweaveOpts{keep.source=TRUE, fig=FALSE} % Ross Ihaka suggestions \DefineVerbatimEnvironment{Sinput}{Verbatim} {xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} % I had been putting figures in the figures/ directory, but the standard % R build script does not copy it and then R CMD check fails \SweaveOpts{prefix.string=compete,width=6,height=4} \newcommand{\myfig}[1]{\includegraphics[height=!, width=\textwidth] {compete-#1.pdf}} \setkeys{Gin}{width=\textwidth} <>= options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=10) #text in graph about the same as regular text options(contrasts=c("contr.treatment", "contr.poly")) #ensure default require("survival") @ \title{Multi-state models and competing risks} \author{Terry Therneau \and Cynthia Crowson \and Elizabeth Atkinson} \newcommand{\code}[1]{\texttt{#1}} \begin{document} \maketitle \section{Multi-state models} \begin{figure} <>= # A note to readers of this code: drawing multi-state figures in this # way via polygon and arrows statements is a major PITA. Don't mimic # the code below, instead do yourself a favor and use a package # designed for the task such as diagram, DiagrammeR, shape or Gmisc. # Survival is a recommended package that is included by lots of others so # I try to limit dependencies in the survival vignettes. # par(mar=c(.1, .1, .1, .1)) frame() oldpar <- par(usr=c(0,100,0,100)) # first figure xx <- c(0, 10, 10, 0) yy <- c(0, 0, 10, 10) polygon(xx +10, yy+70) polygon(xx +30, yy+70) arrows( 22, 75, 28, 75, length=.1) text(c(15, 35), c(75,75), c("Alive", "Dead")) # second figure polygon(xx +60, yy+70) for (j in c(55, 70, 85)) { polygon(xx +80, yy+j) arrows(72, (5*75 +j+5)/6, 78, (100+j*5)/6, length=.1) } text(c(65, 85,85,85), c(70,55,70,85)+5, c("A", "D3", "D2", "D1")) # third figure polygon(xx+10, yy+25) for (j in c(15,35)) { polygon(xx +30, yy+j) arrows(22, (5*30 +j+4)/6, 28, (54+j*5)/6, length=.1) } arrows(28, 2+(65 + 35*5)/6, 22, 2+ (160 + 40)/6, length=.1) arrows(35, 33, 35, 27, length=.1) text(c(15, 35,35), c(30, 20, 40), c("Health", "Death", "Illness")) # fourth for (i in c(50, 68)) polygon(xx+i, yy+25) arrows(62, 30, 67, 30, length=.1) arrows(80, 30, 84, 30, length=.1) text(90, 30, "...", cex=2) text(c(55, 73), c(30, 30), c("0", "1")) par(oldpar) @ \caption{Four multi-state models. The upper left panel depicts simple survival, the upper right is an example of competing risks, the lower left panel is a multi-state illness-death model, and the lower right panel depicts sequential events.} \label{mfig1} \end{figure} A multi-state model is used to model a process where subjects transition from one state to the next. For instance, a standard survival curve can be thought of as a simple multi-state model with two states (alive and dead) and one transition between those two states. A diagram illustrating this process is shown in the top left corner of figure \ref{mfig1}. In these types of diagrams, each box is a state and each arrow is a possible transition. The top right diagram depicts a classic competing risk analysis, where all subjects start on the left and each subject can make a single transition to one of 3 terminal states. The bottom left diagram shows a common multi-state situation known as the illness-death model with recovery. Finally, the lower right diagram represents sequential events, such as repeated infections in the CGD study. In that case one subject had 8 events so there are 9 states corresponding to entry into the study (0 infections) and the first, second, \ldots, eighth events. As will be shown below, there are often multiple choices for the state and transition diagram, and for some data sets it is revealing to look at a problem from multiple views. In addition to deciding the diagram that best matches the research questions, the two other primary decisions are the choice of time scale for the fits, e.g., time from entry in the study vs. time from entry in the state, and what covariates will be used. \section{Multi-state curves} \subsection{Aalen-Johansen estimate} As a starting point for the analysis, it is important to compute and plot estimates of $p(t)$, which is a vector containing the probability of being in each of the states at time $t$. If there is no censoring then $p$ becomes a simple tabulation at time $t$ of all the states. For the general case, we compute this using the Aalen-Johansen estimate via the \code{survfit} function. Mathematically the estimate is simple. For each unique time where an event occurs, form the transition matrix $T(t)$ with elements or rates of $\lambda_{ij}(t) =$ the fraction of subjects who transition from state $i$ to $j$ at time $t$, among those in state $i$ just prior to time $t$. ($T$ is equal to the identity matrix at any time point without an observed transition.) Then \begin{equation} p(t) = p(0) \prod_{s \le t} T(s) \label{AJ} \end{equation} where $p(0)$ is the initial distribution of subjects. Let's work this out for the simple two-state alive $\rightarrow$ {death} model. Let $n(t)$ be the number of subjects still at risk at time $t$ and $d(t)$ the number of deaths at that time point. All subjects start in the alive state and thus $p(0) = (1,0)$ and the transition matrix is \begin{equation*} T(s) = \left( \begin{array}{cc} \frac{n(s)- d(s)}{n(s)} & \frac{d(s)}{n(s)} \\\\ 0 & 1 \end{array} \right) \end{equation*} The second row corresponds to the fact that death is an absorbing state. Writing out the matrices for the first few transitions and multiplying them leads to \begin{equation} p_1(t) = \prod_{s \le t} \left[n(s) - d(s)\right] /n(s) \label{km} \end{equation} which we recognize as the Kaplan-Meier estimate of survival. For the two state alive-dead model the Aalen-Johansen (AJ) estimate has reprised the KM. In the competing risks case $p(t)$ has an alternate form known as the \emph{cumulative incidence} (CI) function \begin{equation} CI_k(t) = \int_0^t \lambda_k(u) S(u) du \label{cuminc} \end{equation} where $\lambda_k$ is the incidence function for outcome $k$, and $S$ is the overall survival curve for ``time to any endpoint''. (The label ``cumulative incidence'' is one of the more unfortunate ones in the survival lexicon, since we normally use `incidence' and `hazard' as interchangeable synonyms but the CI is \emph{not} a cumulative hazard.) Repeating the same matrix exercise for the competing risks, i.e. writing out the Aalen-Johansen computation, exactly recovers the CI formula. The CI is also a special case of the Aalen-Johansen. The AJ estimate is very flexible; subjects can visit multiple states during the course of a study, subjects can start after time 0 (delayed entry), and they can start in any of the states. The \code{survfit} function implements the AJ estimate and will handle all these cases. The standard error of the estimates is computed using an infinitesimal jackknife. Let $D(t)$ be a matrix with one row per subject and one column per state. Each row contains the \emph{change} in $p(t)$ corresponding to subject $i$, i.e., the derivative of $p$ with respect to the $i$th subject's case weight $dp(t)/dw_i$. Then $V(t) = D'WD$ is the estimated variance-covariance matrix of the estimates at time $t$, where $W$ is a diagonal matrix of observation weights. If a single subject is represented by multiple rows in the data set, then $D$ is first collapsed to have one row per subject, the new row for subject $i$ is the sum of the rows for the observations that represented the subject. This is essentially the same algorithm as the robust variance for a Cox model. For simple two state alive -> dead model, the AJ estimate of variance is identical to the traditional Greenwood estimate for the variance of the survival curve $S$. (This was a surprise when we first observed it; proving the equivalence was not straightforward.) The $p(t)$ vector obeys the obvious constraint that its sum at any time is equal to one; each person has to be somewhere. I originally chose to label this as the \emph{current prevalence} estimate, since it estimates what fraction of the subjects are in any given state across time. However the word ``prevalence'' is certain to generate confusion whenever death is one of the states, due to its traditional use as the fraction of living subjects who have a particular condition. We will use the phrase \emph{probability in state} or simply $p$ from this point forward. In the simple two state model Pr(alive) is the usual KM survival estimate, and we have $p_1(t) = 1- p_2(t)$, Pr(alive) = 1 - Pr(dead). Plots for the 2 state case sometimes choose to show Pr(alive) and sometimes Pr(dead). Which one is used often depends on a historical whim of the disease specialty; cardiology journals for instance quite often use Pr(event) resulting in curves that rise starting from zero, while oncology journals invariably use Pr(alive) giving curves that fall downhill from 1. The \code{survfit} routine's historical default for the 2 state case is to print and plot Pr(alive)= $p_1(t)$, which reflects that the author of the routine was working primarily in cancer trials at the time said default was chosen. For simple survival we have gotten used to the idea of using Pr(dead) and Pr(alive) interchangeably, but that habit needs to be left behind for multi-state models, as curves of $1-p_k(t)$ = probability(any other state than $k$) are not useful. In the multi-state case, individual curves can go both up and down. For competing risks the curve for the initial state (leftmost in the diagram) is rarely included in the final plot. Since the curves sum to 1, the full set is redundant. Pr(nothing yet) is usually the least interesting of the set and so it is left off to make the plot less busy. The remaining curves in the competing risks case rise from 0. (This bothers some researchers as it `just looks wrong' to them.) \subsection{Examples} \begin{figure} <>= par(mar=c(.1, .1, .1, .1)) frame() oldpar <- par(usr=c(0,100,0,100)) # first figure xx <- c(0, 10, 10, 0) yy <- c(0, 0, 10, 10) polygon(xx +10, yy+70) temp <- c(60, 80) for (j in 1:2) { polygon(xx + 30, yy+ temp[j]) arrows(22, 70 + 3*j, 28, temp[j] +5, length=.1) } text(c(15, 35, 35), c(75, 65, 85),c("Entry", "Death", "PCM")) text(25, 55, "Competing Risk") # Second figure polygon(xx +60, yy+70) for (j in 1:2) { polygon(xx + 80, yy+ temp[j]) arrows(72, 70+ 3*j, 78, temp[j] +5, length=.1) } text(50+ c(15, 35, 35), c(75, 65, 85),c("Entry", "Death", "PCM")) arrows(85, 78, 85, 72, length=.1) text(75, 55, "Multi-state 1") # third figure polygon(xx+10, yy+25) temp <- c(15, 35) for (j in 1:2) { polygon(2*xx +30, yy + temp[j]) arrows(22, 25 + 3*j, 28, temp[j] +5, length=.1) } text(c(15, 40, 40), c(30, 20, 40),c("Entry", "Death w/o PCM", "PCM")) polygon(2*xx + 60, yy+temp[2]) arrows(52, 40, 58, 40, length=.1) text(70, 40, "Death after PCM") text(40, 10, "Multi-state 2") @ \caption{Three models for the MGUS data.} \label{mfig2} \end{figure} Start with a simple competing risks problem as illustrated in the first diagram of figure \ref{mfig2}. The \code{mgus2} data set contains the time to plasma cell malignancy (PCM) and/or death for 1384 subjects diagnosed with monoclonal gammopathy of undetermined significance (MGUS). Survival and progression time are in months. The code below creates an ordinary Kaplan-Meier curve of post-diagnosis survival for these subjects, along with a histogram of age at diagnosis. The mean age at diagnosis is just over 70 years. <>= oldpar <- par(mfrow=c(1,2)) hist(mgus2$age, nclass=30, main='', xlab="Age") with(mgus2, tapply(age, sex, mean)) mfit1 <- survfit(Surv(futime, death) ~ sex, data=mgus2) mfit1 plot(mfit1, col=c(1,2), xscale=12, mark.time=FALSE, lwd=2, xlab="Years post diagnosis", ylab="Survival") legend("topright", c("female", "male"), col=1:2, lwd=2, bty='n') par(oldpar) @ The xscale and yscale arguments to \code{plot.survfit} affect only the axis labels, not the data. Further additions to the plot region such as \code{legend}, \code{lines}, or \code{text} remain in the original scale. This simplifies programmatic additions such as adding another curve to the plot, while making interactive additions such as a legend somewhat less simple. As a second model for these subjects we will use competing risks with PCM and death without malignancy as the two terminal states, as shown in the upper left of figure \ref{mfig2}. For this model we are only interested in the first event for each subject. Formally we are treating progression to a PCM as an \emph{absorbing state}, i.e., one that subjects never exit. We create a variable \code{etime} containing the time to the first of progression, death, or last follow-up along with an event variable that contains the outcome. The starting data set \code{mgus2} has two pairs of variables \code{(ptime, pstat)} that contain the time to progression and \code{(futime, status)} that contain the time to death or last known alive. The code below creates the necessary \code{etime} and \code{event} variables, then computes and plots the competing risks estimate. <>= etime <- with(mgus2, ifelse(pstat==0, futime, ptime)) event <- with(mgus2, ifelse(pstat==0, 2*death, 1)) event <- factor(event, 0:2, labels=c("censor", "pcm", "death")) table(event) mfit2 <- survfit(Surv(etime, event) ~ sex, data=mgus2) print(mfit2, rmean=240, scale=12) mfit2$transitions plot(mfit2, col=c(1,2,1,2), lty=c(2,2,1,1), mark.time=FALSE, lwd=2, xscale=12, xlab="Years post diagnosis", ylab="Probability in State") legend(240, .6, c("death:female", "death:male", "pcm:female", "pcm:male"), col=c(1,2,1,2), lty=c(1,1,2,2), lwd=2, bty='n') @ The \code{mfit2} call is nearly identical to that for an ordinary Kaplan-Meier, with the exception of the \code{event} variable. \begin{enumerate} \item The event variable was created as a \emph{factor}, whereas for ordinary single state survival the status is either 0/1 or TRUE/FALSE. The first level of the factor must be censoring, which is the status code for those whose follow-up terminated without reaching a new endpoint. Codes for the remaining states can be in any order. The labels for the states are unrestricted, e.g., the first one does not have to be ``censor''. (It will however be treated as censoring, whatever the name.) \item A simple print of the \code{mfit2} object shows the order in which the curves will be displayed. This information was used to choose the line types and colors for the curves. \item The \code{mfit2} object contains curves for all the states, but by default the entry state will not be plotted. The remaining curves all start at 0. \item The transitions component of the result is useful as a data check, e.g., if it showed a transition from death to PCM. \item Each subject's initial state is specified by the \code{istate} argument. When this is omitted all subjects are assumed to start from an entry state named `` '' (the empty string), as seen in the printout above. \end{enumerate} The printout shows that a male subject will spend, on average, 8.7 of his first 20 years post diagnosis in the entry state, 1.1 years in the PCM state and 10.3 of those 20 in the death state. If a cutoff time is not given the default is to use the maximum observed time for all curves, which is 424 months in this case. The result of a multi-state \code{survfit} is a matrix of probabilities with one row per time and one column per state. First are the states found in the event variable (excluding censoring) and then the states found in the \code{istate} variable, removing any duplicates. By default any unnamed state is not plotted -- point 3 above -- for the simple reason that multiple event curves can very quickly get overcrowded with all the multiple lines. Since the three MGUS states of entry/pcm/death must sum to 1 at any given time (everyone has to be somewhere), one of the three curves is redundant and the ``fraction still in the entry state'' curve is normally the least interesting. One can easily add this last state to the plot if desired, e.g., \code{lines(mfit2[,3], col=4, lty=1:2)}, since entry is the third state in the printout. (One can use, e.g., \code{mfit2[, 'pcm']} to select a state as well, but an empty string does not work as the subscript.) A common mistake with competing risks is to use the Kaplan-Meier separately on each event type while treating other event types as censored. The next plot is an example of this for the PCM endpoint. <>= pcmbad <- survfit(Surv(etime, pstat) ~ sex, data=mgus2) plot(pcmbad[2], mark.time=FALSE, lwd=2, fun="event", conf.int=FALSE, xscale=12, xlab="Years post diagnosis", ylab="Fraction with PCM") lines(mfit2[2,1], lty=2, lwd=2, mark.time=FALSE, conf.int=FALSE) legend(0, .25, c("Males, PCM, incorrect curve", "Males, PCM, competing risk"), col=1, lwd=2, lty=c(1,2), bty='n') @ There are two problems with the \code{pcmbad} fit. The first is that it attempts to estimate the expected occurrence of plasma cell malignancy (PCM) if all other causes of death were to be disallowed. In this hypothetical world it is indeed true that many more subjects would progress to PCM (the incorrect curve is higher), but it is also not a world that any of us will ever inhabit. This author views the result in much the same light as discussions of survival after the zombie apocalypse. The second problem is that the computation for this hypothetical case is only correct if all of the competing endpoints are independent, a situation which is almost never true. We thus have an unreliable estimate of an uninteresting quantity. The competing risks curve, on the other hand, estimates the fraction of MGUS subjects who \emph{will experience} PCM, a quantity sometimes known as the lifetime risk, and one which is actually observable. The last example chose to plot only a subset of the curves, something that is often desirable in competing risks problems to avoid a ``tangle of yarn'' plot that simply has too many elements. This is done by subscripting the \code{survfit} object. For subscripting, multi-state curves behave as a matrix with the outcomes as the second subscript. The columns are in order of the levels of \code{event}, i.e., as displayed by our earlier call to \code{table(event)}. The first subscript indexes the groups formed by the right hand side of the model formula, and will be in the same order as simple survival curves. Thus \code{mfit2[2,1]} corresponds to males (2) and the PCM endpoint (1). Curves are listed and plotted in the usual matrix order of R. A third example using the MGUS data treats it as a multi-state model and it shown in the upper right of figure \ref{mfig2}. In this version a subject can have multiple transitions and thus multiple rows in the data set. In this case it is necessary to identify which data rows go with which subject via the \code{id} argument of \code{survfit}; valid estimates of the curves and their standard errors both depend on this. Our model looks like the illness-death model of figure \ref{mfig1} but with ``PCM'' as the upper state and no arrow for a return from that state to health. The necessary data set will have two rows for any subject who has further follow-up after a PCM and a single row for all others. The data set is created below using the \code{tmerge} function, which is discussed in detail in another vignette. We need to decide what to do with the 9 subjects who have PCM and death declared at the same month. (Some of these were cancer cases discovered at autopsy.) They slipped through without comment in the earlier competing risks analysis; only when setting up this second data set did we notice the ties. Looking back at the code, the prior example counted these subjects as a progression. In retrospect this is a defensible choice: even though undetected before death, the disease must have been present for some amount of time previous and so progression did occur first. For the multi-state model we need to be explicit in how this is coded since a sojourn time of 0 within a state is not allowed. Below we push the progression time back by .1 month when there is a tie, but that amount is entirely arbitrary. <>= ptemp <- with(mgus2, ifelse(ptime==futime & pstat==1, ptime-.1, ptime)) newdata <- tmerge(mgus2, mgus2, id=id, death=event(futime, death), pcm = event(ptemp, pstat)) newdata <- tmerge(newdata, newdata, id, enum=cumtdc(tstart)) with(newdata, table(death, pcm)) @ The table above shows that there are no observations in \code{newdata} that have both a PCM and death, i.e., the ties have been resolved. The last \code{tmerge} line above creates a variable \code{enum} which simply counts rows for each person; it will be used later. <>= temp <- with(newdata, ifelse(death==1, 2, pcm)) newdata$event <- factor(temp, 0:2, labels=c("censor", "pcm", "death")) mfit3 <- survfit(Surv(tstart, tstop, event) ~ sex, data=newdata, id=id) print(mfit3, rmean=240, digits=2) mfit3$transitions plot(mfit3[,1], mark.time=FALSE, col=1:2, lty=1:2, lwd=2, xscale=12, xlab="Years post MGUS diagnosis", ylab="Fraction in the PCM state") legend(48, .04, c("female", "male"), lty=1:2, col=1:2, lwd=2, bty='n') @ This plot is quite different in that it shows the fraction of subjects \emph{currently} in the PCM state. Looking at our multi-state diagram this is the fraction of subjects in the upper right PCM box. The curve goes up whenever someone enters the box (progression) and down when they leave (death). Myeloma survival was quite short during the era of this study and the proportion currently in the PCM state rarely rises above 2 percent. The result of \code{print(mfit3)} reveals, as expected, less time spent in the PCM state. In the prior \code{mfit2} model, subjects who enter that state remain there for the duration; in this one they quickly pass through. It is worthwhile to check the \code{transitions} table in the output simply as a data check. In this case it shows subjects going from the entry (unnamed) state to PCM and death along with transitions from PCM to death. This is as expected. An error in creating the input data can lead to surprising counts and an even more surprising curve. We have often found the three curve display below useful in the case of a transient state. It combines the results from competing risk model used above along with a second fit that treats death after PCM as a separate state from death before progression, the \emph{multi-state 2} model of figure \ref{mfig2}. In this plot the fraction of subjects currently in the PCM state is shown by the distance between the two curves. Only males are shown in the plot to minimize overlap. <>= # Death after PCM will correspond to data rows with # enum = 2 and event = death d2 <- with(newdata, ifelse(enum==2 & event=='death', 4, as.numeric(event))) e2 <- factor(d2, labels=c("censor", "pcm", "death w/o pcm", "death after pcm")) mfit4 <- survfit(Surv(tstart, tstop, e2) ~ sex, data=newdata, id=id) plot(mfit2[2,], lty=c(1,2), xscale=12, mark.time=FALSE, lwd=2, xlab="Years post diagnosis", ylab="Probability in State") lines(mfit4[2,3], mark.time=FALSE, col=2, lty=1, lwd=2, conf.int=FALSE) legend(200, .5, c("Death w/o PCM", "ever PCM", "Death after PCM"), col=c(1,1,2), lty=c(2,1,1), lwd=2, bty='n', cex=.82) @ \subsection{Further notes} The Aalen-Johansen method used by \code{survfit} does not account for interval censoring, also known as panel data, where a subject's current state is recorded at some fixed time such as a medical center visit but the actual times of transitions are unknown. Such data requires further assumptions about the transition process in order to model the outcomes and has a more complex likelihood. The \code{msm} package, for instance, deals with data of this type. If subjects reliably come in at regular intervals then the difference between the two results can be small, e.g., the \code{msm} routine estimates time until progression \emph{occurred} whereas \code{survfit} estimates time until progression was \emph{observed}. \begin{itemize} \item When using multi-state data to create Aalen-Johansen estimates, individuals are not allowed to have gaps in the middle of their time line. An example of this would be a data set with (0, 30, pcm] and (50,70, death] as the two observations for a subject where the time from 30-70 is not accounted for. \item Subjects must stay in the same group over their entire observation time, i.e., variables on the right hand side of the equation cannot be time-dependent. \item A transition to the same state is allowed, e.g., observations of (0,50, 1], (50, 75, 3], (75, 89, 4], (89, 93, 4] and (93, 100, 4] for a subject who goes from entry to state 1, then to state 3, and finally to state 4. However, a warning message is issued for the data set in this case, since stuttering may instead be the result of a coding mistake. The same result is obtained if the last three observations were collapsed to a single row of (75, 100, 4]. \end{itemize} \section{Rate models} For simple two-state survival, the Cox model leads to three relationships \begin{align} \lambda(t) &= \lambda_0(t) e^{X\beta} \label{hazard} \\ \Lambda(t) &= \Lambda_0(t) e^{X\beta} \label{cumhaz}\\ S(t) &= \exp(-\Lambda(t)) \label{surv} \end{align} where $\lambda$, $\Lambda$ and $S$ are the hazard, cumulative hazard and survival functions, respectively. There is a single linear predictor which governs both the rate $\lambda$ (the arrow in figure \ref{mfig1}) and probability of residing in the left hand box of the figure. For multi-state models this simplicity no longer holds; proportional hazards does not lead to proportional $p(t)$ curves. The task before us is more complex. The analysis of multi-state data has four key steps. In order of importance: \begin{enumerate} \item Draw a box and arrow figure describing the model. \item Think through the rates (arrows). \begin{enumerate} \item Which covariates should be attached to each rate? Sometimes a covariate is important for one transition, but not for another. \item For which transitions should one or more of the covariates be constrained to have the same coefficient? Sometimes there will be a biologic rationale for this. For other studies an equivalence is forced simply because we have too many unknowns and cannot accommodate them all. (This is the often the same reason that models contain very few interaction terms). \item Which, if any, of the transitions should share the same baseline hazard? Most of the time the baseline rates are all assumed to be different. \item Should there be random effects, and if so what is an appropriate correlation structure? Do some pairs of transitions have a shared effect, some pairs separate effects and others no random effect? Mixed effects Cox models tend to need larger sample size --- does the data set have enough events? \end{enumerate} \item Build an appropriate data set. \item Fit the data. Examine multiple summaries of the model fit, including the predicted occupancy curves. \end{enumerate} Step 1 is key to the entire endeavor. We saw in figure \ref{mfig2} and the examples above that multiple views of a multi-state process can be useful, and this will hold for modeling as well. Step 3 will often be the one that demands the most attention to detail. \subsection{MGUS example} Start with the simplest model for the MGUS data: a competing risks model (upper left diagram of figure \ref{mfig2}), distinct baseline hazards for the two rates, no shared coefficients, and three covariates. <>= options(show.signif.stars = FALSE) # display intelligence cfit2 <- coxph(Surv(etime, event=="death") ~ age + sex + mspike, mgus2) summary(cfit2, scale=c(10, 1, 1)) # scale age in decades @ The effect of age and sex on non-PCM mortality is profound, which is not a surprise given the median starting age of \Sexpr{median(mgus2$age)}. Risk rises \Sexpr{round(exp(10*coef(cfit2)[1]),1)} fold per decade of age and the death rate for males is \Sexpr{round(exp(coef(cfit2)[2]),1)} times as great as that for females. The size of the serum monoclonal spike has almost no impact on non-PCM mortality. A 1 unit increase changes mortality by only 6\%. <>= cfit1 <- coxph(Surv(etime, event=="pcm") ~ age + sex + mspike, mgus2) cfit1 quantile(mgus2$mspike, na.rm=TRUE) @ The mspike size has a major impact on progression, however; each 1 gram change increases risk by \Sexpr{round(exp(coef(cfit1)[3]) ,1)} fold. The interquartile range of \code{mspike} is 0.9 gram so this risk increase is clinically important. The effect of age on the progression rate is much less pronounced, with a coefficient only 1/4 that for mortality, while the effect of sex on progression is completely negligible. The effect of sex on the \emph{lifetime} probability of PCM is not zero, however. Because of a longer lifetime, a female with MGUS will on average spend more total years at risk for PCM than the average male, and so has a larger lifetime risk of PCM. The average rate of progression is about 1\% per year, as shown below, while the mean post diagnosis lifetime is 19 months longer for females. The overall effect is a 1.6\% increase in lifetime risk. <>= pfit1 <- pyears(Surv(ptime, pstat) ~ sex, mgus2, scale=12) round(100* pfit1$event/pfit1$pyears, 1) # PCM rate per year temp <- summary(mfit1, rmean="common") #print the mean survival time round(temp$table[,1:6], 1) @ Notice that each \code{coxph} fit essentially ignores the other event type(s). In the figure, each rate (arrow) depends only on the box from which it originates and the events which it enumerates. Rates are instantaneous quantities, and depend only on the set of subjects who are at risk at at a given moment; if someone is not at risk it really does not matter why. When computing $p(t)$, on the other hand, all the rates must be considered at once. The Aalen-Johansen estimate applies as before, but now the individual entries $\lambda_{ij}(t)$ in each cell of the transition matrix are taken from the relevant fit. As is also the case with predicted survival curves from a simple Cox model, predicted probability-in-state curves correspond to a set of prespecified covariate values. As an example we will generate the curves for four hypothetical subjects: male and female, age 60 and 80, and serum m-spike of 1.2 grams. These are the approximate quartiles of age, and the median mspike. The Aalen-Johansen estimate for this simple 3-state competing risks setup works with a matrix of this form: \begin{equation*} \left( \begin{array}{ccc} & \lambda_{12}{t} & \lambda_{13}(t) \\ 0 & & 0 \\ 0 & 0 & \end{array} \right) \end{equation*} As before, the diagonal elements are chosen so that each row sums to 1. Standard survival curve calculations for a Cox model can be used to obtain $\lambda_{12}$, the rate of transition to the PCM state for our four subjects, and $\lambda_{13}$ = the rate of transition to the ``death before PCM'' state. These are placed into a matrix and combined using a third call. The standard errors from the individual curves won't be used and the survfit routine is a bit faster if we skip them. <>= newdata <- expand.grid(sex=c("F", "M"), age=c(60, 80), mspike=1.2) newdata temp <- matrix(list(), 3,3) dimnames(temp) <- list(from=c("Entry", "PCM", "Death"), to =c("Entry", "PCM", "Death")) temp[1,2] <- list(survfit(cfit1, newdata, std.err=FALSE)) temp[1,3] <- list(survfit(cfit2, newdata, std.err=FALSE)) csurv <- survfit(temp, p0 =c(1,0,0)) plot(csurv[,2], xmax=25*12, xscale=12, xlab="Years after MGUS diagnosis", ylab="PCM", col=1:2, lty=c(1,1,2,2), lwd=2) legend(10, .14, outer(c("female", "male "), c("diagnosis at age 60", "diagnosis at age 80"), paste, sep=", "), col=1:2, lty=c(1,1,2,2), bty='n', lwd=2) @ The individual survival curves that result from \code{survfit(cfit1)} and \code{survfit(cfit2)} are not actually of interest, since each is a Cox model analog of the pcmbad curve we criticized earlier. The cumulative hazard portion of the results is what is used to build an Aalen-Johansen estimate. (Calling \code{survfit} on a set of \code{survfit} objects is, I admit, a bit confusing. It would perhaps have been better to name the second routine ``AalenJohansen'', but we use this often and didn't want to type that long a name.) Sex has nearly no effect on the hazard of PCM, i.e., on any given day the risk of conversion for a male is essentially the same as for a female of the same age. Yet we see above that the fitted Cox models predict a higher lifetime risk for females, and an age effect on lifetime risk that is far from proportional. Very few subjects acquire PCM more than 15 years after a MGUS diagnosis at age 80 for the obvious reason: very few of them will still be alive. Creating the `list' form matrix above is quite easy, in particular we do not need to fill in elements on the diagonal, nor those for which no transitions occur, e.g., from death back to the entry state. The resulting \code{survfit} object is easy to plot or print using standard calls. The approach has a number of caveats, however. \begin{itemize} \item It does not produce standard errors for the curves, as a consequence of being two steps removed from the data. \item It is easy to ``fool'' the program. For instance if you were to get curves for females and males from \code{cfit1}, but the curves from \code{cfit2} were in the reverse order of male then female, results will still be produced but they would not be valid. The user is responsible for setting the problem up correctly. \item The R syntax for a matrix of lists is rather fussy, e.g., you can't leave the \code{list} function out of the lines that assign elements to \code{temp} above. \end{itemize} The \code{mstate} package addresses these issues, at the price of a somewhat more complex syntax. <>= # Print out a M/F results at 20 years temp <- summary(csurv, time=20*12)$pstate cbind(newdata, PCM= round(100*temp[,2], 1)) @ The above table shows that females are modeled to have a higher risk of 20 year progression, even though their hazard at any given moment is nearly identical to males. The difference at 20 years is on the order of our ``back of the napkin'' person-years estimate of 1\% progression per year * 1.7 more years of life for the females, but the progression fraction varies substantially by group. \section{Fine-Gray model} For the competing risk case the Fine-Gray model provides an alternate way of looking at the data. As we saw above, the impact of a particular covariate on the final values $P$ can be complex, even if the models for the hazards are relatively simple. The primary idea of the Fine-Gray approach is to turn the multi-state problem into a collection of two-state ones. In the upper right diagram of figure 1, draw a circle around all of the states except the chosen endpoint and collapse them into a single meta-state. For the MGUS data these are \begin{itemize} \item Model 1 \begin{itemize} \item left box: All subjects in the entry or ``death first'' state \item right box: PCM \end{itemize} \item Model 2 \begin{itemize} \item left box: All subjects in the entry or ``PCM first'' state \item right box: Death (without PCM) \end{itemize} \end{itemize} An interesting aspect of this is that the fit can be done as a two stage process: the first stage creates a special data set while the second fits a weighted \code{coxph} or \code{survfit} model to the data. The data set can be created using the \code{finegray} command. <>= # (first three lines are identical to an earlier section) etime <- with(mgus2, ifelse(pstat==0, futime, ptime)) event <- with(mgus2, ifelse(pstat==0, 2*death, 1)) event <- factor(event, 0:2, labels=c("censor", "pcm", "death")) pcmdat <- finegray(Surv(etime, event) ~ ., data=mgus2, etype="pcm") pcmdat[1:4, c(1:3, 11:14)] deathdat <- finegray(Surv(etime, event) ~ ., data=mgus2, etype="death") dim(pcmdat) dim(deathdat) dim(mgus2) @ The \code{finegray} command has been used to create two data sets: one for the PCM endpoint and one for the death endpoint. In each, four new variables have been added containing a survival time \code{(fgstart, fgstop, fgstatus)} with an `ordinary' status of 0/1, along with a case weight and a large number of new rows. We can use this new data set as yet another way to compute multi-state survival curves, though there is no good reason to use this rather roundabout approach instead of the simpler \code{survfit(Surv(etime, event) \textasciitilde sex)}. <>= # The PCM curves of the multi-state model pfit2 <- survfit(Surv(fgstart, fgstop, fgstatus) ~ sex, data=pcmdat, weight=fgwt) # The death curves of the multi-state model dfit2 <- survfit(Surv(fgstart, fgstop, fgstatus) ~ sex, data=deathdat, weight=fgwt) @ The two new curves are almost identical to the prior estimates, and in fact would be identical if we had accounted for the slightly different censoring patterns in males and females (by adding \code{strata(sex)} to the right hand side of the \code{finegray} formulas). A Cox model fit to the constructed data set yields the Fine-Gray models for PCM and for death. <>= fgfit1 <- coxph(Surv(fgstart, fgstop, fgstatus) ~ sex, data=pcmdat, weight= fgwt) summary(fgfit1) fgfit2 <- coxph(Surv(fgstart, fgstop, fgstatus) ~ sex, data=deathdat, weight= fgwt) fgfit2 mfit2 <- survfit(Surv(etime, event) ~ sex, data=mgus2) #reprise the AJ plot(mfit2[,1], col=1:2, lwd=2, xscale=12, conf.times=c(5, 15, 25)*12, xlab="Years post diagnosis", ylab="Fraction with PCM") ndata <- data.frame(sex=c("F", "M")) fgsurv1 <- survfit(fgfit1, ndata) lines(fgsurv1, fun="event", lty=2, lwd=2, col=1:2) legend("topleft", c("Female, Aalen-Johansen", "Male, Aalen-Johansen", "Female, Fine-Gray", "Male, Fine-Gray"), col=1:2, lty=c(1,1,2,2), bty='n') # rate models with only sex pfitr <- coxph(Surv(etime, event=="pcm") ~ sex, mgus2) dfitr <- coxph(Surv(etime, event=="death") ~ sex, mgus2) temp <- matrix(list(), 3,3) temp[1,2] <- list(survfit(pfitr, ndata, std.err=FALSE)) temp[1,3] <- list(survfit(dfitr, ndata, std.err=FALSE)) rcurve <- survfit(temp, p0=c(entry=1, pcm=0, death=0)) @ The FG model states that males have a less \emph{observed} PCM, by a factor of \Sexpr{round(exp(coef(fgfit1)), 2)}, and that this hazard ratio is constant over time. An overlaid plot of the non-parametric Aalen-Johansen estimates for the PCM state (from \code{survfit}) along with predicted curves from the Fine-Gray model show that proportional hazards is not unreasonable for this particular fit. The predicted values from the rate model, computed just above but not plotted on the curve, also fit well with the data. When there is only a single categorical 0/1 covariate the Fine-Gray model reduces to Gray's test of the subdistribution function, in the same way that a \code{coxph} fit with a single categorical predictor is equivalent to the log-rank test. The mathematics behind the Fine-Gray estimate starts with the functions $F_k(t) = p_k(t)$, where $p$ is the probability in state function estimated by the AJ estimate. This can be thought of as the distribution function for the improper random variable $T^*= I(\mbox{event type}=k)T + I(\mbox{event type}\ne k)\infty$. Fine and Gray refer to $F_k$ as a subdistribution function. In analogy to the survival probability in the two state model define \begin{equation} \gamma_k(t) = - d \log[1-F_k(t)]/dt \label{FG}I \end{equation} and assume that $\gamma_k(t;x) = \gamma_{k0}(t) \exp(X\beta)$. In a 2 state alive $\longrightarrow$ death model, $\gamma$ becomes the usual hazard function $\lambda$. In the same way that our multivariate Cox model \code{cfit2} made the simplifying assumption that the impact of male sex is to increase the hazard for death by a factor of \Sexpr{round(exp(coef(cfit2)['sexM']), 2)}, independent of the subject's age or serum mspike value, the Fine-Gray model assumes that each covariate's effect on $\log(1-F)$ is a constant, independent of other variables. Both model's assumptions are wonderfully simplifying with respect to understanding a covariate, since we can think about each one separately from the others. This is, of course, under the assumption that the model is correct: additivity across covariates, linearity, and proportional hazards all hold. In a multi-state model, however, these assumptions cannot hold for both the per-transition and Fine-Gray models formulations at the same time; if it is true for one, it will not be true for the other. Now consider a multivariate fit on age, sex, and serum m-spike. <>= fgfit2a <- coxph(Surv(fgstart, fgstop, fgstatus) ~ age + sex + mspike, data=pcmdat, weight=fgwt) fgfit2b <- coxph(Surv(fgstart, fgstop, fgstatus) ~ age + sex + mspike, data=deathdat, weight=fgwt) round(rbind(PCM= coef(fgfit2a), death=coef(fgfit2b)), 3) @ The Fine-Gray fits show an effect of all three variables on the subdistribution rates. Males have a lower lifetime risk of PCM before death and a higher risk of death before PCM, while a high serum m-spike works in the opposite direction. The Cox models showed no effect of sex on the instantaneous hazard of PCM and none for serum m-spike on the death rate. However, as shown in the last section, the Cox models do predict a greater lifetime risk for females. We had also seen that older subjects are less likely to experience PCM due to the competing risk of death; this is reflected in the FG model as a negative coefficient for age. Now compute predicted survival curves for the model, and show them alongside the predictions from the multi-state model. <>= oldpar <- par(mfrow=c(1,2)) newdata <- expand.grid(sex= c("F", "M"), age=c(60, 80), mspike=1.2) fsurv1 <- survfit(fgfit2a, newdata) # time to progression curves plot(fsurv1, xscale=12, col=1:2, lty=c(1,1,2,2), lwd=2, fun='event', xlab="Years", ylab="Fine-Gray predicted", xmax=12*25, ylim=c(0, .15)) legend(1, .15, c("Female, 60", "Male, 60","Female: 80", "Male, 80"), col=c(1,2,1,2), lty=c(1,1,2,2), lwd=2, bty='n') plot(csurv[,2], xscale=12, col=1:2, lty=c(1,1,2,2), lwd=2, xlab="Years", ylab="Multi-state predicted", xmax=12*25, ylim=c(0, .15)) legend(1, .15, c("Female, 60", "Male, 60","Female: 80", "Male, 80"), col=c(1,2,1,2), lty=c(1,1,2,2), lwd=2, bty='n') par(oldpar) @ The predictions as a function of age group are quite different for the Fine-Gray model: new PCM cases are predicted 20+ years after diagnosis in both the old and young age groups, while they are predicted to cease in the multi-state fit. The average of the curves is nearly the same at each age, but the global proportional hazards assumption of the FG model forces the curves to remain parallel. We can check the proportional hazards assumption of the models using the \code{cox.zph} function, linearity of the continuous variables age and mspike by using non-linear terms such as \code{pspline} or \code{ns}, and additivity by exploring interactions. All are obvious and important next steps. For instance, the proportional hazards assumption for age shows clear violations. <>= zph.fgfit2a <- cox.zph(fgfit2a) zph.fgfit2a plot(zph.fgfit2a[1]) abline(h=coef(fgfit2a)[1], lty=2, col=2) @ A weakness of the Fine-Gray approach is that since the two endpoints are modeled separately, the results do not have to be consistent. Below is a graph of the predicted fraction who have experienced neither endpoint. For subjects diagnosed at age 80 the Fine-Gray models predict that more than 100\% will either progress or die by 30 years. Predictions based on the Aalen-Johansen approach do not have this issue. <>= fsurv2 <- survfit(fgfit2b, newdata) # time to progression curves xtime <- 0:(30*12) #30 years y1a <- 1 - summary(fsurv1, times=xtime)$surv #predicted pcm y1b <- 1 - summary(fsurv2, times=xtime)$surv #predicted deaths before pcm y1 <- (y1a + y1b) #either matplot(xtime/12, y1, col=1:2, lty=c(1,1,2,2), type='l', xlab="Years post diagnosis", ylab="FG: either endpoint") abline(h=1, col=3) legend("bottomright", c("Female, 60", "Male, 60","Female: 80", "Male, 80"), col=c(1,2,1,2), lty=c(1,1,2,2), lwd=2, bty='n') @ The primary strength of the Fine-Gray model with respect to the Cox model approach is that if lifetime risk is a primary question, then the model has given us a simple and digestible answer to that question: ``females have a 1.2 fold higher lifetime risk of PCM, after adjustment for age and serum m-spike''. This simplicity is not without a price, however, and these authors are not proponents of the approach. There are five issues. \begin{enumerate} \item The attempt to capture a complex process as a single value is grasping for a simplicity that does not exist for many (perhaps most) data sets. The necessary assumptions in a multivariate Cox model of proportional hazards, linearity of continuous variables, and no interactions are strong ones. For the FG model these need to hold for a combined process --- the mixture of transition rates to each endpoint --- which turns out to be a more difficult barrier. \item The sum of predictions need not be consistent. \item From the per-transition models one can work forward and compute $p(t)$, the occupancy probabilities for each state over time; both the hazard ratios and $p$ are useful summaries of the data. We don't have tools to work backwards from a Fine-Gray fit to the per transition hazards. \item The approach is viable only for competing risks and not for other multi-state models. \item The risk sets are odd. \end{enumerate} The last of these is perhaps the most frequently listed issue with the Fine-Gray model, but it is actually a minor complaint. The state probabilities $p(t)$ in a multi-state model are implicitly fractions of the total population we started with: someone who dies in month 1 is still a part of the denominator for the fraction of subjects with PCM at 20 years. In the Fine-Gray formulas this subject explicitly appears in risk set denominators at a later time, which looks odd but is more of an artifact. The first issue is substantial, however, and checking the model assumptions of a Fine-Gray fit is mandatory. The second point is alarming, but it does not have a practical impact unless there is long follow-up. \section{Stacked data sets} How does one fit risk models that have shared coefficients or baseline hazards? One approach is to fit the set of Cox models for the rates `all at once' on a combined data set. For the simple competing risks MGUS fit above, assume that we wanted to add hemoglobin to the fit, with a common coefficient for both the PCM and death endpoint. (Anemia is a feature of both PCM and old age.) Create a stacked data set with $2n$ observations. The first $n$ rows are the data set we would use for a time to PCM analysis, with a simple 0/1 status variable encoding the PCM outcome. The second $n$ rows are the data set we would have used for the `death before PCM' fits, with status encoding the death-before-PCM endpoint. A last variable, \code{group}, is `pcm' for the first $n$ observations and `death' for the remainder. Then fit a model <>= temp1 <- data.frame(mgus2, time=etime, status=(event=="pcm"), group='pcm') temp2 <- data.frame(mgus2, time=etime, status=(event=="death"), group="death") stacked <- rbind(temp1, temp2) allfit <- coxph(Surv(time, status) ~ hgb + (age + sex)*strata(group), data=stacked) @ This fits a common effect for hemoglobin (hgb) but separate age and sex effects for the two endpoints, along with separate baseline hazards. \section{Other software} \subsection{The mstate package} As the number of states + transitions (arrows + boxes) gets larger then the `by hand' approach used above for creating a stacked data set, labeling coefficients, and producing multi-state curves becomes a challenge. (It is still fairly easy to do, just not as easy to ensure it has been done \emph{correctly}.) The \code{mstate} package starts with a definition of the matrix of possible transitions and uses that to drive tools that build and analyze the stacked data set in a more automated fashion. We recommend it for more complex models. (The tutorial above is about at our personal threshold.) A second advantage of \code{mstate} is that all the Cox model fits are now in one well indexed object, which allows for calculation of proper confidence intervals for the state probabilities $p(t)$. (Since all of the steps used the same transition matrix template, the necessary computations are scripted and reliable.) \subsection{The \code{msm} package} There are two broad classes of multi-state data: \begin{itemize} \item Panel data arises when subjects have regular visits, with the current state assessed at each visit. We don't know when the transitions between states occur, or if other states may have been visited in the interim --- only the subject's state at specific times. \item Survival data arises when we observe the transition times; death, for example. \end{itemize} The overall model (boxes and arrows), the quantities of interest (transition rates and $p(t)$), and the desired printout and graphs are identical for the two cases. Much of the work in creating a data set is also nearly the same. The underlying likelihood equations and resulting analytical methods for solving the problem are, however, completely different. The \code{msm} package addresses panel data, while \code{survival}, \code{mstate}, and a host of others are devoted to survival data. \section{Conclusions} When working with acute diseases, such as advanced cancer or end-stage liver disease, there is often a single dominating endpoint. Ordinary single event Kaplan-Meier curves and Cox models are then efficient and sufficient tools for much of the analysis. Such data was the primary use case for survival analysis earlier in the authors' careers. Data with multiple important endpoints is now common, and multi-state methods are an important addition to the statistical toolbox. As shown above, they are now readily available and easy to use. It is sometimes assumed that the presence of competing risks \emph{requires} the use of a Fine-Gray model (we have seen it in referee reports), but this is not correct. The model may often be useful, but is one available option among many. Grasping the big picture for a multi-state data set is always a challenge and we should make use of as many tools as possible. We are often reminded of the story of a centenarian on his 100th birthday proclaiming that he was looking forward to many more years ahead because ``I read the obituaries every day, and you almost never see someone over 100 listed there''. It is not always easy to jump between observed deaths, hazard rates, and lifetime risk. %\bibliographystyle{plain} %\bibliography{refer} \end{document} survival/vignettes/tests.Rnw0000644000175100001440000026325012650522315016016 0ustar hornikusers\documentclass{article}[11pt] \usepackage{Sweave} \usepackage{amsmath} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} %\VignetteIndexEntry{Cox models and ``type 3'' Tests} \SweaveOpts{prefix.string=tests,width=6,height=4, keep.source=TRUE, fig=FALSE} % Ross Ihaka suggestions \DefineVerbatimEnvironment{Sinput}{Verbatim} {xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} \SweaveOpts{width=6,height=4} \setkeys{Gin}{width=\textwidth} <>= options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text options(contrasts=c("contr.treatment", "contr.poly")) #reset default @ \title{Contrasts, populations, and ``type III'' tests} \author{Terry M Therneau \\ \emph{Mayo Clinic}} \newcommand{\code}[1]{\texttt{#1}} \newcommand{\myfig}[1]{\includegraphics[height=!, width=\textwidth] {tests-#1.pdf}} \newcommand{\ybar}{\overline{y}} \begin{document} \maketitle \tableofcontents \section{Introduction} \begin{table} \centering \begin{tabular} {crrrrr} & \multicolumn{5}{c}{Group} \\ &A & B & C & D & E \\ <>= library(survival) age2 <- cut(flchain$age, c(49, 59, 69, 79, 89, 120), labels=c("50-59", "60-69", "70-79", "80-89", "90+")) flchain$flc <- flchain$kappa + flchain$lambda tab1 <- with(flchain, tapply(flc, list(sex, age2), mean)) cat("female&" , paste(round(tab1[1,], 1), collapse=" & "), "\\\\ \n") cat("male &" , paste(round(tab1[2,], 1), collapse=" & "), "\n") @ \end{tabular} \caption{Fitted values from a linear model with two factors.} \label{tab1} \end{table} One of the annoying design shortfalls of R, inherited from S, is how modeling functions deal with categorical predictors. For a simple model such as \code{y ~ age + treatment} where the latter is a categorical, we will normally want to compare pairs of treatments. One way to do this is to set up the columns of 0/1 dummy variables that represent treatment so that the comparisons of interest appear directly as coefficients in the fit. If for instance there were three treatments, a control and two active agents then the two natural comparisons are control vs. agent1 and control vs. agent2. R does this for us without a hitch and nearly automatically, with several options to help control exactly how said 0/1 variables are created. But what if there were 4 treatments and we want to look at all 6 pairwise comparisons? This cannot be set up so that all 6 will appear as one coefficient in the fit, one needs a mechanism to compute these 6 estimates or \emph{contrasts} after the fit. As a more complex case consider the simple data shown in table \ref{tab1}, which are fitted values from a linear model on two factors along with their interaction. There are any number of comparisons that we might want to make in the data set: a trend test across the groups, overall or separately for each sex, all pairwise comparisons between groups, etc. A standard mechanism for this after-the-fit estimates has been lacking. There are several addons that address parts of the question such as \code{pairwise.t.tests} or \code{TukeyHSD}, but they are not applicable to coxph models. The \code{yates} function was motivated by the more perplexing problem of population contrasts, which it also addresses. This note started with an interchange on the R-help. A user asked ``how do I do a type III test using the Cox model'', and I replied that this was not a well defined question. If he/she could define exactly what it was that they were after, then I would look into it. To which the response was that ``SAS does it''. A grant deadline was looming so the discussion did not get any further at that point, but it eventually led to a much longer investigation on my part, which is summarized in this note. There are three central ideas as it turns out: populations, computation, and the mapping linear models ideas onto the Cox model. The first idea, and perhaps the central one, is using the model fit from a current data set to predict for a new population. This plays an important role in predicted survival curves, see for instance the vignette on that topic or chapter 10 of our book \cite{Therneau00}; recognizing that ``type 3'' tests are simply another variant on that theme was a pivotal step in my understanding. This immediately leads to the important subtopic of ``prediction for \emph{which} population''. The SAS type 3 computations corresponds to a very particular and inflexible choice. The second theme is computational: given some summary measure and a population for which you wish to predict it, the result will be some sort of weighted average. There are two primary ways to set up this computation. In a linear model one of them can be reduced to a particular contrast $C \hat\beta$ in the fitted coefficients $\hat\beta$, which is an appealing choice since follow-up computations such as the variance of the estimate become particularly simple. A common, simple, but unreliable algorithm for creating $C$ has been a major source of confusion (hereafter referred to as the NSTT: not safe type three). The last theme is how the linear models formulae map to the Cox model case. In particular, there is a strong temptation to use $C \hat\beta$ with $C$ taken from linear models machinery and $\hat\beta$ from a fitted Cox model. The problem is that this implicitly requires a replacement of $E[\exp(X)]$ with $\exp(E[X])$. For a Cox model $C \beta$ is certainly a valid statistic for any $C$, we just have no clear idea of what it is testing. For the impatient readers among you I'll list the main conclusions of this report at the start. \begin{itemize} \item SAS type 3 predicts for a population with a uniform distribution across all categorical predictors. Scholarly papers discussing fundamental issues with using such an approach as a default analysis method have appeared almost biannually in the statistics literature, with little apparent effect on the usage of the method. SAS documentation of type 3 is almost entirely focused on the algorithm they use for computing $C$ and ignores the population issue. \item Population predictions very often make sense, including the question the type 3 approach is attempting to address. There are valid ways to compute these estimates for a Cox model, they are closely related the inverse probability weight (IPW) methods used in propensity scores and marginal structural models. \item The algorithm used to compute $C$ by the SAS glm procedure is sophisticated and reliable. The SAS phreg procedure uses the linear models approach of $C \hat\beta$ to compute a ``type 3'' contrast, with $C$ computed via the NSTT. The combination is a statistical disaster. (This is true for SAS version 9.4; I will update this note if things change.) \end{itemize} \section{Linear approximations and the Cox model} \label{sect:transfer} One foundation of my concern has to do with the relationship between linear models and coxph. The solution to the Cox model equations can be represented as an iteratively reweighted least-squares problem, with an updated weight matrix and adjusted dependent variable at each iteration, rather like a GLM model. This fact has been rediscovered multiple times, and leads to the notion that since the last iteration of the fit \emph{looks} just like a set of least-squares equations, then various least squares ideas could be carried over to the proportional hazards model by simply writing them out using these final terms. In practice, sometimes this works and sometimes it doesn't. The Wald statistic is one example of the former type, which is completely reliable as long as the coefficients $\beta$ are not too large\footnote{ In practice failure only occurs in the rare case that one of the coefficients is tending to infinity. However, in that case the failure is complete: the likelihood ratio and score tests behave perfectly well but the Wald test is worthless.}. A counter example is found in two ideas used to examine model adequacy: adjusted variable plots and constructed variable plots, each of which was carried over to the Cox model case by reprising the linear-model equations. After a fair bit of exploring I found neither is worth doing \cite{Therneau00}. Copying over a linear models formula simply did not work in this case. \begin{figure} \myfig{data} \caption{Average free light chain for males and females. The figure shows both a smooth and the means within deciles of age.} \label{fig:data} \end{figure} \section{Data set} We will motivate our discussion with the simple case of a two-way analysis. The \code{flchain} data frame contains the results of a small number of laboratory tests done on a large fraction of the 1995 population of Olmsted County, Minnesota aged 50 or older \cite{Kyle06, Dispenzieri12}. The R data set contains a 50\% random sample of this larger study and is included as a part of the survival package. The primary purpose of the study was to measure the amount of plasma immunoglobulins and its components. Intact immunoglobulins are composed of a heavy chain and light chain portion. In normal subjects there is overproduction of the light chain component by the immune cells leading to a small amount of \emph{free light chain} in the circulation. Excessive amounts of free light chain (FLC) are thought to be a marker of disregulation in the immune system. Free light chains have two major forms denoted as kappa and lambda, we will use the sum of the two. An important medical question is whether high levels of FLC have an impact on survival, which will be explored using a Cox model. To explore linear models we will compare FLC values between males and females. A confounding factor is that free light chain values rise with age, in part because it is eliminated by the kidneys and renal function declines with age. The age distribution of males and females differs, so we will need to adjust our simple comparison between the sexes for age effects. The impact of age on mortality is of course even greater and so correction for the age imbalance is is critical when exploring the impact of FLC on survival. Figure \ref{fig:data} shows the trend in free light chain values as a function of age. For illustration of linear models using factors, we have also created a categorical age value using deciles of age. The table of counts shows that the sex distribution becomes increasingly unbalanced at the older ages, from about 1/2 females in the youngest group to a 4:1 ratio in the oldest. <>= library(survival) library(splines) age2 <- cut(flchain$age, c(49, 59, 69, 79, 89, 120), labels=c("50-59", "60-69", "70-79", "80-89", "90+")) counts <- with(flchain, table(sex, age2)) counts # flchain$flc <- flchain$kappa + flchain$lambda male <- (flchain$sex=='M') mlow <- with(flchain[male,], smooth.spline(age, flc)) flow <- with(flchain[!male,], smooth.spline(age, flc)) plot(flow, type='l', ylim=range(flow$y, mlow$y), xlab="Age", ylab="FLC") lines(mlow, col=2) cellmean <- with(flchain, tapply(flc, list(sex, age2), mean, na.rm=T)) matpoints(c(55,65,75, 85, 95), t(cellmean), pch='fm', col=1:2) round(cellmean, 2) @ Notice that the male/female difference in FLC varies with age, \Sexpr{round(cellmean[1,1],1)} versus \Sexpr{round(cellmean[2,1],1)} at age 50--59 and \Sexpr{round(cellmean[1,5],1)} versus \Sexpr{round(cellmean[2,5],1)} at age 90. The data does not fit a simple additive model; there are ``interactions'' to use statistical parlance. An excess of free light chain is thought to be at least partly a reflection of immune senescence, and due to our hormonal backgrounds men and women simply do not age in quite the same way. \section{Population averages} The question of how to test for a main effect in the presence of interaction is an old one. At one time this author considered the phrase ``main effect in the presence of interaction'' to be an oxymoron, but long experience with clinical data sets has led me to the opposite conclusion. Real data always has interactions. The treatment effect of a drug will not be exactly the same for old and young, thin and obese, physically active and sedentary, etc. Explicit recognition of this is an underlying rationale of the current drive towards ``personalized medicine'', though that buzzword often focuses only on genetic differences. Any given data set may often be too small to explore these variations and our statistical models will of necessity smooth over the complexity, but interactions are nevertheless still present. Consider the data shown in figure \ref{fig:data} above, which shows a particular laboratory test value by age and sex. We see that the sex effect varies by age. Given this, what could be meant by a ``main effect'' of sex? One sensible approach is to select a fixed \emph{population} for the ages, and then compute the average sex effect over that population. Indeed this is precisely what many computations do behind the scenes, e.g. the ``type 3'' estimates found in linear models. There are three essential components to the calculation: a reference population for the confounders, a summary measure of interest, and a computational algorithm. To understand how linear models methods may (or may not) extend to the proportional hazards model it is useful consider all three facets; each is revealing. Four possible choices for a target population of ages are given below. \begin{enumerate} \item Empirical: the age distribution of the sample at hand, also called the data distribution. In our sample this would be the age distribution of all \Sexpr{nrow(flchain)} subjects, ignoring sex. \item SAS: a uniform distribution is assumed over all categorical adjusters, and the data distribution for continuous ones. \item External reference: a fixed external population, e.g. the age distribution of the US 2010 census. \item MVUE: minimum variance unbiased; the implicit population corresponding to a multivariate least squares fit. \end{enumerate} Method 3 is common in epidemiology, method 1 is found in traditional survey sampling and in other common cases as we will see below. The type 3 estimates of SAS correspond to population 2. If there an interaction between two categorical variables x1 and x2, then the uniform distribution is taken to be over all combinations formed by the pair, and similarly for higher order interactions. \section{Linear models and populations} If we ignore the age effect, then everyone agrees on the best estimate of mean FLC: the simple average of FLC values within each sex. The male-female difference is estimated as the difference of these means. This is what is obtained from a simple linear regression of FLC on sex. Once we step beyond this and adjust for age, the relevant linear models can be looked at in several ways; we will explore three of them below: contrasts, case weights, and nesting. This ``all roads lead to Rome'' property of linear models is one of their fascinating aspects, at least mathematically. \subsection{Case weights} \begin{figure} \myfig{pop} \caption{Three possible adjusting populations for the FLC data set, a empirical reference in black, least squares based one in red, and the US 2000 reference population as `u'.} \label{fig:pop} \end{figure} How do we form a single number summary of ``the effect of sex on FLC''? Here are four common choices. \begin{enumerate} \item Unadjusted. The mean for males minus the mean for females. The major problem with this is that a difference in age distributions will bias the result. Looking at figure \ref{fig:data} imagine that this were two treatments A and B rather than male/female, and that the upper one had been given to predominantly 50-65 year olds and the lower predominantly to subjects over 80. An unadjusted difference would actually reverse the true ordering of the curves. \item Population adjusted. An average difference between the curves, weighted by age. Three common weightings are \begin{enumerate} \item External reference. It is common practice in epidemiology to use an external population as the reference age distribution, for instance the US 2000 census distribution. This aids in comparing results between studies. \item Empirical population. The overall population structure of the observed data. \item Least squares. The population structure that minimizes the variance of the estimated female-male difference. \end{enumerate} \end{enumerate} The principle idea behind case weights is to reweight the data such that confounders become balanced, i.e., ages are balanced when examining the sex effect and sex is balanced when examining age. Any fitted least squares estimate can be rewritten as a weighted sum of the data points with weight matrix $W= (X'X)^{-1}X'$. $W$ has $p$ rows, one per coefficient, each row is the weight vector for the corresponding element of $\hat\beta$. So we can backtrack and see what population assumption was underneath any given fit by looking at the weights for the relevant coefficient(s). Consider the two fits below. In both the second coefficient is an estimate of the overall difference in FLC values between the sexes. (The relationship in figure \ref{fig:data} is clearly curved so we have foregone the use of a simple linear term for age; there is no point in fitting an obviously incorrect model.) Since $\beta_2$ is a contrast the underlying weight vectors have negative values for the females and positive for the males. <<>>= us2000 <- rowSums(uspop2[51:101,,'2000']) fit1 <- lm(flc ~ sex, flchain, x=TRUE) fit2 <- lm(flc ~ sex + ns(age,4), flchain, x=TRUE) c(fit1$coef[2], fit2$coef[2]) wt1 <- solve(t(fit1$x)%*%fit1$x, t(fit1$x))[2,] # unadjusted wt2 <- solve(t(fit2$x)%*%fit2$x, t(fit2$x))[2,] # age-adjusted table(wt1, flchain$sex) @ To reconstruct the implied population density, one can use the density function with \code{wt1} or \code{wt2} as the case weights. Examination of \code{wt1} immediately shows that the values are $-1/n_f$ for females and $1/n_m$ for males where $n_f$ and $n_m$ are number of males and females, respectively. The linear model \code{fit1} is the simple difference in male and female means; the implied population structure for males and females is the unweighted density of each. Because this data set is very large and age is coded in years we can get a density estimate for fit2 by simple counting. The result is coded below and shown in figure \ref{fig:pop}. The empirical reference and least squares reference are nearly identical. This is not a surprise. Least squares fits produce minimum variance unbiased estimates (MVUE), and the variance of a weighted average is minimized by using weights proportional to the sample size, thus the MVUE estimate will give highest weights to those ages with a lot of people. The weights are not \emph{exactly} proportional to sample size for each age. As we all know, for a given sample size $n$ a study comparing two groups will have the most power with equal allocation between the groups. Because the M/F ratio is more unbalanced at the right edge of the age distribution the MVUE estimate gives just a little less weight there, but the difference between it and the overall data set population will be slight for all but those pathological cases where there is minimal overlap between M/F age distributions. (And in that case the entire discussion about what ``adjustment'' can or should mean is much more difficult.) <>= us2000 <- rowSums(uspop2[51:101,,'2000']) tab0 <- table(flchain$age) tab2 <- tapply(abs(wt2), flchain$age, sum) matplot(50:100, cbind(tab0/sum(tab0), tab2/sum(tab2)), type='l', lty=1, xlab="Age", ylab="Density") us2000 <- rowSums(uspop2[51:101,,'2000']) matpoints(50:100, us2000/sum(us2000), pch='u') legend(60, .02, c("Empirical reference", "LS reference"), lty=1, col=1:2, bty='n') @ The LS calculation does a population adjustment automatically for us behind the scenes via the matrix algebra of linear models. If we try to apply population reference adjustment directly a problem immediately arises: in the US reference \Sexpr{round(100*us2000[46]/sum(us2000),2)}\% of the population is aged 95 years, and our sample has no 95 year old males; it is not possible to re weight the sample so as to exactly match the US population reference. This occurs in any data set that is divided into small strata. The traditional epidemiology approach to this is to use wider age intervals of 5 or 10 years. Weights are chosen for each age/sex strata such that the sum of weights for females = sum of weights for males within each age group (balance), and the total sum of weights in an age group is equal to the reference population. The next section goes into this further. An increasingly popular approach for producing results that are standardized to the empirical reference population (i.e. the data distribution) is to use a smoothed age effect, obtained through inverse probability weights which are based on logistic regression, e.g. in the causal models literature and propensity score literature. This approach is illustrated in a vignette on adjusted survival curves which is also in the survival package. \subsection{Categorical predictors and contrasts} When the adjusting variable or variables are categorical --- a factor in R or a class variable in SAS --- then two more aspects come into play. The first is that any estimate of interest can be written in terms of the cell means. Formally, the cell means are a \emph{sufficient statistic} for the data. For our data set and using the categorized variable \code{age2} let $\theta_{ij}$ parameterize these means. $$ \begin{tabular}{cccccc} &50--59 & 60--69 & 70-79 & 80-89 & 90+ \\ \hline Female & $\theta_{11}$ & $\theta_{12}$ & $\theta_{13}$& $\theta_{14}$& $\theta_{15}$ \\ Male & $\theta_{21}$ & $\theta_{22}$ & $\theta_{23}$& $\theta_{24}$ & $\theta_{25}$ \\ \end{tabular} $$ For a design with three factors we will have $\theta_{ijk}$, etc. Because it is a sufficient statistic, any estimate or contrast of interest can be written as a weighted sum of the $\theta$s. Formulas for the resulting estimates along with their variances and tests were worked out by Yates in 1934 \cite{Yates34} and are often referred to as a Yates weighted means estimates. For higher order designs the computations can be rearranged in a form that is manageable on a desk calculator, and this is in fact the primary point of that paper. (Interestingly, his computational process turns out to be closely related to the fast Fourier transform.) The second facet of categorical variables is that another adjustment is added to the list of common estimates: \begin{enumerate} \item Unadjusted \item Population adjusted \begin{enumerate} \item External reference \item Empirical (data set) reference \item Least squares \item Uniform. A population in which each combination of the factors has the same frequency of occurrence. \end{enumerate} \end{enumerate} The uniform population plays a special role in the case of designed experiments, where equal allocation corresponds to the optimal study design. The Yates estimates are particularly simple in this case. For a hypothetical population with equal numbers in each age category the estimated average FLC for females turns out to be $\mu_f = \sum_j \theta_{1j} /5$ and the male - female contrast is $\sum_j(\theta_{2j}-\theta_{1j})/5$. We will refer to these as the ``Yates'' estimates and contrast for an effect. Conversely, the estimated age effects, treating sex as a confounding effect and assuming an equal distribution of females and males as the reference population, gives an estimated average FLC for the 60-69 year olds of $\mu_{60-69}= (\theta_{12} + \theta_{22})/2$, and etc for the other age groups. We can obtain the building blocks for Yates estimates by using the interaction function and omitting the intercept. <>= yatesfit <- lm(flc ~ interaction(sex, age2) -1, data=flchain) theta <- matrix(coef(yatesfit), nrow=2) dimnames(theta) <- dimnames(counts) round(theta,2) @ For a linear model fit, any particular weighted average of the coefficients along with its variance and the corresponding sums of squares can be computed using the \code{contrast} function given below. Let $C$ be a contrast matrix with $k$ rows, each containing one column per coefficient. Then $C\theta$ is a vector of length $k$ containing the weighted averages and $V = \hat\sigma^2 C (X'X)^{-1}C'$ is its variance matrix. The sums of squares is the increase in the sum of squared residuals if the fit were restricted to the subspace $C\theta =0$. Formulas are from chapter 5 of Searle \cite{Searle71}. Some authors reserve the word \emph{contrast} for the case where each row of $C$ sums to zero and use \emph{estimate} for all others; I am being less restrictive since the same computation serves for both. <<>>= qform <- function(beta, var) # quadratic form b' (V-inverse) b sum(beta * solve(var, beta)) contrast <- function(cmat, fit) { varmat <- vcov(fit) if (class(fit) == "lm") sigma2 <- summary(fit)$sigma^2 else sigma2 <- 1 # for the Cox model case beta <- coef(fit) if (!is.matrix(cmat)) cmat <- matrix(cmat, nrow=1) if (ncol(cmat) != length(beta)) stop("wrong dimension for contrast") estimate <- drop(cmat %*% beta) #vector of contrasts ss <- qform(estimate, cmat %*% varmat %*% t(cmat)) *sigma2 list(estimate=estimate, ss=ss, var=drop(cmat %*% varmat %*% t(cmat))) } yates.sex <- matrix(0, 2, 10) yates.sex[1, c(1,3,5,7,9)] <- 1/5 #females yates.sex[2, c(2,4,6,8,10)] <- 1/5 #males contrast(yates.sex, yatesfit)$estimate # the estimated "average" FLC for F/M contrast(yates.sex[2,]-yates.sex[,1], yatesfit) # male - female contrast @ <>= # Create the estimates table -- lots of fits emat <- matrix(0., 6, 3) dimnames(emat) <- list(c("Unadjusted", "MVUE: continuous age", "MVUE: categorical age", "Empirical (data) reference", "US200 reference", "Uniform (Yates)"), c("est", "se", "SS")) #unadjusted emat[1,] <- c(summary(fit1)$coef[2,1:2], anova(fit1)["sex", "Sum Sq"]) # MVUE -- do the two fits fit2 <- lm(flc ~ ns(age,4) + sex, flchain) emat[2,] <- c(summary(fit2)$coef[6, 1:2], anova(fit2)["sex", "Sum Sq"]) fit2 <- lm(flc ~ age2 + sex, flchain) emat[3,] <- c(summary(fit2)$coef[6, 1:2], anova(fit2)["sex", "Sum Sq"]) #Remainder, use contrasts tfun <- function(wt) { cvec <- c(matrix(c(-wt, wt), nrow=2, byrow=TRUE)) temp <- contrast(cvec, yatesfit) c(temp$est, sqrt(temp$var), temp$ss) } emat[4,] <- tfun(colSums(counts)/sum(counts)) usgroup <- tapply(us2000, rep(1:5, c(10,10,10,10,11)), sum)/sum(us2000) emat[5,]<- tfun(usgroup) emat[6,] <- tfun(rep(1/5,5)) @ \begin{table} \centering \begin{tabular}{l|ccc} & estimate & sd & SS \\ \hline <>= temp <- dimnames(emat)[[1]] for (i in 1:nrow(emat)) cat(temp[i], sprintf(" &%5.3f", emat[i,1]),sprintf(" &%6.5f", emat[i,2]), sprintf(" & %6.1f", emat[i,3]), "\\\\ \n") @ \end{tabular} \caption{Estimates of the male-female difference along with their standard errors. The last 4 rows are based on categorized age.} \label{tab:allest} \end{table} Table \ref{tab:est} shows all of the estimates of the male/female difference we have considered so far along with their standard errors. Because it gives a much larger weight to the 90+ age group than any of the other estimates, and that group has the largest M-F difference, the projected difference for a uniform population (Yates estimate) yields the largest contrast. It pays a large price for this in terms of standard error, however, and is over twice the value of the other approaches. As stated earlier, any least squares parameter estimate can be written as a weighted sum of the y values. Weighted averages have minimal variance when all of the weights are close to 1. The unadjusted estimate adheres to this precisely and the data-reference and MVUE stay as close as possible to constant weights, subject to balancing the population. The Yates estimate, by treating every cell equally, implicitly gives much larger weights to the oldest ages. Table \ref{tab:est} shows the effective observation weights used for each of the age categories. <>= casewt <- array(1, dim=c(2,5,4)) # case weights by sex, age group, estimator csum <- colSums(counts) casewt[,,2] <- counts[2:1,] / rep(csum, each=2) casewt[,,3] <- rep(csum, each=2)/counts casewt[,,4] <- 1/counts #renorm each so that the mean weight is 1 for (i in 1:4) { for (j in 1:2) { meanwt <- sum(casewt[j,,i]*counts[j,])/ sum(counts[j,]) casewt[j,,i] <- casewt[j,,i]/ meanwt } } @ \begin{table} \centering \begin{tabular}{rlrrrrr} &&50--59& 60--69 & 70--79 & 80--89 & 90+ \\ \hline <>= tname <- c("Unadjusted", "Min var", "Empirical", "Yates") for (i in 1:2) { for (j in 1:4) { cat("&",tname[j], " & ", paste(sprintf("%4.2f", casewt[i,,j]), collapse= " & "), "\\\\\n") if (j==1) cat(c("Female", "Male")[i]) } if (i==1) cat("\\hline ") } @ \end{tabular} \caption{Observation weights for each data point corresponding to four basic approaches. All weights are normed so as to have an average value of 1.} \label{tab:est} \end{table} Looking at table \ref{tab:est} notice the per observation weights for the $\ge 90$ age group, which is the one with the greatest female/male imbalance in the population. For all but the unbalanced estimate (which ignores age) the males are given a weight that is approximately 3 times that for females in order to re balance the shortage of males in that category. However, the absolute values of the weights differ considerably. \subsection{Different codings} Because the cell means are a sufficient statistic, all of the estimates based on categorical age can be written in terms of the cell means $\hat\theta$. The Yates contrast is the simplest to write down: $$ \begin{tabular} {rrrrrr} & 50--59 & 60--69 & 70--79 & 80--89 & 90+ \\ \hline Female & -1/5 & -1/5 & -1/5 & -1/5 & -1/5 \\ Male & 1/5 & 1/5 & 1/5 & 1/5 & 1/5 \end{tabular} $$ %(Note that for calculating a sum of squares we will get the exact same %result from a matrix using $\pm 1$ rather than $\pm 1/5$; %the Yates contrast is often written this way.) For the data set weighting the values of 1/5 are replaced by $n_{+j}/n_{++}$, the overall frequency of each age group, where a $+$ in the subscript stands for addition over that subscript in the table of counts. The US population weights use the population frequency of each age group. The MVUE contrast has weights of $w_j/\sum w_j$ where $w_j = 1/(1/n_{1j} + 1/n_{2j})$, which are admittedly not very intuitive. $$ \begin{tabular}{rrrrrr} & 50--59 & 60--69 & 70--79 & 80--89 & 90+ \\ \hline <>= temp <- 1/colSums(1/counts) temp <- temp/sum(temp) cat("Female", sprintf(" & %5.3f", -temp), "\\\\ \n") cat("Male", sprintf(" & %5.3f", temp), "\\\\ \n") @ \end{tabular} $$ In the alternate model \code{y \textasciitilde sex + age2} the MVUE contrast is much simpler, namely (0, 1, 0,0,0,0,0), and can be read directly off the printout as $\beta/se(\beta)$. The computer's calculation of $(X'X)^{-1}$ has derived the ``complex'' MVUE weights for us without needing to lift a pencil. The Yates contrast, however, cannot be created from the coefficients of the simpler model at all. This observation holds in general: a contrast that is simple to write down in one coding may appear complicated in another, or not even be possible. The usual and more familiar coding for a two way model is \begin{equation} y_{ij} = \mu + \alpha_i + \beta_j + \gamma_{ij} \label{std} \end{equation} What do the Yates' estimates look like in this form? Let $e_i$ be the Yates estimate for row $i$ and $k$ the number of columns in the two way table of $\theta$ values. Then \begin{align*} e_i &= (1/k)\sum_{j=1}^k \theta_{ij} \\ &= \mu + \alpha_i + \sum_j \left(\beta_j + \gamma_{ij}\right)/k \end{align*} and the Yates test for row effect is \begin{align} 0 &= e_i - e_{i'} \quad \forall i,i' \nonumber \\ &= (\alpha_i - \alpha_{i'}) + (1/k)\sum_j(\gamma_{ij} - \gamma_{i'j}) \label{ycont} \end{align} Equation \eqref{std} is over determined and all computer programs add constraints in order to guarantee a unique solution. However those constraints are applied, however, equation \eqref{ycont} holds. The default in R is treatment contrasts, which use the first level of any factor as a reference level. Under this constraint the reference coefficients are set to zero, i.e., all coefficients of equations \eqref{std} and \eqref{ycont} above where $i=1$ or $j=1$. We have been computing the male - female contrast, corresponding to $i=2$ and $i'=1$ in equation \eqref{ycont}, and the Yates contrast for sex becomes $\alpha_2 + 1/5(\gamma_{22} +\gamma_{23} +\gamma_{24} +\gamma_{25})$. The code below verifies that this contrast plus the usual R fit replicates the results in table \ref{tab:allest}. <>= fit3 <- lm(flc ~ sex * age2, flchain) coef(fit3) contrast(c(0,1, 0,0,0,0, .2,.2,.2,.2), fit3) #Yates @ The usual constraint is SAS is to use the last level of any class variable as the reference group, i.e., all coefficients with $i=2$ or $j=5$ in equations \eqref{std} and \eqref{ycont} are set to zero. <>= options(contrasts=c("contr.SAS", "contr.poly")) sfit1 <- lm(flc ~ sex, flchain) sfit2 <- lm(flc ~ sex + age2, flchain) sfit3 <- lm(flc ~ sex * age2, flchain) contrast(c(0,-1, 0,0,0,0, -.2,-.2,-.2,-.2), sfit3) # Yates for SAS coding @ The appendix contains SAS code and output for the three models \code{sfit1, sfit2} and \code{sfit3} above. The \code{E3} option was added to the SAS model statements, which causes a symbolic form of the contrasts that were used for ``type III'' results to be included in the printout. Look down the column labeled ``SEX'' and you will see exactly the coefficients used just above, after a bit of SAS to English translation. \begin{itemize} \item The SAS printout is labeled per equation \eqref{std}, so L1= column 1 of the full $X$ matrix = intercept. L2 = column 2 = females, L3 = column 3 = males, L4= column 4 = age 50--59, etc. \item In the symbolic printout they act as though sum constraints were in force: the last column of age is labeled with a symbolic value that would cause the age coefficients to sum to zero. However, in actuality these coefficients are set to zero. The table of parameter estimates at the end of the printout reveals this; forced zeros have a blank for their standard error. \item When calculating the contrast one can of course skip over the zero coefficients, and the R functions do not include them in the coefficient vector. Remove all of these aliased rows from the SAS symbolic printout to get the actual contrast that is used; this will agree with my notation. \item The SAS printout corresponds to a female-male contrast and I have been using male-female for illustration. This changes the signs of the contrast coefficients but not the result. \end{itemize} The \code{estimate} statement in the SAS code required that all of the coefficients be listed, even the aliased ones (someone more proficient in SAS may know a way to avoid this and enter only the non-aliased values.) %A general principle is that a given hypothesis may be represented as %a simple contrast in one coding but be complex in another. %The unadjusted test is a trivial contrast in the sfit1 coding, but a %complex one in the sfit3 coding. %The Yates test cannot be expressed as a contrast using the sfit1 or sfit2 %coding, is simple and obvious in the cell means coding, and has %simple but non obvious coefficients in the sfit3 coding. %Que sera sera. So, how do we actually compute the Yates contrast in a computer program? We will take it as a give that no one wants to memorize contrast formulas. Appendix \ref{sect:coding} describes three algorithms for the computation. One of these three (NSTT) is completely unreliable, but is included because it is so often found in code. If one uses the sum constraints commonly found in textbooks, which corresponds to the \code{contr.sum} constraint in R and to \code{effect} constraints in SAS, and there are no missing cells, then the last term in equation \eqref{ycont} is zero and the simple contrast $\alpha_i =0$ will be equal to the Yates contrast for sex. I often see this method recommended on R help in response to the question of ``how to obtain type III'', computed either by use of the \code{drop1} command or the \code{Anova} function found within the car package, but said advice almost never mentions the need for this particular non-default setting of the contrasts option\footnote{The Companion to Applied Regression (car) package is designed to be used with the book of the same name by John Fox, and the book does clarify the need for sum constraints.}. When applied to other codings the results of this procedure can be surprising. <>= options(contrasts = c("contr.treatment", "contr.poly")) #R default fit3a <- lm(flc ~ sex * age2, flchain) options(contrasts = c("contr.SAS", "contr.poly")) fit3b <- lm(flc~ sex * age2, flchain) options(contrasts=c("contr.sum", "contr.poly")) fit3c <- lm(flc ~ sex * age2, flchain) # nstt <- c(0,1, rep(0,8)) #test only the sex coef = the NSTT method temp <- rbind(unlist(contrast(nstt, fit3a)), unlist(contrast(nstt, fit3b)), unlist(contrast(nstt, fit3c)))[,1:2] dimnames(temp) <- list(c("R", "SAS", "sum"), c("effect", "SS")) print(temp) # drop1(fit3a, .~.) @ For the case of a two level effect such as sex, the NSTT contrast under the default R coding is a comparison of males to females in the first age group \textbf{only}, and under the default SAS coding it is a comparison of males to females within the \textbf{last} age group. Due to this easy creation of a test statistic which has no relation to the global comparison one expects from the ``type 3'' label the acronym \emph{not safe type three}(NSTT) was chosen, ``not SAS'' and ``nonsense'' are alternate mnemonics. \subsection{Sums of squares and projections} \label{sect:anova} The most classic exposition of least squares is as a set of projections, each on to a smaller space. Computationally we represent this as a series of model fits, each fit summarized by the change from the prior fit in terms of residual sum of squares. <>= options(show.signif.stars = FALSE) #exhibit intelligence sfit0 <- lm(flc ~ 1, flchain) sfit1b <- lm(flc ~ age2, flchain) anova(sfit0, sfit1b, sfit2, sfit3) @ The second row is a test for the age effect. The third row of the above table summarizes the improvement in fit for the model with sex + age2 over the model with just age2, a test of ``sex, adjusted for age''. This test is completely identical to the minimum variance contrast, and is in fact the way in which that SS is normally obtained. The test for a sex effect, unadjusted for age, is identical to an anova table that compares the intercept-only fit to one with sex, i.e., the second line from a call to \code{anova(sfit0, sfit1)}. The anova table for a nested sequence of models $A$, $A+B$, $A + B +C$, \ldots has a simple interpretation, outside of contrasts or populations, as an improvement in fit. Did the variable(s) $B$ add significantly to the goodness of fit for a model with just $A$, was $C$ an important addition to a model that already includes $A$ and $B$? The assessment of improvement is based on the likelihood ratio test (LRT), and extends naturally to all other models based on likelihoods. The tests based on a target population (external, data population, or Yates) do not fit naturally into this approach, however. %Obtaining the Yates contrast using a sequential sums of squares approach %is possible but a bit contrived. %Our final fit in the table will be \code{sfit3}, but %the one prior to it needs to be from a constrained version of \code{sfit3}, %whose solution lies in the space spanned by the Yates contrast %$\beta_2 + \beta_7/5 + \beta_8/5 + \beta_9/5 + \beta_{10}/5 = 0$. %There is no simple way to write down an ordinary LS model equation that %will do this, and instead one must use one a program for constrained %linear regression; these are far less familiar. %There are many algorithms to fit a constrained linear regression, one is %to transform the problem as $X\beta = (XQ)(Q'\beta) = Z \phi$ %where $Q$ is an orthogonal transformation matrix. %If the first column of $Q$ is chosen as a scaled version of the Yates %contrast, then setting that contrast equal to zero is the same as %the constraint $\phi_1 =0$; it suffices to fit a model using all but the %first column of $Z$. \subsection{What is SAS type 3?} We are now in a position to fully describe the SAS sums of squares. \begin{itemize} \item Type 1 is the output of the ANOVA table, where terms are entered in the order specified in the model. \item Type 2 is the result of a two stage process \begin{enumerate} \item Order the terms by level: 0= intercept, 1= main effects, 2= 2 way interactions, \ldots. \item For terms of level k, print the MVUE contrast from a model that includes all terms of levels $0-k$. Each of these will be equivalent to the corresponding line of a sequential ANOVA table where the term in question was entered as the last one of its level. \end{enumerate} \item Type 3 and 4 are also a 2 stage process \begin{enumerate} \item Segregate the terms into those for which a Yates contrast can be formed versus those for which it can not. The second group includes the intercept, any continuous variables, and any factor (class) variables that do not participate in interactions with other class variables. \item For variables in the first group compute Yates contrasts. For those in the second group compute the type 2 results. \end{enumerate} \end{itemize} SAS has two different algorithms for computing the Yates contrast, which correspond to the \code{ATT} and \code{STT} options of the \code{yates} function. SAS describes the two contrast algorithms in their document ``The four types of estimable functions'' \cite{SASguide}, one of which defines type 3 and the other type 4. I found it very challenging to recreate their algorithm from this document. Historical knowledge of the underlying linear model algorithms used by SAS is a useful and almost necessary adjunct, as many of the steps in the document are side effects of their calculation. When there are missing cells, then it is not possible to compute a contrast that corresponds to a uniform distribution over the cells, and thus the standard Yates contrast is also not defined. The SAS type 3 and 4 algorithms still produce a value, however. What exactly this result ``means'' and whether it is a good idea has been the subject of lengthy debates which I will not explore here. Sometimes the type 3 and type 4 algorithms will agree but often do not when there are missing cells, which further muddies the waters. Thus we have 3 different tests: the MVUE comparison which will be close but not exactly equal to the data set population, Yates comparisons which correspond to a uniform reference population, and the SAS type 3 (STT) which prints out a chimeric blend of uniform population weighting for those factor variables that participate in interactions and the MVUE weighting for all the other terms. \subsection{Which estimate is best?} Deciding which estimate is the best is complicated. Unfortunately a lot of statistical textbooks emphasize the peculiar situation of balanced data with exactly the same number of subjects in each cell. Such data is \emph{extremely} peculiar if you work in medicine; in 30 years work and several hundred studies I have seen 2 instances. In this peculiar case the unadjusted, MVUE, empirical reference and Yates populations are all correspond to a uniform population and so give identical results. No thinking about which estimate is best is required. This has led many to avoid the above question, instead pining for that distant Eden where the meaning of ``row effect'' is perfectly unambiguous. But we are faced with real data and need to make a choice. The question has long been debated in depth by wiser heads than mine. In a companion paper to his presentation at the joint statistical meetings in 1992, Macnaughton \cite{Macnaughton92} lists 54 references to the topic between 1952 and 1991. Several discussion points recur: \begin{enumerate} \item Many take the sequential ANOVA table as primary, i.e., a set of nested models along with likelihood ratio tests (LRT), and decry all comparisons of ``main effects in the presence of interaction.'' Population weightings other than the LS one do not fit nicely into the nested framework. \item Others are distressed by the fact that the MVUE adjusting population is data dependent, so that one is ``never sure exactly what hypothesis being tested''. \item A few look at the contrast coefficients themselves, with a preference for simple patterns since they ``are interpretable''. \item No one approach works for all problems. Any author who proposes a uniform rule is quickly presented with counterexamples. \end{enumerate} Those in group 1 argue strongly against the Yates weighting and those in group 2 argue for the Yates contrast. Group 3 is somewhat inexplicable to me since any change in the choice of constraint type will change all the patterns. I fear that an opening phrase from the 1986 overview/review of Herr \cite{Herr86} is still apropos, ``In an attempt to understand how we have arrived at our present state of ignorance \ldots''. There are some cases where the Yates approach is clearly sensible, for instance a designed experiment which has become unbalanced due to a failed assay or other misadventure that has caused a few data points to be missing. There are cases such as the FLC data where the Yates contrast makes little sense at all --- the hypothetical population with equal numbers of 50 and 90 year olds is one that will never be seen--- so it is rather like speculating on the the potential covariate effect in dryads and centaurs. The most raucous debate has circled around the case of testing for a treatment effect in the presence of multiple enrolling centers. Do we give each patient equal weight (MVUE) or each center equal weight (Yates). A tongue-in-cheek but nevertheless excellent commentary on the subject is given by the old curmudgeon, aka Guernsey McPearson \cite{Senn1, Senn2}. A modern summary with focus on the clinical trials arena is found in chapter 14 of the textbook by Senn \cite{Senn07} I have found two papers particularly useful in thinking about this. Senn \cite{Senn00} points out the strong parallels between tests for main effects when there may be interactions and meta analyses, cross connecting these two approaches is illuminating. A classic reference is the 1978 paper by Aitkin \cite{Aitkin78}. This was read before the Royal Statistical Society and includes remarks by 10 discussants forming a who's who of statistical theory (F Yates, J Nelder, DR Cox, DF Andrews, KR Gabriel, \ldots). The summary of the paper states that ``It is shown that a standard method of analysis used in many ANOVA programs, equivalent to Yates method of weighted squares of means, may lead to inappropriate models''; the paper goes on to carefully show why no one method can work in all cases. Despite the long tradition among RSS discussants of first congratulating the speaker and then skewering every one their conclusions, not one defense of the always-Yates approach is raised! This includes the discussion by Yates himself, who protests that his original paper advocated the proposed approach with reservations, it's primary advantage being that the computations could be performed on a desk calculator. I have two primary problems with the SAS type 3 approach. The first and greatest is that their documentation recommends the method with no reference to this substantial and sophisticated literature discussing strengths and weaknesses of the Yates contrast. This represents a level of narcissism which is completely unprofessional. %Recommending the type III approach as best for all cases, as they do, has %caused actual harm. The second is that their documentation explains the method is a way that is almost impenetrably opaque. If this is the only documentation one has, there will not be 1 statistician in 20 who would be able to explain the actual biological hypothesis which is being addressed by a type 3 test. \section{Cox models} \subsection{Tests and contrasts} Adapting the Yates test to a Cox model is problematic from the start. First, what do we mean by a ``balanced population''? In survival data, the variance of the hazard ratio for each particular sex/age combination is proportional to the number of deaths in that cell rather than the number of subjects. Carrying this forward to the canonical problem of adjusting a treatment effect for enrolling center, does this lead to equal numbers of subjects or equal numbers of events? Two centers might have equal numbers of patients but different number of events because one initiated the study at a later time (less follow up per subject), or it might have the same follow up time but a lower death rate. Should we reweight in one case (which one), both, or neither? The second issue is that the per-cell hazard ratio estimates are no longer a minimally sufficient statistic, so underlying arguments about a reference population no longer directly translate into a contrast of the parameters. A third but more minor issue is that the three common forms of the test statistic --- Wald, score, and LRT --- are identical in a linear model but not for the Cox model, so which should we choose? To start, take a look at the overall data and compute the relative death rates for each age/sex cell. <>= options(contrasts= c("contr.treatment", "contr.poly")) # R default cfit0 <- coxph(Surv(futime, death) ~ interaction(sex, age2), flchain) cmean <- matrix(c(0, coef(cfit0)), nrow=2) cmean <- rbind(cmean, cmean[2,] - cmean[1,]) dimnames(cmean) <- list(c("F", "M", "M/F ratio"), dimnames(counts)[[2]]) signif(exp(cmean),3) @ Since the Cox model is a relative risk model all of the death rates are relative to one of the cells, in this case the 50--59 year old females has been arbitrarily chosen as the reference cell and so has a defined rate of 1.00. Death rates rise dramatically with age for both males and females (no surprise), with males always slightly ahead in the race to a coffin. The size of the disadvantage for males decreases in the last 2 decades, however. The possible ways to adjust for age in comparing the two sexes are \begin{enumerate} \item The likelihood ratio test. This is analogous to the sequential ANOVA table in a linear model, and has the strongest theoretical justification. \item A stratified Cox model, with age group as the stratification factor. This gives a more general and rigorous adjustment for age. Stratification on institution is a common approach in clinical trials. \item The Wald or score test for the sex coefficient, in a model that adjusts for age. This is analogous to Wald tests in the linear model, and is asymptotically equivalent the the LRT. \item The test from a reweighted model, using case weights. Results using this approach have been central to causal model literature, particularly adjustment for covariate imbalances in observational studies. (Also known as \emph{marginal structural models}). Adjustment to a uniform population is also possible. \item A Yates-like contrast in the Cox model coefficients. \begin{itemize} \item A reliable algorithm such as cell means coding. \item Unreliable approach such as the NSTT \end{itemize} \end{enumerate} I have listed these in order from the most to the least available justification, both in terms of practical experience and available theory. The two standard models are for sex alone, and sex after age. Likelihood ratio tests for these models are the natural analog to anova tables for the linear model, and are produced by the same R command. Here are results for the first three, along with the unadjusted model that contains sex only. <>= options(contrasts=c("contr.SAS", "contr.poly")) cfit1 <- coxph(Surv(futime, death) ~ sex, flchain) cfit2 <- coxph(Surv(futime, death) ~ age2 + sex, flchain) cfit3 <- coxph(Surv(futime, death) ~ sex + strata(age2), flchain) # Unadjusted summary(cfit1) # # LRT anova(cfit2) # # Stratified anova(cfit3) summary(cfit3) # # Wald test signif(summary(cfit2)$coefficients, 3) # anova(cfit1, cfit2) @ Without adjustment for age the LRT for sex is only \Sexpr{round(2*diff(cfit1$loglik),1)}, and after adjustment for %$ a it increases to \Sexpr{round(anova(cfit2)[3,2],2)}. Since females are older, not adjusting for age almost completely erases the evidence of their actual survival advantage. Results of the LRT are unchanged if we change to any of the other possible codings for the factor variables (not shown). Adjusting for age group using a stratified model gives almost identical results to the sequential LRT, in this case. The Wald tests for sex are equal to $[\beta/ se(\beta)]^2$ using the sex coefficient from the fits, \Sexpr{round(summary(cfit1)$coef[1,4]^2,2)} and \Sexpr{round(summary(cfit2)$coef[5,4]^2,2)} for the unadjusted and adjusted models, respectively. Unlike a linear model they are not exactly equal to the anova table results based on the log-likelihood, but tell the same story. Now consider weighted models, with both empirical and uniform distributions as the target age distribution. The fits require use of a robust variance, since we are approaching it via a survey sampling computation. The tapply function creates a per-subject index into the case weight table created earlier. <>= wtindx <- with(flchain, tapply(death, list(sex, age2))) cfitpop <- coxph(Surv(futime, death) ~ sex, flchain, robust=TRUE, weight = (casewt[,,3])[wtindx]) cfityates <- coxph(Surv(futime, death) ~ sex, flchain, robust=TRUE, weight = (casewt[,,4])[wtindx]) # # Glue it into a table for viewing # tfun <- function(fit, indx=1) { c(fit$coef[indx], sqrt(fit$var[indx,indx])) } coxp <- rbind(tfun(cfit1), tfun(cfit2,5), tfun(cfitpop), tfun(cfityates)) dimnames(coxp) <- list(c("Unadjusted", "Additive", "Empirical Population", "Uniform Population"), c("Effect", "se(effect)")) signif(coxp,3) @ The population estimates based on reweighting lie somewhere between the unadjusted and the sequential results. We expect that balancing to the empirical population will give a solution that is similar to the age + sex model, in the same way that the close but not identical to the MVUE estimate in a linear model. Balancing to a hypothetical population with equal numbers in each age group yields a substantially smaller estimate of effect. since it gives large weights to the oldest age group, where in this data set the male/female difference is smallest. Last, look at constructed contrasts from a cell means model. We can either fit this using the interaction, or apply the previous contrast matrix to the coefficients found above. Since the ``intercept'' of a Cox model is absorbed into the baseline hazard our contrast matrix will have one less column. <<>>= cfit4 <- coxph(Surv(futime, death) ~ sex * age2, flchain) # Uniform population contrast ysex <- c(0,-1, 0,0,0,0, -.2,-.2,-.2,-.2) #Yates for sex, SAS coding contrast(ysex[-1], cfit4) # Verify using cell means coding cfit4b <- coxph(Surv(futime, death) ~ interaction(sex, age2), flchain) temp <- matrix(c(0, coef(cfit4b)),2) # the female 50-59 is reference diff(rowMeans(temp)) #direct estimate of the Yates # temp2 <- rbind(temp, temp[2,] - temp[1,]) dimnames(temp2) <- list(c('female', 'male', 'difference'), levels(age2)) round(temp2, 3) # # # NSTT contrast contrast(c(1,0,0,0,0,0,0,0,0), cfit4) @ In the case of a two level covariate such as sex, the NSTT algorithm plus the SAS coding yields an estimate and test for a difference in sex for the \emph{first} age group; the proper contrast is an average. Since it gives more weight to the larger ages, where the sex effect is smallest, the Yates-like contrast is smaller than the result from an additive model \code{cfit2}. Nevertheless, this contrast and the sequential test are more similar for the survival outcome than for the linear models. This is due to the fact that the variances of the individual hazards for each sex/age combination are proportional to the number of deaths in that cell rather than the number of subjects per cell. A table of the number of deaths is not as imbalanced as the table of subject counts, and so the Yates and MLE ``populations'' are not as far apart as they were for the linear regression. There are fewer subjects at the higher ages but they die more frequently. Why is the Yates-like contrast so different than the result of creating a uniform age distribution using case weights followed by an MLE estimate? Again, the MLE estimate has death counts as the effective weights; the case-weighted uniform population has smaller weights for the youngest age group and that group also has the lowest death rate, resulting in lower influence for that group and an estimate shrunken towards the 90+ difference of \Sexpr{round(temp2[3,5], 3)}. All told, for survival models adjustment to a uniform population is a slippery target. \subsection{SAS phreg results} Now for the main event: what does SAS do? First, for the simple case of an additive model the SAS results are identical to those shown above. The coefficients, variances and log-likelihoods for cfit2 are identical to the phreg output for an additive model, as found in the appendix. As would be expected from the linear models case, the ``type III'' results for the additive model are simply the Wald tests for the fit, repackaged with a new label. Now look at the model that contains interactions. We originally surmised that a contrast calculation would be the most likely way in which the phreg code would implement type 3, as it is the easiest to integrate with existing code. Results are shown in the last SAS fit of the appendix. Comparing these results of the SAS printout labeled as ``Type III Wald'' to the contrasts calculated above shows that phreg is using the NSTT method. This is a bit of a shock. All of the SAS literature on type III emphasizes the care with which they form the calculation so as to always produce a Yates contrast (or in the case of missing cells a Yates-like one), and there was no hint in the documentation that phreg does anything different. As a double check direct contrast statements corresponding to the Yates and NSTT contrasts were added to the SAS code, and give confirmatory results. A further run which forced sum constraints by adding \code{'/ effect'} to the SAS class statement (not shown) restored the correct Yates contrast, as expected. As a final check, look at the NSTT version of the LRT, which corresponds to simply dropping the sex column from the $X$ matrix. <>= xmat4 <- model.matrix(cfit4) cfit4b <- coxph(Surv(futime, death) ~ xmat4[,-1], flchain) anova(cfit4b, cfit4) @ This agrees with the LR ``type 3'' test of the phreg printout. \subsection{Conclusion} Overall, both rebalanced estimates and coefficient contrasts are interesting exercises for the Cox model, but their actual utility is unclear. It is difficult to make a global optimality argument for either one, particularly in comparison to the sequential tests which have the entire weight of likelihood theory as a justification. Case reweighted estimates do play a key role when attempting to adjust for non-random treatment assignment, as found in the literature for causal analysis and marginal structural models; a topic and literature far too extensive and nuanced for discussion in this note. No special role is apparent, at least to this author, for regular or even sporadic use of a Yates contrast in survival models. The addition of such a feature and label to the SAS phreg package is a statistical calamity, one that knowledgeable and conscientious statistical practitioners will likely have to fight for the rest of their careers. In the common case of a treatment comparison, adjusted for enrolling center, the default ``type III'' printout from phreg corresponds to a comparison of treatments within the last center; the only contribution of the remainder of the data set is to help define the baseline hazard function and the effect of any continuous adjusters that happen to be in the model. The quadruple whammy of a third rate implementation (the NSTT), defaults that lead to a useless and misleading result, no documentation of the actual computation that is being done, and irrational reverence for the type III label conspire to make this a particularly unfortunate event. \appendix \section{Computing the Yates estimate} \label{sect:coding} We will take it as a given that no one wants to memorize contrast formulas, and so we need a way to compute Yates contrasts automatically in a computer program. The most direct method is to encode the original fit in terms of the cell means, as has been done throughout this report. The Yates contrast is then simply an average of estimates across the appropriate margin. However, we normally will want to solve the linear or Cox model fit in a more standard coding and then compute the Yates contrast after the fact. Note that any population re norming requires estimates of the cell means, whether they were explicit parameters or not, i.e., the model fit must include interaction terms. Here are three algorithms for this post-hoc computation. All of them depend, directly or indirectly, on the breakdown found earlier in equation \eqref{std}. \begin{align} y_{ij} &= \mu + \alpha_i + \beta_j + \gamma_{ij} + \epsilon \label{a1} \\ &= \theta_{ij} + \epsilon \label{a2}\\ \theta_{ij} &= \mu + \alpha_i + \beta_j + \gamma_{ij} \label{a3} \\ \end{align} Equation \eqref{a1} is the standard form from our linear models textbooks, equation \eqref{a2} is the cell means form, and \eqref{a3} is the result of matching them together. Using this equivalence a Yates test for row effects will be \begin{align} 0 &= e_i - e_{i'} \quad \forall i,i' \nonumber \\ &= (\alpha_i - \alpha_{i'}) + (1/k)\sum_j(\gamma_{ij} - \gamma_{i'j}) \label{ycont2} \end{align} where the subscripts $i$ and $i'$ range over the rows and $k$ is the number of columns. To illustrate the methods we will use 3 small data sets defined below. All are unbalanced. The second data set removes the aD observation and so has a zero cell, the third removes the diagonal and has 3 missing cells. <>= data1 <- data.frame(y = rep(1:6, length=20), x1 = factor(letters[rep(1:3, length=20)]), x2 = factor(LETTERS[rep(1:4, length=10)]), x3 = 1:20) data1$x1[19] <- 'c' data1 <- data1[order(data1$x1, data1$x2),] row.names(data1) <- NULL with(data1, table(x1,x2)) # data2 -- single missing cell indx <- with(data1, x1=='a' & x2=='D') data2 <- data1[!indx,] #data3 -- missing the diagonal data3 <- data1[as.numeric(data1$x1) != as.numeric(data1$x2),] @ \subsection{NSTT method} The first calculation method is based on a simple observation. If we impose the standard sums constraint on equation \eqref{a1} which is often found in textbooks (but nowhere else) of $\sum_i \alpha_i = \sum_j \beta_j = 0$, $\sum_i\gamma_{ij} =0 \; \forall j$ and $\sum_j \gamma_{ij} = 0 \; \forall i$, then the last term in equation \eqref{ycont2} is identically 0. Thus the Yates contrast corresponds exactly to a test of $\alpha=0$. In R we can choose this coding by using the \code{contr.sum} option. This approach has the appearance of simplicity: we can do an ordinary test for row effects within an interaction model. Here is R code that is often proposed for ``type III'' computation, which is based on the same process. <<>>= options(contrasts=c("contr.sum", "contr.poly")) fit1 <- lm(y ~ x1*x2, data1) drop1(fit1, .~.) @ The problem with this approach is that it depends critically on use of the sum constraints. If we apply the same code after fitting the data set under the more usual constraints a completely different value ensues. <<>>= options(contrasts=c("contr.SAS", "contr.poly")) fit2 <- lm(y ~ x1*x2, data1) drop1(fit2, .~.) options(contrasts=c("contr.treatment", "contr.poly")) fit3 <- lm(y ~ x1*x2, data1) drop1(fit3, .~.) @ Both common choices of contrasts give a different answer than contr.sum, and both are useless. I thus refer to this as the Not Safe Type Three (NSTT) algorithm, ``not SAS type three'' and ``nonsense type three'' are two other sensible expansions. This approach should NEVER be used in practice. \subsection{ATT} The key idea of the averaging approach (Averaged Type Three) is to directly evaluate equation \eqref{ycont2}. The first step of the computation is shown below <>= X <- model.matrix(fit2) ux <- unique(X) ux indx <- rep(1:3, c(4,4,4)) effects <- t(rowsum(ux, indx)/4) # turn sideways to fit the paper better effects yates <- effects[,-1] - effects[,1] yates @ The data set ux has 12 rows, one for each of the 12 unique x*x2 combinations. Because data1 was sorted, the first 4 rows correspond to x=1, the next 4 to x=2 and the next to x=3 which is useful for illustration but has no impact on the computation. The average of rows 1-4 (column 1 of \code{effects} above) is the estimated average response for subjects with x1=a, assuming a uniform distribution over the 12 cells. Any two differences between the three effects is an equivalent basis for computing the Yates contrast. We can verify that the resulting estimates correspond to a uniform target population by directly examining the case weights for the estimate. Each of them gives a total weight of 1/4 to each level of x2. Each element of $\beta\beta$ is a weighted average of the data, revealed by the rows of the matrix $(X'X)^{-1}X'$. The estimate are a weighted sum of the coefficients, so are also a weighted average of the $y$ values. <<>>= wt <- solve(t(X) %*% X, t(X)) # twelve rows (one per coef), n columns casewt <- t(effects) %*% wt # case weights for the three "row efffects" for (i in 1:3) print(tapply(casewt[i,], data1$x2, sum)) @ \subsection{STT} The SAS type III method takes a different approach, based on a a dependency matrix $D$. Start by writing the $X$ matrix for the problem using all of the parameters in equation \eqref{a1}. For our flc example this will have columns for intercept (1), sex (2), age group (5) and the age group by sex interaction (10) = 18 columns. Now define the lower triangular square matrix $D$ such that \begin{itemize} \item If the $i$th column of $X$ can be written as a linear combination of columns 1 through $i-1$, then row $i$ of $D$ contains that linear combination and $D_{ii}=0$. \item If the $i$th column is not linearly dependent on earlier ones then $D_{ii}=1$ and $D_{ij}=0$ for all $j \ne i$. \end{itemize} Columns of $D$ that correspond to linearly dependent columns of $X$ will be identically zero and can be discarded (or not) at this point. The result of this operation replicates table 12.2 in the SAS reference \cite{SASguide} labeled ``the form of estimable functions''. To obtain the Yates contrasts for an effect replace the appropriate columns of $D$ with the residuals from a regression on all columns to the right of it. Simple inspection shows that the columns of $D$ corresponding to any given effect will already be orthogonal to other effects in $D$ \emph{except} those for interactions that contain it; so the regression does not have to include all columns to the right. It is easy to demonstrate that this gives the uniform population contrast (Yates) for a large number of data sets, but I have not yet constructed a proof. (I suspect it could be approached using the Rao-Blackwell theorem.) \subsection{Bystanders} What about a model that has a extra predictor, such as \code{x3} in our example data and in the fit below? <<>>= fit4 <- lm(y ~ x1*x2 + x3, data=data1) @ The standard approach is to ignore this variable when setting up ``type III'' tests: the contrast for \code{x1} will be the same as it was in the prior model, with a 0 row in the middle for the x3 coefficient. \subsection{Missing cells} When there are combinations of factors with 0 subjects in that group, it is not possible to create a uniform population via reweighting of either subjects or parameters. There is thus no Yates contrast corresponding to the hypothetical population of interest. For that matter, adjustment to any fixed population is no longer possible, such as the US 2000 reference, unless groups are pooled so as to remove any counts of zero, and even then the estimate could be problematic due to extreme weights. This fact does not stop each of the above 3 algorithms from executing and producing a number. This raises two further issues. First, what does that number \emph{mean}? Much ink has been spilled on this subject, but I personally have never been able to come to grips with a satisfactory explanation and so have nothing to offer on the topic. I am reluctant to use such estimates. The second issue is that the computational algorithms become more fragile. \begin{itemize} \item The NSTT algorithm is a disaster in waiting, so no more needs to be said about situations where its behavior may be even worse. \item When fitting the original model, there will be one or more NA coefficients due to the linear dependencies that arise. A natural extension of the ATT method is to leave these out of the sums when computing each average. However, there are data sets for which the particular set of coefficients returned as missing will depend on the order in which variables were listed in the model statement, which in turn will change the ATT result. \item For the STT method, our statement that certain other columns in $D$ will be orthogonal to the chosen effect is no longer true. To match SAS, the orthogonalization step above should include only those effects further to the right that contain the chosen effect (the one we are constructing a contrast vector for). As a side effect, this makes the STT result invariant to the order of the variables in the model statement. \end{itemize} \section{SAS computations} The following code was executed in version 9.3 of SAS. \begin{verbatim} options ls=70; libname save "sasdata"; title "Sex only"; proc glm data=save.flc; class sex; model flc = sex; title "Sex only"; proc glm data=save.flc; class sex age2; model flc = age2 sex /solution E1 E2 E3; title "Second fit, no interaction"; proc glm data=save.flc; class sex age2; model flc = sex age2 sex*age2/solution E1 E2 E3; estimate 'yates' sex 1 -1 sex*age2 .2 .2 .2 .2 .2 -.2 -.2 -.2 -.2 -.2; title "Third fit, interaction"; proc phreg data=save.flc; class sex age2; model futime * death(0) = sex age2/ ties=efron; title "Phreg fit, sex and age, additive"; proc phreg data=save.flc; class sex age2; model futime * death(0) = sex age2 sex*age2 / ties=efron type3(all); estimate 'Yates sex' sex 1 sex*age2 .2 .2 .2 .2; contrast 'NSTT sex ' sex 1 ; contrast 'NSTT age' age2 1 0 0 0 , age2 0 1 0 0 , age2 0 0 1 0 , age2 0 0 0 1; title "Phreg fit, sex and age with interaction"; proc phreg data=save.flc; class sex age2/ param=effect; model futime * death(0) = sex age2 sex*age2 / ties=efron; title "Phreg, using effect coding"; \end{verbatim} The SAS output is voluminous, covering over a dozen pages. A subset is extracted below, leaving out portions that are unimportant to our comparison. First the GLM model for sex only. There are no differences between type 1 and type 3 output for this model. \small \begin{verbatim} ... Number of Observations Read 7874 Number of Observations Used 7874 ... Dependent Variable: flc Sum of Source DF Squares Mean Square F Value Model 1 142.19306 142.19306 42.27 Error 7872 26481.86345 3.36406 Corrected Total 7873 26624.05652 \end{verbatim} \normalsize The second fit with sex and then age. \small \begin{verbatim} Type I Estimable Functions -----------------Coefficients------------------ Effect age2 sex Intercept 0 0 age2 1 L2 0 age2 2 L3 0 age2 3 L4 0 age2 4 L5 0 age2 5 -L2-L3-L4-L5 0 sex F -0.2571*L2-0.2576*L3-0.1941*L4-0.0844*L5 L7 sex M 0.2571*L2+0.2576*L3+0.1941*L4+0.0844*L5 -L7 Type II Estimable Functions ---Coefficients---- Effect age2 sex Intercept 0 0 age2 1 L2 0 age2 2 L3 0 age2 3 L4 0 age2 4 L5 0 age2 5 -L2-L3-L4-L5 0 sex F 0 L7 sex M 0 -L7 Type III Estimable Functions ---Coefficients---- Effect age2 sex Intercept 0 0 age2 1 L2 0 age2 2 L3 0 age2 3 L4 0 age2 4 L5 0 age2 5 -L2-L3-L4-L5 0 sex F 0 L7 sex M 0 -L7 Dependent Variable: flc Sum of Source DF Squares Mean Square F Value Model 5 2212.13649 442.42730 142.60 Error 7868 24411.92003 3.10268 Corrected Total 7873 26624.05652 Source DF Type I SS Mean Square F Value age2 4 1929.642183 482.410546 155.48 sex 1 282.494304 282.494304 91.05 Source DF Type II SS Mean Square F Value age2 4 2069.943424 517.485856 166.79 sex 1 282.494304 282.494304 91.05 Source DF Type III SS Mean Square F Value age2 4 2069.943424 517.485856 166.79 sex 1 282.494304 282.494304 91.05 Standard Parameter Estimate Error t Value Pr > |t| Intercept 5.503757546 B 0.17553667 31.35 <.0001 age2 1 -2.587424744 B 0.17584961 -14.71 <.0001 age2 2 -2.249164537 B 0.17684133 -12.72 <.0001 age2 3 -1.770342603 B 0.17834253 -9.93 <.0001 age2 4 -1.082104827 B 0.18584656 -5.82 <.0001 age2 5 0.000000000 B sex F -0.383454133 B 0.04018624 -9.54 <.0001 sex M 0.000000000 B \end{verbatim} \normalsize The third linear models fit, containing interactions. For first portion I have trimmed off long printout on the right, i.e. the estimable functions for the age2*sex effect since they are not of interest. \small \begin{verbatim} Type I Estimable Functions --------------------Coefficients-------- Effect sex age2 Intercept 0 0 sex F L2 0 sex M -L2 0 age2 1 -0.0499*L2 L4 age2 2 -0.0373*L2 L5 age2 3 0.0269*L2 L6 age2 4 0.0482*L2 L7 age2 5 0.0121*L2 -L4-L5-L6-L7 sex*age2 F 1 0.3786*L2 0.6271*L4+0.1056*L5+0.0796*L6+0.0346*L7 sex*age2 F 2 0.2791*L2 0.0778*L4+0.5992*L5+0.0587*L6+0.0255*L7 sex*age2 F 3 0.2182*L2 0.0527*L4+0.0528*L5+0.6245*L6+0.0173*L7 sex*age2 F 4 0.1055*L2 0.0188*L4+0.0188*L5+0.0142*L6+0.7006*L7 sex*age2 F 5 0.0186*L2 -0.7764*L4-0.7764*L5-0.777*L6-0.7781*L7 sex*age2 M 1 -0.4285*L2 0.3729*L4-0.1056*L5-0.0796*L6-0.0346*L7 sex*age2 M 2 -0.3164*L2 -0.0778*L4+0.4008*L5-0.0587*L6-0.0255*L7 sex*age2 M 3 -0.1913*L2 -0.0527*L4-0.0528*L5+0.3755*L6-0.0173*L7 sex*age2 M 4 -0.0573*L2 -0.0188*L4-0.0188*L5-0.0142*L6+0.2994*L7 sex*age2 M 5 -0.0065*L2 -0.2236*L4-0.2236*L5-0.223*L6-0.2219*L7 Type II Estimable Functions --------------------Coefficients--------------------- Effect sex age2 Intercept 0 0 sex F L2 0 sex M -L2 0 age2 1 0 L4 age2 2 0 L5 age2 3 0 L6 age2 4 0 L7 age2 5 0 -L4-L5-L6-L7 sex*age2 F 1 0.41*L2 0.6271*L4+0.1056*L5+0.0796*L6+0.0346*L7 sex*age2 F 2 0.3025*L2 0.0778*L4+0.5992*L5+0.0587*L6+0.0255*L7 sex*age2 F 3 0.2051*L2 0.0527*L4+0.0528*L5+0.6245*L6+0.0173*L7 sex*age2 F 4 0.073*L2 0.0188*L4+0.0188*L5+0.0142*L6+0.7006*L7 sex*age2 F 5 0.0093*L2 -0.7764*L4-0.7764*L5-0.777*L6-0.7781*L7 sex*age2 M 1 -0.41*L2 0.3729*L4-0.1056*L5-0.0796*L6-0.0346*L7 sex*age2 M 2 -0.3025*L2 -0.0778*L4+0.4008*L5-0.0587*L6-0.0255*L7 sex*age2 M 3 -0.2051*L2 -0.0527*L4-0.0528*L5+0.3755*L6-0.0173*L7 sex*age2 M 4 -0.073*L2 -0.0188*L4-0.0188*L5-0.0142*L6+0.2994*L7 sex*age2 M 5 -0.0093*L2 -0.2236*L4-0.2236*L5-0.223*L6-0.2219*L7 Type III Estimable Functions ---------------------Coefficients--------------------- Effect sex age2 sex*age2 Intercept 0 0 0 sex F L2 0 0 sex M -L2 0 0 age2 1 0 L4 0 age2 2 0 L5 0 age2 3 0 L6 0 age2 4 0 L7 0 age2 5 0 -L4-L5-L6-L7 0 sex*age2 F 1 0.2*L2 0.5*L4 L9 sex*age2 F 2 0.2*L2 0.5*L5 L10 sex*age2 F 3 0.2*L2 0.5*L6 L11 sex*age2 F 4 0.2*L2 0.5*L7 L12 sex*age2 F 5 0.2*L2 -0.5*L4-0.5*L5-0.5*L6-0.5*L7 -L9-L10-L11-L12 sex*age2 M 1 -0.2*L2 0.5*L4 -L9 sex*age2 M 2 -0.2*L2 0.5*L5 -L10 sex*age2 M 3 -0.2*L2 0.5*L6 -L11 sex*age2 M 4 -0.2*L2 0.5*L7 -L12 sex*age2 M 5 -0.2*L2 -0.5*L4-0.5*L5-0.5*L6-0.5*L7 L9+L10+L11+L12 Source DF Type I SS Mean Square F Value sex 1 142.193063 142.193063 45.97 age2 4 2069.943424 517.485856 167.30 sex*age2 4 87.218363 21.804591 7.05 Source DF Type II SS Mean Square F Value sex 1 282.494304 282.494304 91.33 age2 4 2069.943424 517.485856 167.30 sex*age2 4 87.218363 21.804591 7.05 Source DF Type III SS Mean Square F Value sex 1 126.961986 126.961986 41.05 age2 4 1999.446491 499.861623 161.60 sex*age2 4 87.218363 21.804591 7.05 Standard Parameter Estimate Error t Value Pr > |t| yates -0.58972607 0.09204824 -6.41 <.0001 Standard Parameter Estimate Error t Value Pr > |t| Intercept 6.003043478 B 0.36672295 16.37 <.0001 sex F -1.024512614 B 0.41553944 -2.47 0.0137 sex M 0.000000000 B age2 1 -3.176876326 B 0.36950532 -8.60 <.0001 age2 2 -2.787597918 B 0.37048599 -7.52 <.0001 age2 3 -2.088127335 B 0.37292760 -5.60 <.0001 age2 4 -1.353746449 B 0.38703805 -3.50 0.0005 age2 5 0.000000000 B sex*age2 F 1 0.813889663 B 0.42023749 1.94 0.0528 sex*age2 F 2 0.716160958 B 0.42189464 1.70 0.0896 sex*age2 F 3 0.330651265 B 0.42487846 0.78 0.4365 sex*age2 F 4 0.313230835 B 0.44127621 0.71 0.4778 sex*age2 F 5 0.000000000 B sex*age2 M 1 0.000000000 B sex*age2 M 2 0.000000000 B sex*age2 M 3 0.000000000 B sex*age2 M 4 0.000000000 B sex*age2 M 5 0.000000000 B \end{verbatim} \normalsize The phreg printout for the additive model with age and sex. \small \begin{verbatim} Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 2357.5239 5 <.0001 Score 3823.3905 5 <.0001 Wald 2374.5250 5 <.0001 Type 3 Tests Wald Effect DF Chi-Square Pr > ChiSq sex 1 69.9646 <.0001 age2 4 2374.5211 <.0001 Analysis of Maximum Likelihood Estimates Parameter Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq sex F 1 -0.36617 0.04378 69.9646 <.0001 age2 1 1 -4.18209 0.12180 1179.0289 <.0001 age2 2 1 -3.23859 0.11418 804.5068 <.0001 age2 3 1 -2.17521 0.10963 393.6524 <.0001 age2 4 1 -1.15226 0.11072 108.3077 <.0001 \end{verbatim} \normalsize The model with age*sex interaction. \small \begin{verbatim} Model Fit Statistics Without With Criterion Covariates Covariates -2 LOG L 37736.900 35374.050 AIC 37736.900 35392.050 SBC 37736.900 35443.188 Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio 2362.8497 9 <.0001 Score 3873.5113 9 <.0001 Wald 2357.9498 9 <.0001 Type 3 Tests LR Statistics Effect DF Chi-Square Pr > ChiSq sex 1 0.4607 0.4973 age2 4 932.1371 <.0001 sex*age2 4 5.3258 0.2555 Score Statistics Effect DF Chi-Square Pr > ChiSq sex 1 0.4757 0.4904 age2 4 1506.8699 <.0001 sex*age2 4 5.2516 0.2624 Wald Statistics Effect DF Chi-Square Pr > ChiSq sex 1 0.4833 0.4869 age2 4 964.6007 <.0001 sex*age2 4 5.2322 0.2643 Analysis of Maximum Likelihood Estimates Parameter Standard Parameter DF Estimate Error Chi-Square sex F 1 -0.16537 0.23789 0.4833 age2 1 1 -4.02699 0.22585 317.9171 age2 2 1 -3.04796 0.21843 194.7187 age2 3 1 -1.99577 0.21577 85.5504 age2 4 1 -1.10659 0.22256 24.7216 sex*age2 F 1 1 -0.21121 0.26896 0.6167 sex*age2 F 2 1 -0.29334 0.25518 1.3214 sex*age2 F 3 1 -0.25663 0.24829 1.0684 sex*age2 F 4 1 -0.04339 0.25527 0.0289 Contrast DF Chi-Square Pr > ChiSq NSTT sex 1 0.4833 0.4869 NSTT age 4 964.6007 <.0001 Likelihood Ratio Statistics for Type 1 Analysis LR Source -2 Log L DF Chi-Square Pr > ChiSq (Without Covariates) 37736.8997 sex 37733.0932 1 3.8066 0.0511 age2 35379.3758 4 2353.7173 <.0001 sex*age2 35374.0501 4 5.3258 0.2555 Standard Label Estimate Error z Value Pr > |z| Yates -0.3263 0.06149 -5.31 <.0001 \end{verbatim} \normalsize \begin{thebibliography}{9} \bibitem{Aitkin78} M. Aitkin (1978). The analysis of unbalanced cross classifications (with discussion). \emph{J Royal Stat Soc A} 141:195-223. \bibitem{Dispenzieri12} A. Dispenzieri, J. Katzmann, R. Kyle, D. Larson, T. Therneau, C. Colby, R. Clark, .G Mead, S. Kumar, L..J Melton III and S.V. Rajkumar (2012). Use of monoclonal serum immunoglobulin free light chains to predict overall survival in the general population, \emph{Mayo Clinic Proc} 87:512--523. \bibitem{Herr86} D. G. Herr (1986). On the History of ANOVA in Unbalanced, Factorial Designs: The First 30 Years. \emph{Amer Statistician} 40:265-270. \bibitem{Kyle06} R. Kyle, T. Therneau, S.V. Rajkumar, D. Larson, M. Plevak, J. Offord, A. Dispenzieri, J. Katzmann, and L.J. Melton, III (2006), Prevalence of monoclonal gammopathy of undetermined significance, \emph{New England J Medicine} 354:1362--1369. \bibitem{Macnaughton92} D. B. Macnaughton (1992). Which sum of squares are best in an unbalanced analysis of variance. www.matstat.com/ss. \bibitem{Nelder77} J. Nelder (1977). A reformulation of linear models (with discussion). \emph{J Royal Stat Soc A} 140:48--76. \bibitem{SASguide} SAS Institute Inc. (2008), The four types of estimable functions. SAS/STAT 9.2 User's Guide, chapter 15. \bibitem{Searle71} S. R. Searle, \emph{Linear Models}, Wiley, New York, 1971. \bibitem{Senn1} S. Senn. Multi-centre trials and the finally decisive argument. www.senns.demon.co.uk/wprose.html\#FDA. \bibitem{Senn2} S. Senn. Good mixed centre practice. www.senns.demon.co.uk/wprose.html\#Mixed. \bibitem{Senn07} S. Senn. Statistical Issues in Drug Development, Wiley, New York, 2007. \bibitem{Senn00} S. Senn. The many modes of meta. Drug Information J 34:535-549, 2000. \bibitem{Therneau00} T. M. Therneau and P. M. Grambsch, \emph{Modeling Survival Data: Extending the Cox Model}, Springer-Verlag, New York, 2000. \bibitem{Yates34} F. Yates (1934). The analysis of multiple classifications with unequal numbers in the different classes. \emph{J Am Stat Assoc}, 29:51--66. \end{thebibliography} \end{document} survival/vignettes/timedep.Rnw0000644000175100001440000015252613043667011016306 0ustar hornikusers\documentclass{article} \usepackage{amsmath} \usepackage{Sweave} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} \newcommand{\code}[1]{\texttt{#1}} %\VignetteIndexEntry{Using Time Dependent Covariates} \title{Using Time Dependent Covariates and Time Dependent Coefficients in the Cox Model} \author{Terry Therneau \and Cynthia Crowson \and Elizabeth Atkinson\\ \emph{Mayo Clinic}} \begin{document} \maketitle \SweaveOpts{prefix.string=compete,width=6,height=4} \setkeys{Gin}{width=\textwidth} \SweaveOpts{keep.source=TRUE} <>= options(width=60, continue=" ") makefig <- function(file, top=1, right=1, left=4) { pdf(file, width=9.5, height=7, pointsize=18) par(mar=c(4, left, top, right) +.1) } library(survival) @ \section{Introduction} This vignette covers 3 different but interrelated concepts: \begin{itemize} \item An introduction to time dependent covariates, along with some of the most common mistakes. \item Tools for creating time-dependent covariates, or rather the data sets used to encode them. \item Time dependent coefficients. \end{itemize} \section{Time dependent covariates} One of the strengths of the Cox model is its ability to encompass covariates that change over time. The practical reason that time-dependent covariates work is based on the underlying way in which the Cox model works: at each event time the program compares the current covariate values of the subject who had the event to the current values of all others who were at risk at that time. One can think of it as a lottery model, where at each death time there is a drawing to decide which subject ``wins'' the event. Each subject's risk score $\exp(X\beta)$ determines how likely they are to win, e.g., how many ``tickets'' they have purchased for the drawing. The model tries to assign a risk score to each subject that best predicts the outcome of each drawing based on \begin{itemize} \item The risk set: which subjects are present for each event; the set of those able to ``win the prize''. \item The covariate values of each subject just prior to the event time. \end{itemize} The model has a theoretical foundation in martingale theory, a mathematical construct which arose out of the study of games of chance. A key underlying condition for a martingale like game is that present actions depend only on the past. The decision of whether to play (is one in the risk set or not) and the size of a bet (covariates) can depend in any way on prior bets and patterns of won/lost, but cannot look into the future. If this holds then multiple properties can be proven about the resulting process. A simple way to code time-dependent covariates uses intervals of time. Consider a subject with follow-up from time 0 to death at 185 days, and assume that we have a time dependent covariate (creatinine) that was measured at day 0, 90 and 120 with values of .9, 1.5, and 1.2 mg/dl. A way to encode that data for the computer is to break the subject's time into 3 time intervals 0-90, 90-120, 120-185, with one row of data for each interval. The data might look like the following <>= tdata <- data.frame(subject=c(5,5,5), time1=c(0,90, 120), time2 = c(90, 120, 185), death=c(0,0,1), creatinine=c(0.9, 1.5, 1.2)) tdata @ We read this as stating that over the interval from 0 to 90 the creatinine for subject ``5'' was 0.9 (last known level), and that this interval did not end in a death. The underlying code treats intervals as open on the left and closed on the right, e.g. the creatinine on exactly day 90 is 0.9. One way to think of this is that all changes for a given day (covariates or status) are recorded at the end of the day. The key rule for time dependent covariates in a Cox model is simple and essentially the same as that for gambling: \emph{you cannot look into the future}. A covariate may change in any way based on past data or outcomes, but it may not reach forward in time. In the above simple data set this means that we cannot add a linear interpolation between the creatinine values 0.9 and 1.5 to get a predicted value of 1.1 on day 100; on day 100 the later value of 1.5 has not yet been seen. A an example consider a recent analysis from the Mayo Clinic study of aging (MCSA), a study which enrolled a stratified random sample from the population of Olmsted County and then has followed them forward in time. The occurrence of mild cognitive impairment (MCI), dementia, and death are all of interest. The paper starts out with a table comparing baseline covariates for those who never progress to MCI versus those who ever did, there is also a table of baseline covariates versus survival. Both of these are fine: if you think in terms of an R formula they could be written with future outcomes on the left hand side of the formula and past information on the right. A table that compared the survival of those who did or did not progress to MCI, however, would be invalid. It corresponds to a model with a future occurrence on both sides of the equation. One of the more well known examples of this error is analysis by treatment response: at the end of a trial a survival curve is made comparing those who had an early response to treatment (shrinkage of tumor, lowering of cholesterol, or whatever) to those who did not, and it discovered that responders have a better curve. A Cox model fit to the same data will demonstrate a strong ``significant'' effect. The problem arises because any early deaths, those that occur before response can be assessed, will all be assigned to the non-responder group, even deaths that have nothing to do with the condition under study. Below is a simple example based on the advanced lung cancer data set. Assume that subjects came in monthly for 12 cycles of treatment, and randomly declare a ``response'' for 5\% of the subjects at each visit. <>= set.seed(1953) # a good year nvisit <- floor(pmin(lung$time/30.5, 12)) response <- rbinom(nrow(lung), nvisit, .05) > 0 badfit <- survfit(Surv(time/365.25, status) ~ response, data=lung) plot(badfit, mark.time=FALSE, lty=1:2, xlab="Years post diagnosis", ylab="Survival") legend(1.5, .85, c("Responders", "Non-responders"), lty=2:1, bty='n') @ What is most surprising about this error is the \emph{size} of the false effect that is produced. A Cox model using the above data reports a hazard ratio of 1.9 fold with a p-value of less than 1 in 1000. The alarm about this incorrect approach has been sounded often \cite{Anderson83, Buyse96, Suissa08} but the analysis is routinely re-discovered. A slightly subtler form of the error is discussed in Redmond et al \cite{Redmond83}. The exploration was motivated by a flawed analysis presented in Bonadonna et. al \cite{Bref} which looked at the effect of total dose. breast cancer chemotherapy patients were divided into three groups based on whether the patient eventually received $>85$\%, 65--85\% or $<65$\% of the dose planned at the start of their treatment. Per the above, this approach leads to a severe bias since early deaths do not finish all their cycles of chemotherapy and hence by definition get a lower dose. A proportional hazards model using total dose received shows a very strong effect for dose, so much so that it could encourage a treating physician to defer necessary dose reductions in response to treatment toxicity. Redmond looked at a variant of this: create a variable $p$ for each subject which is the fraction of the target dose \emph{up to} the last entry for that subject. A subject who died after recieving only 6 weeks of a planned 12 week regimen could still score 100\%. This looks like it should cure the bias issue, but as it turns out it leads to bias in the other direction. The reason is that dose reductions due to toxicity occur more often in the later cycles of treatment, and thus living longer leads to smaller values of $p$. A proportional hazards regression fit to $p$ implies that a smaller dose is protective! The proper approach is to code the predictor as a time-dependent covariate. For treatment response this will be a variable that starts at 0 for all subjects and is recoded to 1 only when the response occurs. For dose it would measure cumulative dose to date. There are many variations on the error: interpolation of the values of a laboratory test linearly between observation times, removing subjects who do not finish the treatment plan, imputing the date of an adverse event as midway between observation times, etc. Using future data will often generate large positive or negative bias in the coefficients, but sometimes it generates little bias at all. It is nearly impossible to predict a priori which of these will occur in any given data set. Using such a covariate is similar to jogging across a Los Angeles freeway: disaster is not guaranteed --- but it is likely. The most common way to encode time-dependent covariates is to use the (start, stop] form of the model. <>= fit <- coxph(Surv(time1, time2, status) ~ age + creatinine, data=mydata) @ In data set \code{mydata} a patient might have the following observations \begin{center} \begin{tabular}{ccccccc} subject & time1 & time2 & status & age & creatinine & \ldots \\ \hline 1 & 0 & 15 & 0 & 25 & 1.3 \\ 1 & 15& 46 & 0 & 25 & 1.5 \\ 1 & 46& 73 & 0 & 25 & 1.4 \\ 1 & 73& 100& 1 & 25 & 1.6 \\ \end{tabular} \end{center} In this case the variable \code{age} = age at entry to the study stays the same from line to line, while the value of creatinine varies and is treated as 1.3 over the interval $(0, 15]$, 1.5 over $(15, 46]$, etc. The intervals are open on the left and closed on the right, which means that the creatinine is taken to be 1.3 on day 15. The status variable describes whether or not each interval ends in an event. One common question with this data setup is whether we need to worry about correlated data, since a given subject has multiple observations. The answer is no, we do not. The reason is that this representation is simply a programming trick. The likelihood equations at any time point use only one copy of any subject, the program picks out the correct row of data at each time. There two exceptions to this rule: \begin{itemize} \item When subjects have multiple events, then the rows for the events are correlated within subject and a cluster variance is needed. \item When a subject appears in overlapping intervals. This however is almost always a data error, since it corresponds to two copies of the subject being present in the same strata at the same time, e.g., she could meet herself at a party. \end{itemize} A subject can be at risk in multiple strata at the same time, however. This corresponds to being simultaneously at risk for two distinct outcomes. \section{Building time-dependent sets with tmerge} \subsection{The function} A useful function for building data sets is \code{tmerge}, which is part of the survival library. The idea is to build up a time dependent data set one endpoint at at time. The primary arguments are \begin{itemize} \item data1: the base data set that will be added onto \item data2: the source for new information \item id: the subject identifier in the new data \item \ldots: additional arguments that add variables to the data set \item tstart, tstop: used to set the time range for each subject \item options \end{itemize} The created data set has three new variables (at least), which are \code{id}, \code{tstart} and \code{tstop}. The key part of the call are the ``\ldots'' arguments which each can be one of four types: tdc() and cumtdc() add a time dependent variable, event() and cumevent() add a new endpoint. In the survival routines time intervals are open on the left and closed on the right, i.e., (tstart, tstop]. Time dependent covariates apply from the start of an interval and events occur at the end of an interval. If a data set already had intervals of (0,10] and (10, 14] a new time dependent covariate or event at time 8 would lead to three intervals of (0,8], (8,10], and (10,14]; the new time-dependent covariate value would be added to the second interval, a new event would be added to the first one. The basic form of the function is <>= newdata <- tmerge(data1, data2, id, newvar=tdc(time, value), ...) @ Where \code{data1} is the starting data set and additions to the data are taken from \code{data2}. The idea behind the function is that each addition will be ``slipped in'' to the original data in the same way that one would slide a new card into an existing deck of cards. It is a complex function, and we illustrate it below with a set of examples that sequentially reveal its features. \subsection{CGD data set} Chronic granulomatous disease (CGD) is a heterogeneous group of uncommon inherited disorders characterized by recurrent pyogenic infections that usually begin early in life and may lead to death in childhood. In 1986, Genentech, Inc. conducted a randomized, double-blind, placebo-controlled trial in 128 CGD patients who received Genentech's humanized interferon gamma (rIFN-g) or placebo three %' times daily for a year. Data were collected on all serious infections until the end of followup, which occurred before day 400 for most patients. One patient was taken off on the day of his last infection; all others have some followup after their last episode. Below are the first 10 observations, see the help page for \texttt{cgd0} for the full list of variable names. The last few columns contain the duration of follow-up for the subject followed by infection times. Subject 1 was followed for 414 days and had infections on days 219 and 373, subject 2 had 7 infections and subject 3 had none. \small \begin{verbatim} 1 204 082888 1 2 12 147.0 62.0 2 2 2 2 414 219 373 2 204 082888 0 1 15 159.0 47.5 2 2 1 2 439 8 26 152 241 249 322 350 3 204 082988 1 1 19 171.0 72.7 1 2 1 2 382 4 204 091388 1 1 12 142.0 34.0 1 2 1 2 388 5 238 092888 0 1 17 162.5 52.7 1 2 1 1 383 246 253 6 245 093088 1 2 44 153.3 45.0 2 2 2 2 364 7 245 093088 0 1 22 175.0 59.7 1 2 1 2 364 292 8 245 093088 1 1 7 111.0 17.4 1 2 1 2 363 9 238 100488 0 1 27 176.0 82.8 2 2 1 1 349 294 10 238 100488 1 1 5 113.0 19.5 1 2 1 1 371 \end{verbatim} \normalsize The data set is included as \code{cgd0} in the survival library. Here is the R printout of the first four subjects. <<>>= cgd0[1:4,] @ We want to turn this into a data set that has survival in a counting process form. \begin{itemize} \item Each row of the resulting data set represents a time interval (time1, time2] which is open on the left and closed on the right. Covariate values for that row are the covariate values that apply over that interval. \item The event variable for each row $i$ is 1 if the time interval ends with an event and 0 otherwise. \end{itemize} We don't need variables etime1--etime7 in the final data set, so they are left out of the data1 argument in the first call. <>= dim(cgd0) newcgd <- tmerge(data1=cgd0[, 1:13], data2=cgd0, id=id, tstop=futime) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime1)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime2)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime3)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime4)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime5)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime6)) newcgd <- tmerge(newcgd, cgd0, id=id, infect = event(etime7)) newcgd <- tmerge(newcgd, newcgd, id, enum=cumtdc(tstart)) dim(newcgd) newcgd[1:5,c(1, 4:6, 13:17)] attr(newcgd, "tcount") coxph(Surv(tstart, tstop, infect) ~ treat + inherit + steroids + + cluster(id), newcgd) @ These lines show the canonical way to use tmerge: each call adds one more bit of information to the data set. \begin{itemize} \item The first call sets the \emph{time range} for each subject to be from 0 (default) to last follow-up. If a later call tried to add an event outside that range, at time = -2 say, that addition would be ignored. The range can be set explicitly by using the tstop and (optional) tstart arguments, or implicitly as will be done in the heart transplant example below. This first result has \Sexpr{nrow(cgd0)} rows, the same number as \code{cgd0}. \item Each additional call then adds either an endpoint or a covariate, splitting individual rows of the input in two as necessary. An \code{event} or \code{cumevent} directive adds events, while a \code{tdc} or \code{cumtdc} one adds a time dependent covariate. Events happen at the ends of intervals and time-dependent covariates change at the start of an interval. \item Additions from \code{data2} with a missing time value are ignored. \item The result of \code{tmerge} is a data frame with a few extra attributes. One of these, tcount, is designed to help visualize the process and was printed out after the last step above. Assume that a subject already had 3 intervals of (2,5), (5,10) and (14,40). A new event added at time 1 would be ``early'' while one at time 50 is after any interval and would be recorded as ``late''. An event at time 3 is within an interval, one at 5 is on the border of two intervals, one at 14 is at the leading edge of an interval, one at time 10 in on the trailing edge and at time 11 is in a gap. In this data set all new additions fell strictly within prior intervals. We also see that etime6 and etime7 each added only a single event to the data. \item If two observations in data2 for a single person share exactly the same time, the created value will be the later contribution for tdc() or event() calls, cumtdc() and cumevent() will add. The ``tied'' column tells how often this happened; in some data sets this behavior might not be desired and one would need to break the ties before calling tmerge. \item The last tmerge call adds a simple time-dependent variable \code{enum} which is a running observation count for each subject. This can often be a useful variable in later models or processing, e.g. \code{enum==1} selects off the first row for each subject. \item The extra attributes of the data frame are ephemeral: they will be lost as soon as any further manipulation is done. This is intentional. \item One can verify that the resulting data set is equivalent to \code{cgd}, a (start, stop] version of the CGD data in the survival library which had been created by hand several years earlier. \end{itemize} The \code{tmerge} function processes arguments sequentially, and the above example can be rewritten as below. There is no computational advantage of one form versus the other. <>= test <- tmerge(cgd0[, 1:13], cgd0, id=id, tstop=futime, infect = event(etime1), infect= event(etime2), infect = event(etime3), infect= event(etime4), infect = event(etime5), infect= event(etime6), infect = event(etime7)) test <- tmerge(test, test, id= id, enum = cumtdc(tstart)) all.equal(newcgd, test) @ \subsection{Stanford heart transplant} The \code{jasa} data set contains information from the Stanford heart transplant study, in the form that it appeared in the paper of Crowley and Hu \cite{Crowley77}. The data set has one line per subject which contains the baseline covariates along with dates of enrollment, transplant, and death or last follow-up. We want to create \code{transplant} as a time dependent covariate. As is often the case with real data, this data set contains a few anomalies that need to be dealt with when setting up an analysis data set. \begin{enumerate} \item One subject died on the day of entry. However (0,0) is an illegal time interval for the \code{coxph} routine. It suffices to have them die on day 0.5. An alternative is to add 1 day to everyone's follow-up, e.g., subject 2 who enrolled on Jan 2 1968 and died on Jan 7 would be credited with 6 days. (This is what Kalbfleisch and Prentice do in their textbook.) The result of the final \code{coxph} call is the same from either strategy. \item A subject transplanted on day 10 is considered to have been on medical treatment for days 1--10 and as transplanted starting on day 11. That is, except for patient 38 who died on the same day as their procedure. They should be treated as a transplant death; the problem is resolved by moving this transplant back .5 day. \item The treatment coefficients in table 6.1 of the definitive analysis found in Kalbfleisch and Prentice \cite{Kalbfleisch02} will only be obtained if covariates are defined in precisely the same way, since their models include interactions. (Table 5.2 in the original edition of the book). For age this is (age in days)/ 365.25 - 48 years, and for year of enrollment it is the number of years since the start of the study: (entry date - 1967/10/1)/365.25. (Until I figured this out I would get occasional ``why is coxph giving the wrong answers'' emails.) \end{enumerate} Since time is in days the fractional time of 0.5 could be any value between 0 and 1, our choice will not affect the results. <>= jasa$subject <- 1:nrow(jasa) #we need an identifier variable tdata <- with(jasa, data.frame(subject = subject, futime= pmax(.5, fu.date - accept.dt), txtime= ifelse(tx.date== fu.date, (tx.date -accept.dt) -.5, (tx.date - accept.dt)), fustat = fustat )) sdata <- tmerge(jasa, tdata, id=subject, death = event(futime, fustat), trt = tdc(txtime), options= list(idname="subject")) attr(sdata, "tcount") sdata$age <- sdata$age -48 sdata$year <- as.numeric(sdata$accept.dt - as.Date("1967-10-01"))/365.25 # model 6 of the table in K&P coxph(Surv(tstart, tstop, death) ~ age*trt + surgery + year, data= sdata, ties="breslow") @ This example shows a special case for the \code{tmerge} function that is quite common: if the first created variable is an event then the time range for each subject is inferred to be from 0 to the event time: explicit \code{tstop} and \code{tstart} arguments are not required. It also makes use of a two argument form of \code{event}. Each of the \code{event}, \code{cumevent}, \code{tdc} and \code{cumtdc} functions may have a second argument, which if present will be used as the value for the event code or time dependent covariate. If this second argument is not present a value of 1 is used. If a created variable is not already in data1, the starting value \emph{before} the first definition of that variable is a NA for a \code{tdc} or \code{cumtdc} call that has two arguments and 0 in all other cases. If the variable being created is already a part of data1, then our updates make changes to that variable. Be careful of this. This feature is what allowed for the \code{infection} indicator to be build up incrementally in the cgd example above, but quite surprising results can occur when you think a new variable is being created de novo but its name is already in use. For example, if we name the new variable `transplant' in the third line of \code{sdata} above it collides with an existing variable in the \code{jasa} data set; the result is to not create a time-dependent transplant variable at all. (The author made this mistake himself when creating this vignette, and then spent several hours searching the tmerge code for an error that wasn't there.) The \code{tcount} table for the above fit shows all the deaths at the trailing edge of their interval, which is expected since the time of death or last follow-up was used to define each subject's interval of risk. Two of the transplants happened on day 0 and are listed as occurring on the leading edge of the first follow-up interval for the subject. The other 67 transplants were strictly within the (0, last follow up) interval of each subject. \subsection{PBC data} The \code{pbc} data set contains baseline data and follow-up status for a set of subjects with primary biliary cirrhosis, while the \code{pbcseq} data set contains repeated laboratory values for those subjects. The first data set contains data on 312 subjects in a clinical trial plus 106 that agreed to be followed off protocol, the second data set has data only on the trial subjects. <>= temp <- subset(pbc, id <= 312, select=c(id:sex, stage)) # baseline pbc2 <- tmerge(temp, temp, id=id, death = event(time, status)) #set range pbc2 <- tmerge(pbc2, pbcseq, id=id, ascites = tdc(day, ascites), bili = tdc(day, bili), albumin = tdc(day, albumin), protime = tdc(day, protime), alk.phos = tdc(day, alk.phos)) fit1 <- coxph(Surv(time, status==2) ~ log(bili) + log(protime), pbc) fit2 <- coxph(Surv(tstart, tstop, death==2) ~ log(bili) + log(protime), pbc2) rbind('baseline fit' = coef(fit1), 'time dependent' = coef(fit2)) @ We start the build with a baseline data set that has a subset of the variables. This is due to my own frugality --- I happen to like data sets that are more trim. It is not a requirement of the tmerge function, however, and a user is certainly free to skip the first step above and build \code{pbc2} directly from data set \code{pbc}. The coefficients of bilirubin and prothrombin time are somewhat larger in the time-dependent analysis than the fit using only baseline values. In this autoimmune disease there is steady progression of liver damage, accompanied by a steady rise in these two markers of dysfunction. The baseline analysis captures patients' disease status at the start, the time-dependent analysis is able to account for those who progress more quickly. In the pbc data set the status variable is 0= censored, 1= liver transplant and 2= death; the above analyses were models of time to death, censoring at transplant. (At the time of the PBC study liver transplantation was still in its infancy and it is fair to view the 19/312 subjects who received the procedure as a random sample. In the modern era there are far more waiting recipients than organs and available livers are directed to those patients who illness is most dire; censoring at transplant would not lead to an interpretable result.) By default \code{tmerge} ignores any updates from \code{data2} that have a missing value for either the time or the value. In the pbcseq data set there are several observations with a missing alkaline phosphotase value. A consequence of this behavior is that the pbc2 data set effectively uses ``last value carried forward'' values for alk.phos, replacing those missing values. Subject 6 for instance has a total follow-up of 2503, and alk.phos values of 682 and NA on days 1492 and 2453, respectively; in the final data set it is coded 682 from day 1492 until last follow up. One can change this default by adding \code{options=list(na.rm=FALSE)} to the second call above, in which case the alkaline phosphotase value over the interval (2453, 2503] will become missing. Any \code{tdc} calls with a missing time are still ignored, independent of the na.rm value, since we would not know where to insert them. <<>>= attr(pbc2, "tcount") @ <>= #grab a couple of numbers for the paragraph below atemp <- attr(pbc2, "tcount")[2:3,] @ The tcount results are interesting. For the first addition of ascites we have \Sexpr{atemp[1, 'leading']} observations on a leading edge of follow up, which is all of the baseline lab values at time 0, and \Sexpr{atemp[1, 'within']} further additions within the subjects' follow-up interval. The latter cause a new break point to be added at each of these intermediate laboratory dates, for subsequent additions these \Sexpr{atemp[1, 'within']} times lie on a boundary of two intervals. Another \Sexpr{atemp[1, 'late']} non-missing alkaline phosphotase values occurred after the last follow-up date of the pbc data set and are ignored. Bilirubin is missing on no subjects, so it's addition creates a few more unique break points in the follow-up, namely those clinical visits for which the ascites value was missing. The data for the pbcseq data set was assembled at a later calendar time than the primary data set. Since having lab test results is a certain marker that the patient is still alive, would a better analysis have used this test information to extend the last follow-up date for these \Sexpr{atemp[2,'late']} ``late'' subjects with a later laboratory date? Not necessarily. Odd things happen in survival analysis when risk sets are extended piecemeal. A basic tenet of the Cox model is that if someone is marked as being ``at risk'' over some interval $(s, t)$, this means that ``if they had had an event over that interval, we would have recorded it.'' Say someone ended their initial follow-up time at 3000 days and then had a lab test at 3350 days (subjects returned about once a year). If we only extend the time of those who had a test, then saying that this subject was at risk during the interval (3000, 3350) is false: if they had died in that interval, they would not have had the lab test and would not obtained the extension, nor would their death have been updated in the original \code{pbc} data set. The cutoff rule of \code{tmerge} is purposefully conservative to avoid creating such anomalies. In the case of the PBC data set this author happens to know that active follow-up \emph{was} continued for all subjects, both those that did and did not return for further laboratory tests. This updated follow-up information is included in the pbcseq data and could have been used to set a wider time range. Such is not always the case, however. Automatic additions to a data set via electronic systems can be particularly troublesome. One case from the author's experience involved a study of patient outcomes after organ transplant. Cases were actively followed up for 3 years, at which time priorities shifted and the clerical staff responsible for the active follow-up were reassigned. Automatic updates from a state death index continued to accumulate, however. A Kaplan-Meier curve computed at 5 years showed the remarkable result of a 3 year survival of .9 followed by a precipitous drop to 0 at 5 years! This is because there was, by definition, 100\% mortality in all those subjects with more than 3 years of supposed follow-up. \subsection{Time delay and other options} The \code{options} argument to the tmerge routine is a list with one or more of the following five elements, listed below along with their default values. \begin{itemize} \item idname = 'id' \item tstartname = 'tstart' \item tstopname = 'tstop' \item na.rm = TRUE \item delay = 0 \end{itemize} The first three of these are the variable names that will be used for the identifier, start, and stop variables which are added to the output data set. They only need to be specified one time within a series of tmerge calls in order to effect a change. The na.rm option has been discussed above; it affects tdc() and cumtdc() directives within a single tmerge call. The delay option causes any tdc or cumtdc action in the tmerge call to be delayed by a fixed amount. The final two tmerge calls below are \emph{almost} identical in their action: <>= temp <- subset(pbc, id <= 312, select=c(id:sex, stage)) pbc2 <- tmerge(temp, temp, id=id, death = event(time, status)) pbc2a <- tmerge(pbc2, pbcseq, id=id, ascites = tdc(day, ascites), bili = tdc(day, bili), options= list(delay=14)) pbc2b <- tmerge(pbc2, pbcseq, id=id, ascites = tdc(day+14, ascites), bili = tdc(day+14, bili)) @ The difference between \code{pbc2a} and \code{pbc2b} is that the first call does not defer baseline values for each subject, i.e., any value with a time that is on or before the the subject's first time point, as that will introduce intervals with a missing value into the result. The more important question is \emph{why} one would wish to delay or lag a time dependent covariate. One reason is to check for cases of reverse causality. It is sometimes the case that a covariate measured soon before death is not a predictor of death but rather is simply a marker for an event that is already in progress. A simple example would the the time dependent covariate ``have called the family for a final visit''. A less obvious one from the author's experience occurs when a clinical visit spans more than one day, the endpoint is progression, and one or more laboratory results that were used to define ``progression'' get recorded in the data set 1-2 days before the progression event. (They were perhaps pulled automatically from a laboratory information system). One then ends up with the tautology of a test value predicting its own result. Even more subtle biases can occur via coding errors. For any data set containing constructed time-dependent covariates, it has become the author's practice to re-run the analyses after adding a 7-14 day lag to key variables. When the results show a substantial change, and this is not infrequent, understanding why this occurred is an critical step. Even if there is not an actual error, one has to question the value of a covariate that can predict death within the next week but fails for a longer horizon. \subsection{Cumulative events} The action of the \code{cumevent} operator is different than \code{cumtdc} in several ways. Say that we have a subject with outcomes of one type at times 5, 10, and 15 and another type at times 6 and 15, with a follow-up interval of 0 to 20. For illustration I'll call the first event 'asthma' and the second 'IBD' (a disease flare in inflammatory bowel disease). A resulting data set would have the following form: \begin{center} \begin{tabular}{rcccc} &\multicolumn{2}{c}{cumtdc} & \multicolumn{2}{c}{cumevent} \\ interval & asthma & IBD & asthma & IBD \\ \hline (0, 5] & 0 &0 & 1 & 0 \\ (5, 6] & 1 &0 & 0 & 1 \\ (6, 10]& 1 &1 & 2 & 0 \\ (10, 15] & 2& 1& 3 & 2 \\ (15, 20] & 3& 2& 0 & 0 \end{tabular} \end{center} Events happen at the ends of an interval and time-dependent covariates change the following intervals. More importantly, time-dependent covariates persist while events do not, a \code{cumevent} action simply changes the label attached to an event. \subsubsection{REP} The motivating case for \code{tmerge} came from a particular problem: the Rochester Epidemiology Project has tracked all subjects living in Olmsted County, Minnesota, from 1965 to the present. For an investigation of cumulative comorbidity we had three data sets \begin{itemize} \item base: demographic data such as sex and birth date \item timeline: one or more rows for each subject containing age intervals during which they were a resident of the county. The important variables are id, age1 and age2; each (age1, age2) pair marks an interval of residence. Disjoint intervals are not uncommon. \item outcome: one row for the first occurrence of each outcome of interest. The outcomes were 20 comorbid conditions as defined by a particular research initiative from the National Institutes of Health. \end{itemize} The structure for building the data is shown below. (The data for this example unfortunately cannot be included with the survival library so the code is shown but not executed.) <>= newd <- tmerge(data1=base, data2=timeline, id=repid, tstart=age1, tstop=age2, options(id="repid")) newd <- tmerge(newd, outcome, id=repid, mcount = cumtdc(age)) newd <- tmerge(newd, subset(outcome, event='diabetes'), diabetes= tdc(age)) newd <- tmerge(newd, subset(outcome, event='arthritis'), arthritis= tdc(age)) @ The first call to tmerge adds the time line for each observation to the baseline data. For this first call both data1 and data2 must contain a copy of the id variable (here \code{repid}), and data1 is constrained to have only a single line for each id value. (Subjects have a single baseline.) Each subsequent call adds a new variable to the data set. The second line creates a covariate which is a cumulative count of the number of comorbidities thus far for each subject. The third line creates a time dependent covariate (tdc) which will be 0 until the age of diabetes and is 1 thereafter, the fourth line creates a time dependent variable for the presence of arthritis. Time dependent covariates that occur before the start of a subject's follow-up interval or during a gap in time do not generate a new time point, but they do set the value of that covariate for future times. Events that occur in a gap are not counted. The rationale is that during a subject's time within the county we would like the variable ``prior diagnosis of diabetes'' to be accurate, even if that diagnosis occurred during a prior period when the subject was not a resident. For events outside of the time line, we have no way to know who the appropriate comparison group is, and so must ignore those events. (Formally, the risk set would be the set of all non-residents who, if they were to have had an event at the same age, we would find out about it because they will later move to the county, have a medical encounter here, and have that event written into the ``prior conditions'' section of their medical record.) \section{Time dependent coefficients} Time dependent covariates and time dependent coefficients are two different extensions of a Cox model, as shown in the two equations below. \begin{align} \lambda(t) &= \lambda_0(t) e^{\beta X(t)} \label{tdcovar} \\ \lambda(t) &= \lambda_0(t) e^{\beta(t) X} \label{tdbeta} \end{align} Equation \eqref{tdcovar} is a time dependent covariate, a commonly used and well understood usage. Equation \eqref{tdbeta} has a time dependent coefficient. These models are much less common, but represent one way to deal with non-proportional hazards -- the proportional hazard assumption is precisely that the coefficient does not change over time: $\beta(t) = c$. The \code{cox.zph} function will plot an estimate of $\beta(t)$ for a study and is used to diagnose and understand non-proportional hazards. Here for example is a test case using the veterans cancer data. <>= options(show.signif.stars = FALSE) # display user intelligence vfit <- coxph(Surv(time, status) ~ trt + prior + karno, veteran) vfit quantile(veteran$karno) zp <- cox.zph(vfit, transform= function(time) log(time +20)) zp plot(zp[3]) # a plot for the 3rd variable in the fit abline(0,0, col=2) abline(h= vfit$coef[3], col=3, lwd=2, lty=2) @ Karnofsky score is a very important predictor, but its effect is not constant over time as shown by both the test and the plot. Early on it has a large negative effect: the risk of someone at the first quartile is approximately exp(35*.03377) = 3.2 fold times that of someone at the third quartile, but by 200 days this has waned and is not much different from zero. One explanation is that, in this very acute illness, any measure that is over 6 months old is no longer relevant. The proportional hazards model estimates an average hazard over time, the value of which is shown by the dashed horizontal line. The use of an average hazard is often reasonable, the proportional hazards assumption is after all never precisely true. In this case, however, the departure is quite large and a time dependent coefficient is a more useful summary of the actual state. The cox.zph plot is excellent for diagnosis but does not, however, produce a formal fit of $\beta(t)$. What if we want to fit the model? \subsection{Step functions} One of the simplest extensions is a step function for $\beta(t)$, i.e., different coefficients over different time intervals. An easy way to do this is to use the \code{survSplit} function to break the data set into time dependent parts. We will arbitrarily divide the veteran's data into 3 epochs of the first 3 months, 3-6 months, and greater than 6 months. <>= vet2 <- survSplit(Surv(time, status) ~ ., data= veteran, cut=c(90, 180), episode= "tgroup", id="id") vet2[1:7, c("id", "tstart", "time", "status", "tgroup", "age", "karno")] @ The first subject died at 72 days, his data is unchanged. The second and third subjects contribute time to each of the three intervals. <>= vfit2 <- coxph(Surv(tstart, time, status) ~ trt + prior + karno:strata(tgroup), data=vet2) vfit2 cox.zph(vfit2) @ A fit to the revised data shows that the effect of baseline Karnofsky score is essentially limited to the first two months. The \code{cox.zph} function shows no further time dependent effect of Karnofsky score. This last is of course no surprise, since we used the original graph to pick the cut points. A ``test'' that the coefficients for the three intervals are different will be biased by this sequential process and should be viewed with caution. Survival curves post fit require a little more care. The default curve uses the mean covariate values, which is always problematic and completely useless in this case. Look at the set of saved means for the model: <>= vfit2$means @ The default curve will be for someone on treatment arm \Sexpr{round(vfit2$means[1], 2)}, %$ which applies to no one, and a single set of ``blended'' values of the Karnofsky score, each times the three Karnofsky coefficients. This is easily rectified by creating a new data set with time intervals. <>= quantile(veteran$karno) cdata <- data.frame(tstart= rep(c(0,30,60), 2), time = rep(c(30,60, 100), 2), status= rep(0,6), #necessary, but ignored tgroup= rep(1:3, 2), trt = rep(1,6), prior= rep(0,6), karno= rep(c(40, 75), each=3), curve= rep(1:2, each=3)) cdata sfit <- survfit(vfit2, newdata=cdata, id=curve) km <- survfit(Surv(time, status) ~ I(karno>60), veteran) plot(km, xmax=120, col=1:2, lwd=2, xlab="Days from enrollment", ylab="Survival") lines(sfit, col=1:2, lty=2, lwd=2) @ In the new data set the \code{tgroup} variable correctly tracks time intervals. The default behavior for survival curves based on a coxph model is to create one curve for each line in the input data; the \code{id} option causes it to use a set of lines for each curve. Karnofsky scores at the 25th and 75th percentiles roughly represent the average score for the lower half of the subjects and that for the upper half, respectively, and are plotted over the top of the Kaplan-Meier curves for those below and above the median. At 30 days the Cox model curves essentially become parallel. \subsection{Continuous time-dependent coefficients} If $\beta(t)$ is assumed to have a simple functional form we can fool an ordinary Cox model program in to doing the fit. The particular form $\beta(t) = a + b\log(t)$ has for instance often been assumed. Then $\beta(t) x = ax + b \log(t) x = ax + b z$ for the special time dependent covariate $z = \log(t) x$. The time scale for the \code{cox.zph} plot used further above of $\log(t + 20)$ was chosen to make the first 200 days of the plot roughly linear. Per the figure this simple linear model does not fit over the entire range, but we will forge ahead and use it as an example anyway. (After all, most who fit the log(t) form have not bothered to even look at a plot.) An obvious but incorrect approach is <>= vfit3 <- coxph(Surv(time, status) ~ trt + prior + karno + I(karno * log(time + 20)), data=veteran) @ This mistake has been made often enough the the \code{coxph} routine has been updated to print an error message for such attempts. The issue is that the above code does not actually create a time dependent covariate, rather it creates a time-static value for each subject based on their value for the covariate \code{time}; no differently than if we had constructed the variable outside of a \code{coxph} call. This variable most definitely breaks the rule about not looking into the future, and one would quickly find the circularity: large values of \code{time} predict long survival, because long survival leads to large values for \code{time}. A true time-dependent covariate can be constructed using the \emph{time-transform} functionality of coxph. <>= vfit3 <- coxph(Surv(time, status) ~ trt + prior + karno + tt(karno), data=veteran, tt = function(x, t, ...) x * log(t+20)) vfit3 @ The time dependent coefficient is estimated to be $\beta(t) =$ \Sexpr{round(coef(vfit3)[3], 3)} + \Sexpr{round(coef(vfit3)[4], 3)} * log(t + 20). We can add said line to the \code{cox.zph} plot. Not surprisingly, the result is rather too high for time $>$ 200 and underestimates the initial slope. Still the fit is better than a horizontal line, as confirmed by the p-value for the slope term in \code{vfit3}. (The p-value for that term from cox.zph is nearly identical, as it must be, since the tests in cox.zph are for a linear effect on the chosen time scale.) <>= plot(zp[3]) abline(coef(vfit3)[3:4], col=2) @ This same coding dichotomy exists in SAS phreg, by the way. Adding \code{time} to the right hand side of the model statement will create the time-fixed (incorrect) variable, while a programming statement within phreg that uses \code{time} as a variable will generate time-dependent objects. The error is less likely there because phreg's model statement has no equivalent to the \code{I()} function, i.e., you cannot simply write ``log(time)'' on the right hand side. \section{Predictable time-dependent covariates} Occasionally one has a time-dependent covariate whose values in the future are predictable. The most obvious of these is patient age, occasionally this may also be true for the cumulative dose of a drug. If age is entered as a linear term in the model, then the effect of changing age can be ignored in a Cox model, due to the structure of the partial likelihood. Assume that subject $i$ has an event at time $t_i$, with other subject $j \in R_i$ at risk at that time, with $a$ denoting age. The partial likelihood term is \begin{equation*} \frac{e^{\beta * a_i}}{\sum_{j \in R_i} e^{\beta* a_j}} = \frac{e^{\beta * (a_i + t_i)}}{\sum_{j \in R_i} e^{\beta* (a_j + t_i)}} \end{equation*} We see that using time-dependent age (the right hand version) or age at baseline (left hand), the partial likelihood term is identical since $\exp(\beta t_i)$ cancels out of the fraction. However, if the effect of age on risk is \emph{non-linear}, this cancellation does not occur. Since age changes continuously, we would in theory need a very large data set to completely capture the effect, an interval per day to match the usual resolution for death times. In practice this level of resolution is not necessary; though we all grow older, risk does not increase so rapidly that we need to know our age to the day! One method to create a time-changing covariate is to use the \emph{time-transform} feature of coxph. Below is an example using the pbc data set. The longest follow-up time in that data set is over 13 years, follow-up time is in days, and we might worry that the intermediate data set would be huge. The program only needs the value of the time dependent covariate(s) for each subject at the times of events, however, so the maximum number of rows in the intermediate data set is the number of subjects times the number of unique event times. <>= pfit1 <- coxph(Surv(time, status==2) ~ log(bili) + ascites + age, pbc) pfit2 <- coxph(Surv(time, status==2) ~ log(bili) + ascites + tt(age), data=pbc, tt=function(x, t, ...) { age <- x + t/365.25 cbind(age=age, age2= (age-50)^2, age3= (age-50)^3) }) pfit2 anova(pfit2) # anova(pfit1, pfit2) #this fails 2*(pfit2$loglik - pfit1$loglik)[2] @ Since initial age is in years and time is in days, it was important to scale within the pspline function. The likelihood ratio of 10.8 on 2 degrees of freedom shows that the additional terms are mildly significant. When there are one or more terms on the right hand side of the equation marked with the tt() operator, the program will pre-compute the values of that variable for each unique event time. A user-defined function is called with arguments of \begin{itemize} \item the covariate: whatever is inside the tt() call \item the event time \item the event number: if there are multiple strata and the same event time occurs in two of them, they can be treated separately \item the weight for the observation, if the call used weights \end{itemize} There is a single call to the function with a large $x$ vector, it contains an element for each subject at risk at each event time. If there are multiple tt() terms in the formula, then the tt argument should be a list of functions with the requisite number of elements. An alternate way to fit the above model is to create the expanded data set directly and then do an ordinary \code{coxph} call on the expanded data. The disadvantage of this is the very large data set, of course, but an advantage is that further processing of the model is available, such as residuals or survival curves. A reasonable strategy is to use \code{tt()} expressions for initial analysis and then expanded data sets to follow up on selected models. <>= dtimes <- sort(unique(with(pbc, time[status==2]))) tdata <- survSplit(Surv(time, status==2) ~., pbc, cut=dtimes) tdata$c.age <- tdata$age + tdata$time/365.25 -50 #current age, centered at 50 pfit3 <- coxph(Surv(tstart, time, event) ~ log(bili) + ascites + c.age + I(c.age^2) + I(c.age^3), data=tdata) rbind(coef(pfit2), coef(pfit3)) @ There are other interesting uses for the time-transform capability. One example is O'Brien's logit-rank test procedure \cite{obrien78}. He proposed replacing the covariate at each event time with a logit transform of its ranks. This removes the influence of any outliers in the predictor $x$. For this case we ignore the event time argument and concentrate on the groupings. <<>>= function(x, t, riskset, weights){ obrien <- function(x) { r <- rank(x) (r-.5)/(.5+length(r)-r) } unlist(tapply(x, riskset, obrien)) } @ This relies on the fact that the input arguments to tt() are ordered by the event number or risk set. This function is used as a default if no tt argument is present in the coxph call, but there are tt terms in the model formula. (Doing so allowed me to depreciate the survobrien function). Another interesting usage is to replace the data by simple ranks, not rescaled to 0--1. <<>>= function(x, t, riskset, weights) unlist(tapply(x, riskset, rank)) @ The score statistic for this model is $(C-D)/2$, where $C$ and $D$ are the number of concordant and discordant pairs, see the survConcordance function. The score statistic from this fit is then a test for significance of the concordance statistics, and is in fact the basis for the standard error reported by survConcordance. The O'Brien test can be viewed as concordance statistic that gives equal %' weight to each event time, whereas the standard concordance weights each event proportionally to the size of the risk set. (The Cox score statistic depends on the mean $x$ at each event time; since ranks go from 1 to number at risk the mean also scales.) Although handy, the computational impact of the tt argument should be considered before using it. The Cox model requires computation of a weighted mean and variance of the covariates at each event time, a process that is inherently $O(ndp^2)$ where $n$ = the sample size, $d$ = the number of events and $p$= the number of covariates. Much of the algorithmic effort in coxph() is to use updating methods for the mean and variance matrices, reducing the compute time to $O((n+d) p^2)$. When a tt term appears updating is not possible; for even moderate size data sets the impact of $nd$ versus $n+d$ can be surprising. The time-transform is a newer addition and still has some rough edges. At this moment the $x=TRUE$ argument is needed to get proper residuals and predicted values, and termplot is unable to properly reconstruct the data to plot a fit. Please communicate any concerns or interesting examples to the author. \begin{thebibliography}{9} \bibitem{Anderson83} Anderson JR, Cain KC, and Gelber RD. Analysis of survival by tumor response. J Clinical Oncology 1:710--719, 1983. \bibitem{Buyse96} M Buyse and P Piedbois. The relationship between response to treatment and survival time. Stat in Med 15:2797--2812, 1996. \bibitem{Crowley77} J Crowley and M Hu. Covariance analysis of heart transplant survival data. J American Statistical Assoc, 72:27--36, 1977. \bibitem{Gail72} M H Gail. Does cardiac transplantation prolong life? A reassessment. Annals Int Medicine 76:815-17, 1972. \bibitem{Kalbfleisch02} J Kalbfleisch and R Prentice. The statistical analysis of failure time data, second edition. Wiley, 2002. \bibitem{obrien78} O'Brien, Peter. A non-parametric test for association with censored data, Biometrics 34:243--250, 1978. \bibitem{Redmond83} Redmond C, Fisher B, Wieand HS. The methodologic dilemma in retrospectively correlating the amount of chemotherapy received in adjuvant therapy protocols with disease free survival: a commentary. Cancer Treatment Reports 67:519--526, 1983. \bibitem{Suissa08} S Suissa. Immortal time bias in pharmacoepidemiology. Am J Epi, 167:492-499, 2008. \end{thebibliography} \end{document} survival/vignettes/splines.Rnw0000644000175100001440000003233513017617770016337 0ustar hornikusers\documentclass{article} \usepackage{amsmath} \usepackage{Sweave} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} \SweaveOpts{keep.source=TRUE, fig=FALSE} %\VignetteIndexEntry{Splines, plots, and interactions} % Ross Ihaka suggestions \DefineVerbatimEnvironment{Sinput}{Verbatim} {xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} \SweaveOpts{prefix.string=splines,width=6,height=4} \setkeys{Gin}{width=\textwidth} \newcommand{\code}[1]{\texttt{#1}} <>= options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text options(contrasts=c("contr.treatment", "contr.poly")) #reset default @ \title{Spline terms in a Cox model} \author{Terry Therneau} \begin{document} \maketitle This is a trio of topics that comes up just often enough in my work that I end up re-discovering how to do it correctly about once a year. A note showing how may be useful to others, it is certainly a useful reference for me. \section{Plotting smooth terms} Here is a simple example using the MGUS data. I prefer a simpler color palette than the default found in termplot. <>= require(survival) mfit <- coxph(Surv(futime, death) ~ sex + pspline(age, df=4), data=mgus) mfit termplot(mfit, term=2, se=TRUE, col.term=1, col.se=1) @ Note that the \code{term=2} option is passed directly from the \code{termplot} routine to a \code{predict(fit, type='terms')} call. For coxph models, the \code{predict} function allows terms to be specified either by position or name. Other routines, e.g. \code{gam}, respond only to a name. (This can be a bit of a pain since it must exactly match the \emph{printed} call in both spelling and spacing; and the printed spacing may not match what the user typed.) Three questions are whether the curve is significantly non-linear, how the curve is centered and whether we can easily plot it on the hazard as opposed to the log hazard scale. The first question is answered by the printout, the solution to the others is to use the plot=FALSE option of termplot, which returns the data points that would be plotted back to the user. <>= ptemp <- termplot(mfit, se=TRUE, plot=FALSE) attributes(ptemp) ptemp$age[1:4,] @ The termplot function depends on a call to predict with type='terms', which returns a centered set of predictions. Like a simple linear model fit, the intercept is a separate term, which is found in the ``constant'' attribute above, and each column of the result is centered so that the average predicted value is zero. Since any given $x$ value may appear multiple times in the data and thus in the result of predict, and the termplot function removes duplicates, the data returned by \code{termplot} may not be precisely centered at zero. Now suppose we want to redraw this on log scale with age 50 as the reference, i.e., the risk is 1 for a 50 year old. Since the Cox model is a relative hazards model we can choose whatever center we like. (If there were no one of exactly age 50 in the data set the first line below would need to do an interpolation, e.g. by using the approx function.) <>= ageterm <- ptemp$age # this will be a data frame center <- with(ageterm, y[x==50]) ytemp <- ageterm$y + outer(ageterm$se, c(0, -1.96, 1.96), '*') matplot(ageterm$x, exp(ytemp - center), log='y', type='l', lty=c(1,2,2), col=1, xlab="Age at diagnosis", ylab="Relative death rate") @ Voila! We now have a plot that is interpretable with respect to a fixed reference. The approach is appropriate for any term, not just psplines. The above plot uses log scale for the y axis which is appropriate for the question of whether a non-linear age effect was even necessary for this model (it is not), one could remove the log argument to emphasize the Gomperzian effect of age on mortality. \section{Monotone splines} Consider the following model using the \code{mgus2} data set. <>= fit <- coxph(Surv(futime, death) ~ age + pspline(hgb, 4), mgus2) fit termplot(fit, se=TRUE, term=2, col.term=1, col.se=1, xlab="Hemoglobin level") @ Low hemoglobin or anemia is a recognized marker of frailty in older age, so the rise in risk for low levels is not surprising. The rise on the right hand portion of the curve is less believable --- the normal range of HGB is 12-15.5 for women and 13.5 to 17.5 for men, why would we expect a rise there? A monotone fit that forces the curve to be horizontal from 14 onward fits well within the confidence bands, so we might want to force monotonicity. There are two tools for this within the pspline function. The first is to decrease the overall degrees of freedom and the second is to use \code{combine} option to force equality of selected coefficients. Start by decreasing the degrees of freedom. The pspline function automatically picks the number of basis (nterms) to be ``sufficiently large'' for the given degrees of freedom. We fix it at a single value for the rest of this example to better isolate the effects of degrees of freedom and of constraints. <>= termplot(fit, se=TRUE, col.term=1, col.se=1, term=2, xlab="Hemoglobin level", ylim=c(-.4, 1.3)) df <- c(3, 2.5, 2) for (i in 1:3) { tfit <- coxph(Surv(futime, death) ~ age + pspline(hgb, df[i], nterm=8), mgus2) temp <- termplot(tfit, se=FALSE, plot=FALSE, term=2) lines(temp$hgb$x, temp$hgb$y, col=i+1, lwd=2) } legend(14, 1, paste("df=", c(4, df)), lty=1, col=1:4, lwd=2) @ This has reduced, but not eliminated, the right hand rise at the expense of a less sharp transition at the value of 14. The \code{combine} option makes use of a property of the P-spline basis, which is that the curve will be monotone if and only if the coefficients are monotone. We can then use a pool adjacent violators algorithm to sequentially force equality for those coefficients which go the wrong way. Look at the coefficients for the fit with 2.5 degrees of freedom. <>= fit2a <- coxph(Surv(futime, death) ~ age + pspline(hgb, 2.5, nterm=8), mgus2) coef(fit2a) plot(1:10, coef(fit2a)[-1]) @ Now force the last 3 to be equal, then the last 4, and see how this changes the fit. <>= temp <- c(1:7, 8,8,8) fit2b <- coxph(Surv(futime, death) ~ age + pspline(hgb, 2.5, nterm=8, combine=temp), data= mgus2) temp2 <- c(1:6, 7,7,7,7) fit2c <- coxph(Surv(futime, death) ~ age + pspline(hgb, 2.5, nterm=8, combine=temp2), data= mgus2) matplot(1:10, cbind(coef(fit2a)[-1], coef(fit2b)[temp+1], coef(fit2c)[temp2+1]), type='b', pch='abc', xlab="Term", ylab="Pspline coef") @ We see that constraining the last four terms along with a degrees of freedom of is almost enough to force monotonicity; it may be sufficient if our goal is a simple plot for display. This dance between degrees of freedom, number of terms, and constraints has a component of artistry. When all three values become large the result will begin to approach a step function, reminiscent of non-parametric isotonic regression, whereas small values begin to approach a linear fit. The best compromise of smoothness and constraints will be problem specific. \section{Splines in an interaction} As an example we will use the effect of age on survival in the \texttt{flchain} data set, a population based sample of subjects from Olmsted County, Minnesota. If we look at a simple model using age and sex we see that both are very significant. <>= options(show.signif.stars=FALSE) # display intelligence fit1 <- coxph(Surv(futime, death) ~ sex + pspline(age, 3), data=flchain) fit1 termplot(fit1, term=2, se=TRUE, col.term=1, col.se=1, ylab="log hazard") @ We used a \code{pspline} term rather than \code{ns}, say, because the printout for a pspline nicely segregates the linear and non-linear age effects. The non-linearity is not very large, as compared to the linear portion, but still may be important. We would like to go forward and fit separate age curves for the males and the females, since the above fit makes an untested assumption that the male/female ratio of death rates will be the same at all ages. The primary problem is that a formula of \texttt{sex * pspline(age)} does not work; the coxph routine is not clever enough to do the right thing automatically for \code{pspline} interactions. (Perhaps some future version will be sufficiently intelligent, but don't hold your breath). As a first solution we will use regression splines, i.e., splines that can be represented using a basis matrix. <>= options(show.signif.stars=FALSE) # display statistical intellegence require(splines, quietly=TRUE) nfit1 <- coxph(Surv(futime, death) ~ sex + age, flchain) nfit2 <- coxph(Surv(futime, death) ~ sex + ns(age, df=3), flchain) nfit3 <- coxph(Surv(futime, death) ~ sex * ns(age, df=3), flchain) anova(nfit1, nfit2, nfit3) @ The nonlinear term is significant but the interaction is not. Nevertheless we would like to plot the two estimated curves for \code{nfit3}, expecting that they will be approximately parallel. The \code{termplot} routine is not able to deal with models that have an interaction and will bow out with a warning message; we use explicit prediction instead, which is nearly as easy. <>= pdata <- expand.grid(age= 50:99, sex=c("F", "M")) pdata[1:5,] ypred <- predict(nfit3, newdata=pdata, se=TRUE) yy <- ypred$fit + outer(ypred$se, c(0, -1.96, 1.96), '*') matplot(50:99, exp(matrix(yy, ncol=6)), type='l', lty=c(1,1,2,2,2,2), lwd=2, col=1:2, log='y', xlab="Age", ylab="Relative risk") legend(55, 20, c("Female", "Male"), lty=1, lwd=2, col=1:2, bty='n') abline(h=1) @ The \code{ns} function generates a basis of dummy variables to represent the spline, which will work automatically in interactions. The coefficients that result are not very interpretable, but the result of predict is invariant to this. The issues as compared to using \code{termplot} are \begin{enumerate} \item We need to provide our own set of predictor values for the plot, whereas \code{termplot} would automatically use the set of unique age and sex values. \item Keeping track of the indexing. The predict function produces two vectors each of length \code{nrow(pdata)} with a predicted value and its standard error, one value for each row of \code{pdata}. The data set is in order of females, then males. We fold it into an appropriate matrix for use with matplot. \item The vertical centering of the curves corresponds to an average population predictor of$\eta = X\beta =0$; i.e., the average over the subjects in the data set. This is a consequence of the variable centering that \code{coxph} does for numerical stability. To center at some particular (age, sex) pair obtain the predicted value for that fictional subject and subtract the resulting value from \code{yy}. \end{enumerate} To create the same figure with \code{pspline} curves it is necessary to code the males and females as two separate terms. To do this create our own dummy variables to handle the interaction. <>= agem <- with(flchain, ifelse(sex=="M", age, 60)) agef <- with(flchain, ifelse(sex=="F", age, 60)) fit2 <- coxph(Surv(futime, death) ~ sex + pspline(agef, df=3) + pspline(agem, df=3), data=flchain) anova(fit2, fit1) @ You might well ask why we used 60 as a dummy value of \texttt{agem} for the females instead of 0? If a value of 0 is used it forces the pspline function to create a basis set that includes all the empty space between 0 and 50, and do predictions at 0; these last can become numerically unstable leading to errors or incorrect values. Best is to pick a value close to the mean, though any value within the range will do. For this plot we will use a 65 year old female as the reference. <>= # predictions pdata2 <- pdata pdata2$agem <- with(pdata2, ifelse(sex=="M", age, 60)) pdata2$agef <- with(pdata2, ifelse(sex=="F", age, 60)) ypred2 <- predict(fit2, pdata2, se=TRUE) yy <- ypred2$fit + outer(ypred2$se, c(0, -1.96, 1.96), '*') # reference refdata <- data.frame(sex='F', agef=65, agem=60) ref <- predict(fit2, newdata=refdata, type="lp") # plot matplot(50:99, exp(matrix(yy-ref, ncol=6)), type='l', lty=c(1,1,2,2,2,2), lwd=2, col=1:2, log='y', xlab="Age", ylab="Relative risk") legend(55, 20, c("Female", "Male"), lty=1, lwd=2, col=1:2, bty='n') abline(h=1) @ The final curves for males and female are not quite parallel, most of the difference is at the highest ages, however, where there are very few subjects. One thing the plot does not display is that the spacing between the male and female points also has a standard error. This moves the entire bundle of three red curves up and down. It is not clear how best to add this information into the plot. For questions of parallelism and shape, as here, it seemed best to ignore it, which is what the termplot function also does. If someone were reading individual male/female differences off the plot a different choice would be appropriate. \end{document} survival/vignettes/mstate.rda0000644000175100001440000006240012710413422016136 0ustar hornikusers‹íÝÜW}çÿçô 0ÆtaL%‚B.†ÐDØô*¹ÁE¶dlºÜ»­Þ%?’M’Íf³Þl6É&٬¦mª“Íf³ÿ4§76Q*¤áÿçj~ß'z3sï},ƒ“ð¼^GG÷Þ™3§½Ïœ)÷Îé¯~ç üÎÏÍÍù¹ù7ðßèùÇÍŹçµç½~ýyssáQ¼J„‡òáë.1^‹Æ«Øg™P a¼ö8å‡Nh×›{áá„e„GI§{"áÑ„“!œLx,áq„Çž@x"áI„'–žB8…ðT©„§žNxᙄgVžMxṄ美°’ð| _Oø /"|#áÅ„—^Jxáå„W¾‰°Š0"¼’páU„W¾™ðÂk ¯#Œëè „o!¼‘ð&› ßJXMx át„·ÞFx;á„wÞEx7á=„÷ÞGx?á„5„µ„3 gÎ&œC8—ðA‡´Ù܇ !œO¸€p!á"Â:ÂÅ„Kë —>J¸Œp9ác„>Aø$áS„O>CØH¸‚p%á*ÂÕ„k×®#\O¸p#á&ÂÍ„[·n#l"l&l!l%l#l'ì ì$ì"ì&ì!ì%ì#ì' ÜN˜'$"ÜA¸“ðY·¾ð„GøN¿'|á?¾›ð wþá{ÿ™ð½„ÿBø>Â÷~€ð_ ?Hø!ÂþáGÿp˜ð£„ÏþáÇ?Nø ÂO~Šð? ?MøÂÏ~Žðó„_ ÜMøEÂ/þá— ÿ›ð+„ÿCøUÂÿ%ü„_#ü:á7¿Iø-Â=„ß&üáw ¿Gø}ÂþðG„?&ü áO Ÿ'ü?Ÿþœp„ð„¿$üᯠCø[Â_$üáï ÿ@øGÂ?¾D¸·¥ïøÇáßáßáßáßáßáßáßáßáßáßáßÇ 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%\VignetteIndexEntry{Roundoff error and tied times} <>= options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text library(survival, quietly=TRUE) @ \title{Roundoff error and Tied Times} \author{Terry M Therneau} \begin{document} \maketitle \section{Round off error} The heart of the issue can be shown with a simple example. Calculate the following set of intervals for subjects with the same birth date who were enrolled in a study from September 14 through October 23, and then followed for 2--3 months. <>= birth <- as.Date("1973/03/10") start <- as.Date("1998/09/13") + 1:40 end <- as.Date("1998/12/03") + rep(1:10, 4) interval <- (end-start) table(interval) @ Each interval has a different start and end date, but there are only 4 unique interval lengths, each of which appears 10 times. Now convert this to an age scale. <>= start.age <- as.numeric(start-birth)/365.25 end.age <- as.numeric(end -birth)/365.25 age.interval <- end.age - start.age length(unique(age.interval)) table(match(age.interval, sort(unique(age.interval)))) @ There are now eight different age intervals instead of 4, and the 8 unique values appear between 1 and 9 times each. We have become a victim of floating point precision. The exact results above, i.e. how many 'unique' time intervals are found, may depend on your computer system. Some users prefer to use time in days and some prefer time in years, and those users reasonably expect survival analysis results to be identical on the two scales. Both the coxph and survfit routines treat tied event times in a special way, however, and this roundoff can make actual ties appear as non-tied values. In that case results will differ. Parametric survival routines such as \code{survreg} are not affected by the problem since they do not treat ties differently than other values. In survival version 2.40 this issue has been addressed for the coxph and survfit routines; input times are subjected to the same logic found in the all.equal routine in order to determine actual ties. This may change the results for some data sets. For the following test case cox1 and cox2 have identical results in in version 2.40 but different results in prior versions of the survival package. <<>>= ndata <- data.frame(id=1:30, birth.dt = rep(as.Date("1953/03/10"), 30), enroll.dt= as.Date("1993/03/10") + 1:30, end.dt = as.Date("1996/10/21") + 1:30 + rep(1:10, 3), status= rep(0:1, length=30), x = 1:30) ndata$enroll.age <- with(ndata, as.numeric(enroll.dt - birth.dt))/365.25 ndata$end.age <- with(ndata, as.numeric(end.dt - birth.dt))/365.25 fudays <- with(ndata, as.numeric(end.dt - enroll.dt)) fuyrs <- with(ndata, as.numeric(end.age- enroll.age)) cox1 <- coxph(Surv(fudays, status) ~ x, data=ndata) cox2 <- coxph(Surv(fuyrs, status) ~ x, data=ndata) @ A downside to the new procedure is that the code will now give an error message for some constructed data sets. An example sent by one user had several time intervals of length 1e-9, which is less than the roundoff precision used by the \code{all.equal} routine and consequently turned them into illegal intervals of zero length. The \code{timefix} argument of \code{coxph.control} can be used to address this. This general issue of floating point precision arises often enough in R that it is part of the frequently asked questions, see FAQ 7.31 on CRAN. The author of the survival routines (me) has always used days as the scale for analysis -- just by habit, not for any particluarly scientific reason -- so the issue had never appeared in my work nor in the survival package's test suite. Due to user input, near ties had been addressed earlier in the survfit routine, but only when the status variable was 0/1, not when it is a factor. The new code uses a single routine \code{aeqSurv} to deal with ties in a uniform way for all the affected functions. As a final footnote, the simple data set above also gives different results when using the SAS phreg procedure and I suspect the problem exists in other software as well --- the R routines are not alone.\footnote{I have reported this to SAS as of November 2016 and was told that they plan to address the problem.} As a consequence, the maintainer expects to get new emails that ``we have found a bug in your code: it gives a different answer than SAS''. (This is an actual quote.) \end{document} survival/vignettes/validate.Rnw0000644000175100001440000013372613017617770016461 0ustar hornikusers\documentclass{article}[11pt] \usepackage{Sweave} \usepackage{amsmath} \addtolength{\textwidth}{1in} \addtolength{\oddsidemargin}{-.5in} \setlength{\evensidemargin}{\oddsidemargin} \SweaveOpts{keep.source=TRUE, fig=FALSE} % Ross Ihaka suggestions \DefineVerbatimEnvironment{Sinput}{Verbatim} {xleftmargin=2em} \DefineVerbatimEnvironment{Soutput}{Verbatim}{xleftmargin=2em} \DefineVerbatimEnvironment{Scode}{Verbatim}{xleftmargin=2em} \fvset{listparameters={\setlength{\topsep}{0pt}}} \renewenvironment{Schunk}{\vspace{\topsep}}{\vspace{\topsep}} \SweaveOpts{prefix.string=adjcurve,width=6,height=4} \setkeys{Gin}{width=\textwidth} %\VignetteIndexEntry{Validation} <>= options(continue=" ", width=60) options(SweaveHooks=list(fig=function() par(mar=c(4.1, 4.1, .3, 1.1)))) pdf.options(pointsize=8) #text in graph about the same as regular text require(survival, quietly=TRUE) @ \newcommand{\imat}{H} % use H for the hessian rather than script I \newcommand{\Cvar}{H^{-1}} % use H for the hessian rather than script I \newcommand{\splus}{R} % ``the survival package'' would be an alternate \newcommand{\xbar}{\overline x} \newcommand{\lhat}{\hat \Lambda} \def\bhat{\hat\beta} %define "bhat" to mean "beta hat" \def\Mhat{\widehat M} %define "Mhat" to mean M-hat \newcommand{\code}[1]{\texttt{#1}} \title{Validation} \author{Terry M Therneau} \date{Dec 2015} \begin{document} \maketitle \section{Introduction} \begin{quotation} `When I use a word,' Humpty Dumpty said, in rather a scornful tone, `it means just what I choose it to mean - neither more nor less.' `The question is,' said Alice, `whether you can make words mean so many different things.' `The question is,' said Humpty Dumpty, `which is to be master - that's all.' -Lewis Caroll, \emph{Through the Looking Glass} \end{quotation} ``Validatation'' is a label which is used for many different things in scientific research, so much so that the word is essentially meaningless without further clarification. One of the more common meanings assigned to it in the software realm is ``repeatability'', i.e. that a new release of a given package or routine will give the same results as it did the week before. Users of the software often assume the word implies a more rigorous criterion, namely that the routine gives \emph{correct} answers. Validation of the latter type is rare, however; and I surmise that a primary reason for this is that working out correct answers is boring, tedious work. This note contains a set of examples, often very simple, that have evolved over multiple decades. They have proven extremely useful in debugging the methods, not least because all the intermediate steps of each calculation are transparent, and have been incorporated into the formal test suite for the survival package as the files \code{book1.R}, \code{book2.R}, etc. They also continue to be a resource for package's defence: I have been told multiple times that some person or group cannot use R in their work because ``SAS is validated'' while R is not. The survival package passes all of the tests below and SAS passes many but not all of them. It is my hope that the formal test cases will be a resource for developers on multiple platforms. Portions of this work were included as an appendix in the textbook of Therneau and Grambsch \cite{Therneau2000} precisely for this reason. \section{Basic formulas} All these examples have a single covariate. Let $x_i$ be the covariate for each subject, $r_i= exp(x_i \beta)$ the risk score for the subject, and $w_i$ the case weight, if any. Let $Y_i(t)$ be 1 if subject $i$ is at risk at time $t$ and 0 otherwise, and $\delta_i(t)$ be the death indicator which is 1 if subject $i$ has an event at time $t$. At each death time we have the following quantities: \begin{align} d(t) &= \sum_i Y_i(t) w_i r_i \\ LPL(t) &= \left( \sum_i \delta_i(t) \log(r_i) \right) / \log(d(t)) \\ \xbar(t) &= \left( \sum_i Y_i(t) w_i r_i x_i \right) /d(t) \\ U(t) &= \sum_i \delta_i(t) (x_i - \xbar(t)) \label{U1} \\ H(t) &= \sum_i Y_i(t) (x_i - \xbar(t))^2 / d(t) \\ &= \left(\sum_i Y_i(t) x_i^2/d(t) \right)- \xbar(t)^2 \label{H2} \\ \lambda(t) &= \sum_i \delta_i(t)/ d(t) \end{align} The denominator $d$ is the weighted number of subjects at the time, $LPL$ is the contribution to the log partial likelihood at time $t$, and $\xbar$ and $H$ are the weighted mean and variance of the covariate $x$ at each time. The sum of $H(t)$ over the death times is the second derivative of the LPL, also known as the Hessian matrix. $U$ is the contribution to the first derivative of the LPL at time $t$ and $\lambda$ is the increment in the baseline hazard function. \section{Test data 1} This data set of $n=6$ subjects has a single 0/1 covariate $x$. There is one tied death time, one time with both a death and a censored observation, one with only a death, and one with only censoring. (This is as small as a data set can be and still cover these four important cases.) Let $r = \exp(\beta)$ be the risk score for a subject with $x=1$; the risk score is $\exp(0) =1$ for those with $x=0$. Table \ref{tab:val1} shows the data set along with the mean and increment to the hazard at each time point. \begin{table}[b] \centering \begin{tabular}{ccc|cc|cc} &&& \multicolumn{2}{c|}{$\xbar(t)$} & \multicolumn{2}{c}{$d\lhat_0(t)$} \\ Time& Status& $x$& Breslow& Efron& Breslow& Efron \\ \hline 1&1&1&$r/(r+1)$ & $r/(r+1)$& $1/(3r+3)$ & $1/(3r+3)$ \\ 1&0&1&&&&\\ 6&1&1& $r/(r+3)$ & $r/(r+3)$ & $1/(r+3)$& $1/(r+3)$ \\ 6&1&0& $r/(r+3)$ & $r/(r+5)$ & $1/(r+3)$& $1/(r+5)$ \\ 8&0&0&&&& \\ 9&1&0&0&0& 1& 1\\ \end{tabular} \caption{Test data 1} \label{tab:val1} \end{table} \subsection{Breslow estimates} \label{sect:valbreslow} The log partial likelihood (LPL) has a term for each event; each term is the log of the ratio of the score for the subject who had an event over the sum of scores for those who did not. The LPL, first derivative $U$ of the LPL and second derivative (or Hession) $\imat$ are: \begin{eqnarray*} LPL &=& \{\beta- \log(3r+3)\} + \{\beta - \log(r+3)\} + \{0-\log(r+3)\} + \{0-0\} \\ &=& 2\beta - \log(3r+3) - 2\log(r+3). \\ \\ U &=& \left(1-\frac{r}{r+1}\right) + \left(1-\frac{r}{r+3}\right) + \left(0-\frac{r}{r+3} \right) + (0-0) \\ &=& \frac{-r^2 + 3r + 6}{(r+1)(r+3)} .\\ \\ -\imat&=& \left\{\frac{r}{r+1} - \left( \frac{r}{r+1} \right )^2\right\} +2 \left\{\frac{r}{r+3} - \left( \frac{r}{r+3} \right )^2\right\} + (0-0) \\ &=& \frac{r}{(r+1)^2} + \frac{6r}{(r+3)^2}. \end{eqnarray*} (For a 0/1 covariate the variance formula \eqref{H2} simplifies to $\xbar - \xbar^2$, but only in that case. We used this fact above.) The following function computes these quantities. <>= breslow1 <- function(beta) { # first test data set, Breslow approximation r = exp(beta) lpl = 2*beta - (log(3*r +3) + 2*log(r+3)) U = (6+ 3*r - r^2)/((r+1)*(r+3)) H = r/(r+1)^2 + 6*r/(r+3)^2 c(beta=beta, loglik=lpl, U=U, H=H) } beta <- log((3 + sqrt(33))/2) temp <- rbind(breslow1(0), breslow1(beta)) dimnames(temp)[[1]] <- c("beta=0", "beta=solution") temp @ The maximum partial likelihood occurs when $U(\beta)=0$, namely $r^2 -3r -6 =0$. Using the usual formula for a quadratic equation gives $r=(1/2)(3 + \sqrt{33})$ and $\bhat = \log(r) \approx 1.475285$. The above call to \code{breslow1} verifies that the first derivative is zero at this point. Newton--Raphson iteration has increments of $-\Cvar U$. Starting with the usual initial estimate of $\beta=0$, the first iteration is $\beta=8/5$ and further ones are shown below. <<>>= iter <- matrix(0, nrow=6, ncol=4, dimnames=list(paste("iter", 0:5), c("beta", "loglik", "U", "H"))) # Exact Newton-Raphson beta <- 0 for (i in 1:6) { iter[i,] <- breslow1(beta) beta <- beta + iter[i,"U"]/iter[i,"H"] } iter # coxph fits test1 <- data.frame(time= c(1, 1, 6, 6, 8, 9), status=c(1, 0, 1, 1, 0, 1), x= c(1, 1, 1, 0, 0, 0)) temp <- matrix(0, nrow=6, ncol=4, dimnames=list(1:6, c("iter", "beta", "loglik", "H"))) for (i in 0:5) { tfit <- coxph(Surv(time, status) ~ x, data=test1, ties="breslow", iter.max=i) temp[i+1,] <- c(tfit$iter, coef(tfit), tfit$loglik[2], 1/vcov(tfit)) } temp @ The \code{coxph} routine declares convergence after 4 iterations for this data set, so the last two calls with \code{iter.max} of 4 and 5 give identical results. The martingale residuals are defined as $O-E$ = observed - expected, where the observed is the number of events for the subject (0 or 1) and $E$ is the expected number assuming that the model is completely correct. For the first death all 6 subjects are at risk, and the martingale formulation views the outcome as a lottery in which the subjects hold $r$, $r$, $r$, 1, 1 and 1 tickets, respectively. The contribution to $E$ for subject 1 at time 1 is thus $r/(r+3)$. Carrying this forward the residuals can be written as simple function of the cumulative baseline hazard $\Lambda_0(t)$, the Nelson cumulative hazard estimator with case weights of $w_ir_i$; this is shown in the `Breslow' column of table \ref{tab:val1}. (Also known as the Aalen estimate, Breslow estimate, and all possible combinations of the three names.) Then the residual can be written as \begin{equation} M_i = \delta_i - \exp(x_i\beta)\lhat(t_i) \label{mart} \end{equation} Each of the two subjects who die at time 6 are credited with the full hazard increment at time 6. Residuals at $\beta=0$ and $\bhat$ are shown in the table below. <>= mresid1 <- function(r) { status <- c(1,0,1,1,0,1) xbeta <- c(r,r,r,1,1,1) temp1 <- 1/(3*r +3) temp2 <- 2/(r+3) + temp1 status - xbeta*c(temp1, temp1, temp2, temp2, temp2, 1+ temp2) } r0 <- mresid1(1) r1 <- round(mresid1((3 + sqrt(33))/2), 6) @ \begin{center} \begin{tabular}{c|lrr} Subject &\multicolumn{1}{c}{$\Lambda_0$} & $\Mhat(0)$ & $\Mhat(\bhat)$ \\ \hline 1& $1/(3r+3)$ & $5/6$ & \Sexpr{r1[1]} \\ 2& $1/(3r+3)$ & $-1/6$ & \Sexpr{r1[2]} \\ 3& $1/(3r+3) + 2/(r+3)$ &$1/3$ & \Sexpr{r1[3]} \\ 4& $1/(3r+3) + 2/(r+3)$ &$1/3$ & \Sexpr{r1[4]} \\ 5& $1/(3r+3) + 2/(r+3)$ & $-2/3$ & \Sexpr{r1[5]} \\ 6 & $1/(3r+3) + 2/(r+3) +1$ & $-2/3$ & \Sexpr{r1[6]} \end{tabular} \end{center} The score statistic $U$ can be written as a two way sum involving the covariate(s) and the martingale residuals \begin{equation} U = \sum_{i=1}^n \int [x_i - \xbar(t)] dM_i(t) \label{score} \end{equation} The martingale residual $M$ has jumps at the observed deaths, leading to the table below with 6 rows and 3 columns. The score residuals $L_i$ are defined as the per-patient contributions to this total, i.e., the row sums, and the Schoenfeld residuals are the per-time point contributions, i.e., the column sums. \begin{center} \begin{tabular}{cccc} &\multicolumn{3}{c}{Time} \\ Subject & 1 & 6 & 9 \\ \hline 1&$ \left(1- \frac{r}{r+1} \right) \left(1- \frac{r}{3r+3} \right)$ &0&0 \\ 2& $\left(1- \frac{r}{r+1} \right) \left(0- \frac{r}{3r+3} \right)$ &0&0 \\ 3& $\left(1- \frac{r}{r+1} \right) \left(0- \frac{r}{3r+3} \right)$ & $\left(1- \frac{r}{r+3} \right) \left(1- \frac{2r}{r+3} \right)$ & 0\\ 4& $\left(0- \frac{r}{r+1} \right) \left(0- \frac{1}{3r+3} \right)$ & $\left(0- \frac{r}{r+3} \right) \left(1- \frac{2}{r+3} \right)$ & 0\\ 5& $\left(0- \frac{r}{r+1} \right) \left(0- \frac{1}{3r+3} \right)$ & $\left(0- \frac{r}{r+3} \right) \left(0- \frac{2}{r+3} \right)$ & 0\\ 6& $\left(0- \frac{r}{r+1} \right) \left(0- \frac{1}{3r+3} \right)$ & $\left(0- \frac{r}{r+3} \right) \left(0- \frac{2}{r+3} \right)$ & (0 - 0) (1-1) \end{tabular} \end{center} At $\beta=0$ the score residuals are 5/12, -1/12, 7/24, -1/24, 5/24 and 5/24. Showing that the three column sums are identical to the three terms of equation \eqref{U1} is left as an exercise for the reader, namely $1- \xbar(1)$, $(1- \xbar(6)) + (0- \xbar(6))$ and $1 - \xbar(9)$. The computer program returns 4 residuals, one per event, rather than one per death time as this has proven to be more useful for plots and other downstream computations. In the multivariate case there will be a matrix like the above for each covariate. Let $L$ be the $n$ by $p$ matrix made up of the collection of row sums where $n$ is the number of subjects and $p$ is the number of covariates, this is the matrix of score residuals. The dfbeta residuals are the $n$ by $p$ matrix $D = L \Cvar$; $\imat$ has been defined above for this data set. $D$ is an approximate measure of the influence of each observation on the solution vector. Similarly, the scaled Schoenfeld residuals are the (number of events) by $p$ matrix obtained by multiplying the Schoenfeld residuals by $\Cvar$. As stated above there is a close connection between the Nelson--Aalen estimate estimate of cumulative hazard and the Breslow approximation for ties. The baseline hazard is shown as the column $\Lambda_0$ in table \ref{tab:val1}. The estimated hazard for a subject with covariate $x_i$ is $\Lambda_i(t) = \exp(x_i \beta) \Lambda_0(t)$ and the survival estimate for the subject is $S_i(t)= \exp(-\Lambda_i(t))$. The variance of the cumulative hazard is the sum of two terms. Term 1 is a natural extension of the Nelson--Aalen estimator to the case where there are weights. It is a running sum, with an increment at each death of $1/(\sum Y_i(t)r_i(t))^2$. For a subject with covariate $x_i$ this term is multiplied by $[\exp(x_i \beta)]^2$. The second term is $c\Cvar c'$, where $\imat$ is the information matrix of the Cox model and $c$ is a vector. The second term accounts for the fact that the weights themselves have a variance; $c$ is the derivative of $S(t)$ with respect to $\beta$ and can be formally written as $$ \exp(x\beta) \int_0^t (\bar x(s) - x_i) d\hat\Lambda_0 (s)\,. $$ This can be recognized as $-1$ times the score residual process for a subject with $x_i$ as covariates and no events; it measures leverage of a particular observation on the estimate of $\beta$. It is intuitive that a small score residual --- an observation whose covariates has little influence on $\beta$ --- results in a small added variance; that is, $\beta$ has little influence on the estimated survival. \begin{center} \begin{tabular}{c|l} Time & Term 1 \\ \hline 1& $1/(3r+3)^2$ \\ 6& $1/(3r+3)^2 + 2/(r+3)^2$ \\ 9& $1/(3r+3)^2 + 2/(r+3)^2 + 1/1^2$ \\ \multicolumn{2}{c}{} \\ Time & $c$ \\ \hline 1& $(r/(r+1))* 1/(3r+3)$ \\ 6& $(r/(r+1))* 1/(3r+3) + (r/(r+3))* 2/(r+3)$ \\ 9& $(r/(r+1))* 1/(3r+3) + (r/(r+3))* 2/(r+3) + 0*1$\\ \end{tabular} \end{center} For $\beta=0$, $x=0$: \begin{center} \begin{tabular}{c|lll} Time & \multicolumn{2}{c}{Variance}&\\ \hline 1 & 1/36 &+ $1.6*(1/12)^2 $ &= 7/180\\ 6 & (1/36 + 2/16) &+ $1.6*(1/12 + 2/16)^2 $ &= 2/9\\ 9 & (1/36 + 2/16 + 1)&+ $1.6*(1/12 + 2/16 + 0)^2$&= 11/9\\ \end{tabular} \end{center} For $\beta=1.4752849$, $ x=0$ \begin{center} \begin{tabular}{c|lll} Time & \multicolumn{2}{c}{Variance}&\\ \hline 1 & 0.0038498 &+ .004021 &= 0.007871\\ 2 & 0.040648 &+ .0704631 &= 0.111111\\ 4 & 1.040648 &+ .0704631 &= 1.111111\\ \end{tabular} \end{center} \subsection{Efron approximation} The Efron approximation \cite{Efron77} differs from the Breslow only at day 6, where two deaths occur. A useful way to view the approximation is to recast the problem as a lottery model. On day 1 there were 6 subjects in the lottery and 1 ticket was drawn, at which time the winner became ineligible for further drawings and withdrew. On day 6 there were 4 subjects in the drawing (at risk) and two tickets (deaths) were drawn. The Breslow approximation considers all four subjects to be eligible for both drawings, which implies that one of them could in theory have won both, that is, died twice. This is of clearly impossible. The Efron approximation treats the two drawings on day 6 as sequential. All four living subjects are at risk for the first of them, then the winner is withdrawn. Three subjects are eligible for the second drawing, either subjects 3, 5, and 6 or subjects 2, 5, and 6, but we do not know which. In some sense then, subjects 3 and 4 each have ``.5 probability" of being at risk for the second event at time 6. In the computation, we treat the two deaths at time 6 as two separate times (two terms in the loglik), with subjects 3 and 4 each having a case weight of 1/2 for the second one. The mean covariate for the second event is then $$ \frac{1*r/2 + 0*1/2 + 0*1 + 0*1 } {r/2 + 1/2 + 1+1} = \frac{r}{r+5} $$ and the main quantities are \begin{eqnarray*} LL &=& \{\beta- \log(3r+3)\} + \{\beta - \log(r+3)\} + \{0-\log(r/2 +5/2)\} + \{0-0\} \\ &=& 2\beta - \log(3r+3) - \log(r+3) - \log(r/2 +5/2)\\ \\ U &=& \left(1-\frac{r}{r+1}\right) + \left(1-\frac{r}{r+3}\right) + \left(0-\frac{r}{r+5}\right) + (0-0) \\ &=& \frac{-r^3 + 23r + 30}{(r+1)(r+3)(r+5)} \\ \\ I&=& \left\{\frac{r}{r+1} - \left( \frac{r}{r+1} \right )^2\right\} + \left\{\frac{r}{r+3} - \left( \frac{r}{r+3} \right )^2\right\} \\ && + \left\{\frac{r}{r+5} - \left( \frac{r}{r+5} \right )^2\right\}. \end{eqnarray*} The solution corresponds to the one positive root of $U(\beta)=0$, which is $r=2\sqrt{23/3}\cos(\phi/3)$ where $\phi=\arccos\{(45/23)\sqrt{3/23}\}$ via the standard formula for the roots of a cubic equation. This yields $r \approx 5.348721$ or $\bhat = \log(r) \approx 1.676857$. Plugging this value into the formulas above yields $$ \begin{array}{ll} LL(0)=-4.276666 & LL(\bhat)=-3.358979 \\ U(0) = 52/48 & U(\bhat) = 0 \\ \imat(0) = 83/144 & \imat(\bhat) = 0.652077. \end{array} $$ The martingale residuals are again $O-E$, but the expected part of the calculation changes. For the first drawing at time 6 the total number of ``tickets'' in the drawing is $r+1+1+1$; subject 4 has an increment of $r/(r+3)$ and the others $1/(r+3)$ to their expected value. For the second event at time 6 subjects 3 and 4 have a weight of 1/2, the total number of tickets is $(r+5)/2$ and the consequent increment in the cumulative hazard is $2/(r+5)$. This $\beta=0$ this calculation is equivalent to the Fleming-Harrington \cite{Fleming84} estimate of cumulative hazard. Subjects 3 and 4 receive 1/2 of this second increment to $E$ and subjects 5 and 6 the full increment. Efron \cite{Efron77} did not discuss residuals so did not investigate this aspect of the approximation, we nevertheless sometime refer to this using combinations of Fleming, Harrington, Efron in the same way as the Nelson-Aalen-Breslow estimate. The martingale residuals are \begin{center} \begin{tabular}{cl} Subject & $M_i$ \\ \hline 1 & $1 - r/(3r+3)$ \\ 2 & $0 - r/(3r+3)$ \\ 3 & $1 - r/(3r+3) - r/(r+3) - r/(r+5)$ \\ 4 & $1 - 1/(3r+3) - 1/(r+3) - 1/(r+5)$ \\ 5 & $0 - 1/(3r+3) - 1/(r+3) - 2/(r+5)$ \\ 6 & $0 - 1/(3r+3) - 1/(r+3) - 2/(r+5) - 1$ \\ \end{tabular} \end{center} giving residuals at $\beta=0$ of 5/6, -1/6, 5/12, 5/12, -3/4 and -3/4. The matrix defining the score and Schoenfeld residuals has the same first column (time 1) and last column as before, with the following contributions at time 6. \begin{center} \begin{tabular}{ccc} &\multicolumn{2}{c}{Time} \\ Subject & 6 (first) & 6 (second)\\ \hline 1&0 & 0 \\ 2&0 & 0 \\ 3& $\left(1- \frac{r}{r+3} \right) \left(1- \frac{r}{r+3} \right)$ & $\left(1- \frac{r}{r+5} \right) \left(1- \frac{2r}{r+5} \right)/2$ \\ 4& $\left(0- \frac{r}{r+3} \right) \left(0- \frac{1}{r+3} \right)$ & $\left(0- \frac{r}{r+5} \right) \left(1- \frac{2}{r+5} \right)/2$ \\ 5& $\left(0- \frac{r}{r+3} \right) \left(0- \frac{1}{r+3} \right)$ & $\left(0- \frac{r}{r+5} \right) \left(0- \frac{2}{r+5} \right)$ \\ 6& $\left(0- \frac{r}{r+3} \right) \left(0- \frac{1}{r+3} \right)$ & $\left(0- \frac{r}{r+5} \right) \left(0- \frac{2}{r+5} \right)$ \end{tabular} \end{center} The score residuals at $\beta=0$ are 5/12, -1/12, 55/144, -5/144, 29/144 and 29/144. It is an error to generate residuals for the Efron method by using formula \eqref{mart}, which was derived from the Breslow approximation. It is clear that some packages do exactly this, however, which can be verified using formulas from above. (Statistical forensics is another use for our results.) What are the consequences of this? On a formal level the resulting ``martingale residuals'' no longer have an expected value of 0 and thus are not martingales, so one loses theoretical backing for derived plots or statistics. The score, Schoenfeld, dfbeta and scaled Schoenfeld residuals are based on the martingale residual so suffer the same loss. On a practical level, when the fraction of ties is small it is quite often the case that $\bhat$ is nearly the same when using the Breslow and Efron approach. We have normally found the correct and ad hoc residuals to be similar as well in that case, sufficiently so that explorations of functional form (martingale residuals), leverage and robust variance (dfbeta) and proportional hazards (scaled Schoenfeld) led to the same conclusions. This will not hold when there are a moderate to large number of ties. The variance formula for the baseline hazard function in the Efron case is evaluated the same way as before, as the sum of $(\mbox{hazard increment})^2$, treating a tied death as multiple separate hazard increments. In term 1 of the variance, the variance increment at time 6 is now $1/(r+3)^2 + 4/(r+5)^2$ rather than $2/(r+3)^2$. The increment to $d$ at time 6 is $(r/(r+3))* 1/(r+3) + (r/(r+5))* 2/(r+5)$. (Numerically, the result of this computation is intermediate between the Nelson--Aalen variance and the Greenwood variance used in the Kaplan--Meier.) For $\beta=0$, $x=0$, let $v= \Cvar = 144/83$. \begin{center} \begin{tabular}{c|ll} Time & \multicolumn{2}{c}{Variance}\\ \hline 1 & 1/36 \\ & \quad + $v(1/12)^2 $ &= \phantom{0}119/2988\\ 6 & (1/36 + 1/16 + 4/25)& \\ &\quad + $v(1/12 + 1/16+ 1/18)^2$ &= 1996/6225\\ 9 & (1/36 + 1/16 + 4/25 + 1) \\& \quad + $v(1/12 + 1/16 + 1/18 +0)^2$&= 8221/6225\\ \end{tabular} \end{center} For $\beta=1.676857$, $ x=0$. \begin{center} \begin{tabular}{c|ll} Time & \multicolumn{2}{c}{Variance}\\ \hline 1 & 0.00275667 + .00319386 & = 0.0059505\\ 2 & 0.05445330 + .0796212 & = 0.134075\\ 4 & 1.05445330 + .0796212 &= 1.134075\\ \end{tabular} \end{center} \subsection{Exact partial likelihood} Returning to the lottery analogy, for the two deaths at time 6 the exact partial likelihood computes the direct probability that those two subjects would be selected given that a pair will be chosen. The numerator is $r_3 r_4$, the product of the risk scores of the subjects with an event, and the denominator is the sum over all 6 pairs who could have been chosen: $r_3r_4 + r_3r_5 + r_3r_6 + r_4 r_5 + r_4r_6 + r_5r_6$. (If there were 10 tied deaths from a pool of 60 available the sum will have over 75 billion terms, each a product of 10 values; a truly formidable computation!) In our case, three of the four subjects at risk at time 6 have a risk score of $\exp(0x)=1$ and one a risk score of $r$, and the denominator is $r +r+ r+1 +1 +1$. \begin{eqnarray*} LL &=& \{\beta- \log(3r+3)\} + \{\beta - \log(3r+3)\} + \{0-0\} \\ &=& 2\{\beta - \log(3r+3)\}. \\ \\ U &=& \left(1-\frac{r}{r+1}\right) + \left(1-\frac{r}{r+1}\right) + (0-0)\\ &=& \frac{2}{r+1}. \\ \\ -\imat&=& \frac{2r}{(r+1)^2}. \\ \end{eqnarray*} The solution $U(\beta)=0$ corresponds to $r=\infty$, with a loglikelihood that asymptotes to $-2\log(3)$ = 2.1972. The Newton--Raphson iteration has increments of $(r+1)/r$ leading to the following iteration for $\bhat$: <>= temp <- matrix(0, 8, 3) dimnames(temp) <- list(paste0("iteration ", 0:7, ':'), c("beta", "loglik", "H")) bhat <- 0 for (i in 1:8) { r <- exp(bhat) temp[i,] <- c(bhat, 2*(bhat - log(3*r +3)), 2*r/(r+1)^2) bhat <- bhat + (r+1)/r } round(temp,3) @ The Newton-Raphson iteration quickly settles down to addition of a constant increment to $\bhat$ at each step while the partial likelihood approaches an asymptote: this is a fairly common case when the Cox MLE is infinite. A solution at $\bhat=10$ or 15 is hardly different in likelihood from the true maximum, and most programs will stop iterating around this point. The information matrix, which measures the curvature of the likelihood function at $\beta$, rapidly goes to zero as $\beta$ grows. It is difficult to describe a satisfactory definition of the expected number of events for each subject and thus a definition of the proper martingale residual for the exact calculation. Among other things it should lead to a consistent score residual, i.e., ones that sum to the total score statistic $U$ \begin{align*} L_i &= \int (x_i - \xbar(t)) dM_i(t) \\ \sum L_i &= U \end{align*} The residuals defined above for the Breslow and Efron approximations have this property, for instance. The exact partial likelihood contribution to $U$ for a set of set of $k$ tied deaths, however, is a sum of all subsets of size $k$; how would one partition this term as a simple sum over subjects? The exact partial likelihood is infrequently used and examination of post fit residuals is even rarer. The survival package (and all others that I know of) takes the easy road in this case and uses equation \eqref{mart} along with the Nelson-Aalen-Breslow hazard to form residuals. They are certainly not correct, but the viable options were to use this, the Efron residuals, or print an error message. At $\bhat=\infty$ the Breslow residuals are still well defined. Subjects 1 to 3, those with a covariate of 1, experience a hazard of $r/(3r+3)=1/3$ at time 1. Subject 3 accumulates a hazard of 1/3 at time 1 and a further hazard of 2 at time 6. The remaining subjects are at an infinitely lower risk during days 1 to 6 and accumulate no hazard then, with subject 6 being credited with 1 unit of hazard at the last event. The residuals are thus $1-1/3=2/3$, $0-1/3$, $1-7/3= -4/3$, $1-0$, 0, and 0, respectively, for the six subjects. \section{Test data 2} This data set also has a single covariate, but in this case a (start, stop] style of input is employed. Table \ref{tab:val2} shows the data sorted by the end time of the risk intervals. The columns for $\xbar$ and hazard are the values at the event times; events occur at the end of each interval for which status = 1. \begin{table}\centering \begin{tabular}{ccc|ccc} &&&Number& \\ Time&Status&$x$&at Risk& $\xbar$& $d\lhat$ \\ \hline (1,2] &1 &1 &2 &$r/(r+1)$ & $1/(r+1)$\\ (2,3] &1 &0 &3 & $r/(r+2)$ & $1/(r+2)$ \\ (5,6] &1 &0 &5 & $3r/(3r+2)$ & $1/(3r+2)$ \\ (2,7] &1 &1 &4 & $3r/(3r+1)$ & $1/(3r+1)$ \\ (1,8] &1 &0 &4 & $3r/(3r+1)$ & $1/(3r+1)$ \\ (7,9] &1 &1 &5 & $3r/(3r+2)$ & $2/(3r+2)$ \\ (3,9] &1 &1 && \\ (4,9] &0 &1 && \\ (8,14]&0 &0 &2& 0&0 \\ (8,17]&0 &0 &1& 0&0 \\ \end{tabular} \caption{Test data 2} \label{tab:val2} \end{table} \subsection{Breslow approximation} For the Breslow approximation we have \begin{eqnarray*} LL &=& \log\left(\frac{r}{r+1}\right) +\log\left(\frac{1}{r+2}\right) +\log\left(\frac{1}{3r+2}\right) +\\ && \log\left(\frac{r}{3r+1}\right) +\log\left(\frac{1}{3r+1}\right) +2\log\left(\frac{r}{3r+2}\right) \\ &=& 4\beta - \log(r+1) - \log(r+3)- 3\log(3r+2) -2\log(3r+1). \\ \\ U &=& \left(1-\frac{r}{r+1}\right) + \left(0-\frac{r}{r+2}\right) + \left(0-\frac{3r}{3r+2}\right) + \\ && \left(1-\frac{3r}{3r+1}\right) + \left(0-\frac{3r}{3r+1}\right) + 2\left(1-\frac{3r}{3r+2}\right) \\ \\ \\ \imat &=& \frac{r}{(r+1)^2} + \frac{2r}{(r+2)^2} + \frac{6r}{(3r+2)^2} + \frac{3r}{(3r+1)^2} \\ && \frac{3r}{(3r+1)^2} + \frac{12r}{(3r+2)^2} . \\ \end{eqnarray*} In this case $U$ is a quartic equation and we find the solution numerically. <>= ufun <- function(r) { 4 - (r/(r+1) + r/(r+2) + 3*r/(3*r+2) + 6*r/(3*r+1) + 6*r/(3*r+2)) } rhat <- uniroot(ufun, c(.5, 1.5), tol=1e-8)$root bhat <- log(rhat) c(rhat=rhat, bhat=bhat) @ The solution is at $U(\bhat)=0$ or $r \approx .9189477$; $\bhat = \log(r) \approx -.084526$. Then <>= true2 <- function(beta, newx=0) { r <- exp(beta) loglik <- 4*beta - log(r+1) - log(r+2) - 3*log(3*r+2) - 2*log(3*r+1) u <- 1/(r+1) + 1/(3*r+1) + 4/(3*r+2) - ( r/(r+2) +3*r/(3*r+2) + 3*r/(3*r+1)) imat <- r/(r+1)^2 + 2*r/(r+2)^2 + 6*r/(3*r+2)^2 + 3*r/(3*r+1)^2 + 3*r/(3*r+1)^2 + 12*r/(3*r+2)^2 hazard <-c( 1/(r+1), 1/(r+2), 1/(3*r+2), 1/(3*r+1), 1/(3*r+1), 2/(3*r+2) ) xbar <- c(r/(r+1), r/(r+2), 3*r/(3*r+2), 3*r/(3*r+1), 3*r/(3*r+1), 3*r/(3*r+2)) # The matrix of weights, one row per obs, one col per time # deaths at 2,3,6,7,8,9 wtmat <- matrix(c(1,0,0,0,1,0,0,0,0,0, 0,1,0,1,1,0,0,0,0,0, 0,0,1,1,1,0,1,1,0,0, 0,0,0,1,1,0,1,1,0,0, 0,0,0,0,1,1,1,1,0,0, 0,0,0,0,0,1,1,1,1,1), ncol=6) wtmat <- diag(c(r,1,1,r,1,r,r,r,1,1)) %*% wtmat x <- c(1,0,0,1,0,1,1,1,0,0) status <- c(1,1,1,1,1,1,1,0,0,0) xbar <- colSums(wtmat*x)/ colSums(wtmat) n <- length(x) # Table of sums for score and Schoenfeld resids hazmat <- wtmat %*% diag(hazard) #each subject's hazard over time dM <- -hazmat #Expected part for (i in 1:6) dM[i,i] <- dM[i,i] +1 #observed dM[7,6] <- dM[7,6] +1 # observed mart <- rowSums(dM) # Table of sums for score and Schoenfeld resids # Looks like the last table of appendix E.2.1 of the book resid <- dM * outer(x, xbar, '-') score <- rowSums(resid) scho <- colSums(resid) # We need to split the two tied times up, to match coxph scho <- c(scho[1:5], scho[6]/2, scho[6]/2) var.g <- cumsum(hazard*hazard /c(1,1,1,1,1,2)) var.d <- cumsum( (xbar-newx)*hazard) surv <- exp(-cumsum(hazard) * exp(beta*newx)) varhaz <- (var.g + var.d^2/imat)* exp(2*beta*newx) list(loglik=loglik, u=u, imat=imat, xbar=xbar, haz=hazard, mart=mart, score=score, rmat=resid, scho=scho, surv=surv, var=varhaz) } val2 <- true2(bhat) rtemp <- round(val2$mart, 6) @ $$ \begin{array}{ll} LL(0)= \Sexpr{round(true2(0)$loglik, 6)} & LL(\bhat)= \Sexpr{round(val2$loglik,6)} \\ U(0) = -2/15 & U(\bhat) = 0 \\ \imat(0) = 2821/1800 & \imat(\bhat) = \Sexpr{round(val2$imat,6)} %$ \end{array} $$ \def\haz{\hat \lambda} The martingale residuals are (status--cumulative hazard) or $O-E = \delta_i - \int Y_i(s) r_i d\lhat(s)$. Let $\haz_1, \ldots, \haz_6$ be the six increments to the cumulative hazard listed in Table \ref{tab:val2}. Then the cumulative hazards and martingale residuals for the subjects are as follows. \begin{center} \begin{tabular}{c|lrr} Subject &$\Lambda_i$ & $\Mhat(0)$ & $\Mhat(\bhat)$ \\ \hline 1& $r\haz_1$ & 1--30/60 & \Sexpr{rtemp[1]} \\ 2& $\haz_2 $ & 1--20/60 & \Sexpr{rtemp[2]}\\ 3& $\haz_3 $ & 1--12/60 & \Sexpr{rtemp[3]} \\ 4& $r(\haz_2 + \haz_3 + \haz_4)$& 1--47/60 & \Sexpr{rtemp[4]}\\ 5& $\haz_1+\haz_2+\haz_3+\haz_4+\haz_5$& 1--92/60 & \Sexpr{rtemp[5]}\\ 6 &$r*(\haz_5 + \haz_6) $& 1--39/60 & \Sexpr{rtemp[6]} \\ 7& $r*(\haz_3+\haz_4+\haz_5+ \haz_6)$& 1--66/60& \Sexpr{rtemp[7]}\\ 8& $r*(\haz_3+\haz_4+\haz_5+ \haz_6)$& 0--66/60&\Sexpr{rtemp[8]} \\ 9& $\haz_6$ & 0--24/60 & \Sexpr{rtemp[9]} \\ 10& $\haz_6$ & 0--24/60 & \Sexpr{rtemp[10]} \end{tabular} \end{center} The score and Schoenfeld residuals can be laid out in a tabular fashion. Each entry in the table is the value of $\{x_i - \xbar(t_j)\} d\Mhat_i(t_j)$ for subject $i$ and event time $t_j$. The row sums of the table are the score residuals for the subject; the column sums are the Schoenfeld residuals at each event time. Below is the table for $\beta= \log(2)$ ($r=2$). This is a slightly more stringent test than the table for $\beta=0$, since in this latter case a program could be missing a factor of $r = \exp(\beta)=1$ and give the correct answer. However, the results are much more compact than those for $\bhat$, since the solutions are exact fractions. %\newcommand{\pf}[2]{$\left(\frac{#1}{#2}\right)$} %positive fraction %\newcommand{\nf}[2]{$\left(\frac{-#1}{#2}\right)$} %negative fraction \newcommand{\pf}[2]{$\phantom{-}\frac{#1}{#2}$} %positive fraction \newcommand{\nf}[2]{$-\frac{#1}{#2}$} %negative fraction \renewcommand{\arraystretch}{1.5} \begin{center} \begin{tabular}{c|cccccc|c} & \multicolumn{6}{c|}{Event Time} & Score\\ Id&2&3&6&7&8&9& Resid \\ \hline 1&\pf{1}{9} &&&&&& $\phantom{-}\frac{1}{9}$ \\ 2&&\nf{3}{8} &&&&& $-\frac{3}{8}$ \\ 3&&&\nf{21}{32}&&&& $-\frac{21}{32}$ \\ 4&&\nf{1}{4} & \nf{1}{16} & \pf{5}{49} &&& $-\frac{165}{784} $\\ 5&\pf{2}{9}& \pf{1}{8} & \pf{3}{32} & \pf{6}{49} & \nf{36}{49}&& $-\frac{2417}{14112} $\\ 6&&&&& \nf{2}{49} & \pf{1}{8} & $\phantom{-}\frac{33}{392}$ \\ 7&&& \nf{1}{16} & \nf{2}{49}& \nf{2}{49} & \pf{1}{8} & $-\frac{15}{784}$ \\ 8&&& \nf{1}{16} & \nf{2}{49}& \nf{2}{49} & \nf{1}{8} & $-\frac{211}{784}$ \\ 9&&&&&& \pf{3}{16} &$ \phantom{-}\frac{3}{16}$ \\ 10&&&&&& \pf{3}{16} & $\phantom{-}\frac{3}{16}$ \\ \hline & \pf{1}{3} &\nf{1}{2} & \nf{3}{4} & \pf{1}{7} & \nf{6}{7} & \pf{1}{2} & \nf{95}{84} \\ &&&&&&& \\ & $\frac{1}{r+1}$ & $\frac{-r}{r+2}$ & $\frac{-3r}{r+2}$ & $\frac{1}{3r+1}$ & $\frac{3r}{3r+1}$ & $\frac{4}{3r+2}$ \end{tabular} \end{center} Both the Schoenfeld and score residuals sum to the score statistic $U(\beta)$. As discussed further above, programs will return two Schoenfeld residuals at time 7, one for each subject who had an event at that time. \subsection{Efron approximation} This example has only one tied death time, so only the term(s) for the event at time 9 change. The main quantities at that time point are as follows. \begin{center} \begin{tabular}{r|cc} &Breslow & Efron \\ \hline $LL$ & $2\log\left(\frac{r}{3r+2}\right)$ & $\log\left(\frac{r}{3r+2}\right) + \log\left(\frac{r}{2r+2}\right)$ \\ $U$ & $\frac{2}{3r+2}$& $\frac{1}{3r+2} + \frac{1}{2r+2}$ \\ $\imat$& $2\frac{6r}{(3r+2)^2} $ &$\frac{6r}{(3r+2)^2} + \frac{4r}{(2r+2)^2}$\\ $d\lhat$ & $\frac{2}{3r+2} $ & $\frac{1}{3r+2} + \frac{1}{2r+2}$ \end{tabular} \end{center} \renewcommand{\arraystretch}{1} \section{Test data 3} This is very similar to test data 1, but with the addition of case weights. There are 9 observations, $x$ is a 0/1/2 covariate, and weights range from 1 to 4. As before, let $r = \exp(\beta)$ be the risk score for a subject with $x=1$. Table \ref{tab:val3} shows the data set along with the mean and increment to the hazard at each point. \begin{table} \centering \begin{tabular}{cccc|cc} Time&Status&$X$ & Wt& $\xbar(t)$ & $d\lhat_0(t)$ \\ \hline 1& 1& 2 & 1& $(2r^2+11r) d\lhat_0 =\xbar_1$ & $1/(r^2 + 11r +7)$ \\ 1& 0& 0 & 2&& \\ 2& 1& 1 & 3& $11r/(11r+5) = \xbar_2$ & $10/(11r+5)$ \\ 2& 1& 1 & 4&& \\ 2& 1& 0 & 3&& \\ 2& 0& 1 & 2&& \\ 3& 0& 0 & 1&& \\ 4& 1& 1 & 2& $2r/(2r+1)= \xbar_3$ & $ 2/(2r+1)$ \\ 5& 0& 0 & 1 & \\ \end{tabular} \caption{Test data 3} \label{tab:val3} \end{table} \subsection{Breslow estimates} The likelihood is a product of terms, one for each death, of the form $$ \left( \frac{e^{X_i \beta}}{\sum_j Y_j(t_i) w_j e^{X_j \beta}} \right) ^{w_i} $$ For integer weights, this gives the same results as would be obtained by replicating each observation the specified number of times, which is in fact one motivation for the definition. The definitions for the score vector $U$ and information matrix $\imat$ simply replace the mean and variance with weighted versions of the same. Let $PL(\beta,w)$ be the log partial liklihood when all the observations are given a common case weight of $w$; it is easy to prove that $PL(\beta,w) = wPL(\beta,1) - d\log(w)$ where $d$ is the number of events. One consequence of this is that $PL$ can be positive for weights that are less than 1, a case which sometimes occurs in survey sampling applications. (This can be a big surprise the first time one encounters it.) \begin{eqnarray*} LL &=& \{2\beta - \log(r^2 + 11r +7)\} + 3\{\beta - \log(11r+5)\} \\ && + 4\{\beta - \log(11r+5)\} +3\{0 - \log(11r+5)\} \\ && + 2\{\beta - \log(2r+1) \} \\ &=& 11\beta - \log(r^2 + 11r +7) -10\log(11r+5) - 2\log(2r+1) \\\\ U &=& (2- \xbar_1) + 3(0-\xbar_2) + 4(1-\xbar_2) + 3(1-\xbar_2) + 2(1-\xbar_3) \\ &=& 11 - [(2r^2+11r)/(r^2+11r+7) + 10(11r/(11r+5)) + 2(2r/(2r+1))] \\ I &=& [(4r^2 + 11r)/(r^2 + 11r +7) - \xbar_1^2] + 10(\xbar_2 - \xbar_2^2) + 2(\xbar_3 - \xbar_3^2) \\ \end{eqnarray*} The solution corresponds to $U(\beta)=0$ and can be computed using a simple search for the zero of the equation. <>= ufun <- function(r) { xbar <- c( (2*r^2 + 11*r)/(r^2 + 11*r +7), 11*r/(11*r + 5), 2*r/(2*r +1)) 11- (xbar[1] + 10* xbar[2] + 2* xbar[3]) } rhat <- uniroot(ufun, c(1,3), tol= 1e-9)$root bhat <- log(rhat) c(rhat=rhat, bhat=bhat) @ From this we have <>= wfun <- function(r) { beta <- log(r) pl <- 11*beta - (log(r^2 + 11*r + 7) + 10*log(11*r +5) + 2*log(2*r +1)) xbar <- c((2*r^2 + 11*r)/(r^2 + 11*r +7), 11*r/(11*r +5), 2*r/(2*r +1)) U <- 11 - (xbar[1] + 10*xbar[2] + 2*xbar[3]) H <- ((4*r^2 + 11*r)/(r^2 + 11*r +7)- xbar[1]^2) + 10*(xbar[2] - xbar[2]^2) + 2*(xbar[3]- xbar[3]^2) c(loglik=pl, U=U, H=H) } temp <- matrix(c(wfun(1), wfun(rhat)), ncol=2, dimnames=list(c("loglik", "U", "H"), c("beta=0", "beta-hat"))) round(temp, 6) @ When $\beta=0$, the three unique values for $\xbar$ at $t=1$, 2, and 4 are 13/19, 11/16 and 2/3, respectively, and the increments to the cumulative hazard are 1/19, 10/16 = 5/8, and 2/3, see table \ref{tab:val3}. The martingale and score residuals at $\beta=0$ and $\bhat$ are \begin{center} \begin{tabular}{cc|lr} Id &Time& \multicolumn{1}{c}{$M(0)$} &\multicolumn{1}{c}{$M(\bhat)$} \\ \hline A&1 & $1-1/19 = 18/19 $&0.85531\\ B&1 & $0-1/19 = -1/19 $&-0.02593\\ C&2 & $1-(1/19 + 5/8)= 49/152 $&0.17636 \\ D&2 & $1-(1/19 + 5/8)= 49/152 $&0.17636\\ E&2 & $1-(1/19 + 5/8)= 49/152 $&0.65131\\ F&2 & $0-(1/19 + 5/8)= -103/152 $&-0.82364\\ G&3 & $0-(1/19 + 5/8)= -103/152 $&-0.34869\\ H&4 & $1-(1/19 + 5/8 +2/3)= -157/456 $&-0.64894\\ I&5 & $0-(1/19 + 5/8 +2/3)= -613/456 $&-0.69808\\ \end{tabular} \end{center} Score residuals at $\beta=0$ are \begin{center} \begin{tabular}{cc|r} Id &Time& Score \\ \hline A&1 &$(2-13/19)(1-1/19)$\\ B&1 &$(0-13/19)(0-1/19)$\\ C&2 &$ (1-13/19)(0-1/19) + (1-11/16)(1-5/8) $ \\ D&2 &$(1-13/19)(0-1/19) + (1-11/16)(1-5/8)$ \\ E&2 &$(0-13/19)(0-1/19) + (0-11/16)(1-5/8)$ \\ F&2 &$(1-13/19)(0-1/19) + (1-11/16)(0-5/8)$ \\ G&3 &$(1-13/19)(0-1/19) + (0-11/16)(0-5/8)$ \\ H&4 &$(1-13/19)(0-1/19) + (1-11/16)(0-5/8) $ \\ && $ + (1-2/3)(1-2/3)$ \\ I&5 &$(1-13/19)(0-1/19) + (1-11/16)(0-5/8)$ \\ & &$+ (0-2/3)(0-2/3) $ \\ \end{tabular} \end{center} {\splus} also returns unweighted residuals by default, with an option to return the weighted version; it is the weighted sum of residuals that totals zero, $\sum w_i \Mhat_i=0$. Whether the weighted or the unweighted form is more useful depends on the intended application, neither is more ``correct'' than the other. {\splus} does differ for the dfbeta residuals, for which the default is to return weighted values. For the third observation in this data set, for instance, the unweighted dfbeta is an approximation to the change in $\bhat$ that will occur if the case weight is changed from 2 to 3, corresponding to deletion of one of the three ``subjects'' that this observation represents, and the weighted form approximates a change in the case weight from 0 to 3, i.e., deletion of the entire observation. The increments of the Nelson-Aalen estimate of the hazard are shown in the rightmost column of table \ref{tab:val3}. The hazard estimate for a hypothetical subject with covariate $X^\dagger$ is $\Lambda_i(t) = \exp(X^\dagger \beta) \Lambda_0(t)$ and the survival estimate is $S_i(t)= \exp(-\Lambda_i(t))$. The two term of the variance, for $X^\dagger=0$, are Term1 + $d'Vd$: \begin{center} \begin{tabular}{c|l} Time & Term 1 \\ \hline 1& $1/(r^2 + 11r+7)^2$ \\ 2& $1/(r^2 + 11r+7)^2 + 10/(11r+5)^2$ \\ 4& $1/(r^2 + 11r+7)^2 + 10/(11r+5)^2 + 2/(2r+1)^2$ \\ \multicolumn{2}{c}{} \\ Time & $d$ \\ \hline 1& $(2r^2+11r)/(r^2+11r+7)^2$ \\ 2& $(2r^2+11r)/(r^2+11r+7)^2 + 110r/(11r+5)^2$ \\ 4& $(2r^2+11r)/(r^2+11r+7)^2 + 110r/(11r+5)^2 + 4r/(2r+1)^2$ \end{tabular} \end{center} For $\beta=\log(2)$ and $X^\dagger =0$, where $k\equiv$ the variance of $\bhat$ = 1/2.153895 this reduces to \begin{center} \begin{tabular}{c|ll} Time & \multicolumn{2}{c}{Variance}\\ \hline 1 & 1/1089 &+ $k(30/1089)^2$ \\ 2 & (1/1089+ 10/729) &+ $k(30/1089+ 220/729)^2 $ \\ 4 & (1/1089+ 10/729 + 2/25)&+ $k(30/1089+ 220/729 + 8/25)^2$\\ \end{tabular} \end{center} giving numeric values of 0.0012706, 0.0649885, and 0.2903805, respectively. \subsection{Efron approximation} For the Efron approximation the combination of tied times and case weights can be approached in at least two ways. One is to treat the case weights as replication counts. There are then 10 tied deaths at time 2 in the data above, and the Efron approximation involves 10 different denominator terms. Let $a= 7r+3$, the sum of risk scores for the 3 observations with an event at time 2 and $b=4r+2$, the sum of risk scores for the other subjects at risk at time 2. For the replication approach, the loglikelihood is \begin{eqnarray*} LL &=& \{2\beta - \log(r^2 + 11r +7)\} + \\ && \{7\beta - \log(a+b) - \log(.9a+b) - \ldots - \log(.1a+b) \} + \\ && \{2\beta - \log(2r+1) - \log(r+1)\}. \end{eqnarray*} A test program can be created by comparing results from the weighted data set (9 observations) to the unweighted replicated data set (19 observations). This is the approach taken by SAS \code{phreg} using the \code{freq} statement. It's advantage is that the appropriate result for all of the weighted computations is perfectly clear the disadvantage is that the only integer case weights are supported. (A secondary advantage is that I did not need to create another algebraic derivation for this appendix.) A second approach, used in {\splus}, allows for non-integer weights. The data is considered to be 3 tied observations, and the log-likelihood at time 2 is the sum of 3 weighted terms. The first term of the three is one of \begin{eqnarray*} && 3 [\beta - \log(a+b)] \\ && 4 [\beta - \log(a+b)] \\ &{\rm or}&3 [0 - \log(a+b)], \end{eqnarray*} depending on whether the event for observation C, D or E actually happened first (had we observed the time scale more exactly); the leading multiplier of 3, 4 or 3 is the case weight. The second term is one of \begin{eqnarray*} && 4 [\beta - \log(4s+3+b)] \\ && 3 [0 - \log(4s+3+b)] \\ && 3 [\beta - \log(3s+3+b)] \\ && 3 [\beta - \log(3s+3+b)] \\ && 3 [0 - \log(4s+3+b)] \\ &{\rm or}&4 [\beta - \log(4s+3+b)]. \end{eqnarray*} The first choice corresponds to an event order of observation C then D (subject D has the event, with D and E still at risk), the second to $C \rightarrow E$, then $D\rightarrow C$, $D\rightarrow E$, $E \rightarrow C$ and $E \rightarrow D$, respectively. For a weighted Efron approximation first replace the argument to the $\log$ function by its average argument, just as in the unweighted case. Once this is done the average term in the above corresponds to using an average weight of 10/3. The final log-likelihood and score statistic are \begin{eqnarray*} LL &=& \{2\beta - \log(r^2 + 11r +7)\} \\ && + \{7\beta - (10/3)[\log(a+b) + \log(2a/3 +b) + \log(a/3+b)] \} \\&& + 2\{\beta - \log(2r+1) \} \\ \\ U &=& (2- \xbar_1) + 2(1-\xbar_3) \\ && + 7 - (10/3)[\xbar_2 + 26r/(26r+12) + 19r/(19r+9)] \\ &=& 11 -(\xbar_1 + (10/3)(\xbar_2 + \xbar_{2b} +\xbar_{2c}) + 2\xbar_3)\\ \\ I &=& [(4s^2+11s)/(s^2+11s+7)- \xbar_1^2] \\ &&+ (10/3)[ (\xbar_2- \xbar_2^2) + (\xbar_{2b}- \xbar_{2b}^2) + (\xbar_{2b}- \xbar_{2b}^2) \\ &&+2(\xbar_3 - \xbar_3^2) \\ \end{eqnarray*} The solution is at $\beta=.87260425$, and $$ \begin{array}{ll} LL(0)=-30.29218 & LL(\bhat)=-29.41678 \\ U(0) = 2.148183 & U(\bhat) = 0 \\ \imat(0) = 2.929182 & \imat(\bhat) = 1.969447 \,. \end{array} $$ The hazard increment and mean at times 1 and 4 are identical to those for the Breslow approximation, as shown in table \ref{tab:val3}. At time 2, the number at risk for the first, second and third portions of the hazard increment are $n_1= 11r+5$, $n_2= (2/3)(7r+3) + 4r+2 = (26r+12)/3$, and $n_3=(1/3)(7r+3) + 4r+2 = (19r+9)/3$. Subjects F--I experience the full hazard at time 2 of $(10/3)(1/n_1 + 1/n_2 + 1/n_3)$, subjects B--D experience $(10/3)(1/n_1 + 2/3n_2 + 1/3n_3)$. Thus, at $\beta=0$ the martingale residuals are \begin{center} \begin{tabular}{cc|ll} Id& Time & \multicolumn{1}{c}{$\Mhat(0)$} \\ \hline A & 1 & 1 - 1/19 & = 18/19 \\ B & 1 & 0 - 1/19 & = -1/19 \\ C & 2 & 1 - (1/19 + 10/48 + 20/114 + 10/84)& =473/1064 \\ D & 2 & 1 - (1/19 + 10/48 + 20/114 + 10/84)& =473/1064 \\ E & 2 & 1 - (1/19 + 10/48 + 20/114 + 10/84) &=473/1064 \\ F & 2 & 0 - (1/19 + 10/48 + 10/38\phantom{4} + 10/28)& =-2813/3192 \\ G & 3 & 0 - (1/19 + 10/48 + 10/38\phantom{4} + 10/28) &=-2813/3192 \\ H & 4 & 1 - (1/19 + 10/48 + 10/38\phantom{4} + 10/28 + 2/3) &=-1749/3192 \\ I & 5 & 0 - (1/19 + 10/48 + 10/38\phantom{4} + 10/28 + 2/3) &=-4941/3192 \end{tabular} \end{center} The hazard estimate for a hypothetical subject with covariate $X^\dagger$ is $\Lambda_i(t) = \exp(X^\dagger \beta) \Lambda_0(t)$, $\Lambda_0$ has increments of $1/(r^2 + 11r +7$, $(10/3)(1/n_1 + 1/n_2 + 1/n_3)$ and $2/(2r+1)$. This increment at time 2 is a little larger than the Breslow jump of $10/d1$. The first term of the variance will have an increment of $[\exp((X^\dagger \beta)(]^2 (10/3)(1/n_1^2 + 1/n_2^2 + 1/n_3^2)$ at time 2. The increment to the cumulative distance from the center $d$ will be \begin{eqnarray*} && [X^\dagger - \frac{11r}{11r+5}] \frac{10}{3 n_1} \\ &+& [X^\dagger -\frac{(2/3)7r + 4r}{n2} ] (10/3)(1/n_2) \\ &+& [X^\dagger -\frac{(1/3)7r + 4r}{n2} ] (10/3)(1/n_3) \end{eqnarray*} For $X^\dagger = 1$ and $\beta=\pi/3$ we get cumulative hazard and variance below. 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5ustar hornikuserssurvival/build/vignette.rds0000644000175100001440000000067013070714003015577 0ustar hornikusers‹­R¹N1Ýœä”ÒÐ \‘Òð(Q„„’€(±â rصW¶su|6aœµwHTPøzóìyžy¯­(ŠÊQ¥†s·•Nuç8Q5jâÚ¡l9_©5 &bã°ö\&)˜j&«Øð£Ó˜ Ð!Ç€6!Ð5˜áÉ«miuÖ4挺„Çú.îÙr¥ 02E•™dhåj¿~´ÂnµÁë$‘ bM¨`$ûïDqýáÙ½ [š¤1¸™fº!i, .ö. 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License: LGPL (>= 2) URL: https://github.com/therneau/survival NeedsCompilation: yes Packaged: 2017-04-04 12:56:36 UTC; therneau Author: Terry M Therneau [aut, cre], Thomas Lumley [ctb, trl] (original S->R port and maintainer until 2009) Repository: CRAN Date/Publication: 2017-04-04 19:31:37 UTC survival/man/0000755000175100001440000000000013070714004012712 5ustar hornikuserssurvival/man/survexp.Rd0000644000175100001440000002025612571571667014747 0ustar hornikusers\name{survexp} \alias{survexp} \alias{print.survexp} \title{ Compute Expected Survival } \description{ Returns either the expected survival of a cohort of subjects, or the individual expected survival for each subject. } \usage{ survexp(formula, data, weights, subset, na.action, rmap, times, method=c("ederer", "hakulinen", "conditional", "individual.h", "individual.s"), cohort=TRUE, conditional=FALSE, ratetable=survival::survexp.us, scale=1, se.fit, model=FALSE, x=FALSE, y=FALSE) } \arguments{ \item{formula}{ formula object. The response variable is a vector of follow-up times and is optional. The predictors consist of optional grouping variables separated by the \code{+} operator (as in \code{survfit}), and is often \code{~1}, i.e., expected survival for the entire group. } \item{data}{ data frame in which to interpret the variables named in the \code{formula}, \code{subset} and \code{weights} arguments. } \item{weights}{ case weights. This is most useful when conditional survival for a known population is desired, e.g., the data set would contain all unique age/sex combinations and the weights would be the proportion of each. } \item{subset}{ expression indicating a subset of the rows of \code{data} to be used in the fit. } \item{na.action}{ function to filter missing data. This is applied to the model frame after \code{subset} has been applied. Default is \code{options()$na.action}. } \item{rmap}{ an optional list that maps data set names to the ratetable names. See the details section below. } \item{times}{ vector of follow-up times at which the resulting survival curve is evaluated. If absent, the result will be reported for each unique value of the vector of times supplied in the response value of the \code{formula}. } \item{method}{computational method for the creating the survival curves. The \code{individual} option does not create a curve, rather it retrieves the predicted survival \code{individual.s} or cumulative hazard \code{individual.h} for each subject. The default is to use \code{method='ederer'} if the formula has no response, and \code{method='hakulinen'} otherwise.} \item{cohort}{logical value. This argument has been superseded by the \code{method} argument. To maintain backwards compatability, if is present and FALSE, it implies \code{method='individual.s'}.} \item{conditional}{logical value. This argument has been superseded by the \code{method} argument. To maintain backwards compatability, if it is present and TRUE it implies \code{method='conditional'}.} \item{ratetable}{ a table of event rates, such as \code{survexp.mn}, or a fitted Cox model. Note the \code{survival::} prefix in the default argument is present to avoid the (rare) case of a user who expects the default table but just happens to have an object named "survexp.us" in their own directory.} \item{scale}{ numeric value to scale the results. If \code{ratetable} is in units/day, \code{scale = 365.25} causes the output to be reported in years. } \item{se.fit}{ compute the standard error of the predicted survival. This argument is currently ignored. Standard errors are not a defined concept for population rate tables (they are treated as coming from a complete census), and for Cox models the calculation is hard. Despite good intentions standard errors for this latter case have not been coded and validated. } \item{model,x,y}{ flags to control what is returned. If any of these is true, then the model frame, the model matrix, and/or the vector of response times will be returned as components of the final result, with the same names as the flag arguments. }} \value{ if \code{cohort=TRUE} an object of class \code{survexp}, otherwise a vector of per-subject expected survival values. The former contains the number of subjects at risk and the expected survival for the cohort at each requested time. The cohort survival is the hypothetical survival for a cohort of subjects enrolled from the population at large, but matching the data set on the factors found in the rate table. } \details{ Individual expected survival is usually used in models or testing, to `correct' for the age and sex composition of a group of subjects. For instance, assume that birth date, entry date into the study, sex and actual survival time are all known for a group of subjects. The \code{survexp.us} population tables contain expected death rates based on calendar year, sex and age. Then \preformatted{ haz <- survexp(fu.time ~ 1, data=mydata, rmap = list(year=entry.dt, age=(birth.dt-entry.dt)), method='individual.h')) } gives for each subject the total hazard experienced up to their observed death time or last follow-up time (variable fu.time) This probability can be used as a rescaled time value in models: \preformatted{ glm(status ~ 1 + offset(log(haz)), family=poisson) glm(status ~ x + offset(log(haz)), family=poisson) } In the first model, a test for intercept=0 is the one sample log-rank test of whether the observed group of subjects has equivalent survival to the baseline population. The second model tests for an effect of variable \code{x} after adjustment for age and sex. The ratetable being used may have different variable names than the user's data set, this is dealt with by the \code{rmap} argument. The rate table for the above calculation was \code{survexp.us}, a call to \code{summary{survexp.us}} reveals that it expects to have variables \code{age} = age in days, \code{sex}, and \code{year} = the date of study entry, we create them in the \code{rmap} line. The sex variable was not mapped, therefore the function assumes that it exists in \code{mydata} in the correct format. (Note: for factors such as sex, the program will match on any unique abbreviation, ignoring case.) Cohort survival is used to produce an overall survival curve. This is then added to the Kaplan-Meier plot of the study group for visual comparison between these subjects and the population at large. There are three common methods of computing cohort survival. In the "exact method" of Ederer the cohort is not censored, for this case no response variable is required in the formula. Hakulinen recommends censoring the cohort at the anticipated censoring time of each patient, and Verheul recommends censoring the cohort at the actual observation time of each patient. The last of these is the conditional method. These are obtained by using the respective time values as the follow-up time or response in the formula. } \references{ Berry, G. (1983). The analysis of mortality by the subject-years method. \emph{Biometrics}, 39:173-84. Ederer, F., Axtell, L. and Cutler, S. (1961). The relative survival rate: a statistical methodology. \emph{Natl Cancer Inst Monogr}, 6:101-21. Hakulinen, T. (1982). Cancer survival corrected for heterogeneity in patient withdrawal. \emph{Biometrics}, 38:933-942. Therneau, T. and Grambsch, P. (2000). Modeling survival data: Extending the Cox model. Springer. Chapter 10. Verheul, H., Dekker, E., Bossuyt, P., Moulijn, A. and Dunning, A. (1993). Background mortality in clinical survival studies. \emph{Lancet}, 341: 872-875. } \seealso{ \code{\link{survfit}}, \code{\link{pyears}}, \code{\link{survexp.us}}, \code{\link{survexp.fit}}. } \examples{ # # Stanford heart transplant data # We don't have sex in the data set, but know it to be nearly all males. # Estimate of conditional survival fit1 <- survexp(futime ~ 1, rmap=list(sex="male", year=accept.dt, age=(accept.dt-birth.dt)), method='conditional', data=jasa) summary(fit1, times=1:10*182.5, scale=365) #expected survival by 1/2 years # Estimate of expected survival stratified by prior surgery survexp(~ surgery, rmap= list(sex="male", year=accept.dt, age=(accept.dt-birth.dt)), method='ederer', data=jasa, times=1:10 * 182.5) ## Compare the survival curves for the Mayo PBC data to Cox model fit ## pfit <-coxph(Surv(time,status>0) ~ trt + log(bili) + log(protime) + age + platelet, data=pbc) plot(survfit(Surv(time, status>0) ~ trt, data=pbc), mark.time=FALSE) lines(survexp( ~ trt, ratetable=pfit, data=pbc), col='purple') } \keyword{survival} survival/man/survreg.control.Rd0000644000175100001440000000161711732700061016363 0ustar hornikusers\name{survreg.control} \alias{survreg.control} %- Also NEED an `\alias' for EACH other topic documented here. \title{Package options for survreg and coxph} \description{ This functions checks and packages the fitting options for \code{\link{survreg}} } \usage{ survreg.control(maxiter=30, rel.tolerance=1e-09, toler.chol=1e-10, iter.max, debug=0, outer.max=10) } %- maybe also `usage' for other objects documented here. \arguments{ \item{maxiter}{maximum number of iterations } \item{rel.tolerance}{relative tolerance to declare convergence } \item{toler.chol}{Tolerance to declare Cholesky decomposition singular} \item{iter.max}{same as \code{maxiter}} \item{debug}{print debugging information} \item{outer.max}{maximum number of outer iterations for choosing penalty parameters} } \value{ A list with the same elements as the input } \seealso{ \code{\link{survreg}}} \keyword{survival} survival/man/mgus2.Rd0000644000175100001440000000265113017617770014257 0ustar hornikusers\name{mgus2} \alias{mgus2} \docType{data} \title{Monoclonal gammapothy data} \description{Natural history of 1341 sequential patients with monoclonal gammapothy of undetermined significance (MGUS). } \usage{data("mgus2")} \format{ A data frame with 1384 observations on the following 10 variables. \describe{ \item{\code{id}}{subject identifier} \item{\code{age}}{age at diagnosis, in years} \item{\code{sex}}{a factor with levels \code{F} \code{M}} \item{\code{hgb}}{hemoglobin} \item{\code{creat}}{creatinine} \item{\code{mspike}}{size of the monoclonal serum splike} \item{\code{ptime}}{time until progression to a plasma cell malignancy (PCM) or last contact, in months} \item{\code{pstat}}{occurrence of PCM: 0=no, 1=yes } \item{\code{futime}}{time until death or last contact, in months} \item{\code{death}}{occurrence of death: 0=no, 1=yes} } } \details{ This is a larger follow-on study of the condition also found in data set \code{mgus}. } \source{Mayo Clinic data courtesy of Dr. Robert Kyle. All patient identifiers have been removed, age rounded to the nearest year, and follow-up times rounded to the nearest month.} \references{ R. Kyle, T. Therneau, V. Rajkumar, J. Offord, D. Larson, M. Plevak, and L. J. Melton III, A long-terms study of prognosis in monoclonal gammopathy of undertermined significance. New Engl J Med, 346:564-569 (2002). } \keyword{datasets} survival/man/lines.survfit.Rd0000644000175100001440000001227012760114003016014 0ustar hornikusers\name{lines.survfit} \alias{lines.survfit} \alias{points.survfit} \alias{lines.survexp} \title{ Add Lines or Points to a Survival Plot } \description{ Often used to add the expected survival curve(s) to a Kaplan-Meier plot generated with \code{plot.survfit}. } \usage{ \method{lines}{survfit}(x, type="s", mark=3, col=1, lty=1, lwd=1, cex=1, mark.time=FALSE, xscale=1, firstx=0, firsty=1, xmax, fun, conf.int=FALSE, conf.times, conf.cap=.005, conf.offset=.012, ...) \method{lines}{survexp}(x, type="l", ...) \method{points}{survfit}(x, xscale, xmax, fun, censor=FALSE, col=1, pch, ...) } \arguments{ \item{x}{ a survival object, generated from the \code{survfit} or \code{survexp} functions. } \item{type}{ the line type, as described in \code{lines}. The default is a step function for \code{survfit} objects, and a connected line for \code{survexp} objects. All other arguments for \code{lines.survexp} are identical to those for \code{lines.survfit}. } \item{mark, col, lty, lwd, cex}{ vectors giving the mark symbol, color, line type, line width and character size for the added curves. Of this set only color is applicable to \code{points}. } \item{pch}{plotting characters for points, in the style of \code{matplot}, i.e., either a single string of characters of which the first will be used for the first curve, etc; or a vector of characters or integers, one element per curve. } \item{censor}{should censoring times be displayed for the \code{points} function? } \item{...}{other graphical parameters} \item{mark.time}{ controls the labeling of the curves. If \code{FALSE}, no labeling is done. If \code{TRUE}, then curves are marked at each censoring time. If \code{mark.time} is a numeric vector, then curves are marked at the specified time points. } \item{xscale}{ this parameter is no longer necessary and is ignored. See the note in \code{\link{plot.survfit}}. } \item{firstx, firsty}{ the starting point for the survival curves. If either of these is set to \code{NA} or < blank > the plot will start at the first time point of the curve. } \item{xmax}{ the maximum horizontal plot coordinate. This shortens the curve before plotting it, so unlike using the \code{xlim} graphical parameter, warning messages about out of bounds points are not generated. } \item{fun}{ an arbitrary function defining a transformation of the survival curve. For example \code{fun=log} is an alternative way to draw a log-survival curve (but with the axis labeled with log(S) values). Four often used transformations can be specified with a character argument instead: "log" is the same as using the \code{log=T} option, "event" plots cumulative events (f(y) = 1-y), "cumhaz" plots the cumulative hazard function (f(y) = -log(y)) and "cloglog" creates a complimentary log-log survival plot (f(y) = log(-log(y))) along with log scale for the x-axis. } \item{conf.int}{ if \code{TRUE}, confidence bands for the curves are also plotted. If set to \code{"only"}, then only the CI bands are plotted, and the curve itself is left off. This can be useful for fine control over the colors or line types of a plot. } \item{conf.times}{optional vector of times at which to place a confidence bar on the curve(s). If present, these will be used instead of confidence bands.} \item{conf.cap}{width of the horizontal cap on top of the confidence bars; only used if conf.times is used. A value of 1 is the width of the plot region.} \item{conf.offset}{the offset for confidence bars, when there are multiple curves on the plot. A value of 1 is the width of the plot region. If this is a single number then each curve's bars are offset by this amount from the prior curve's bars, if it is a vector the values are used directly.} } \value{ a list with components \code{x} and \code{y}, containing the coordinates of the last point on each of the curves (but not of the confidence limits). This may be useful for labeling. } \section{Side Effects}{ one or more curves are added to the current plot. } \seealso{ \code{\link{lines}}, \code{\link{par}}, \code{\link{plot.survfit}}, \code{\link{survfit}}, \code{\link{survexp}}. } \details{ When the \code{survfit} function creates a multi-state survival curve the resulting object has class `survfitms'. The only difference in the plots is that that it defaults to a curve that goes from lower left to upper right (starting at 0), where survival curves default to starting at 1 and going down. All other options are identical. } \examples{ fit <- survfit(Surv(time, status==2) ~ sex, pbc,subset=1:312) plot(fit, mark.time=FALSE, xscale=365.25, xlab='Years', ylab='Survival') lines(fit[1], lwd=2) #darken the first curve and add marks # Add expected survival curves for the two groups, # based on the US census data # The data set does not have entry date, use the midpoint of the study efit <- survexp(~ ratetable(sex=sex,age=age*365.35,year=as.Date('1979/1/1')) + sex, data=pbc, times=(0:24)*182) temp <- lines(efit, lty=2, lwd=2:1) text(temp, c("Male", "Female"), adj= -.1) #labels just past the ends title(main="Primary Biliary Cirrhosis, Observed and Expected") } \keyword{survival} survival/man/print.summary.survfit.Rd0000644000175100001440000000144111732700061017533 0ustar hornikusers\name{print.summary.survfit} \alias{print.summary.survfit} \title{ Print Survfit Summary } \description{ Prints the result of \code{summary.survfit}. } \usage{ \method{print}{summary.survfit}(x, digits = max(options() $digits-4, 3), ...) } \arguments{ \item{x}{ an object of class \code{"summary.survfit"}, which is the result of the \code{summary.survfit} function. } \item{digits}{ the number of digits to use in printing the numbers. } \item{\dots}{for future methods} } \value{ \code{x}, with the invisible flag set to prevent printing. } \section{Side Effects}{ prints the summary created by \code{summary.survfit}. } \seealso{ \code{\link{options}}, \code{\link{print}}, \code{\link{summary.survfit}}. } \keyword{print} % docclass is function % Converted by Sd2Rd version 37351. survival/man/colon.Rd0000644000175100001440000000510712607725322014330 0ustar hornikusers\name{colon} \alias{colon} \title{Chemotherapy for Stage B/C colon cancer} \usage{colon} \description{These are data from one of the first successful trials of adjuvant chemotherapy for colon cancer. Levamisole is a low-toxicity compound previously used to treat worm infestations in animals; 5-FU is a moderately toxic (as these things go) chemotherapy agent. There are two records per person, one for recurrence and one for death} \format{ \tabular{ll}{ id:\tab id\cr study:\tab 1 for all patients\cr rx:\tab Treatment - Obs(ervation), Lev(amisole), Lev(amisole)+5-FU\cr sex:\tab 1=male\cr age:\tab in years\cr obstruct:\tab obstruction of colon by tumour\cr perfor:\tab perforation of colon\cr adhere:\tab adherence to nearby organs\cr nodes:\tab number of lymph nodes with detectable cancer\cr time:\tab days until event or censoring\cr status:\tab censoring status\cr differ:\tab differentiation of tumour (1=well, 2=moderate, 3=poor)\cr extent:\tab Extent of local spread (1=submucosa, 2=muscle, 3=serosa, 4=contiguous structures)\cr surg:\tab time from surgery to registration (0=short, 1=long)\cr node4:\tab more than 4 positive lymph nodes\cr etype:\tab event type: 1=recurrence,2=death\cr }} \note{The study is originally described in Laurie (1989). The main report is found in Moertel (1990). This data set is closest to that of the final report in Moertel (1991). A version of the data with less follow-up time was used in the paper by Lin (1994). } \references{ JA Laurie, CG Moertel, TR Fleming, HS Wieand, JE Leigh, J Rubin, GW McCormack, JB Gerstner, JE Krook and J Malliard. Surgical adjuvant therapy of large-bowel carcinoma: An evaluation of levamisole and the combination of levamisole and fluorouracil: The North Central Cancer Treatment Group and the Mayo Clinic. J Clinical Oncology, 7:1447-1456, 1989. DY Lin. Cox regression analysis of multivariate failure time data: the marginal approach. Statistics in Medicine, 13:2233-2247, 1994. CG Moertel, TR Fleming, JS MacDonald, DG Haller, JA Laurie, PJ Goodman, JS Ungerleider, WA Emerson, DC Tormey, JH Glick, MH Veeder and JA Maillard. Levamisole and fluorouracil for adjuvant therapy of resected colon carcinoma. New England J of Medicine, 332:352-358, 1990. CG Moertel, TR Fleming, JS MacDonald, DG Haller, JA Laurie, CM Tangen, JS Ungerleider, WA Emerson, DC Tormey, JH Glick, MH Veeder and JA Maillard, Fluorouracil plus Levamisole as an effective adjuvant therapy after resection of stage II colon carcinoma: a final report. Annals of Internal Med, 122:321-326, 1991. } \keyword{survival} survival/man/survreg.distributions.Rd0000644000175100001440000001032313013633731017602 0ustar hornikusers\name{survreg.distributions} \alias{survreg.distributions} \title{Parametric Survival Distributions} \usage{ survreg.distributions } \description{ List of distributions for accelerated failure models. These are location-scale families for some transformation of time. The entry describes the cdf \eqn{F} and density \eqn{f} of a canonical member of the family. } \format{ There are two basic formats, the first defines a distribution de novo, the second defines a new distribution in terms of an old one. \tabular{ll}{ name:\tab name of distribution\cr variance:\tab function(parms) returning the variance (currently unused)\cr init(x,weights,...):\tab Function returning an initial\cr \tab estimate of the mean and variance \cr \tab (used for initial values in the iteration)\cr density(x,parms):\tab Function returning a matrix with columns \eqn{F},\cr \tab \eqn{1-F},\eqn{f},\eqn{f'/f},\eqn{f''/f}\cr quantile(p,parms):\tab Quantile function\cr scale:\tab Optional fixed value for the scale parameter\cr parms:\tab Vector of default values and names for any additional parameters\cr deviance(y,scale,parms):\tab Function returning the deviance for a\cr \tab saturated model; used only for deviance residuals. } and to define one distribution in terms of another \tabular{ll}{ name:\tab name of distribution\cr dist:\tab name of parent distribution\cr trans:\tab transformation (eg log)\cr dtrans:\tab derivative of transformation\cr itrans:\tab inverse of transformation\cr scale:\tab Optional fixed value for scale parameter\cr } } \details{ There are four basic distributions:\code{extreme}, \code{gaussian}, \code{logistic} and \code{t}. The last three are parametrised in the same way as the distributions already present in \R. The extreme value cdf is \deqn{F=1-e^{-e^t}.} When the logarithm of survival time has one of the first three distributions we obtain respectively \code{weibull}, \code{lognormal}, and \code{loglogistic}. The location-scale parameterization of a Weibull distribution found in \code{survreg} is not the same as the parameterization of \code{\link{rweibull}}. The other predefined distributions are defined in terms of these. The \code{exponential} and \code{rayleigh} distributions are Weibull distributions with fixed \code{scale} of 1 and 0.5 respectively, and \code{loggaussian} is a synonym for \code{lognormal}. For speed parts of the three most commonly used distributions are hardcoded in C; for this reason the elements of \code{survreg.distributions} with names of "Extreme value", "Logistic" and "Gaussian" should not be modified. (The order of these in the list is not important, recognition is by name.) As an alternative to modifying \code{survreg.distributions} a new distribution can be specified as a separate list. This is the preferred method of addition and is illustrated below. } \seealso{\code{\link{survreg}}, \code{\link{pweibull}}, \code{\link{pnorm}},\code{\link{plogis}}, \code{\link{pt}}, \code{\link{survregDtest}} } \examples{ # time transformation survreg(Surv(time, status) ~ ph.ecog + sex, dist='weibull', data=lung) # change the transformation to work in years # intercept changes by log(365), everything else stays the same my.weibull <- survreg.distributions$weibull my.weibull$trans <- function(y) log(y/365) my.weibull$itrans <- function(y) 365*exp(y) survreg(Surv(time, status) ~ ph.ecog + sex, lung, dist=my.weibull) # Weibull parametrisation y<-rweibull(1000, shape=2, scale=5) survreg(Surv(y)~1, dist="weibull") # survreg scale parameter maps to 1/shape, linear predictor to log(scale) # Cauchy fit mycauchy <- list(name='Cauchy', init= function(x, weights, ...) c(median(x), mad(x)), density= function(x, parms) { temp <- 1/(1 + x^2) cbind(.5 + atan(x)/pi, .5+ atan(-x)/pi, temp/pi, -2 *x*temp, 2*temp*(4*x^2*temp -1)) }, quantile= function(p, parms) tan((p-.5)*pi), deviance= function(...) stop('deviance residuals not defined') ) survreg(Surv(log(time), status) ~ ph.ecog + sex, lung, dist=mycauchy) } \keyword{survival} survival/man/attrassign.Rd0000644000175100001440000000333312055773252015376 0ustar hornikusers\name{attrassign} \alias{attrassign.default} \alias{attrassign} \alias{attrassign.lm} \title{Create new-style "assign" attribute} \description{ The \code{"assign"} attribute on model matrices describes which columns come from which terms in the model formula. It has two versions. R uses the original version, but the alternate version found in S-plus is sometimes useful. } \usage{ \method{attrassign}{default}(object, tt,...) \method{attrassign}{lm}(object,...) } %- maybe also `usage' for other objects documented here. \arguments{ \item{object}{model matrix or linear model object} \item{tt}{terms object} \item{...}{ignored} } \value{ A list with names corresponding to the term names and elements that are vectors indicating which columns come from which terms } \details{ For instance consider the following \preformatted{ survreg(Surv(time, status) ~ age + sex + factor(ph.ecog), lung) } R gives the compact for for assign, a vector (0, 1, 2, 3, 3, 3); which can be read as ``the first column of the X matrix (intercept) goes with none of the terms, the second column of X goes with term 1 of the model equation, the third column of X with term 2, and columns 4-6 with term 3''. The alternate (S-Plus default) form is a list \preformatted{ $(Intercept) 1 $age 2 $sex 3 $factor(ph.ecog) 4 5 6 } } \seealso{\code{\link{terms}},\code{\link{model.matrix}}} \examples{ formula <- Surv(time,status)~factor(ph.ecog) tt <- terms(formula) mf <- model.frame(tt,data=lung) mm <- model.matrix(tt,mf) ## a few rows of data mm[1:3,] ## old-style assign attribute attr(mm,"assign") ## alternate style assign attribute attrassign(mm,tt) } \keyword{models} survival/man/rats2.Rd0000644000175100001440000000137412052731313014242 0ustar hornikusers\name{rats2} \alias{rats2} \docType{data} \title{Rat data from Gail et al.} \description{48 rats were injected with a carcinogen, and then randomized to either drug or placebo. The number of tumors ranges from 0 to 13; all rats were censored at 6 months after randomization. } \usage{rats2} \format{ \tabular{ll}{ rat:\tab id\cr trt:\tab treatment,(1=drug, 0=control) \cr observation:\tab within rat\cr start:\tab entry time\cr stop:\tab exit time\cr status:\tab event status, 1=tumor, 0=censored\cr } } \source{ MH Gail, TJ Santner, and CC Brown (1980), An analysis of comparative carcinogenesis experiments based on multiple times to tumor. \emph{Biometrics} \bold{36}, 255--266. } \keyword{survival} \keyword{datasets} survival/man/rats.Rd0000644000175100001440000000221712453556344014173 0ustar hornikusers\name{rats} \alias{rats} \docType{data} \title{Rat treatment data from Mantel et al} \description{Rat treatment data from Mantel et al. Three rats were chosen from each of 100 litters, one of which was treated with a drug, and then all followed for tumor incidence. } \usage{rats} \format{ \tabular{ll}{ litter:\tab litter number from 1 to 100\cr rx:\tab treatment,(1=drug, 0=control) \cr time:\tab time to tumor or last follow-up\cr status:\tab event status, 1=tumor and 0=censored\cr sex:\tab male or female } } \source{ N. Mantel, N. R. Bohidar and J. L. Ciminera. Mantel-Haenszel analyses of litter-matched time to response data, with modifications for recovery of interlitter information. Cancer Research, 37:3863-3868, 1977. } \references{ E. W. Lee, L. J. Wei, and D. Amato, Cox-type regression analysis for large number of small groups of correlated failure time observations, in "Survival Analysis, State of the Art", Kluwer, 1992. } \note{Since only 2/150 of the male rats have a tumor, most analyses use only females (odd numbered litters), e.g. Lee et al.} \keyword{survival} \keyword{datasets} survival/man/survreg.Rd0000644000175100001440000001127612604477535014726 0ustar hornikusers\name{survreg} \alias{survreg} \alias{model.frame.survreg} \alias{labels.survreg} \alias{print.survreg.penal} \alias{print.summary.survreg} \alias{survReg} \alias{anova.survreg} \alias{vcov.survreg} \alias{anova.survreglist} \title{ Regression for a Parametric Survival Model } \description{ Fit a parametric survival regression model. These are location-scale models for an arbitrary transform of the time variable; the most common cases use a log transformation, leading to accelerated failure time models. } \usage{ survreg(formula, data, weights, subset, na.action, dist="weibull", init=NULL, scale=0, control,parms=NULL,model=FALSE, x=FALSE, y=TRUE, robust=FALSE, score=FALSE, \dots) } \arguments{ \item{formula}{ a formula expression as for other regression models. The response is usually a survival object as returned by the \code{Surv} function. See the documentation for \code{Surv}, \code{lm} and \code{formula} for details. } \item{data}{ a data frame in which to interpret the variables named in the \code{formula}, \code{weights} or the \code{subset} arguments. } \item{weights}{optional vector of case weights} \item{subset}{ subset of the observations to be used in the fit } \item{na.action}{ a missing-data filter function, applied to the model.frame, after any \code{subset} argument has been used. Default is \code{options()\$na.action}. } \item{dist}{ assumed distribution for y variable. If the argument is a character string, then it is assumed to name an element from \code{\link{survreg.distributions}}. These include \code{"weibull"}, \code{"exponential"}, \code{"gaussian"}, \code{"logistic"},\code{"lognormal"} and \code{"loglogistic"}. Otherwise, it is assumed to be a user defined list conforming to the format described in \code{\link{survreg.distributions}}. } \item{parms}{ a list of fixed parameters. For the t-distribution for instance this is the degrees of freedom; most of the distributions have no parameters. } \item{init}{ optional vector of initial values for the parameters. } \item{scale}{ optional fixed value for the scale. If set to <=0 then the scale is estimated. } \item{control}{ a list of control values, in the format produced by \code{\link{survreg.control}}. The default value is \code{survreg.control()} } \item{model,x,y}{ flags to control what is returned. If any of these is true, then the model frame, the model matrix, and/or the vector of response times will be returned as components of the final result, with the same names as the flag arguments.} \item{score}{return the score vector. (This is expected to be zero upon successful convergence.) } \item{robust}{Use robust 'sandwich' standard errors, based on independence of individuals if there is no \code{cluster()} term in the formula, based on independence of clusters if there is.} \item{\dots}{ other arguments which will be passed to \code{survreg.control}. }} \value{ an object of class \code{survreg} is returned. } \details{ All the distributions are cast into a location-scale framework, based on chapter 2.2 of Kalbfleisch and Prentice. The resulting parameterization of the distributions is sometimes (e.g. gaussian) identical to the usual form found in statistics textbooks, but other times (e.g. Weibull) it is not. See the book for detailed formulas. } \seealso{ \code{\link{survreg.object}}, \code{\link{survreg.distributions}}, \code{\link{pspline}}, \code{\link{frailty}}, \code{\link{ridge}} } \examples{ # Fit an exponential model: the two fits are the same survreg(Surv(futime, fustat) ~ ecog.ps + rx, ovarian, dist='weibull', scale=1) survreg(Surv(futime, fustat) ~ ecog.ps + rx, ovarian, dist="exponential") # # A model with different baseline survival shapes for two groups, i.e., # two different scale parameters survreg(Surv(time, status) ~ ph.ecog + age + strata(sex), lung) # There are multiple ways to parameterize a Weibull distribution. The survreg # function embeds it in a general location-scale family, which is a # different parameterization than the rweibull function, and often leads # to confusion. # survreg's scale = 1/(rweibull shape) # survreg's intercept = log(rweibull scale) # For the log-likelihood all parameterizations lead to the same value. y <- rweibull(1000, shape=2, scale=5) survreg(Surv(y)~1, dist="weibull") # Economists fit a model called `tobit regression', which is a standard # linear regression with Gaussian errors, and left censored data. tobinfit <- survreg(Surv(durable, durable>0, type='left') ~ age + quant, data=tobin, dist='gaussian') } \references{ Kalbfleisch, J. D. and Prentice, R. L., The statistical analysis of failure time data, Wiley, 2002. } \keyword{survival} survival/man/uspop2.Rd0000644000175100001440000000205413013633731014436 0ustar hornikusers\name{uspop2} \alias{uspop2} \docType{data} \title{Projected US Population} \description{US population by age and sex, for 2000 through 2020} \usage{data(uspop2)} \format{ The data is a matrix with dimensions age, sex, and calendar year. Age goes from 0 through 100, where the value for age 100 is the total for all ages of 100 or greater. } \details{ This data is often used as a "standardized" population for epidemiology studies.} \source{ NP2008_D1: Projected Population by Single Year of Age, Sex, Race, and Hispanic Origin for the United States: July 1, 2000 to July 1, 2050, www.census.gov/population/projections. } \examples{ us50 <- uspop2[51:101,, "2000"] #US 2000 population, 50 and over age <- as.integer(dimnames(us50)[[1]]) smat <- model.matrix( ~ factor(floor(age/5)) -1) ustot <- t(smat) \%*\% us50 #totals by 5 year age groups temp <- c(50,55, 60, 65, 70, 75, 80, 85, 90, 95) dimnames(ustot) <- list(c(paste(temp, temp+4, sep="-"), "100+"), c("male", "female")) } \seealso{\code{\link{uspop}}} \keyword{datasets} survival/man/cipoisson.Rd0000644000175100001440000000407113017026563015220 0ustar hornikusers\name{cipoisson} \alias{cipoisson} \title{Confidence limits for the Poisson} \description{Confidence interval calculation for Poisson rates.} \usage{ cipoisson(k, time = 1, p = 0.95, method = c("exact", "anscombe")) } \arguments{ \item{k}{Number of successes} \item{time}{Total time on trial} \item{p}{Probability level for the (two-sided) interval} \item{method}{The method for computing the interval.} } \value{a vector, matrix, or array. If both \code{k} and \code{time} are single values the result is a vector of length 2 containing the lower an upper limits. If either or both are vectors the result is a matrix with two columns. If \code{k} is a matrix or array, the result will be an array with one more dimension; in this case the dimensions and dimnames (if any) of \code{k} are preserved. } \details{ The likelihood method is based on equation 10.10 of Feller, which relates poisson probabilities to tail area of the gamma distribution. The Anscombe approximation is based on the fact that sqrt(k + 3/8) is has a nearly constant variance of 1/4, along with a continuity correction. There are many other proposed intervals: Patil and Kulkarni list and evaluate 19 different suggestions from the literature!. The exact intervals can be overly broad for very small values of \code{k}, many of the other approaches try to shrink the lengths, with varying success. } \examples{ cipoisson(4) # 95\\\% confidence limit # lower upper # 1.089865 10.24153 ppois(4, 10.24153) #chance of seeing 4 or fewer events with large rate # [1] 0.02500096 1-ppois(3, 1.08986) #chance of seeing 4 or more, with a small rate # [1] 0.02499961 } \references{ F.J. Anscombe (1949). Transformations of Poisson, binomial and negative-binomial data. Biometrika, 35:246-254. W.F. Feller (1950). An Introduction to Probability Theory and its Applications, Volume 1, Chapter 6, Wiley. V. V. Patil and H.F. Kulkarni (2012). Comparison of confidence intervals for the poisson mean: some new aspects. Revstat 10:211-227. } \seealso{ \code{\link[stats]{ppois}}, \code{\link[stats]{qpois}} } survival/man/survfitcoxph.fit.Rd0000644000175100001440000000567313017617770016556 0ustar hornikusers\name{survfitcoxph.fit} \alias{survfitcoxph.fit} \title{ A direct interface to the `computational engine' of survfit.coxph } \description{ This program is mainly supplied to allow other packages to invoke the survfit.coxph function at a `data' level rather than a `user' level. It does no checks on the input data that is provided, which can lead to unexpected errors if that data is wrong. } \usage{ survfitcoxph.fit(y, x, wt, x2, risk, newrisk, strata, se.fit, survtype, vartype, varmat, id, y2, strata2, unlist=TRUE) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{y}{the response variable used in the Cox model. (Missing values removed of course.) } \item{x}{covariate matrix used in the Cox model } \item{wt}{weight vector for the Cox model. If the model was unweighted use a vector of 1s. } \item{x2}{matrix describing the hypothetical subjects for which a curve is desired. Must have the same number of columns as \code{x}. } \item{risk}{the risk score exp(X beta) from the fitted Cox model. If the model had an offset, include it in the argument to exp. } \item{newrisk}{risk scores for the hypothetical subjects } \item{strata}{strata variable used in the Cox model. This will be a factor. } \item{se.fit}{if \code{TRUE} the standard errors of the curve(s) are returned } \item{survtype}{1=Kalbfleisch-Prentice, 2=Nelson-Aalen, 3=Efron. It is usual to match this to the approximation for ties used in the \code{coxph} model: KP for `exact', N-A for `breslow' and Efron for `efron'. } \item{vartype}{1=Greenwood, 2=Aalen, 3=Efron } \item{varmat}{the variance matrix of the coefficients } \item{id}{optional; if present and not NULL this should be a vector of identifiers of length \code{nrow(x2)}. A mon-null value signifies that \code{x2} contains time dependent covariates, in which case this identifies which rows of \code{x2} go with each subject. } \item{y2}{survival times, for time dependent prediction. It gives the time range (time1,time2] for each row of \code{x2}. Note: this must be a Surv object and thus contains a status indicator, which is never used in the routine, however. } \item{strata2}{vector of strata indicators for \code{x2}. This must be a factor. } \item{unlist}{if \code{FALSE} the result will be a list with one element for each strata. Otherwise the strata are ``unpacked'' into the form found in a \code{survfit} object.} } \value{a list containing nearly all the components of a \code{survfit} object. All that is missing is to add the confidence intervals, the type of the original model's response (as in a coxph object), and the class. } \note{The source code for for both this function and \code{survfit.coxph} is written using noweb. For complete documentation see the \code{inst/sourcecode.pdf} file. } \author{Terry Therneau} \seealso{\code{\link{survfit.coxph}} } \keyword{survival} survival/man/ratetable.Rd0000644000175100001440000000200012760114003015132 0ustar hornikusers\name{ratetable} \alias{ratetable} \alias{[.ratetable} \alias{[.ratetable2} \alias{print.ratetable} \alias{is.na.ratetable} \alias{summary.ratetable} \title{Ratetable reference in formula} \description{ This function matches variable names in data to those in a ratetable for \code{\link{survexp}} } \usage{ ratetable(...) } \arguments{ \item{\dots}{tags matching dimensions of the ratetable and variables in the data frame (see example)} } \value{ A data frame } \seealso{\code{\link{survexp}},\code{\link{survexp.us}},\code{\link{is.ratetable}}} \examples{ fit <- survfit(Surv(time, status) ~ sex, pbc,subset=1:312) # The data set does not have entry date, use the midpoint of the study efit <- survexp(~ ratetable(sex=sex,age=age*365.35,year=as.Date('1979/1/1')) + sex, data=pbc, times=(0:24)*182) \dontrun{ plot(fit, mark.time=F, xscale=365.25, xlab="Years post diagnosis", ylab="Survival") lines(efit, col=2) # Add the expected survival line } } \keyword{survival}%-- one or more ... survival/man/residuals.survreg.Rd0000644000175100001440000000531111732700061016671 0ustar hornikusers\name{residuals.survreg} \alias{residuals.survreg} \alias{residuals.survreg.penal} \title{Compute Residuals for `survreg' Objects} \description{ This is a method for the function \code{\link{residuals}} for objects inheriting from class \code{survreg}. } \usage{ \method{residuals}{survreg}(object, type=c("response", "deviance","dfbeta","dfbetas", "working","ldcase","ldresp","ldshape", "matrix"), rsigma=TRUE, collapse=FALSE, weighted=FALSE, ...) } \arguments{ \item{object}{ an object inheriting from class \code{survreg}. } \item{type}{ type of residuals, with choices of \code{"response"}, \code{"deviance"}, \code{"dfbeta"}, \code{"dfbetas"}, \code{"working"}, \code{"ldcase"}, \code{"lsresp"}, \code{"ldshape"}, and \code{"matrix"}. See the LaTeX documentation (\code{survival/doc/survival.ps.gz}) for more detail. } \item{rsigma}{ include the scale parameters in the variance matrix, when doing computations. (I can think of no good reason not to). } \item{collapse}{ optional vector of subject groups. If given, this must be of the same length as the residuals, and causes the result to be per group residuals. } \item{weighted}{ give weighted residuals? Normally residuals are unweighted. }\item{...}{other unused arguments}} \value{ A vector or matrix of residuals is returned. Response residuals are on the scale of the original data, working residuals are on the scale of the linear predictor, and deviance residuals are on log-likelihood scale. The dfbeta residuals are a matrix, where the ith row gives the approximate change in the coefficients due to the addition of subject i. The dfbetas matrix contains the dfbeta residuals, with each column scaled by the standard deviation of that coefficient. The matrix type produces a matrix based on derivatives of the log-likelihood function. Let \eqn{L} be the log-likelihood, \eqn{p} be the linear predictor \eqn{X\beta}{X \%*\% coef}, and \eqn{s} be \eqn{\log(\sigma)}. Then the 6 columns of the matrix are \eqn{L}, \eqn{dL/dp},\eqn{\partial^2L/\partial p^2}{ddL/(dp dp)}, \eqn{dL/ds}, \eqn{\partial^2L/\partial s^2}{ddL/(ds ds)} and \eqn{\partial^2L/\partial p\partial s}{ddL/(dp ds)}. Diagnostics based on these quantities are discussed in an article by Escobar and Meeker. The main ones are the likelihood displacement residuals for perturbation of a case weight (\code{ldcase}), the response value (\code{ldresp}), and the \code{shape}. } \references{ Escobar, L. A. and Meeker, W. Q. (1992). Assessing influence in regression analysis with censored data. \emph{Biometrics} \bold{48}, 507-528. } \seealso{\code{\link{predict.survreg}}} \examples{ fit <- survreg(Surv(time,status) ~x, aml) rr <- residuals(fit, type='matrix') } \keyword{survival} % Converted by Sd2Rd version 0.3-2. survival/man/survfit.matrix.Rd0000644000175100001440000000656113026501446016223 0ustar hornikusers\name{survfit.matrix} \alias{survfit.matrix} \title{Create Aalen-Johansen estimates of multi-state survival from a matrix of hazards.} \description{ This allows one to create the Aalen-Johansen estimate of P, a matrix with one column per state and one row per time, starting with the individual hazard estimates. Each row of P will sum to 1. } \usage{ \method{survfit}{matrix}(formula, p0, method = c("discrete", "matexp"), ...) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{formula}{a matrix of lists, each element of which is either NULL or a survival curve object. } \item{p0}{the initial state vector. The names of this vector are used as the names of the states in the output object. If there are multiple curves then \code{p0} can be a matrix with one row per curve. } \item{method}{ use a product of discrete hazards, or a product of matrix exponentials. See details below. } \item{...}{further arguments for other methods} } \details{ On input the matrix should contain a set of predicted curves for each possible transition, and NULL in other positions. Each of the predictions will have been obtained from the relevant Cox model. This approach for multistate curves is easy to use but has some caveats. First, the input curves must be consistent. The routine checks as best it can, but can easy be fooled. For instance, if one were to fit two Cox models, obtain predictions for males and females from one, and for treatment A and B from the other, this routine will create two curves but they are not meaningful. A second issue is that standard errors are not produced. The names of the resulting states are taken from the names of the vector of initial state probabilities. If they are missing, then the dimnames of the input matrix are used, and lacking that the labels '1', '2', etc. are used. For the usual Aalen-Johansen estimator the multiplier at each event time is the matrix of hazards H (also written as I + dA). When using predicted survival curves from a Cox model, however, it is possible to get predicted hazards that are greater than 1, which leads to probabilities less than 0. If the \code{method} argument is not supplied and the input curves are derived from a Cox model this routine instead uses the approximation expm(H-I) as the multiplier, which always gives valid probabilities. (This is also the standard approach for ordinary survival curves from a Cox model.) } \value{a survfitms object} \author{Terry Therneau} \note{The R syntax for creating a matrix of lists is very fussy.} \seealso{\code{\link{survfit}}} \examples{ etime <- with(mgus2, ifelse(pstat==0, futime, ptime)) event <- with(mgus2, ifelse(pstat==0, 2*death, 1)) event <- factor(event, 0:2, labels=c("censor", "pcm", "death")) cfit1 <- coxph(Surv(etime, event=="pcm") ~ age + sex, mgus2) cfit2 <- coxph(Surv(etime, event=="death") ~ age + sex, mgus2) # predicted competing risk curves for a 72 year old with mspike of 1.2 # (median values), male and female. # The survfit call is a bit faster without standard errors. newdata <- expand.grid(sex=c("F", "M"), age=72, mspike=1.2) AJmat <- matrix(list(), 3,3) AJmat[1,2] <- list(survfit(cfit1, newdata, std.err=FALSE)) AJmat[1,3] <- list(survfit(cfit2, newdata, std.err=FALSE)) csurv <- survfit(AJmat, p0 =c(entry=1, PCM=0, death=0)) } \keyword{survival } survival/man/print.survfit.Rd0000644000175100001440000000713012461741246016052 0ustar hornikusers\name{print.survfit} \alias{print.survfit} \title{ Print a Short Summary of a Survival Curve } \description{ Print number of observations, number of events, the restricted mean survival and its standard error, and the median survival with confidence limits for the median. } \usage{ \method{print}{survfit}(x, scale=1, digits = max(options()$digits - 4,3), print.rmean=getOption("survfit.print.rmean"), rmean = getOption('survfit.rmean'),...) } \arguments{ \item{x}{ the result of a call to the \code{survfit} function. } \item{scale}{ a numeric value to rescale the survival time, e.g., if the input data to survfit were in days, \code{scale=365} would scale the printout to years. } \item{digits}{Number of digits to print} \item{print.rmean,rmean}{Options for computation and display of the restricted mean.} \item{\dots}{for future results} } \value{ x, with the invisible flag set to prevent printing. (The default for all print functions in R is to return the object passed to them; print.survfit complies with this pattern. If you want to capture these printed results for further processing, see the \code{table} component of \code{summary.survfit}.) } \section{Side Effects}{ The number of observations, the number of events, the median survival with its confidence interval, and optionally the restricted mean survival (\code{rmean}) and its standard error, are printed. If there are multiple curves, there is one line of output for each. } \details{ The mean and its variance are based on a truncated estimator. That is, if the last observation(s) is not a death, then the survival curve estimate does not go to zero and the mean is undefined. There are four possible approaches to resolve this, which are selected by the \code{rmean} option. The first is to set the upper limit to a constant, e.g.,\code{rmean=365}. In this case the reported mean would be the expected number of days, out of the first 365, that would be experienced by each group. This is useful if interest focuses on a fixed period. Other options are \code{"none"} (no estimate), \code{"common"} and \code{"individual"}. The \code{"common"} option uses the maximum time for all curves in the object as a common upper limit for the auc calculation. For the \code{"individual"}options the mean is computed as the area under each curve, over the range from 0 to the maximum observed time for that curve. Since the end point is random, values for different curves are not comparable and the printed standard errors are an underestimate as they do not take into account this random variation. This option is provided mainly for backwards compatability, as this estimate was the default (only) one in earlier releases of the code. Note that SAS (as of version 9.3) uses the integral up to the last \emph{event} time of each individual curve; we consider this the worst of the choices and do not provide an option for that calculation. The median and its confidence interval are defined by drawing a horizontal line at 0.5 on the plot of the survival curve and its confidence bands. The intersection of the line with the lower CI band defines the lower limit for the median's interval, and similarly for the upper band. If any of the intersections is not a point, then we use the smallest point of intersection, e.g., if the survival curve were exactly equal to 0.5 over an interval. } \section{References}{ Miller, Rupert G., Jr. (1981). \emph{Survival Analysis.} New York:Wiley, p 71. } \seealso{ \code{\link{summary.survfit}}, \code{\link{quantile.survfit}} } \keyword{survival} % docclass is function % Converted by Sd2Rd version 37351. survival/man/summary.survexp.Rd0000644000175100001440000000266113013633731016422 0ustar hornikusers\name{summary.survexp} \alias{summary.survexp} \title{Summary function for a survexp object} \description{ Returns a list containing the values of the survival at specified times. } \usage{ \method{summary}{survexp}(object, times, scale = 1, ...) } \arguments{ \item{object}{ the result of a call to the \code{survexp} function } \item{times}{ vector of times; the returned matrix will contain 1 row for each time. Missing values are not allowed. } \item{scale}{ numeric value to rescale the survival time, e.g., if the input data to \code{survfit} were in days, \code{scale = 365.25} would scale the output to years. } \item{\dots}{For future methods} } \details{ A primary use of this function is to retrieve survival at fixed time points, which will be properly interpolated by the function. } \value{ a list with the following components: \item{surv}{ the estimate of survival at time t. } \item{time}{ the timepoints on the curve. } \item{n.risk}{ In expected survival each subject from the data set is matched to a hypothetical person from the parent population, matched on the characteristics of the parent population. The number at risk is the number of those hypothetical subject who are still part of the calculation. } } \author{Terry Therneau} \seealso{\code{\link{survexp}} } % Add one or more standard keywords, see file 'KEYWORDS' in the % R documentation directory. \keyword{ survival } survival/man/aeqSurv.Rd0000644000175100001440000000255613026563540014647 0ustar hornikusers\name{aeqSurv} \alias{aeqSurv} \title{Adjudicate near ties in a Surv object} \description{The check for tied survival times can fail due to floating point imprecision, which can make actual ties appear to be distinct values. Routines that depend on correct identification of ties pairs will then give incorrect results, e.g., a Cox model. This function rectifies these. } \usage{ aeqSurv(x, tolerance = sqrt(.Machine$double.eps)) } \arguments{ \item{x}{a Surv object} \item{tolerance}{the tolerance used to detect values that will be considered equal} } \details{ This routine is called by both \code{survfit} and \code{coxph} to deal with the issue of ties that get incorrectly broken due to floating point imprecision. See the short vignette on tied times for a simple example. Use the \code{timefix} argument of \code{survfit} or \code{coxph.control} to control the option if desired. The rule for `equality' is identical to that used by the \code{all.equal} routine. Pairs of values that are within round off error of each other are replaced by the smaller value. An error message is generated if this process causes a 0 length time interval to be created. } \value{a Surv object identical to the original, but with ties restored.} \author{Terry Therneau} \seealso{\code{\link{survfit}}, \code{\link{coxph.control}}} \keyword{ survival } survival/man/survdiff.Rd0000644000175100001440000000710311732700061015033 0ustar hornikusers\name{survdiff} \alias{survdiff} \alias{print.survdiff} \title{ Test Survival Curve Differences } \description{ Tests if there is a difference between two or more survival curves using the \eqn{G^\rho}{G-rho} family of tests, or for a single curve against a known alternative. } \usage{ survdiff(formula, data, subset, na.action, rho=0) } \arguments{ \item{formula}{ a formula expression as for other survival models, of the form \code{Surv(time, status) ~ predictors}. For a one-sample test, the predictors must consist of a single \code{offset(sp)} term, where \code{sp} is a vector giving the survival probability of each subject. For a k-sample test, each unique combination of predictors defines a subgroup. A \code{strata} term may be used to produce a stratified test. To cause missing values in the predictors to be treated as a separate group, rather than being omitted, use the \code{strata} function with its \code{na.group=T} argument. } \item{data}{ an optional data frame in which to interpret the variables occurring in the formula. } \item{subset}{ expression indicating which subset of the rows of data should be used in the fit. This can be a logical vector (which is replicated to have length equal to the number of observations), a numeric vector indicating which observation numbers are to be included (or excluded if negative), or a character vector of row names to be included. All observations are included by default. } \item{na.action}{ a missing-data filter function. This is applied to the \code{model.frame} after any subset argument has been used. Default is \code{options()$na.action}. } \item{rho}{ a scalar parameter that controls the type of test. }} \value{ a list with components: \item{n}{ the number of subjects in each group. } \item{obs}{ the weighted observed number of events in each group. If there are strata, this will be a matrix with one column per stratum. } \item{exp}{ the weighted expected number of events in each group. If there are strata, this will be a matrix with one column per stratum. } \item{chisq}{ the chisquare statistic for a test of equality. } \item{var}{ the variance matrix of the test. } \item{strata}{ optionally, the number of subjects contained in each stratum. }} \section{METHOD}{ This function implements the G-rho family of Harrington and Fleming (1982), with weights on each death of \eqn{S(t)^\rho}{S(t)^rho}, where \eqn{S(t)}{S} is the Kaplan-Meier estimate of survival. With \code{rho = 0} this is the log-rank or Mantel-Haenszel test, and with \code{rho = 1} it is equivalent to the Peto & Peto modification of the Gehan-Wilcoxon test. If the right hand side of the formula consists only of an offset term, then a one sample test is done. To cause missing values in the predictors to be treated as a separate group, rather than being omitted, use the \code{factor} function with its \code{exclude} argument. } \references{ Harrington, D. P. and Fleming, T. R. (1982). A class of rank test procedures for censored survival data. \emph{Biometrika} \bold{69}, 553-566.} \examples{ ## Two-sample test survdiff(Surv(futime, fustat) ~ rx,data=ovarian) ## Stratified 7-sample test survdiff(Surv(time, status) ~ pat.karno + strata(inst), data=lung) ## Expected survival for heart transplant patients based on ## US mortality tables expect <- survexp(futime ~ ratetable(age=(accept.dt - birth.dt), sex=1,year=accept.dt,race="white"), jasa, cohort=FALSE, ratetable=survexp.usr) ## actual survival is much worse (no surprise) survdiff(Surv(jasa$futime, jasa$fustat) ~ offset(expect)) } \keyword{survival} % Converted by Sd2Rd version 0.3-2. and hand edited. survival/man/bladder.Rd0000644000175100001440000000646613070446751014625 0ustar hornikusers\name{bladder} \docType{data} \alias{bladder} \alias{bladder1} \alias{bladder2} \title{Bladder Cancer Recurrences} \usage{ bladder1 bladder bladder2 } \description{Data on recurrences of bladder cancer, used by many people to demonstrate methodology for recurrent event modelling. Bladder1 is the full data set from the study. It contains all three treatment arms and all recurrences for 118 subjects; the maximum observed number of recurrences is 9. Bladder is the data set that appears most commonly in the literature. It uses only the 85 subjects with nonzero follow-up who were assigned to either thiotepa or placebo, and only the first four recurrences for any patient. The status variable is 1 for recurrence and 0 for everything else (including death for any reason). The data set is laid out in the competing risks format of the paper by Wei, Lin, and Weissfeld. Bladder2 uses the same subset of subjects as bladder, but formatted in the (start, stop] or Anderson-Gill style. Note that in transforming from the WLW to the AG style data set there is a quite common programming mistake that leads to extra follow-up time for 12 subjects: all those with follow-up beyond their 4th recurrence. This "follow-up" is a side effect of throwing away all events after the fourth while retaining the last follow-up time variable from the original data. The bladder2 data set found here does not make this mistake, but some analyses in the literature have done so; it results in the addition of a small amount of immortal time bias and shrinks the fitted coefficients towards zero. } \format{ bladder1 \tabular{ll}{ id:\tab Patient id\cr treatment:\tab Placebo, pyridoxine (vitamin B6), or thiotepa\cr number:\tab Initial number of tumours (8=8 or more)\cr size:\tab Size (cm) of largest initial tumour\cr recur:\tab Number of recurrences \cr start,stop:\tab The start and end time of each time interval\cr status:\tab End of interval code, 0=censored, 1=recurrence, \cr \tab 2=death from bladder disease, 3=death other/unknown cause\cr rtumor:\tab Number of tumors found at the time of a recurrence\cr rsize:\tab Size of largest tumor at a recurrence\cr enum:\tab Event number (observation number within patient)\cr } bladder \tabular{ll}{ id:\tab Patient id\cr rx:\tab Treatment 1=placebo 2=thiotepa\cr number:\tab Initial number of tumours (8=8 or more)\cr size:\tab size (cm) of largest initial tumour\cr stop:\tab recurrence or censoring time\cr enum:\tab which recurrence (up to 4)\cr } bladder2 \tabular{ll}{ id:\tab Patient id\cr rx:\tab Treatment 1=placebo 2=thiotepa\cr number:\tab Initial number of tumours (8=8 or more)\cr size:\tab size (cm) of largest initial tumour\cr start:\tab start of interval (0 or previous recurrence time)\cr stop:\tab recurrence or censoring time\cr enum:\tab which recurrence (up to 4)\cr } } \source{ Andrews DF, Hertzberg AM (1985), DATA: A Collection of Problems from Many Fields for the Student and Research Worker, New York: Springer-Verlag. LJ Wei, DY Lin, L Weissfeld (1989), Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. \emph{Journal of the American Statistical Association}, \bold{84}. } \keyword{datasets} \keyword{survival} survival/man/pbcseq.Rd0000644000175100001440000000661513013633731014472 0ustar hornikusers\name{pbcseq} \alias{pbcseq} \docType{data} \title{Mayo Clinic Primary Biliary Cirrhosis, sequential data} \description{ This data is a continuation of the PBC data set, and contains the follow-up laboratory data for each study patient. An analysis based on the data can be found in Murtagh, et. al. The primary PBC data set contains only baseline measurements of the laboratory parameters. This data set contains multiple laboratory results, but only on the 312 randomized patients. Some baseline data values in this file differ from the original PBC file, for instance, the data errors in prothrombin time and age which were discovered after the original analysis (see Fleming and Harrington, figure 4.6.7). One "feature" of the data deserves special comment. The last observation before death or liver transplant often has many more missing covariates than other data rows. The original clinical protocol for these patients specified visits at 6 months, 1 year, and annually thereafter. At these protocol visits lab values were obtained for a large pre-specified battery of tests. "Extra" visits, often undertaken because of worsening medical condition, did not necessarily have all this lab work. The missing values are thus potentially informative. } \usage{pbc} \format{ \tabular{ll}{ id:\tab case number\cr age:\tab in years\cr sex:\tab m/f\cr trt:\tab 1/2/NA for D-penicillmain, placebo, not randomised\cr time:\tab number of days between registration and the earlier of death,\cr \tab transplantion, or study analysis in July, 1986\cr status:\tab status at endpoint, 0/1/2 for censored, transplant, dead\cr day:\tab number of days between enrollment and this visit date\cr \tab all measurements below refer to this date\cr albumin:\tab serum albumin (mg/dl)\cr alk.phos:\tab alkaline phosphotase (U/liter)\cr ascites:\tab presence of ascites \cr ast:\tab aspartate aminotransferase, once called SGOT (U/ml)\cr bili:\tab serum bilirunbin (mg/dl)\cr chol:\tab serum cholesterol (mg/dl)\cr copper:\tab urine copper (ug/day)\cr edema:\tab 0 no edema, 0.5 untreated or successfully treated\cr \tab 1 edema despite diuretic therapy\cr hepato:\tab presence of hepatomegaly or enlarged liver\cr platelet:\tab platelet count\cr protime:\tab standardised blood clotting time\cr spiders:\tab blood vessel malformations in the skin\cr stage:\tab histologic stage of disease (needs biopsy)\cr trig:\tab triglycerides (mg/dl)\cr } } \source{ T Therneau and P Grambsch, "Modeling Survival Data: Extending the Cox Model", Springer-Verlag, New York, 2000. ISBN: 0-387-98784-3. } \examples{ # Create the start-stop-event triplet needed for coxph first <- with(pbcseq, c(TRUE, diff(id) !=0)) #first id for each subject last <- c(first[-1], TRUE) #last id time1 <- with(pbcseq, ifelse(first, 0, day)) time2 <- with(pbcseq, ifelse(last, futime, c(day[-1], 0))) event <- with(pbcseq, ifelse(last, status, 0)) fit1 <- coxph(Surv(time1, time2, event) ~ age + sex + log(bili), pbcseq) } \references{ Murtaugh PA. Dickson ER. Van Dam GM. Malinchoc M. Grambsch PM. Langworthy AL. Gips CH. "Primary biliary cirrhosis: prediction of short-term survival based on repeated patient visits." Hepatology. 20(1.1):126-34, 1994. Fleming T and Harrington D., "Counting Processes and Survival Analysis", Wiley, New York, 1991. } \keyword{datasets} survival/man/frailty.Rd0000644000175100001440000001174613017617770014701 0ustar hornikusers\name{frailty} \alias{frailty} \alias{frailty.gamma} \alias{frailty.gaussian} \alias{frailty.t} \title{ Random effects terms } \description{ The frailty function allows one to add a simple random effects term to a Cox or survreg model. } \usage{ frailty(x, distribution="gamma", ...) frailty.gamma(x, sparse = (nclass > 5), theta, df, eps = 1e-05, method = c("em","aic", "df", "fixed"), ...) frailty.gaussian(x, sparse = (nclass > 5), theta, df, method =c("reml","aic", "df", "fixed"), ...) frailty.t(x, sparse = (nclass > 5), theta, df, eps = 1e-05, tdf = 5, method = c("aic", "df", "fixed"), ...) } \arguments{ \item{x}{ the variable to be entered as a random effect. It is always treated as a factor. } \item{distribution}{ either the \code{gamma}, \code{gaussian} or \code{t} distribution may be specified. The routines \code{frailty.gamma}, \code{frailty.gaussian} and \code{frailty.t} do the actual work. } \item{\dots}{Arguments for specific distribution, including (but not limited to) } \item{sparse}{ cutoff for using a sparse coding of the data matrix. If the total number of levels of \code{x} is larger than this value, then a sparse matrix approximation is used. The correct cutoff is still a matter of exploration: if the number of levels is very large (thousands) then the non-sparse calculation may not be feasible in terms of both memory and compute time. Likewise, the accuracy of the sparse approximation appears to be related to the maximum proportion of subjects in any one class, being best when no one class has a large membership. } \item{theta}{ if specified, this fixes the variance of the random effect. If not, the variance is a parameter, and a best solution is sought. Specifying this implies \code{method='fixed'}. } \item{df}{ if specified, this fixes the degrees of freedom for the random effect. Specifying this implies \code{method='df'}. Only one of \code{theta} or \code{df} should be specified. } \item{method}{ the method used to select a solution for theta, the variance of the random effect. The \code{fixed} corresponds to a user-specified value, and no iteration is done. The \code{df} selects the variance such that the degrees of freedom for the random effect matches a user specified value. The \code{aic} method seeks to maximize Akaike's information criteria 2*(partial likelihood - df). The \code{em} and \code{reml} methods are specific to Cox models with gamma and gaussian random effects, respectively. Please see further discussion below. } \item{tdf}{ the degrees of freedom for the t-distribution. } \item{eps}{ convergence criteria for the iteration on theta. } } \value{ this function is used in the model statement of either \code{coxph} or \code{survreg}. It's results are used internally. } \details{ The \code{frailty} plugs into the general penalized modeling framework provided by the \code{coxph} and \code{survreg} routines. This framework deals with likelihood, penalties, and degrees of freedom; these aspects work well with either parent routine. Therneau, Grambsch, and Pankratz show how maximum likelihood estimation for the Cox model with a gamma frailty can be accomplished using a general penalized routine, and Ripatti and Palmgren work through a similar argument for the Cox model with a gaussian frailty. Both of these are specific to the Cox model. Use of gamma/ml or gaussian/reml with \code{survreg} does not lead to valid results. The extensible structure of the penalized methods is such that the penalty function, such as \code{frailty} or \code{pspine}, is completely separate from the modeling routine. The strength of this is that a user can plug in any penalization routine they choose. A weakness is that it is very difficult for the modeling routine to know whether a sensible penalty routine has been supplied. Note that use of a frailty term implies a mixed effects model and use of a cluster term implies a GEE approach; these cannot be mixed. The \code{coxme} package has superseded this method. It is faster, more stable, and more flexible. } \section{References}{ S Ripatti and J Palmgren, Estimation of multivariate frailty models using penalized partial likelihood, Biometrics, 56:1016-1022, 2000. T Therneau, P Grambsch and VS Pankratz, Penalized survival models and frailty, J Computational and Graphical Statistics, 12:156-175, 2003. } \seealso{ \link{coxph}, \link{survreg} } \examples{ # Random institutional effect coxph(Surv(time, status) ~ age + frailty(inst, df=4), lung) # Litter effects for the rats data rfit2a <- survreg(Surv(time, status) ~ rx + frailty.gaussian(litter, df=13, sparse=FALSE), rats, subset= (sex=='f')) rfit2b <- survreg(Surv(time, status) ~ rx + frailty.gaussian(litter, df=13, sparse=TRUE), rats, subset= (sex=='f')) } \keyword{survival} survival/man/myeloid.Rd0000644000175100001440000000200713013633731014646 0ustar hornikusers\name{myeloid} \alias{myeloid} \docType{data} \title{Acute myeloid leukemia} \description{ This simulated data set is based on a trial in acute myeloid leukemia. } \format{ A data frame with 646 observations on the following 9 variables. \describe{ \item{\code{id}}{subject identifier, 1-646} \item{\code{trt}}{treatment arm A or B} \item{\code{futime}}{time to death or last follow-up} \item{\code{death}}{1 if \code{futime} is a death, 0 for censoring} \item{\code{txtime}}{time to hematropetic stem cell transplant} \item{\code{crtime}}{time to complete response} \item{\code{rltime}}{time to relapse of disease} } } \details{ This data set is used to illustrate multi-state survival curves. The correlation between within-subject event times strongly resembles that from an actual trial, but none of the actual data values are from that source. } \examples{ coxph(Surv(futime, death) ~ trt, data=myeloid) # See the mstate vignette for a more complete analysis } \keyword{datasets} survival/man/print.summary.coxph.Rd0000644000175100001440000000103511732700061017151 0ustar hornikusers\name{print.summary.coxph} \alias{print.summary.coxph} \title{ Print method for summary.coxph objects } \description{ Produces a printed summary of a fitted coxph model } \usage{ \method{print}{summary.coxph}(x, digits=max(getOption("digits") - 3, 3), signif.stars = getOption("show.signif.stars"), ...) } \arguments{ \item{x}{ the result of a call to \code{summary.coxph} } \item{digits}{significant digits to print} \item{signif.stars}{ Show stars to highlight small p-values } \item{\dots}{For future methods} } survival/man/cluster.Rd0000644000175100001440000000222712453556617014707 0ustar hornikusers\name{cluster} \alias{cluster} \title{ Identify clusters. } \description{ This is a special function used in the context of survival models. It identifies correlated groups of observations, and is used on the right hand side of a formula. Using \code{cluster()} in a formula implies that robust sandwich variance estimators are desired.} \usage{ cluster(x) } \arguments{ \item{x}{ A character, factor, or numeric variable. } } \value{ \code{x} } \details{ The function's only action is semantic, to mark a variable as the cluster indicator. The resulting variance is what is known as the ``working independence'' variance in a GEE model. Note that one cannot use both a frailty term and a cluster term in the same model, the first is a mixed-effects approach to correlation and the second a GEE approach, and these don't mix. } \seealso{ \code{\link{coxph}}, \code{\link{survreg}} } \examples{ marginal.model <- coxph(Surv(time, status) ~ rx + cluster(litter), rats, subset=(sex=='f')) frailty.model <- coxph(Surv(time, status) ~ rx + frailty(litter), rats, subset=(sex=='f')) } \keyword{survival} survival/man/tobin.Rd0000644000175100001440000000134711732700061014322 0ustar hornikusers\name{tobin} \alias{tobin} \docType{data} \title{Tobin's Tobit data} \description{ Economists fit a parametric censored data model called the \sQuote{tobit}. These data are from Tobin's original paper. } \usage{tobin} \format{ A data frame with 20 observations on the following 3 variables. \describe{ \item{durable}{Durable goods purchase} \item{age}{Age in years} \item{quant}{Liquidity ratio (x 1000)} } } \source{ J Tobin (1958), Estimation of relationships for limited dependent variables. \emph{Econometrica} \bold{26}, 24--36. } \examples{ tfit <- survreg(Surv(durable, durable>0, type='left') ~age + quant, data=tobin, dist='gaussian') predict(tfit,type="response") } \keyword{datasets} survival/man/is.ratetable.Rd0000644000175100001440000000210311732700061015553 0ustar hornikusers\name{is.ratetable} \alias{is.ratetable} \alias{Math.ratetable} \alias{Ops.ratetable} \title{ Verify that an object is of class ratetable. } \description{ The function verifies not only the \code{class} attribute, but the structure of the object. } \usage{ is.ratetable(x, verbose=FALSE) } \arguments{ \item{x}{ the object to be verified. } \item{verbose}{ if \code{TRUE} and the object is not a ratetable, then return a character string describing the way(s) in which \code{x} fails to be a proper ratetable object. } } \value{ returns \code{TRUE} if \code{x} is a ratetable, and \code{FALSE} or a description if it is not. } \details{ Rate tables are used by the \code{pyears} and \code{survexp} functions, and normally contain death rates for some population, categorized by age, sex, or other variables. They have a fairly rigid structure, and the \code{verbose} option can help in creating a new rate table. } \seealso{ \code{\link{pyears}}, \code{\link{survexp}}. } \examples{ is.ratetable(survexp.us) # True is.ratetable(cancer) # False } \keyword{survival} survival/man/survexp.fit.Rd0000644000175100001440000000420611732700061015501 0ustar hornikusers\name{survexp.fit} \alias{survexp.fit} \title{ Compute Expected Survival } \description{ Compute expected survival times. } \usage{ survexp.fit(group, x, y, times, death, ratetable) } \arguments{ \item{group}{if there are multiple survival curves this identifies the group, otherwise it is a constant. Must be an integer.} \item{x}{A matrix whose columns match the dimensions of the \code{ratetable}, in the correct order. } \item{y}{ the follow up time for each subject. } \item{times}{ the vector of times at which a result will be computed. } \item{death}{ a logical value, if \code{TRUE} the conditional survival is computed, if \code{FALSE} the cohort survival is computed. See \code{\link{survexp}} for more details. } \item{ratetable}{ a rate table, such as \code{survexp.uswhite}. } } \value{ A list containing the number of subjects and the expected survival(s) at each time point. If there are multiple groups, these will be matrices with one column per group. } \details{ For conditional survival \code{y} must be the time of last follow-up or death for each subject. For cohort survival it must be the potential censoring time for each subject, ignoring death. For an exact estimate \code{times} should be a superset of \code{y}, so that each subject at risk is at risk for the entire sub-interval of time. For a large data set, however, this can use an inordinate amount of storage and/or compute time. If the \code{times} spacing is more coarse than this, an actuarial approximation is used which should, however, be extremely accurate as long as all of the returned values are > .99. For a subgroup of size 1 and \code{times} > \code{y}, the conditional method reduces to exp(-h) where h is the expected cumulative hazard for the subject over his/her observation time. This is used to compute individual expected survival. } \section{Warning}{ Most users will call the higher level routine \code{survexp}. Consequently, this function has very few error checks on its input arguments. } \seealso{ \code{\link{survexp}}, \code{\link{survexp.us}}. } \keyword{survival } % docclass is function % Converted by Sd2Rd version 37351. survival/man/ovarian.Rd0000644000175100001440000000156112466146533014661 0ustar hornikusers\name{ovarian} \alias{ovarian} \docType{data} \title{Ovarian Cancer Survival Data} \usage{ovarian} \description{Survival in a randomised trial comparing two treatments for ovarian cancer} \format{ \tabular{ll}{ futime:\tab survival or censoring time\cr fustat:\tab censoring status\cr age: \tab in years\cr resid.ds:\tab residual disease present (1=no,2=yes)\cr rx:\tab treatment group\cr ecog.ps:\tab ECOG performance status (1 is better, see reference)\cr } } \source{Terry Therneau} \references{ Edmunson, J.H., Fleming, T.R., Decker, D.G., Malkasian, G.D., Jefferies, J.A., Webb, M.J., and Kvols, L.K., Different Chemotherapeutic Sensitivities and Host Factors Affecting Prognosis in Advanced Ovarian Carcinoma vs. Minimal Residual Disease. Cancer Treatment Reports, 63:241-47, 1979. } \keyword{datasets} \keyword{survival} survival/man/anova.coxph.Rd0000644000175100001440000000411211732700061015424 0ustar hornikusers\name{anova.coxph} \alias{anova.coxph} \alias{anova.coxphlist} \title{Analysis of Deviance for a Cox model.} \usage{ \method{anova}{coxph}(object, \dots, test = 'Chisq') } \description{ Compute an analysis of deviance table for one or more Cox model fits. } \arguments{ \item{object}{An object of class \code{coxph}} \item{\dots}{Further \code{coxph} objects} \item{test}{a character string. The appropriate test is a chisquare, all other choices result in no test being done.} } \details{ Specifying a single object gives a sequential analysis of deviance table for that fit. That is, the reductions in the model log-likelihood as each term of the formula is added in turn are given in as the rows of a table, plus the log-likelihoods themselves. A robust variance estimate is normally used in situations where the model may be mis-specified, e.g., multiple events per subject. In this case a comparison of partial-likelihood values does not make sense, and \code{anova} will refuse to print results. If more than one object is specified, the table has a row for the degrees of freedom and loglikelihood for each model. For all but the first model, the change in degrees of freedom and loglik is also given. (This only make statistical sense if the models are nested.) It is conventional to list the models from smallest to largest, but this is up to the user. The table will optionally contain test statistics (and P values) comparing the reduction in loglik for each row. } \value{ An object of class \code{"anova"} inheriting from class \code{"data.frame"}. } \section{Warning}{ The comparison between two or more models by \code{anova} or will only be valid if they are fitted to the same dataset. This may be a problem if there are missing values.} \seealso{ \code{\link{coxph}}, \code{\link{anova}}. } \examples{ fit <- coxph(Surv(futime, fustat) ~ resid.ds *rx + ecog.ps, data = ovarian) anova(fit) fit2 <- coxph(Surv(futime, fustat) ~ resid.ds +rx + ecog.ps, data=ovarian) anova(fit2,fit) } \keyword{models} \keyword{regression} \keyword{survival} survival/man/summary.survfit.Rd0000644000175100001440000000734312357770065016426 0ustar hornikusers\name{summary.survfit} \alias{summary.survfit} \title{ Summary of a Survival Curve } \description{ Returns a list containing the survival curve, confidence limits for the curve, and other information. } \usage{ \method{summary}{survfit}(object, times=, censored=FALSE, scale=1, extend=FALSE, rmean=getOption('survfit.rmean'), ...) } \arguments{ \item{object}{ the result of a call to the \code{survfit} function. } \item{times}{ vector of times; the returned matrix will contain 1 row for each time. The vector will be sorted into increasing order; missing values are not allowed. If \code{censored=T}, the default \code{times} vector contains all the unique times in \code{fit}, otherwise the default \code{times} vector uses only the event (death) times. } \item{censored}{ logical value: should the censoring times be included in the output? This is ignored if the \code{times} argument is present. } \item{scale}{ numeric value to rescale the survival time, e.g., if the input data to \code{survfit} were in days, \code{scale = 365.25} would scale the output to years. } \item{extend}{ logical value: if TRUE, prints information for all specified \code{times}, even if there are no subjects left at the end of the specified \code{times}. This is only valid if the \code{times} argument is present. } \item{rmean}{Show restricted mean: see \code{\link{print.survfit}} for details} \item{\dots}{for future methods} } \value{ a list with the following components: \item{surv}{ the estimate of survival at time t+0. } \item{time}{ the timepoints on the curve. } \item{n.risk}{ the number of subjects at risk at time t-0 (but see the comments on weights in the \code{survfit} help file). } \item{n.event}{ if the \code{times} argument is missing, then this column is the number of events that occurred at time t. Otherwise, it is the cumulative number of events that have occurred since the last time listed until time t+0. } \item{n.entered}{ This is present only for counting process survival data. If the \code{times} argument is missing, this column is the number of subjects that entered at time t. Otherwise, it is the cumulative number of subjects that have entered since the last time listed until time t. } \item{n.exit.censored}{ if the \code{times} argument is missing, this column is the number of subjects that left without an event at time t. Otherwise, it is the cumulative number of subjects that have left without an event since the last time listed until time t+0. This is only present for counting process survival data. } \item{std.err}{ the standard error of the survival value. } \item{conf.int}{ level of confidence for the confidence intervals of survival. } \item{lower}{ lower confidence limits for the curve. } \item{upper}{ upper confidence limits for the curve. } \item{strata}{ indicates stratification of curve estimation. If \code{strata} is not \code{NULL}, there are multiple curves in the result and the \code{surv}, \code{time}, \code{n.risk}, etc. vectors will contain multiple curves, pasted end to end. The levels of \code{strata} (a factor) are the labels for the curves. } \item{call}{ the statement used to create the \code{fit} object. } \item{na.action}{ same as for \code{fit}, if present. } \item{table}{ table of information that is returned from \code{print.survfit} function. } \item{type}{ type of data censoring. Passed through from the fit object. } } \seealso{ \code{\link{survfit}}, \code{\link{print.summary.survfit}} } \examples{ summary( survfit( Surv(futime, fustat)~1, data=ovarian)) summary( survfit( Surv(futime, fustat)~rx, data=ovarian)) } \keyword{survival} survival/man/quantile.survfit.Rd0000644000175100001440000000677713013633731016551 0ustar hornikusers\name{quantile.survfit} \alias{quantile.survfit} \alias{quantile.survfitms} \title{Quantiles from a survfit object} \description{Retrieve quantiles and confidence intervals for them from a survfit object. } \usage{ \method{quantile}{survfit}(x, probs = c(0.25, 0.5, 0.75), conf.int = TRUE, tolerance= sqrt(.Machine$double.eps), ...) \method{quantile}{survfitms}(x, probs = c(0.25, 0.5, 0.75), conf.int = TRUE, tolerance= sqrt(.Machine$double.eps), ...) } \arguments{ \item{x}{a result of the survfit function} \item{probs}{numeric vector of probabilities with values in [0,1]} \item{conf.int}{should lower and upper confidence limits be returned?} \item{tolerance}{tolerance for checking that the survival curve exactly equals one of the quantiles} \item{...}{optional arguments for other methods} } \details{ The kth quantile for a survival curve S(t) is the location at which a horizontal line at height p= 1-k intersects the plot of S(t). Since S(t) is a step function, it is possible for the curve to have a horizontal segment at exactly 1-k, in which case the midpoint of the horizontal segment is returned. This mirrors the standard behavior of the median when data is uncensored. If the survival curve does not fall to 1-k, then that quantile is undefined. In order to be consistent with other quantile functions, the argument \code{prob} of this function applies to the cumulative distribution function F(t) = 1-S(t). Confidence limits for the values are based on the intersection of the horizontal line at 1-k with the upper and lower limits for the survival curve. Hence confidence limits use the same p-value as was in effect when the curve was created, and will differ depending on the \code{conf.type} option of \code{survfit}. If the survival curves have no confidence bands, confidence limits for the quantiles are not available. When a horizontal segment of the survival curve exactly matches one of the requested quantiles the returned value will be the midpoint of the horizontal segment; this agrees with the usual definition of a median for uncensored data. Since the survival curve is computed as a series of products, however, there may be round off error. Assume for instance a sample of size 20 with no tied times and no censoring. The survival curve after the 10th death is (19/20)(18/19)(17/18) ... (10/11) = 10/20, but the computed result will not be exactly 0.5. Any horizontal segment whose absolute difference with a requested percentile is less than \code{tolerance} is considered to be an exact match. } \value{ The quantiles will be a vector if the \code{survfit} object contains only a single curve, otherwise it will be a matrix or array. In this case the last dimension will index the quantiles. If confidence limits are requested, then result will be a list with components \code{quantile}, \code{lower}, and \code{upper}, otherwise it is the vector or matrix of quantiles. } \author{Terry Therneau} \seealso{\code{\link{survfit}}, \code{\link{print.survfit}}, \code{\link{qsurvreg}} } \examples{ fit <- survfit(Surv(time, status) ~ ph.ecog, data=lung) quantile(fit) cfit <- coxph(Surv(time, status) ~ age + strata(ph.ecog), data=lung) csurv<- survfit(cfit, newdata=data.frame(age=c(40, 60, 80)), conf.type ="none") temp <- quantile(csurv, 1:5/10) temp[2,3,] # quantiles for second level of ph.ecog, age=80 quantile(csurv[2,3], 1:5/10) # quantiles of a single curve, same result } \keyword{ survival } survival/man/transplant.Rd0000644000175100001440000000544612630050675015410 0ustar hornikusers\name{transplant} \alias{transplant} \docType{data} \title{Liver transplant waiting list} \description{ Subjects on a liver transplant waiting list from 1990-1999, and their disposition: received a transplant, died while waiting, withdrew from the list, or censored. } \usage{data("transplant")} \format{ A data frame with 815 observations on the following 6 variables. \describe{ \item{\code{age}}{age at addition to the waiting list} \item{\code{sex}}{\code{m} or \code{f}} \item{\code{abo}}{blood type: \code{A}, \code{B}, \code{AB} or \code{O}} \item{\code{year}}{year in which they entered the waiting list} \item{\code{futime}}{time from entry to final disposition} \item{\code{event}}{final disposition: \code{censored}, \code{death}, \code{ltx} or \code{withdraw}} } } \details{ This represents the transplant experience in a particular region, over a time period in which liver transplant became much more widely recognized as a viable treatment modality. The number of liver transplants rises over the period, but the number of subjects added to the liver transplant waiting list grew much faster. Important questions addressed by the data are the change in waiting time, who waits, and whether there was an consequent increase in deaths while on the list. Blood type is an important consideration. Donor livers from subjects with blood type O can be used by patients with A, B, AB or 0 blood types, whereas an Ab liver can only be used by an AB recipient. Thus type O subjects on the waiting list are at a disadvantage, since the pool of competitors is larger for type O donor livers. This data is of historical interest and provides a useful example of competing risks, but it has little relevance to current practice. Liver allocation policies have evolved and now depend directly on each individual patient's risk and need, assessments of which are regularly updated while a patient is on the waiting list. The overall organ shortage remains acute, however. } \examples{ #since event is a factor, survfit creates competing risk curves pfit <- survfit(Surv(futime, event) ~ abo, transplant) pfit[,2] #time to liver transplant, by period plot(pfit[,2], mark.time=FALSE, col=1:4, lwd=2, xmax=735, xscale=30.5, xlab="Months", ylab="Fraction transplanted", xaxt = 'n') temp <- c(0, 6, 12, 18, 24) axis(1, temp, temp) legend(450, .35, levels(transplant$abo), lty=1, col=1:4, lwd=2, bty='n') # competing risks for type O plot(pfit[4,], xscale=30.5, xmax=735, col=1:3, lwd=2) legend(450, .4, c("Death", "Transpant", "Withdrawal"), col=1:3, lwd=2) } \references{ Kim WR, Therneau TM, Benson JT, Kremers WK, Rosen CB, Gores GJ, Dickson ER. Deaths on the liver transplant waiting list: An analysis of competing risks. Hepatology 2006 Feb; 43(2):345-51. } \keyword{datasets} survival/man/flchain.Rd0000644000175100001440000000715112260346575014627 0ustar hornikusers\name{flchain} \alias{flchain} \docType{data} \title{Assay of serum free light chain for 7874 subjects.} \description{ This is a stratified random sample containing 1/2 of the subjects from a study of the relationship between serum free light chain (FLC) and mortality. The original sample contains samples on approximately 2/3 of the residents of Olmsted County aged 50 or greater. } \usage{data(flchain)} \format{ A data frame with 7874 persons containing the following variables. \describe{ \item{\code{age }}{age in years} \item{\code{sex}}{F=female, M=male} \item{\code{sample.yr}}{the calendar year in which a blood sample was obtained} \item{\code{kappa}}{serum free light chain, kappa portion} \item{\code{lambda}}{serum free light chain, lambda portion} \item{\code{flc.grp}}{the FLC group for the subject, as used in the original analysis} \item{\code{creatinine}}{serum creatinine} \item{\code{mgus}}{1 if the subject had been diagnosed with monoclonal gammapothy (MGUS)} \item{\code{futime}}{days from enrollment until death. Note that there are 3 subjects whose sample was obtained on their death date.} \item{\code{death}}{0=alive at last contact date, 1=dead} \item{\code{chapter}}{for those who died, a grouping of their primary cause of death by chapter headings of the International Code of Diseases ICD-9} } } \details{In 1995 Dr. Robert Kyle embarked on a study to determine the prevalence of monoclonal gammopathy of undetermined significance (MGUS) in Olmsted County, Minnesota, a condition which is normally only found by chance from a test (serum electrophoresis) which is ordered for other causes. Later work suggested that one component of immunoglobulin production, the serum free light chain, might be a possible marker for immune disregulation. In 2010 Dr. Angela Dispenzieri and colleagues assayed FLC levels on those samples from the original study for which they had patient permission and from which sufficient material remained for further testing. They found that elevated FLC levels were indeed associated with higher death rates. Patients were recruited when they came to the clinic for other appointments, with a final random sample of those who had not yet had a visit since the study began. An interesting side question is whether there are differences between early, mid, and late recruits. This data set contains an age and sex stratified random sample that includes 7874 of the original 15759 subjects. The original subject identifiers and dates have been removed to protect patient identity. Subsampling was done to further protect this information. } \source{The primary investigator (A Dispenzieri) and statistician (T Therneau) for the study.} \references{ A Dispenzieri, J Katzmann, R Kyle, D Larson, T Therneau, C Colby, R Clark, G Mead, S Kumar, LJ Melton III and SV Rajkumar (2012). Use of monclonal serum immunoglobulin free light chains to predict overall survival in the general population, Mayo Clinic Proceedings 87:512-523. R Kyle, T Therneau, SV Rajkumar, D Larson, M Plevak, J Offord, A Dispenzieri, J Katzmann, and LJ Melton, III, 2006, Prevalence of monoclonal gammopathy of undetermined significance, New England J Medicine 354:1362-1369. } \examples{ data(flchain) age.grp <- cut(flchain$age, c(49,54, 59,64, 69,74,79, 89, 110), labels= paste(c(50,55,60,65,70,75,80,90), c(54,59,64,69,74,79,89,109), sep='-')) table(flchain$sex, age.grp) } \keyword{datasets} survival/man/survival-internal.Rd0000644000175100001440000000464613026572130016703 0ustar hornikusers\name{survival-internal} \alias{survival-internal} \alias{agexact.fit} \alias{as.matrix.ratetable} \alias{coxpenal.df} \alias{coxpenal.fit} \alias{is.na.ratetable2} \alias{is.na.coxph.penalty} \alias{match.ratetable} \alias{survfitCI} \alias{survfitKM} \alias{survreg.fit} \alias{survpenal.fit} \alias{survdiff.fit} \title{Internal survival functions} \description{Internal survival functions} \usage{ survreg.fit(x, y, weights, offset, init, controlvals, dist, scale = 0, nstrat = 1, strata, parms = NULL,assign) survpenal.fit(x, y, weights, offset, init, controlvals, dist, scale = 0, nstrat = 1, strata, pcols, pattr, assign, parms = NULL) survdiff.fit(y, x, strat, rho = 0) match.ratetable(R, ratetable) \method{as.matrix}{ratetable}(x, ...) \method{is.na}{ratetable2}(x) \method{is.na}{coxph.penalty}(x) coxpenal.df(hmat, hinv, fdiag, assign.list, ptype, nvar, pen1, pen2, sparse) coxpenal.fit(x, y, strata, offset, init, control, weights, method, rownames, pcols, pattr, assign) coxph.wtest(var, b, toler.chol = 1e-09) agexact.fit(x, y, strata, offset, init, control, weights, method, rownames) survfitCI(X, Y, weights, id, istate, type=c('kaplan-meier', 'fleming-harrington', 'fh2'), se.fit=TRUE, conf.int= .95, conf.type=c('log', 'log-log', 'plain', 'none'), conf.lower=c('usual', 'peto', 'modified'), influence=FALSE, start.time) survfitKM(x, y, casewt=rep(1,length(x)), type=c('kaplan-meier', 'fleming-harrington', 'fh2'), error=c('greenwood', "tsiatis"), se.fit=TRUE, conf.int= .95, conf.type=c('log', 'log-log', 'plain', 'none'), conf.lower=c('usual', 'peto', 'modified'), start.time, new.time) survfitTurnbull(x, y, casewt, type=c('kaplan-meier', 'fleming-harrington', 'fh2'), error=c('greenwood', "tsiatis"), se.fit=TRUE, conf.int= .95, conf.type=c('log', 'log-log', 'plain', 'none'), conf.lower=c('usual', 'peto', 'modified'), start.time) } \details{The arguments to these routines are not guaranteed to stay the same from release to release -- call them at your own risk!} \keyword{survival} \keyword{internal} survival/man/survfit.formula.Rd0000644000175100001440000002536013026571724016370 0ustar hornikusers\name{survfit.formula} \alias{survfit.formula} \alias{[.survfit} \title{ Compute a Survival Curve for Censored Data } \description{ Computes an estimate of a survival curve for censored data. More multi-state data the Andersen-Johansen estimate is use, for ordinary survival either the Kaplan-Meier or Fleming-Harrington estimate is produced. } \usage{ \method{survfit}{formula}(formula, data, weights, subset, na.action, etype, id, istate, timefix=TRUE, ...) } \arguments{ \item{formula}{ a formula object, which must have a \code{Surv} object as the response on the left of the \code{~} operator and, if desired, terms separated by + operators on the right. One of the terms may be a \code{strata} object. For a single survival curve the right hand side should be \code{~ 1}. } \item{data}{ a data frame in which to interpret the variables named in the formula, \code{subset} and \code{weights} arguments. } \item{weights}{ The weights must be nonnegative and it is strongly recommended that they be strictly positive, since zero weights are ambiguous, compared to use of the \code{subset} argument. } \item{subset}{ expression saying that only a subset of the rows of the data should be used in the fit. } \item{na.action}{ a missing-data filter function, applied to the model frame, after any \code{subset} argument has been used. Default is \code{options()$na.action}. } \item{etype}{ a variable giving the type of event. This has been superseded by multi-state Surv objects; see example below. } \item{id}{ identifies individual subjects, when a given person can have multiple lines of data. } \item{istate}{for multi-state models, identifies the initial state of each subject} \item{timefix}{process times through the \code{aeqSurv} function to eliminate potential roundoff issues.} \item{\dots}{ The following additional arguments are passed to internal functions called by \code{survfit}. \describe{ \item{type}{ a character string specifying the type of survival curve. Possible values are \code{"kaplan-meier"}, \code{"fleming-harrington"} or \code{"fh2"} if a formula is given. This is ignored for competing risks or when the Turnbull estimator is used. } \item{error}{ a character string specifying the error. Possible values are \code{"greenwood"} for the Greenwood formula or \code{"tsiatis"} or \code{"aalen"} for the Tsiatis/Aalen formula, or \code{"robust"} for a robust variance. The last of these is assumed if non-integer case weights are provided. } \item{conf.type}{ One of \code{"none"}, \code{"plain"}, \code{"log"} (the default), or \code{"log-log"}. Only enough of the string to uniquely identify it is necessary. The first option causes confidence intervals not to be generated. The second causes the standard intervals \code{curve +- k *se(curve)}, where k is determined from \code{conf.int}. The log option calculates intervals based on the cumulative hazard or log(survival). The last option bases intervals on the log hazard or log(-log(survival)). } \item{conf.lower}{ a character string to specify modified lower limits to the curve, the upper limit remains unchanged. Possible values are \code{"usual"} (unmodified), \code{"peto"}, and \code{"modified"}. T he modified lower limit is based on an "effective n" argument. The confidence bands will agree with the usual calculation at each death time, but unlike the usual bands the confidence interval becomes wider at each censored observation. The extra width is obtained by multiplying the usual variance by a factor m/n, where n is the number currently at risk and m is the number at risk at the last death time. (The bands thus agree with the un-modified bands at each death time.) This is especially useful for survival curves with a long flat tail. The Peto lower limit is based on the same "effective n" argument as the modified limit, but also replaces the usual Greenwood variance term with a simple approximation. It is known to be conservative. } \item{start.time}{ numeric value specifying a time to start calculating survival information. The resulting curve is the survival conditional on surviving to \code{start.time}. } \item{conf.int}{ the level for a two-sided confidence interval on the survival curve(s). Default is 0.95. } \item{se.fit}{ a logical value indicating whether standard errors should be computed. Default is \code{TRUE}. } \item{influence}{a logical value indicating whether to return the infinitesimal jackknife (influence) values for each subject. These contain the values of the derivative of each value with respect to the case weights of each subject i: \eqn{\partial p/\partial w_i}{dp/dw[i]}, evaluated at the vector of weights \eqn{w=1}. The array will have dimensions (number of subjects, 1+ number of unique times, number of states); be forewarned that this can be huge. If the total number of elements is larger then the maximum integer the underlying C program can not create it. } } } } \value{ an object of class \code{"survfit"}. See \code{survfit.object} for details. Methods defined for survfit objects are \code{print}, \code{plot}, \code{lines}, and \code{points}. } \details{ The estimates used are the Kalbfleisch-Prentice (Kalbfleisch and Prentice, 1980, p.86) and the Tsiatis/Link/Breslow, which reduce to the Kaplan-Meier and Fleming-Harrington estimates, respectively, when the weights are unity. The Greenwood formula for the variance is a sum of terms d/(n*(n-m)), where d is the number of deaths at a given time point, n is the sum of weights for all individuals still at risk at that time, and m is the sum of weights for the deaths at that time. The justification is based on a binomial argument when weights are all equal to one; extension to the weighted case is ad hoc. Tsiatis (1981) proposes a sum of terms d/(n*n), based on a counting process argument which includes the weighted case. The two variants of the F-H estimate have to do with how ties are handled. If there were 3 deaths out of 10 at risk, then the first increments the hazard by 3/10 and the second by 1/10 + 1/9 + 1/8. For the first method S(t) = exp(H), where H is the Nelson-Aalen cumulative hazard estimate, whereas the \code{fh2} method will give results S(t) results closer to the Kaplan-Meier. When the data set includes left censored or interval censored data (or both), then the EM approach of Turnbull is used to compute the overall curve. When the baseline method is the Kaplan-Meier, this is known to converge to the maximum likelihood estimate. The cumulative incidence curve is an alternative to the Kaplan-Meier for competing risks data. For instance, in patients with MGUS, conversion to an overt plasma cell malignancy occurs at a nearly constant rate among those still alive. A Kaplan-Meier estimate, treating death due to other causes as censored, gives a 20 year cumulate rate of 33\% for the 241 early patients of Kyle. This estimates the incidence of conversion if all other causes of death were removed, which is an unrealistic assumption given the mean starting age of 63 and a median follow up of over 21 years. The CI estimate, on the other hand, estimates the total number of conversions that will actually occur. Because the population is older, this is much smaller than the KM, 22\% at 20 years for Kyle's data. If there were no censoring, then CI(t) could very simply be computed as total number of patients with progression by time t divided by the sample size n. } \section{References}{ Dorey, F. J. and Korn, E. L. (1987). Effective sample sizes for confidence intervals for survival probabilities. \emph{Statistics in Medicine} \bold{6}, 679-87. Fleming, T. H. and Harrington, D. P. (1984). Nonparametric estimation of the survival distribution in censored data. \emph{Comm. in Statistics} \bold{13}, 2469-86. Kalbfleisch, J. D. and Prentice, R. L. (1980). \emph{The Statistical Analysis of Failure Time Data.} New York:Wiley. Kyle, R. A. (1997). Moncolonal gammopathy of undetermined significance and solitary plasmacytoma. Implications for progression to overt multiple myeloma\}, \emph{Hematology/Oncology Clinics N. Amer.} \bold{11}, 71-87. Link, C. L. (1984). Confidence intervals for the survival function using Cox's proportional hazards model with covariates. \emph{Biometrics} \bold{40}, 601-610. Turnbull, B. W. (1974). Nonparametric estimation of a survivorship function with doubly censored data. \emph{J Am Stat Assoc}, \bold{69}, 169-173. } \seealso{ \code{\link{survfit.coxph}} for survival curves from Cox models, \code{\link{survfit.object}} for a description of the components of a survfit object, \code{\link{print.survfit}}, \code{\link{plot.survfit}}, \code{\link{lines.survfit}}, \code{\link{coxph}}, \code{\link{Surv}}. } \examples{ #fit a Kaplan-Meier and plot it fit <- survfit(Surv(time, status) ~ x, data = aml) plot(fit, lty = 2:3) legend(100, .8, c("Maintained", "Nonmaintained"), lty = 2:3) #fit a Cox proportional hazards model and plot the #predicted survival for a 60 year old fit <- coxph(Surv(futime, fustat) ~ age, data = ovarian) plot(survfit(fit, newdata=data.frame(age=60)), xscale=365.25, xlab = "Years", ylab="Survival") # Here is the data set from Turnbull # There are no interval censored subjects, only left-censored (status=3), # right-censored (status 0) and observed events (status 1) # # Time # 1 2 3 4 # Type of observation # death 12 6 2 3 # losses 3 2 0 3 # late entry 2 4 2 5 # tdata <- data.frame(time =c(1,1,1,2,2,2,3,3,3,4,4,4), status=rep(c(1,0,2),4), n =c(12,3,2,6,2,4,2,0,2,3,3,5)) fit <- survfit(Surv(time, time, status, type='interval') ~1, data=tdata, weight=n) # # Time to progression/death for patients with monoclonal gammopathy # Competing risk curves (cumulative incidence) fitKM <- survfit(Surv(stop, event=='progression') ~1, data=mgus1, subset=(start==0)) fitCI <- survfit(Surv(stop, status*as.numeric(event), type="mstate") ~1, data=mgus1, subset=(start==0)) # CI curves are always plotted from 0 upwards, rather than 1 down plot(fitCI, xscale=365.25, xmax=7300, mark.time=FALSE, col=2:3, xlab="Years post diagnosis of MGUS") lines(fitKM, fun='event', xmax=7300, mark.time=FALSE, conf.int=FALSE) text(10, .4, "Competing risk: death", col=3) text(16, .15,"Competing risk: progression", col=2) text(15, .30,"KM:prog") } \keyword{survival} survival/man/ridge.Rd0000644000175100001440000000303511732700061014275 0ustar hornikusers\name{ridge} \alias{ridge} \title{ Ridge regression} \usage{ ridge(..., theta, df=nvar/2, eps=0.1, scale=TRUE) } \arguments{ \item{\dots}{predictors to be ridged } \item{theta}{penalty is \code{theta}/2 time sum of squared coefficients } \item{df}{Approximate degrees of freedom } \item{eps}{ Accuracy required for \code{df} } \item{scale}{ Scale variables before applying penalty? } } \description{ When used in a \link{coxph} or \link{survreg} model formula, specifies a ridge regression term. The likelihood is penalised by \code{theta}/2 time the sum of squared coefficients. If \code{scale=T} the penalty is calculated for coefficients based on rescaling the predictors to have unit variance. If \code{df} is specified then \code{theta} is chosen based on an approximate degrees of freedom. } \value{ An object of class \code{coxph.penalty} containing the data and control functions. } \references{ Gray (1992) "Flexible methods of analysing survival data using splines, with applications to breast cancer prognosis" JASA 87:942--951 } \seealso{ \code{\link{coxph}},\code{\link{survreg}},\code{\link{pspline}},\code{\link{frailty}} } \examples{ coxph(Surv(futime, fustat) ~ rx + ridge(age, ecog.ps, theta=1), ovarian) lfit0 <- survreg(Surv(time, status) ~1, cancer) lfit1 <- survreg(Surv(time, status) ~ age + ridge(ph.ecog, theta=5), cancer) lfit2 <- survreg(Surv(time, status) ~ sex + ridge(age, ph.ecog, theta=1), cancer) lfit3 <- survreg(Surv(time, status) ~ sex + age + ph.ecog, cancer) } \keyword{survival }%-- one or more ... survival/man/survregDtest.Rd0000644000175100001440000000301211732700061015677 0ustar hornikusers\name{survregDtest} \alias{survregDtest} \title{Verify a survreg distribution} \description{ This routine is called by \code{survreg} to verify that a distribution object is valid. } \usage{ survregDtest(dlist, verbose = F) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{dlist}{the list describing a survival distribution} \item{verbose}{return a simple TRUE/FALSE from the test for validity (the default), or a verbose description of any flaws.} } \details{ If the \code{survreg} function rejects your user-supplied distribution as invalid, this routine will tell you why it did so. } \value{ TRUE if the distribution object passes the tests, and either FALSE or a vector of character strings if not. } \author{Terry Therneau} \seealso{\code{\link{survreg.distributions}}, \code{\link{survreg}}} \examples{ # An invalid distribution (it should have "init =" on line 2) # surveg would give an error message mycauchy <- list(name='Cauchy', init<- function(x, weights, ...) c(median(x), mad(x)), density= function(x, parms) { temp <- 1/(1 + x^2) cbind(.5 + atan(temp)/pi, .5+ atan(-temp)/pi, temp/pi, -2 *x*temp, 2*temp^2*(4*x^2*temp -1)) }, quantile= function(p, parms) tan((p-.5)*pi), deviance= function(...) stop('deviance residuals not defined') ) survregDtest(mycauchy, TRUE) } \keyword{survival} survival/man/predict.survreg.Rd0000644000175100001440000000547712067401404016346 0ustar hornikusers\name{predict.survreg} \alias{predict.survreg} \alias{predict.survreg.penal} \title{ Predicted Values for a `survreg' Object } \description{ Predicted values for a \code{survreg} object } \usage{ \method{predict}{survreg}(object, newdata, type=c("response", "link", "lp", "linear", "terms", "quantile", "uquantile"), se.fit=FALSE, terms=NULL, p=c(0.1, 0.9), na.action=na.pass, ...) } \arguments{ \item{object}{ result of a model fit using the \code{survreg} function. } \item{newdata}{ data for prediction. If absent predictions are for the subjects used in the original fit. } \item{type}{ the type of predicted value. This can be on the original scale of the data (response), the linear predictor (\code{"linear"}, with \code{"lp"} as an allowed abbreviation), a predicted quantile on the original scale of the data (\code{"quantile"}), a quantile on the linear predictor scale (\code{"uquantile"}), or the matrix of terms for the linear predictor (\code{"terms"}). At this time \code{"link"} and linear predictor (\code{"lp"}) are identical. } \item{se.fit}{ if \code{TRUE}, include the standard errors of the prediction in the result. } \item{terms}{ subset of terms. The default for residual type \code{"terms"} is a matrix with one column for every term (excluding the intercept) in the model. } \item{p}{ vector of percentiles. This is used only for quantile predictions. } \item{na.action}{ applies only when the \code{newdata} argument is present, and defines the missing value action for the new data. The default is to include all observations.} \item{\dots}{for future methods} } \value{ a vector or matrix of predicted values. } \references{ Escobar and Meeker (1992). Assessing influence in regression analysis with censored data. \emph{Biometrics,} 48, 507-528. } \seealso{ \code{\link{survreg}}, \code{\link{residuals.survreg}} } \examples{ # Draw figure 1 from Escobar and Meeker, 1992. fit <- survreg(Surv(time,status) ~ age + I(age^2), data=stanford2, dist='lognormal') with(stanford2, plot(age, time, xlab='Age', ylab='Days', xlim=c(0,65), ylim=c(.1, 10^5), log='y', type='n')) with(stanford2, points(age, time, pch=c(2,4)[status+1], cex=.7)) pred <- predict(fit, newdata=list(age=1:65), type='quantile', p=c(.1, .5, .9)) matlines(1:65, pred, lty=c(2,1,2), col=1) # Predicted Weibull survival curve for a lung cancer subject with # ECOG score of 2 lfit <- survreg(Surv(time, status) ~ ph.ecog, data=lung) pct <- 1:98/100 # The 100th percentile of predicted survival is at +infinity ptime <- predict(lfit, newdata=data.frame(ph.ecog=2), type='quantile', p=pct, se=TRUE) matplot(cbind(ptime$fit, ptime$fit + 2*ptime$se.fit, ptime$fit - 2*ptime$se.fit)/30.5, 1-pct, xlab="Months", ylab="Survival", type='l', lty=c(1,2,2), col=1) } \keyword{survival} survival/man/survConcordance.Rd0000644000175100001440000000705013017617770016356 0ustar hornikusers\name{survConcordance} \alias{survConcordance} \alias{survConcordance.fit} \title{ Compute a concordance measure. } \description{ This function computes the concordance between a right-censored survival time and a single continuous covariate } \usage{ survConcordance(formula, data, weights, subset, na.action) survConcordance.fit(y, x, strata, weight) } \arguments{ \item{formula}{ a formula with a survival time on the left and a single covariate on the right, along with an optional \code{strata()} term. The left hand term can also be a numeric vector. } \item{data}{ a data frame } \item{weights,subset,na.action}{as for \code{coxph}} \item{x, y, strata, weight}{predictor, response, strata, and weight vectors for the direct call} } \value{ an object containing the concordance, followed by the number of pairs that agree, disagree, are tied, and are not comparable. } \details{ The \code{survConcordance.fit} function computes the result but does no data checking whatsoever. It is intended as a hook for other packages that wish to compute concordance, and the data has already been assembled and verified. Concordance is defined as Pr(agreement) for any two randomly chosen observations, where in this case agreement means that the observation with the shorter survival time of the two also has the larger risk score. The predictor (or risk score) will often be the result of a Cox model or other regression. For continuous covariates concordance is equivalent to Kendall's tau, and for logistic regression is is equivalent to the area under the ROC curve. A value of 1 signifies perfect agreement, .6-.7 is a common result for survival data, .5 is an agreement that is no better than chance, and .3-.4 is the performance of some stock market analysts. The computation involves all n(n-1)/2 pairs of data points in the sample. For survival data, however, some of the pairs are incomparable. For instance a pair of times (5+, 8), the first being a censored value. We do not know whether the first survival time is greater than or less than the second. Among observations that are comparable, pairs may also be tied on survival time (but only if both are uncensored) or on the predictor. The final concordance is (agree + tied/2)/(agree + disagree + tied). There is, unfortunately, one aspect of the formula above that is unclear. Should the count of ties include observations that are tied on survival time y, tied on the predictor x, or both? By default the concordance only counts ties in x, treating tied survival times as incomparable; this agrees with the AUC calculation used in logistic regression. The Goodman-Kruskal Gamma statistic is (agree-disagree)/(agree + disagree), ignoring ties. It ranges from -1 to +1 similar to a correlation coefficient. Kendall's tau uses ties of both types. All of the components are returned in the result, however, so people can compute other combinations if interested. (If two observations have the same survival and the same x, they are counted in the tied survival time category). The algorithm is based on a balanced binary tree, which allows the computation to be done in O(n log n) time. } \seealso{ summary.coxph } \examples{ survConcordance(Surv(time, status) ~age, data=lung) options(na.action=na.exclude) fit <- coxph(Surv(time, status) ~ ph.ecog + age + sex, lung) survConcordance(Surv(time, status) ~predict(fit), lung) \dontrun{ n=227 (1 observations deleted due to missing values) Concordance= 0.6371102 , Gamma= 0.2759638 concordant discordant tied risk tied time 12544 7117 126 28 }} \keyword{survival} survival/man/model.frame.coxph.Rd0000644000175100001440000000140611732700061016514 0ustar hornikusers\name{model.frame.coxph} \Rdversion{1.1} \alias{model.frame.coxph} \title{Model.frame method for coxph objects} \description{ Recreate the model frame of a coxph fit. } \usage{ \method{model.frame}{coxph}(formula, ...) } \arguments{ \item{formula}{the result of a \code{coxph} fit} \item{\dots}{other arguments to \code{model.frame}} } \details{ For details, see the manual page for the generic function. This function would rarely be called by a user, it is mostly used inside functions like \code{residual} that need to recreate the data set from a model in order to do further calculations. } \value{the model frame used in the original fit, or a parallel one for new data. } \author{Terry Therneau} \seealso{\code{\link{model.frame}}} \keyword{ survival } survival/man/coxph.detail.Rd0000644000175100001440000000537111732700061015572 0ustar hornikusers\name{coxph.detail} \alias{coxph.detail} \title{ Details of a Cox Model Fit } \description{ Returns the individual contributions to the first and second derivative matrix, at each unique event time. } \usage{ coxph.detail(object, riskmat=FALSE) } \arguments{ \item{object}{ a Cox model object, i.e., the result of \code{coxph}. } \item{riskmat}{ include the at-risk indicator matrix in the output? } } \value{ a list with components \item{time}{ the vector of unique event times } \item{nevent}{ the number of events at each of these time points. } \item{means}{ a matrix with one row for each event time and one column for each variable in the Cox model, containing the weighted mean of the variable at that time, over all subjects still at risk at that time. The weights are the risk weights \code{exp(x \%*\% fit$coef)}. } \item{nrisk}{ number of subjects at risk. } \item{score}{ the contribution to the score vector (first derivative of the log partial likelihood) at each time point. } \item{imat}{ the contribution to the information matrix (second derivative of the log partial likelihood) at each time point. } \item{hazard}{ the hazard increment. Note that the hazard and variance of the hazard are always for some particular future subject. This routine uses \code{object$mean} as the future subject. } \item{varhaz}{ the variance of the hazard increment. } \item{x,y}{ copies of the input data. } \item{strata}{ only present for a stratified Cox model, this is a table giving the number of time points of component \code{time} that were contributed by each of the strata. } \item{riskmat}{ a matrix with one row for each time and one column for each observation containing a 0/1 value to indicate whether that observation was (1) or was not (0) at risk at the given time point. } } \details{ This function may be useful for those who wish to investigate new methods or extensions to the Cox model. The example below shows one way to calculate the Schoenfeld residuals. } \seealso{ \code{\link{coxph}}, \code{\link{residuals.coxph}} } \examples{ fit <- coxph(Surv(futime,fustat) ~ age + rx + ecog.ps, ovarian, x=TRUE) fitd <- coxph.detail(fit) # There is one Schoenfeld residual for each unique death. It is a # vector (covariates for the subject who died) - (weighted mean covariate # vector at that time). The weighted mean is defined over the subjects # still at risk, with exp(X beta) as the weight. events <- fit$y[,2]==1 etime <- fit$y[events,1] #the event times --- may have duplicates indx <- match(etime, fitd$time) schoen <- fit$x[events,] - fitd$means[indx,] } \keyword{survival} survival/man/rhDNase.Rd0000644000175100001440000000756213017617770014554 0ustar hornikusers\name{rhDNase} \alias{rhDNase} \docType{data} \title{rhDNASE data set} \description{ Results of a randomized trial of rhDNase for the treatment of cystic fibrosis. } \format{ A data frame with 767 observations on the following 8 variables. \describe{ \item{\code{id}}{subject id} \item{\code{inst}}{enrolling institution} \item{\code{trt}}{treatment arm: 0=placebo, 1= rhDNase} \item{\code{entry.dt}}{date of entry into the study} \item{\code{end.dt}}{date of last follow-up} \item{\code{fev}}{forced expriatory volume at enrollment, a measure of lung capacity} \item{\code{ivstart}}{days from enrollment to the start of IV antibiotics} \item{\code{ivstop}}{days from enrollment to the cessation of IV antibiotics} } } \details{ In patients with cystic fibrosis, extracellular DNA is released by leukocytes that accumulate in the airways in response to chronic bacterial infection. This excess DNA thickens the mucus, which then cannot be cleared from the lung by the cilia. The accumulation leads to exacerbations of respiratory symptoms and progressive deterioration of lung function. At the time of this study more than 90\% of cystic fibrosis patients eventually died of lung disease. Deoxyribonuclease I (DNase I) is a human enzyme normally present in the mucus of human lungs that digests extracellular DNA. Genentech, Inc. cloned a highly purified recombinant DNase I (rhDNase or Pulmozyme) which when delivered to the lungs in an aerosolized form cuts extracellular DNA, reducing the viscoelasticity of airway secretions and improving clearance. In 1992 the company conducted a randomized double-blind trial comparing rhDNase to placebo. Patients were then monitored for pulmonary exacerbations, along with measures of lung volume and flow. The primary endpoint was the time until first pulmonary exacerbation; however, data on all exacerbations were collected for 169 days. The definition of an exacerbation was an infection that required the use of intravenous (IV) antibiotics. Subjects had 0--5 such episodes during the trial, those with more than one have multiple rows in the data set, those with none have NA for the IV start and end times. A few subjects were infected at the time of enrollment, subject 173 for instance has a first infection interval of -21 to 7. We do not count this first infection as an "event", and the subject first enters the risk set at day 7. Subjects who have an event are not considered to be at risk for another event during the course of antibiotics, nor for an additional 6 days after they end. (If the symptoms reappear immediately after cessation then from a medical standpoint this would not be a new infection.) This data set reproduces the data in Therneau and Grambsch, is does not exactly reproduce those in Therneau and Hamilton due to data set updates. } \references{ T. M. Therneau and P. M. Grambsch, Modeling Survival Data: Extending the Cox Model, Springer, 2000. T. M. Therneau and S.A. Mamilton, rhDNase as an example of recurrent event analysis, Statistics in Medicine, 16:2029-2047, 1997. } \examples{ # Build the start-stop data set for analysis, and # replicate line 2 of table 8.13 first <- subset(rhDNase, !duplicated(id)) #first row for each subject dnase <- tmerge(first, first, id=id, tstop=as.numeric(end.dt -entry.dt)) # Subjects whose fu ended during the 6 day window are the reason for # this next line temp.end <- with(rhDNase, pmin(ivstop+6, end.dt-entry.dt)) dnase <- tmerge(dnase, rhDNase, id=id, infect=event(ivstart), end= event(temp.end)) # toss out the non-at-risk intervals, and extra variables # 3 subjects had an event on their last day of fu, infect=1 and end=1 dnase <- subset(dnase, (infect==1 | end==0), c(id:trt, fev:infect)) agfit <- coxph(Surv(tstart, tstop, infect) ~ trt + fev + cluster(id), data=dnase) } \keyword{datasets} survival/man/retinopathy.Rd0000644000175100001440000000414712657110017015561 0ustar hornikusers\name{retinopathy} \alias{retinopathy} \docType{data} \title{Diabetic Retinopathy} \description{A trial of laser coagulation as a treatment to delay diabetic retinopathy. } \usage{data("retinopathy")} \format{ A data frame with 394 observations on the following 9 variables. \describe{ \item{\code{id}}{numeric subject id} \item{\code{laser}}{type of laser used: \code{xenon} \code{argon}} \item{\code{eye}}{which eye was treated: \code{right} \code{left}} \item{\code{age}}{age at diagnosis of diabetes} \item{\code{type}}{type of diabetes: \code{juvenile} \code{adult}, (diagnosis before age 20)} \item{\code{trt}}{0 = control eye, 1 = treated eye} \item{\code{futime}}{time to loss of vision or last follow-up} \item{\code{status}}{0 = censored, 1 = loss of vision in this eye} \item{\code{risk}}{a risk score for the eye. This high risk subset is defined as a score of 6 or greater in at least one eye.} } } \details{ The 197 patients in this dataset were a 50\% random sample of the patients with "high-risk" diabetic retinopathy as defined by the Diabetic Retinopathy Study (DRS). Each patient had one eye randomized to laser treatment and the other eye received no treatment, and has two observations in the data set. For each eye, the event of interest was the time from initiation of treatment to the time when visual acuity dropped below 5/200 two visits in a row. Thus there is a built-in lag time of approximately 6 months (visits were every 3 months). Survival times in this dataset are the actual time to vision loss in months, minus the minimum possible time to event (6.5 months). Censoring was caused by death, dropout, or end of the study. } \references{ W. J. Huster, R. Brookmeyer and S. G. Self (1989). Modelling paired survival data with covariates, Biometrics 45:145-156. A. L. Blair, D. R. Hadden, J. A. Weaver, D. B. Archer, P. B. Johnston and C. J. Maguire (1976). The 5-year prognosis for vision in diabetes, American Journal of Ophthalmology, 81:383-396. } \examples{ coxph(Surv(futime, status) ~ type + trt + cluster(id), retinopathy) } \keyword{datasets} survival/man/agreg.fit.Rd0000644000175100001440000000261613013633731015060 0ustar hornikusers\name{agreg.fit} \alias{agreg.fit} \alias{coxph.fit} \title{Cox model fitting functions} \description{ These are the the functions called by coxph that do the actual computation. In certain situations, e.g. a simulation, it may be advantageous to call these directly rather than the usual \code{coxph} call using a model formula. } \usage{ agreg.fit(x, y, strata, offset, init, control, weights, method, rownames) coxph.fit(x, y, strata, offset, init, control, weights, method, rownames) } \arguments{ \item{x}{Matix of predictors. This should \emph{not} include an intercept.} \item{y}{a \code{Surv} object containing either 2 columns (coxph.fit) or 3 columns (agreg.fit).} \item{strata}{a vector containing the stratification, or NULL} \item{offset}{optional offset vector} \item{init}{initial values for the coefficients} \item{control}{the result of a call to \code{coxph.control}} \item{weights}{optional vector of weights} \item{method}{method for hanling ties, one of "breslow" or "efron"} \item{rownames}{this is only needed for a NULL model, in which case it contains the rownames (if any) of the original data.} } \details{ This routine does no checking that arguments are the proper length or type. Only use it if you know what you are doing! } \value{ a list containing results of the fit} \author{Terry Therneau} \seealso{\code{\link{coxph}}} \keyword{ survival } survival/man/strata.Rd0000644000175100001440000000250013017617770014511 0ustar hornikusers\name{strata} \alias{strata} \title{ Identify Stratification Variables } \description{ This is a special function used in the context of the Cox survival model. It identifies stratification variables when they appear on the right hand side of a formula. } \usage{ strata(..., na.group=FALSE, shortlabel, sep=', ') } \arguments{ \item{\dots}{ any number of variables. All must be the same length. } \item{na.group}{ a logical variable, if \code{TRUE}, then missing values are treated as a distinct level of each variable. } \item{shortlabel}{if \code{TRUE} omit variable names from resulting factor labels. The default action is to omit the names if all of the arguments are factors, and none of them was named.} \item{sep}{ the character used to separate groups, in the created label } } \value{ a new factor, whose levels are all possible combinations of the factors supplied as arguments. } \details{ The result is identical to the \code{interaction} function, but for the labeling of the factors (\code{strata} is more verbose). } \seealso{ \code{\link{coxph}}, \code{\link{interaction}} } \examples{ a <- factor(rep(1:3,4), labels=c("low", "medium", "high")) b <- factor(rep(1:4,3)) levels(strata(b)) levels(strata(a,b,shortlabel=TRUE)) coxph(Surv(futime, fustat) ~ age + strata(rx), data=ovarian) } \keyword{survival} survival/man/finegray.Rd0000644000175100001440000000747513026563601015030 0ustar hornikusers\name{finegray} \alias{finegray} \title{Create data for a Fine-Gray model} \description{ The Fine-Gray model can be fit by first creating a special data set, and then fitting a weighted Cox model to the result. This routine creates the data set. } \usage{ finegray(formula, data, subset, na.action= na.pass, etype, prefix="fg", count, id, timefix=TRUE) } \arguments{ \item{formula}{a standard model formula, with survival on the left and covariates on the right. } \item{data}{an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. } \item{subset}{ an optional vector specifying a subset of observations to be used in the fitting process. } \item{na.action}{ a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options. } \item{etype}{ the event type for which a data set will be generated. The default is to use whichever is listed first in the multi-state survival object. } \item{prefix}{the routine will add 4 variables to the data set: a start and end time for each interval, status, and a weight for the interval. The default names of these are "fgstart", "fgstop", "fgstatus", and "fgwt"; the \code{prefix} argument determines the initial portion of the new names. } \item{count}{a variable name in the output data set for an optional variable that will contain the the replication count for each row of the input data. If a row is expanded into multiple lines it will contain 1, 2, etc. } \item{id}{optional, the variable name in the data set which identifies subjects.} \item{timefix}{process times through the \code{aeqSurv} function to eliminate potential roundoff issues.} } \details{ The function expects a multi-state survival expression or variable as the left hand side of the formula, e.g. \code{Surv(atime, astat)} where \code{astat} is a factor whose first level represents censoring and remaining levels are states. The output data set will contain simple survival data (status = 0 or 1) for a single endpoint of interest. In the output data set subjects who did not experience the event of interest become censored subjects whose times are artificially extended over multiple intervals, with a decreasing case weight from interval to interval. The output data set will normally contain many more rows than the input. Time dependent covariates are allowed, but not (currently) delayed entry. If there are time dependent covariates, e.g.., the input data set had \code{Surv(entry, exit, stat)} as the left hand side, then an \code{id} statement is required. The program does data checks in this case, and needs to know which rows belong to each subject. See the competing risks vignette for more details. } \value{a data frame} \references{ Fine JP and Gray RJ (1999) A proportional hazards model for the subdistribution of a competing risk. JASA 94:496-509. Geskus RB (2011). Cause-Specific Cumulative Incidence Estimation and the Fine and Gray Model Under Both Left Truncation and Right Censoring. Biometrics 67, 39-49. } \author{Terry Therneau} \seealso{\code{\link{coxph}}, \code{\link{aeqSurv}}} \examples{ # Treat time to death and plasma cell malignancy as competing risks etime <- with(mgus2, ifelse(pstat==0, futime, ptime)) event <- with(mgus2, ifelse(pstat==0, 2*death, 1)) event <- factor(event, 0:2, labels=c("censor", "pcm", "death")) # FG model for PCM pdata <- finegray(Surv(etime, event) ~ ., data=mgus2) fgfit <- coxph(Surv(fgstart, fgstop, fgstatus) ~ age + sex, weight=fgwt, data=pdata) # Compute the weights separately by sex adata <- finegray(Surv(etime, event) ~ . + strata(sex), data=mgus2, na.action=na.pass) } \keyword{survival} survival/man/stanford2.Rd0000644000175100001440000000132011732700061015100 0ustar hornikusers\name{stanford2} \alias{stanford2} \docType{data} \title{More Stanford Heart Transplant data} \description{ This contains the Stanford Heart Transplant data in a different format. The main data set is in \code{\link{heart}}. } \usage{stanford2} \format{ \tabular{ll}{ id: \tab ID number\cr time:\tab survival or censoring time\cr status:\tab censoring status\cr age: \tab in years\cr t5: \tab T5 mismatch score\cr } } \seealso{ \code{\link{predict.survreg}}, \code{\link{heart}} } \source{ LA Escobar and WQ Meeker Jr (1992), Assessing influence in regression analysis with censored data. \emph{Biometrics} \bold{48}, 507--528. Page 519. } \keyword{datasets} \keyword{survival} survival/man/lung.Rd0000644000175100001440000000225211732700061014150 0ustar hornikusers\name{lung} \docType{data} \alias{cancer} \alias{lung} \title{NCCTG Lung Cancer Data} \description{ Survival in patients with advanced lung cancer from the North Central Cancer Treatment Group. Performance scores rate how well the patient can perform usual daily activities. } \usage{ lung cancer } \format{ \tabular{ll}{ inst:\tab Institution code\cr time:\tab Survival time in days\cr status:\tab censoring status 1=censored, 2=dead\cr age:\tab Age in years\cr sex:\tab Male=1 Female=2\cr ph.ecog:\tab ECOG performance score (0=good 5=dead)\cr ph.karno:\tab Karnofsky performance score (bad=0-good=100) rated by physician\cr pat.karno:\tab Karnofsky performance score as rated by patient\cr meal.cal:\tab Calories consumed at meals\cr wt.loss:\tab Weight loss in last six months\cr } } \source{Terry Therneau} \references{ Loprinzi CL. Laurie JA. Wieand HS. Krook JE. Novotny PJ. Kugler JW. Bartel J. Law M. Bateman M. Klatt NE. et al. Prospective evaluation of prognostic variables from patient-completed questionnaires. North Central Cancer Treatment Group. Journal of Clinical Oncology. 12(3):601-7, 1994. } \keyword{datasets} survival/man/cgd0.Rd0000644000175100001440000000274213013633731014027 0ustar hornikusers\name{cgd0} \docType{data} \alias{cgd0} \title{Chronic Granulotomous Disease data} \description{Data are from a placebo controlled trial of gamma interferon in chronic granulotomous disease (CGD). Contains the data on time to serious infections observed through end of study for each patient. } \usage{cgd0} \format{ \describe{ \item{id}{subject identification number} \item{center}{enrolling center } \item{random}{date of randomization } \item{treatment}{placebo or gamma interferon } \item{sex}{sex} \item{age}{age in years, at study entry } \item{height}{height in cm at study entry} \item{weight}{weight in kg at study entry} \item{inherit}{pattern of inheritance } \item{steroids}{use of steroids at study entry,1=yes} \item{propylac}{use of prophylactic antibiotics at study entry} \item{hos.cat}{a categorization of the centers into 4 groups} \item{futime}{days to last follow-up} \item{etime1-etime7}{up to 7 infection times for the subject} } } \details{ The \code{cgdraw} data set (this one) is in the form found in the references, with one line per patient and no recoding of the variables. The \code{cgd} data set has been further processed so as to have one line per event, with covariates such as center recoded as factors to include meaningful labels. } \source{ Fleming and Harrington, Counting Processes and Survival Analysis, appendix D.2. } \seealso{\code{\link{cgd}}} \keyword{datasets} \keyword{survival} survival/man/survreg.object.Rd0000644000175100001440000000445413013633731016156 0ustar hornikusers\name{survreg.object} \alias{survreg.object} \alias{print.survreg} \alias{summary.survreg} \title{ Parametric Survival Model Object } \description{ This class of objects is returned by the \code{survreg} function to represent a fitted parametric survival model. Objects of this class have methods for the functions \code{print}, \code{summary}, \code{predict}, and \code{residuals}. } \section{COMPONENTS}{ The following components must be included in a legitimate \code{survreg} object. \describe{ \item{coefficients}{ the coefficients of the \code{linear.predictors}, which multiply the columns of the model matrix. It does not include the estimate of error (sigma). The names of the coefficients are the names of the single-degree-of-freedom effects (the columns of the model matrix). If the model is over-determined there will be missing values in the coefficients corresponding to non-estimable coefficients. } \item{icoef}{ coefficients of the baseline model, which will contain the intercept and log(scale), or multiple scale factors for a stratified model. } \item{var}{ the variance-covariance matrix for the parameters, including the log(scale) parameter(s). } \item{loglik}{ a vector of length 2, containing the log-likelihood for the baseline and full models. } \item{iter}{ the number of iterations required } \item{linear.predictors}{ the linear predictor for each subject. } \item{df}{ the degrees of freedom for the final model. For a penalized model this will be a vector with one element per term. } \item{scale}{ the scale factor(s), with length equal to the number of strata. } \item{idf}{ degrees of freedom for the initial model. } \item{means}{ a vector of the column means of the coefficient matrix. } \item{dist}{ the distribution used in the fit.} \item{weights}{included for a weighted fit.} } The object will also have the following components found in other model results (some are optional): \code{linear predictors}, \code{weights}, \code{x}, \code{y}, \code{model}, \code{call}, \code{terms} and \code{formula}. See \code{lm}. } \seealso{ \code{\link{survreg}}, \code{\link{lm}} } \keyword{regression} \keyword{survival} % Converted by Sd2Rd version 0.3-2. survival/man/survexp.object.Rd0000644000175100001440000000411313013633731016165 0ustar hornikusers\name{survexp.object} \alias{survexp.object} \title{ Expected Survival Curve Object } \description{ This class of objects is returned by the \code{survexp} class of functions to represent a fitted survival curve. Objects of this class have methods for \code{summary}, and inherit the \code{print}, \code{plot}, \code{points} and \code{lines} methods from \code{survfit}. } \section{Structure}{ The following components must be included in a legitimate \code{survfit} object. } \arguments{ \item{surv}{ the estimate of survival at time t+0. This may be a vector or a matrix. } \item{n.risk}{ the number of subjects who contribute at this time. } \item{time}{ the time points at which the curve has a step. } \item{std.err}{ the standard error of the cumulative hazard or -log(survival). } \item{strata}{ if there are multiple curves, this component gives the number of elements of the \code{time} etc. vectors corresponding to the first curve, the second curve, and so on. The names of the elements are labels for the curves. } \item{method}{the estimation method used. One of "Ederer", "Hakulinen", or "conditional".} \item{na.action}{ the returned value from the na.action function, if any. It will be used in the printout of the curve, e.g., the number of observations deleted due to missing values. } \item{call}{ an image of the call that produced the object. } } \section{Subscripts}{ Survexp objects that contain multiple survival curves can be subscripted. This is most often used to plot a subset of the curves. } \section{Details}{ In expected survival each subject from the data set is matched to a hypothetical person from the parent population, matched on the characteristics of the parent population. The number at risk printed here is the number of those hypothetical subject who are still part of the calculation. In particular, for the Ederer method all hypotheticals are retained for all time, so \code{n.risk} will be a constant. } \seealso{ \code{\link{plot.survfit}}, \code{\link{summary.survexp}}, \code{\link{print.survfit}}, \code{\link{survexp}}. } \keyword{survival} survival/man/untangle.specials.Rd0000644000175100001440000000230411732700061016620 0ustar hornikusers\name{untangle.specials} \alias{untangle.specials} \title{ Help Process the `specials' Argument of the `terms' Function. } \description{ Given a \code{terms} structure and a desired special name, this returns an index appropriate for subscripting the \code{terms} structure and another appropriate for the data frame. } \usage{ untangle.specials(tt, special, order=1) } \arguments{ \item{tt}{ a \code{terms} object. } \item{special}{ the name of a special function, presumably used in the terms object. } \item{order}{ the order of the desired terms. If set to 2, interactions with the special function will be included. }} \value{ a list with two components: \item{vars}{ a vector of variable names, as would be found in the data frame, of the specials. } \item{terms}{ a numeric vector, suitable for subscripting the terms structure, that indexes the terms in the expanded model formula which involve the special. }} \examples{ formula<-Surv(tt,ss)~x+z*strata(id) tms<-terms(formula,specials="strata") ## the specials attribute attr(tms,"specials") ## main effects untangle.specials(tms,"strata") ## and interactions untangle.specials(tms,"strata",order=1:2) } \keyword{survival} % Converted by Sd2Rd version 0.3-2. survival/man/summary.aareg.Rd0000644000175100001440000000641311732700061015761 0ustar hornikusers\name{summary.aareg} \alias{summary.aareg} \title{ Summarize an aareg fit } \description{ Creates the overall test statistics for an Aalen additive regression model } \usage{ \method{summary}{aareg}(object, maxtime, test=c("aalen", "nrisk"), scale=1,...) } \arguments{ \item{object}{ the result of a call to the \code{aareg} function } \item{maxtime}{ truncate the input to the model at time "maxtime" } \item{test}{ the relative time weights that will be used to compute the test } \item{scale}{ scales the coefficients. For some data sets, the coefficients of the Aalen model will be very small (10-4); this simply multiplies the printed values by a constant, say 1e6, to make the printout easier to read. } \item{\dots}{for future methods} } \value{ a list is returned with the following components \item{ table }{ a matrix with rows for the intercept and each covariate, and columns giving a slope estimate, the test statistic, it's standard error, the z-score and a p-value } \item{ test }{ the time weighting used for computing the test statistics } \item{ test.statistic }{ the vector of test statistics } \item{ test.var }{ the model based variance matrix for the test statistic } \item{ test.var2 }{ optionally, a robust variance matrix for the test statistic } \item{ chisq }{ the overall test (ignoring the intercept term) for significance of any variable } \item{ n }{ a vector containing the number of observations, the number of unique death times used in the computation, and the total number of unique death times } } \details{ It is not uncommon for the very right-hand tail of the plot to have large outlying values, particularly for the standard error. The \code{maxtime} parameter can then be used to truncate the range so as to avoid these. This gives an updated value for the test statistics, without refitting the model. The slope is based on a weighted linear regression to the cumulative coefficient plot, and may be a useful measure of the overall size of the effect. For instance when two models include a common variable, "age" for instance, this may help to assess how much the fit changed due to the other variables, in leiu of overlaying the two plots. (Of course the plots are often highly non-linear, so it is only a rough substitute). The slope is not directly related to the test statistic, as the latter is invariant to any monotone transformation of time. } \seealso{ aareg, plot.aareg } \examples{ afit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, data=lung, dfbeta=TRUE) summary(afit) \dontrun{ slope test se(test) robust se z p Intercept 5.05e-03 1.9 1.54 1.55 1.23 0.219000 age 4.01e-05 108.0 109.00 106.00 1.02 0.307000 sex -3.16e-03 -19.5 5.90 5.95 -3.28 0.001030 ph.ecog 3.01e-03 33.2 9.18 9.17 3.62 0.000299 Chisq=22.84 on 3 df, p=4.4e-05; test weights=aalen } summary(afit, maxtime=600) \dontrun{ slope test se(test) robust se z p Intercept 4.16e-03 2.13 1.48 1.47 1.450 0.146000 age 2.82e-05 85.80 106.00 100.00 0.857 0.392000 sex -2.54e-03 -20.60 5.61 5.63 -3.660 0.000256 ph.ecog 2.47e-03 31.60 8.91 8.67 3.640 0.000271 Chisq=27.08 on 3 df, p=5.7e-06; test weights=aalen }} \keyword{survival} survival/man/survexp.us.Rd0000644000175100001440000000257513070710334015356 0ustar hornikusers\name{ratetables} \alias{survexp.us} \alias{survexp.usr} \alias{survexp.mn} \title{ Census Data Sets for the Expected Survival and Person Years Functions } \description{ Census data sets for the expected survival and person years functions. } \details{ \describe{ \item{us}{ total United States population, by age and sex, 1940 to 2004. } \item{usr}{ United States population, by age, sex and race, 1940 to 2004. Race is white, nonwhite, or black. For 1960 and 1970 the black population values were not reported separately, so the nonwhite values were used. } \item{mn}{ total Minnesota population, by age and sex, 1970 to 2004. } } Each of these tables contains the daily hazard rate for a matched subject from the population, defined as \eqn{-\log(1-q)/365.25} where \eqn{q} is the 1 year probability of death as reported in the original tables. For age 25 in 1970, for instance, \eqn{p = 1-q} is is the probability that a subject who becomes 25 years of age in 1970 will achieve his/her 26th birthday. The tables are recast in terms of hazard per day entirely for computational convenience. Each table is stored as an array, with additional attributes, and can be subset and manipulated as standard R arrays. } \examples{ survexp.uswhite <- survexp.usr[,,"white",] } \keyword{survival} \keyword{datasets} survival/man/summary.pyears.Rd0000644000175100001440000000664213046711745016224 0ustar hornikusers\name{summary.pyears} \alias{summary.pyears} \title{Summary function for pyears objecs} \description{Create a printable table of a person-years result.} \usage{ \method{summary}{pyears}(object, header = TRUE, call = header, n = TRUE, event = TRUE, pyears = TRUE, expected = TRUE, rate = FALSE, rr =expected, ci.r = FALSE, ci.rr = FALSE, totals=FALSE, legend = TRUE, vline = FALSE, vertical= TRUE, nastring=".", conf.level = 0.95, scale = 1, ...) } \arguments{ \item{object}{a pyears object} \item{header}{print out a header giving the total number of observations, events, person-years, and total time (if any) omitted from the table} \item{call}{print out a copy of the call} \item{n, event, pyears, expected}{logical arguments: should these elements be printed in the table?} \item{rate, ci.r}{logical arguments: should the incidence rate and/or its confidence interval be given in the table?} \item{rr, ci.rr}{logical arguments: should the hazard ratio and/or its confidence interval be given in the table?} \item{totals}{should row and column totals be added?} \item{legend}{should a legend be included in the printout?} \item{vline}{should vertical lines be included in the printed tables?} \item{vertical}{when there is only a single predictor, should the table be printed with the predictor on the left (vertical=TRUE) or across the top (vertical=FALSE)?} \item{nastring}{what to use for missing values in the table. Some of these are structural, e.g., risk ratios for a cell with no follow-up time.} \item{conf.level}{confidence level for any confidence intervals} \item{scale}{a scaling factor for printed rates} \item{\dots}{optional arguments which will be passed to the \code{format} function; common choices would be digits=2 or nsmall=1.} } \details{ The \code{pyears} function is often used to create initial descriptions of a survival or time-to-event variable; the type of material that is often found in ``table 1'' of a paper. The summary routine prints this information out using one of pandoc table styles. A primary reason for choosing this style is that Rstudio is then able to automatically render the results in multiple formats: html, rtf, latex, etc. If the \code{pyears} call has only a single covariate then the table will have that covariate as one margin and the statistics of interest as the other. If the \code{pyears} call has two predictors then those two predictors are used as margins of the table, while each cell of the table contains the statistics of interest as multiple rows within the cell. If there are more than two predictors then multiple tables are produced, in the same order as the standard R printout for an array. The "N" entry of a pyears object is the number of observations which contributed to a particular cell. When the original call includes \code{tcut} objects then a single observation may contribute to multiple cells. } \section{Notes}{ The pandoc system has four table types: with or without vertical bars, and with single or multiple rows of data in each cell. This routine produces all 4 styles depending on options, but currently not all of them are recognized by the Rstudio-pandoc pipeline. (And we don't yet see why.) } \value{a copy of the object} \author{Terry Therneau and Elizabeth Atkinson} \seealso{\code{\link{cipoisson}}, \code{\link{pyears}}, \code{\link{format}}} \keyword{ survival } survival/man/tmerge.Rd0000644000175100001440000001357013054066311014475 0ustar hornikusers\name{tmerge} \alias{tmerge} \title{Time based merge for survival data} \description{ A common task in survival analysis is the creation of start,stop data sets which have multiple intervals for each subject, along with the covariate values that apply over that interval. This function aids in the creation of such data sets. } \usage{ tmerge(data1, data2, id,\dots, tstart, tstop, options) } \arguments{ \item{data1}{the primary data set, to which new variables and/or observation will be added} \item{data2}{second data set in which the other arguments will be found} \item{id}{subject identifier} \item{\dots}{operations that add new variables or intervals, see below} \item{tstart}{optional variable to define the valid time range for each subject, only used on an initial call} \item{tstop}{optional variable to define the valid time range for each subject, only used on an initial call} \item{options}{a list of options. Valid ones are idname, tstartname, tstopname, delay, na.rm, and tdcstart. See the explanation below.} } \details{ The program is often run in multiple passes, the first of which defines the basic structure, and subsequent ones that add new variables to that structure. For a more complete explanation of how this routine works refer to the vignette on time-dependent variables. There are 4 types of optional arguments: a time dependent covariate (tdc), cumulative count (cumtdc), event (event) or cumulative event (cumevent). Time dependent covariates change their values before an event, events are outcomes. \itemize{ \item{newname = tdc(y, x)}{ A new time dependent covariate variable will created. The argument \code{y} is assumed to be on the scale of the start and end time, and each instance describes the occurrent of a "condition" at that time. The second argument \code{x} is optional. In the case where \code{x} is missing the count variable starts at 0 for each subject and becomes 1 at the time of the event. If \code{x} is present the value of the time dependent covariate is initialized to the \code{tdcstart} option and is reset to the value of \code{x} at each observation. If the option \code{na.rm=TRUE} missing values of \code{x} are first removed. \item{newname = cumtdc(y,x)}{ Similar to tdc, except that the event count is accumulated over time for each subject.} \item{newname = event(y,x)}{ Mark an event at time y. In the usual case that \code{x} is missing the new 0/1 variable will be similar to the 0/1 status variable of a survival time. } \item{newname = cumevent(y,x)}{ Cumulative events}. } } The function adds three new variables to the output data set: \code{tstart}, \code{tstop}, and \code{id}. The \code{options} argument can be used to change these names. The \code{na.rm} option affects creation of time-dependent covariates. Should a data row in \code{data2} that has a missing value for the variable be ignored (na.rm=FALSE, default) or should it generate an observation with a value of NA? The default value leads to "last value carried forward" behavior. The \code{delay} option causes a time-dependent covariate's new value to be delayed, see the vignette for an example. } \value{a data frame with two extra attributes \code{tname} and \code{tcount}. The first contains the names of the key variables; it's persistence from call to call allows the user to avoid constantly reentering the \code{options} argument. The tcount variable contains counts of the match types. New time values that occur before the first interval for a subject are "early", those after the last interval for a subject are "late", and those that fall into a gap are of type "gap". All these are are considered to be outside the specified time frame for the given subject. An event of this type will be discarded. A time-dependent covariate value will be applied to later intervals but will not generate a new time point in the output. The most common type will usually be "within", for those new times that fall inside an existing interval and cause it to be split into two. Observations that fall exactly on the edge of an interval but within the (min, max] time for a subject are counted as being on a "leading" edge, "trailing" edge or "boundary". The first corresponds for instance to an occurrence at 17 for someone with an intervals of (0,15] and (17, 35]. A \code{tdc} at time 17 will affect this interval but an \code{event} at 17 would be ignored. An \code{event} occurrence at 15 would count in the (0,15] interval. The last case is where the main data set has touching intervals for a subject, e.g. (17, 28] and (28,35] and a new occurrence lands at the join. Events will go to the earlier interval and counts to the latter one. A last column shows the number of additions where where the id and time point were identical. These extra attributes are ephemeral and will be discarded if the dataframe is modified in any way. This is intentional. } \author{Terry Therneau} \seealso{\code{\link{neardate}}} \examples{ # The pbc data set contains baseline data and follow-up status # for a set of subjects with primary biliary cirrhosis, while the # pbcseq data set contains repeated laboratory values for those # subjects. # The first data set contains data on 312 subjects in a clinical trial plus # 106 that agreed to be followed off protocol, the second data set has data # only on the trial subjects. temp <- subset(pbc, id <= 312, select=c(id:sex, stage)) # baseline data pbc2 <- tmerge(temp, temp, id=id, endpt = event(time, status)) pbc2 <- tmerge(pbc2, pbcseq, id=id, ascites = tdc(day, ascites), bili = tdc(day, bili), albumin = tdc(day, albumin), protime = tdc(day, protime), alk.phos = tdc(day, alk.phos)) fit <- coxph(Surv(tstart, tstop, endpt==2) ~ protime + log(bili), data=pbc2) } \keyword{ survival } survival/man/ratetableDate.Rd0000644000175100001440000000152011732700061015741 0ustar hornikusers\name{ratetableDate} \alias{ratetableDate} \title{Convert date objects to ratetable form} \description{ This method converts dates from various forms into the internal form used in \code{ratetable} objects. } \usage{ ratetableDate(x) } \arguments{ \item{x}{a date. The function currently has methods for Date, date, POSIXt, timeDate, and chron objects. } } \details{ This function is useful for those who create new ratetables, but is normally invisible to users. It is used internally by the \code{survexp} and \code{pyears} functions to map the various date formats; if a new method is added then those routines will automatically be adapted to the new date type. } \value{a numeric vector, the number of days since 1/1/1960.} \author{Terry Therneau} \seealso{\code{\link{pyears}}, \code{\link{survexp}}} \keyword{survival} survival/man/predict.coxph.Rd0000644000175100001440000001165713026517027015774 0ustar hornikusers\name{predict.coxph} \alias{predict.coxph} \alias{predict.coxph.penal} \title{ Predictions for a Cox model } \description{ Compute fitted values and regression terms for a model fitted by \code{\link{coxph}} } \usage{ \method{predict}{coxph}(object, newdata, type=c("lp", "risk", "expected", "terms", "survival"), se.fit=FALSE, na.action=na.pass, terms=names(object$assign), collapse, reference=c("strata", "sample"), ...) } \arguments{ \item{object}{ the results of a coxph fit. } \item{newdata}{ Optional new data at which to do predictions. If absent predictions are for the data frame used in the original fit. When coxph has been called with a formula argument created in another context, i.e., coxph has been called within another function and the formula was passed as an argument to that function, there can be problems finding the data set. See the note below. } \item{type}{ the type of predicted value. Choices are the linear predictor (\code{"lp"}), the risk score exp(lp) (\code{"risk"}), the expected number of events given the covariates and follow-up time (\code{"expected"}), and the terms of the linear predictor (\code{"terms"}). The survival probability for a subject is equal to exp(-expected). } \item{se.fit}{ if TRUE, pointwise standard errors are produced for the predictions. } \item{na.action}{ applies only when the \code{newdata} argument is present, and defines the missing value action for the new data. The default is to include all observations. When there is no newdata, then the behavior of missing is dictated by the na.action option of the original fit.} \item{terms}{ if type="terms", this argument can be used to specify which terms should be included; the default is all. } \item{collapse}{ optional vector of subject identifiers. If specified, the output will contain one entry per subject rather than one entry per observation. } \item{reference}{reference for centering predictions, see details below} \item{\dots}{For future methods} } \value{ a vector or matrix of predictions, or a list containing the predictions (element "fit") and their standard errors (element "se.fit") if the se.fit option is TRUE. } \details{ The Cox model is a \emph{relative} risk model; predictions of type "linear predictor", "risk", and "terms" are all relative to the sample from which they came. By default, the reference value for each of these is the mean covariate within strata. The primary underlying reason is statistical: a Cox model only predicts relative risks between pairs of subjects within the same strata, and hence the addition of a constant to any covariate, either overall or only within a particular stratum, has no effect on the fitted results. Using the \code{reference="strata"} option causes this to be true for predictions as well. When the results of \code{predict} are used in further calculations it may be desirable to use a fixed reference level. Use of \code{reference="sample"} will use the overall means, and agrees with the \code{linear.predictors} component of the coxph object (which uses the overall mean for backwards compatability with older code). Predictions of \code{type="terms"} are almost invariably passed forward to further calculation, so for these we default to using the sample as the reference. Predictions of type "expected" incorporate the baseline hazard and are thus absolute instead of relative; the \code{reference} option has no effect on these. Models that contain a \code{frailty} term are a special case: due to the technical difficulty, when there is a \code{newdata} argument the predictions will always be for a random effect of zero. } \note{ Some predictions can be obtained directly from the coxph object, and for others it is necessary for the routine to have the entirety of the original data set, e.g., for type = \code{terms} or if standard errors are requested. This extra information is saved in the coxph object if \code{model=TRUE}, if not the original data is reconstructed. If it is known that such residuals will be required overall execution will be slightly faster if the model information is saved. In some cases the reconstruction can fail. The most common is when coxph has been called inside another function and the formula was passed as one of the arguments to that enclosing function. Another is when the data set has changed between the original call and the time of the prediction call. In each of these the simple solution is to add \code{model=TRUE} to the original coxph call. } \seealso{ \code{\link{predict}},\code{\link{coxph}},\code{\link{termplot}} } \examples{ options(na.action=na.exclude) # retain NA in predictions fit <- coxph(Surv(time, status) ~ age + ph.ecog + strata(inst), lung) #lung data set has status coded as 1/2 mresid <- (lung$status-1) - predict(fit, type='expected') #Martingale resid predict(fit,type="lp") predict(fit,type="expected") predict(fit,type="risk",se.fit=TRUE) predict(fit,type="terms",se.fit=TRUE) } \keyword{survival} survival/man/cgd.Rd0000644000175100001440000000306113013633731013742 0ustar hornikusers\name{cgd} \docType{data} \alias{cgd} \alias{cgd.raw} \title{Chronic Granulotomous Disease data} \description{Data are from a placebo controlled trial of gamma interferon in chronic granulotomous disease (CGD). Contains the data on time to serious infections observed through end of study for each patient. } \usage{cgd} \format{ \describe{ \item{id}{subject identification number} \item{center}{enrolling center } \item{random}{date of randomization } \item{treatment}{placebo or gamma interferon } \item{sex}{sex} \item{age}{age in years, at study entry } \item{height}{height in cm at study entry} \item{weight}{weight in kg at study entry} \item{inherit}{pattern of inheritance } \item{steroids}{use of steroids at study entry,1=yes} \item{propylac}{use of prophylactic antibiotics at study entry} \item{hos.cat}{a categorization of the centers into 4 groups} \item{tstart, tstop}{start and end of each time interval } \item{status}{1=the interval ends with an infection } \item{enum}{observation number within subject} } } \details{ The \code{cgd0} data set is in the form found in the references, with one line per patient and no recoding of the variables. The \code{cgd} data set (this one) has been cast into (start, stop] format with one line per event, and covariates such as center recoded as factors to include meaningful labels. } \source{ Fleming and Harrington, Counting Processes and Survival Analysis, appendix D.2. } \seealso{\code{link{cgd0}}} \keyword{datasets} \keyword{survival} survival/man/plot.survfit.Rd0000644000175100001440000001675013013633731015675 0ustar hornikusers\name{plot.survfit} \alias{plot.survfit} \title{ Plot method for \code{survfit} objects } \usage{ \method{plot}{survfit}(x, conf.int=, mark.time=FALSE, mark=3, col=1, lty=1, lwd=1, cex=1, log=FALSE, xscale=1, yscale=1, firstx=0, firsty=1, xmax, ymin=0, fun, xlab="", ylab="", xaxs="S", conf.times, conf.cap=.005, conf.offset=.012, \dots) } \arguments{ \item{x}{ an object of class \code{survfit}, usually returned by the \code{survfit} function. } \item{conf.int}{ determines whether confidence intervals will be plotted. The default is to do so if there is only 1 curve, i.e., no strata. } \item{mark.time}{ controls the labeling of the curves. If set to \code{FALSE}, no labeling is done. If \code{TRUE}, then curves are marked at each censoring time which is not also a death time. If \code{mark.time} is a numeric vector, then curves are marked at the specified time points. } \item{mark}{ vector of mark parameters, which will be used to label the curves. The \code{lines} help file contains examples of the possible marks. The vector is reused cyclically if it is shorter than the number of curves. If it is present this implies \code{mark.time = TRUE}. } \item{col}{ a vector of integers specifying colors for each curve. The default value is 1. } \item{lty}{ a vector of integers specifying line types for each curve. The default value is 1. } \item{lwd}{ a vector of numeric values for line widths. The default value is 1. } \item{cex}{ a numeric value specifying the size of the marks. This is not treated as a vector; all marks have the same size. } \item{log}{ a logical value, if TRUE the y axis wll be on a log scale. Alternately, one of the standard character strings "x", "y", or "xy" can be given to specific logarithmic horizontal and/or vertical axes. } \item{yscale}{ a numeric value used to multiply the labels on the y axis. A value of 100, for instance, would be used to give a percent scale. Only the labels are changed, not the actual plot coordinates, so that adding a curve with "\code{lines(surv.exp(...))}", say, will perform as it did without the \code{yscale} argument. } \item{xscale}{ a numeric value used like \code{yscale} for labels on the x axis. A value of 365.25 will give labels in years instead of the original days. } \item{firstx, firsty}{ the starting point for the survival curves. If either of these is set to \code{NA} the plot will start at the first time point of the curve. By default, the plot program obeys tradition by having the plot start at (0,0). If \code{start.time} argument is used in \code{survfit}, \code{firstx} is set to that value. } \item{xmax}{ the maximum horizontal plot coordinate. This can be used to shrink the range of a plot. It shortens the curve before plotting it, so that unlike using the \code{xlim} graphical parameter, warning messages about out of bounds points are not generated. } \item{ymin}{ lower boundary for y values. Survival curves are most often drawn in the range of 0-1, even if none of the curves approach zero. The parameter is ignored if the \code{fun} argument is present, or if it has been set to \code{NA}. } \item{fun}{ an arbitrary function defining a transformation of the survival curve. For example \code{fun=log} is an alternative way to draw a log-survival curve (but with the axis labeled with log(S) values), and \code{fun=sqrt} would generate a curve on square root scale. Four often used transformations can be specified with a character argument instead: \code{"log"} is the same as using the \code{log=T} option, \code{"event"} plots cumulative events (f(y) = 1-y), \code{"cumhaz"} plots the cumulative hazard function (f(y) = -log(y)), and \code{"cloglog"} creates a complimentary log-log survival plot (f(y) = log(-log(y)) along with log scale for the x-axis). } \item{xlab}{ label given to the x-axis. } \item{ylab}{ label given to the y-axis. } \item{xaxs}{ either \code{"S"} for a survival curve or a standard x axis style as listed in \code{par}. Survival curves are usually displayed with the curve touching the y-axis, but not touching the bounding box of the plot on the other 3 sides. Type \code{"S"} accomplishes this by manipulating the plot range and then using the \code{"i"} style internally. } \item{conf.times}{optional vector of times at which to place a confidence bar on the curve(s). If present, these will be used instead of confidence bands.} \item{conf.cap}{width of the horizontal cap on top of the confidence bars; only used if conf.times is used. A value of 1 is the width of the plot region.} \item{conf.offset}{the offset for confidence bars, when there are multiple curves on the plot. A value of 1 is the width of the plot region. If this is a single number then each curve's bars are offset by this amount from the prior curve's bars, if it is a vector the values are used directly.} \item{\dots}{for future methods} } \value{ a list with components \code{x} and \code{y}, containing the coordinates of the last point on each of the curves (but not the confidence limits). This may be useful for labeling. } \description{ A plot of survival curves is produced, one curve for each strata. The \code{log=T} option does extra work to avoid log(0), and to try to create a pleasing result. If there are zeros, they are plotted by default at 0.8 times the smallest non-zero value on the curve(s). Curves are plotted in the same order as they are listed by \code{print} (which gives a 1 line summary of each). This will be the order in which \code{col}, \code{lty}, etc are used. } \details{ When the \code{survfit} function creates a multi-state survival curve the resulting object also has class `survfitms'. Competing risk curves are a common case. The only difference in the plots is that multi-state defaults to a curve that goes from lower left to upper right (starting at 0), where survival curves by default start at 1 and go down. All other options are identical. When the \code{conf.times} argument is used, the confidence bars are offset by \code{conf.offset} units to avoid overlap. The bar on each curve are the confidence interval for the time point at which the bar is drawn, i.e., different time points for each curve. If curves are steep at that point, the visual impact can sometimes substantially differ for positive and negative values of \code{conf.offset}. } \note{In prior versions the behavior of \code{xscale} and \code{yscale} differed: the first changed the scale both for the plot and for all subsequent actions such as adding a legend, whereas \code{yscale} affected only the axis label. This was normalized in version 2-36.4, and both parameters now only affect the labeling. } \seealso{ \code{\link{points.survfit}}, \code{\link{lines.survfit}}, \code{\link{par}}, \code{\link{survfit}} } \examples{ leukemia.surv <- survfit(Surv(time, status) ~ x, data = aml) plot(leukemia.surv, lty = 2:3) legend(100, .9, c("Maintenance", "No Maintenance"), lty = 2:3) title("Kaplan-Meier Curves\nfor AML Maintenance Study") lsurv2 <- survfit(Surv(time, status) ~ x, aml, type='fleming') plot(lsurv2, lty=2:3, fun="cumhaz", xlab="Months", ylab="Cumulative Hazard") } \keyword{survival} \keyword{hplot} survival/man/summary.coxph.Rd0000644000175100001440000000263311732700061016023 0ustar hornikusers\name{summary.coxph} \alias{summary.coxph} \title{ Summary method for Cox models } \description{ Produces a summary of a fitted coxph model } \usage{ \method{summary}{coxph}(object, conf.int=0.95, scale=1,...) } \arguments{ \item{object}{ the result of a coxph fit } \item{conf.int}{ level for computation of the confidence intervals. If set to FALSE no confidence intervals are printed } \item{scale}{ vector of scale factors for the coefficients, defaults to 1. The confidence limits are for the risk change associated with one scale unit. } \item{\dots}{for future methods} } \value{ An object of class \code{summary.coxph}. } \seealso{ coxph, print.coxph } \examples{ fit <- coxph(Surv(time, status) ~ age + sex, lung) summary(fit) \dontrun{ Call: coxph(formula = Surv(time, status) ~ age + sex, data = lung) n= 228 coef exp(coef) se(coef) z p age 0.017 1.017 0.00922 1.85 0.0650 sex -0.513 0.599 0.16745 -3.06 0.0022 exp(coef) exp(-coef) lower .95 upper .95 age 1.017 0.983 0.999 1.036 sex 0.599 1.670 0.431 0.831 Rsquare= 0.06 (max possible= 0.999 ) Likelihood ratio test= 14.1 on 2 df, p=0.000857 Wald test = 13.5 on 2 df, p=0.00119 Score (logrank) test = 13.7 on 2 df, p=0.00105 }} \keyword{survival} % docclass is function % Converted by Sd2Rd version 37351. survival/man/mgus.Rd0000644000175100001440000000675513017617770014206 0ustar hornikusers\name{mgus} \alias{mgus} \alias{mgus1} \docType{data} \title{Monoclonal gammapothy data} \description{ Natural history of 241 subjects with monoclonal gammapothy of undetermined significance (MGUS). } \usage{ mgus mgus1 } \format{ mgus: A data frame with 241 observations on the following 12 variables. \tabular{ll}{ id:\tab subject id \cr age:\tab age in years at the detection of MGUS \cr sex:\tab \code{male} or \code{female} \cr dxyr:\tab year of diagnosis \cr pcdx:\tab for subjects who progress to a plasma cell malignancy \cr \tab the subtype of malignancy: multiple myeloma (MM) is the \cr \tab most common, followed by amyloidosis (AM), macroglobulinemia (MA),\cr \tab and other lymphprolifative disorders (LP) \cr pctime:\tab days from MGUS until diagnosis of a plasma cell malignancy \cr futime:\tab days from diagnosis to last follow-up \cr death:\tab 1= follow-up is until death \cr alb:\tab albumin level at MGUS diagnosis \cr creat:\tab creatinine at MGUS diagnosis \cr hgb:\tab hemoglobin at MGUS diagnosis \cr mspike:\tab size of the monoclonal protein spike at diagnosis \cr } mgus1: The same data set in start,stop format. Contains the id, age, sex, and laboratory variable described above along with \tabular{ll}{ start, stop:\tab sequential intervals of time for each subject \cr status:\tab =1 if the interval ends in an event \cr event:\tab a factor containing the event type: censor, death, or plasma cell malignancy \cr enum: \tab event number for each subject: 1 or 2 } } \details{ Plasma cells are responsible for manufacturing immunoglobulins, an important part of the immune defense. At any given time there are estimated to be about \eqn{10^6} different immunoglobulins in the circulation at any one time. When a patient has a plasma cell malignancy the distribution will become dominated by a single isotype, the product of the malignant clone, visible as a spike on a serum protein electrophoresis. Monoclonal gammapothy of undertermined significance (MGUS) is the presence of such a spike, but in a patient with no evidence of overt malignancy. This data set of 241 sequential subjects at Mayo Clinic was the groundbreaking study defining the natural history of such subjects. Due to the diligence of the principle investigator 0 subjects have been lost to follow-up. Three subjects had MGUS detected on the day of death. In data set \code{mgus1} these subjects have the time to MGUS coded as .5 day before the death in order to avoid tied times. These data sets were updated in Jan 2015 to correct some small errors. } \source{ Mayo Clinic data courtesy of Dr. Robert Kyle. } \examples{ # Create the competing risk curves for time to first of death or PCM sfit <- survfit(Surv(start, stop, event) ~ sex, mgus1, subset=(enum==1)) print(sfit) # the order of printout is the order in which they plot plot(sfit, xscale=365.25, lty=c(2,1,2,1), col=c(1,1,2,2), xlab="Years after MGUS detection", ylab="Proportion") legend(0, .8, c("Death/male", "Death/female", "PCM/male", "PCM/female"), lty=c(1,1,2,2), col=c(2,1,2,1), bty='n') title("Curves for the first of plasma cell malignancy or death") # The plot shows that males have a higher death rate than females (no # surprise) but their rates of conversion to PCM are essentially the same. } \references{ R Kyle, Benign monoclonal gammopathy -- after 20 to 35 years of follow-up, Mayo Clinic Proc 1993; 68:26-36. } \keyword{datasets} \keyword{survival} survival/man/kidney.Rd0000644000175100001440000000263511732700061014473 0ustar hornikusers\name{kidney} \alias{kidney} \title{Kidney catheter data} \format{ \tabular{ll}{ patient:\tab id\cr time:\tab time\cr status:\tab event status\cr age:\tab in years\cr sex:\tab 1=male, 2=female\cr disease:\tab disease type (0=GN, 1=AN, 2=PKD, 3=Other)\cr frail:\tab frailty estimate from original paper\cr }} \description{ Data on the recurrence times to infection, at the point of insertion of the catheter, for kidney patients using portable dialysis equipment. Catheters may be removed for reasons other than infection, in which case the observation is censored. Each patient has exactly 2 observations. This data has often been used to illustrate the use of random effects (frailty) in a survival model. However, one of the males (id 21) is a large outlier, with much longer survival than his peers. If this observation is removed no evidence remains for a random subject effect. } \section{Note}{ The original paper ignored the issue of tied times and so is not exactly reproduced by the survival package. } \examples{ kfit <- coxph(Surv(time, status)~ age + sex + disease + frailty(id), kidney) kfit0 <- coxph(Surv(time, status)~ age + sex + disease, kidney) kfitm1 <- coxph(Surv(time,status) ~ age + sex + disease + frailty(id, dist='gauss'), kidney) } \source{ CA McGilchrist, CW Aisbett (1991), Regression with frailty in survival analysis. \emph{Biometrics} \bold{47}, 461--66. } \keyword{survival} survival/man/survfit.object.Rd0000644000175100001440000001074413003400762016155 0ustar hornikusers\name{survfit.object} \alias{survfit.object} \alias{survfitms.object} \title{ Survival Curve Object } \description{ This class of objects is returned by the \code{survfit} class of functions to represent a fitted survival curve. For a multi-state model the object has class \code{c('survfitms', 'survfit')}. Objects of this class have methods for the functions \code{print}, \code{summary}, \code{plot}, \code{points} and \code{lines}. The \code{\link{print.survfit}} method does more computation than is typical for a print method and is documented on a separate page. } \section{Structure}{ The following components must be included in a legitimate \code{survfit} or \code{survfitms} object. } \arguments{ \item{n}{ total number of subjects in each curve. } \item{time}{ the time points at which the curve has a step. } \item{n.risk}{ the number of subjects at risk at t. } \item{n.event}{ the number of events that occur at time t. } \item{n.enter}{ for counting process data only, the number of subjects that enter at time t. } \item{n.censor}{ for counting process data only, the number of subjects who exit the risk set, without an event, at time t. (For right censored data, this number can be computed from the successive values of the number at risk). } \item{surv}{ the estimate of survival at time t+0. This may be a vector or a matrix. The latter occurs when a set of survival curves is created from a single Cox model, in which case there is one column for each covariate set. } \item{prev, p0}{ a multi-state survival will have the \code{prev} component instead of \code{surv}. It will be a matrix containing the estimated probability of each state at each time, one column per state. The \code{p0} matrix contains the initial distribution of states. (On further reflection pstate= "probability in state" would have been a much better label than "prevalence", but by that point too many other packages were dependent on the form of the result.) } \item{std.err}{ for a survival curve this contains standard error of the cumulative hazard or -log(survival), for a multi-state curve it contains the standard error of prev. This difference is a reflection of the fact that each is the natural calculation for that case. } \item{cumhaz hazard}{optional. For a multi-state curve this is an k by k array for each time point, where k is the number of states.} \item{upper}{ upper confidence limit for the survival curve or probability } \item{lower}{ lower confidence limit for the survival curve or probability } \item{strata}{ if there are multiple curves, this component gives the number of elements of the \code{time} etc. vectors corresponding to the first curve, the second curve, and so on. The names of the elements are labels for the curves. } \item{start.time}{ the value specified for the \code{start.time} argument, if it was used in the call. } \item{n.all}{ for counting process data, and any time that the \code{start.time} argument was used, this contains the total number of observations that were available. Not all may have been used in creating the curve, in which case this value will be larger than \code{n} above. } \item{conf.type}{ the approximation used to compute the confidence limits. } \item{conf.int}{ the level of the confidence limits, e.g. 90 or 95\%. } \item{transitions}{for multi-state data, the total number of transitions of each type.} \item{na.action}{ the returned value from the na.action function, if any. It will be used in the printout of the curve, e.g., the number of observations deleted due to missing values. } \item{call}{ an image of the call that produced the object. } \item{type}{ type of survival censoring. } \item{influence}{optional, for survfitms objects only. A list with one element per stratum, each element of the list is an array indexed by subject, time, state. The time dimension will have one more element than the \code{prev} matrix, the first row is the subject's influence on the initial prevalence (just before the first time point). If there is only one curve a list is not needed.} } \section{Subscripts}{ Survfit objects that contain multiple survival curves can be subscripted. This is often used to plot a subset of the curves. If the \code{surv} or \code{prev} component is a matrix then the \code{survfit} object will be treated as a matrix, otherwise only a single subscript is used. } \seealso{ \code{\link{plot.survfit}}, \code{\link{summary.survfit}}, \code{\link{print.survfit}}, \code{\link{survfit}}. } \keyword{survival} survival/man/pspline.Rd0000644000175100001440000000745112714073057014674 0ustar hornikusers\name{pspline} \alias{pspline} \alias{psplineinverse} \title{Smoothing splines using a pspline basis} \usage{ pspline(x, df=4, theta, nterm=2.5 * df, degree=3, eps=0.1, method, Boundary.knots=range(x), intercept=FALSE, penalty=TRUE, combine, ...) psplineinverse(x)} \arguments{ \item{x}{for psline: a covariate vector. The function does not apply to factor variables. For psplineinverse x will be the result of a pspline call.} \item{df}{the desired degrees of freedom. One of the arguments \code{df} or \code{theta}' must be given, but not both. If \code{df=0}, then the AIC = (loglik -df) is used to choose an "optimal" degrees of freedom. If AIC is chosen, then an optional argument `caic=T' can be used to specify the corrected AIC of Hurvich et. al. } \item{theta}{roughness penalty for the fit. It is a monotone function of the degrees of freedom, with theta=1 corresponding to a linear fit and theta=0 to an unconstrained fit of nterm degrees of freedom. } \item{nterm}{ number of splines in the basis } \item{degree}{ degree of splines } \item{eps}{accuracy for \code{df} } \item{method}{the method for choosing the tuning parameter \code{theta}. If theta is given, then 'fixed' is assumed. If the degrees of freedom is given, then 'df' is assumed. If method='aic' then the degrees of freedom is chosen automatically using Akaike's information criterion.} \item{\dots}{optional arguments to the control function} \item{Boundary.knots}{the spline is linear beyond the boundary knots. These default to the range of the data.} \item{intercept}{if TRUE, the basis functions include the intercept.} \item{penalty}{if FALSE a large number of attributes having to do with penalized fits are excluded. This is useful to create a pspline basis matrix for other uses.} \item{combine}{an optional vector of increasing integers. If two adjacent values of \code{combine} are equal, then the corresponding coefficients of the fit are forced to be equal. This is useful for monotone fits, see the vignette for more details. } } \description{ Specifies a penalised spline basis for the predictor. This is done by fitting a comparatively small set of splines and penalising the integrated second derivative. Traditional smoothing splines use one basis per observation, but several authors have pointed out that the final results of the fit are indistinguishable for any number of basis functions greater than about 2-3 times the degrees of freedom. Eilers and Marx point out that if the basis functions are evenly spaced, this leads to significant computational simplification, they refer to the result as a p-spline. } \value{ Object of class \code{pspline, coxph.penalty} containing the spline basis, with the appropriate attributes to be recognized as a penalized term by the coxph or survreg functions. For psplineinverse the original x vector is reconstructed. } \seealso{\code{\link{coxph}},\code{\link{survreg}},\code{\link{ridge}}, \code{\link{frailty}} } \references{ Eilers, Paul H. and Marx, Brian D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11, 89-121. Hurvich, C.M. and Simonoff, J.S. and Tsai, Chih-Ling (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion, JRSSB, volume 60, 271--293. } \examples{ lfit6 <- survreg(Surv(time, status)~pspline(age, df=2), cancer) plot(cancer$age, predict(lfit6), xlab='Age', ylab="Spline prediction") title("Cancer Data") fit0 <- coxph(Surv(time, status) ~ ph.ecog + age, cancer) fit1 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,3), cancer) fit3 <- coxph(Surv(time, status) ~ ph.ecog + pspline(age,8), cancer) fit0 fit1 fit3 } \keyword{ survival} survival/man/pyears.Rd0000644000175100001440000001715613017026563014525 0ustar hornikusers\name{pyears} \alias{pyears} \title{ Person Years } \description{ This function computes the person-years of follow-up time contributed by a cohort of subjects, stratified into subgroups. It also computes the number of subjects who contribute to each cell of the output table, and optionally the number of events and/or expected number of events in each cell. } \usage{ pyears(formula, data, weights, subset, na.action, rmap, ratetable, scale=365.25, expect=c('event', 'pyears'), model=FALSE, x=FALSE, y=FALSE, data.frame=FALSE) } \arguments{ \item{formula}{ a formula object. The response variable will be a vector of follow-up times for each subject, or a \code{Surv} object containing the survival time and an event indicator. The predictors consist of optional grouping variables separated by + operators (exactly as in \code{survfit}), time-dependent grouping variables such as age (specified with \code{tcut}), and optionally a \code{ratetable} term. This latter matches each subject to his/her expected cohort. } \item{data}{ a data frame in which to interpret the variables named in the \code{formula}, or in the \code{subset} and the \code{weights} argument. } \item{weights}{ case weights. } \item{subset}{ expression saying that only a subset of the rows of the data should be used in the fit. } \item{na.action}{ a missing-data filter function, applied to the model.frame, after any \code{subset} argument has been used. Default is \code{options()$na.action}. } \item{rmap}{ an optional list that maps data set names to the ratetable names. See the details section below. } \item{ratetable}{ a table of event rates, such as \code{survexp.uswhite}. } \item{scale}{ a scaling for the results. As most rate tables are in units/day, the default value of 365.25 causes the output to be reported in years. } \item{expect}{ should the output table include the expected number of events, or the expected number of person-years of observation. This is only valid with a rate table. } \item{data.frame}{ return a data frame rather than a set of arrays.} \item{model, x, y}{ If any of these is true, then the model frame, the model matrix, and/or the vector of response times will be returned as components of the final result. } } \value{ a list with components: \item{pyears}{ an array containing the person-years of exposure. (Or other units, depending on the rate table and the scale). The dimension and dimnames of the array correspond to the variables on the right hand side of the model equation. } \item{n}{ an array containing the number of subjects who contribute time to each cell of the \code{pyears} array. } \item{event}{ an array containing the observed number of events. This will be present only if the response variable is a \code{Surv} object. } \item{expected}{ an array containing the expected number of events (or person years if \code{expect ="pyears"}). This will be present only if there was a \code{ratetable} term. } \item{data}{ if the \code{data.frame} option was set, a data frame containing the variables \code{n}, \code{event}, \code{pyears} and \code{event} that supplants the four arrays listed above, along with variables corresponding to each dimension. There will be one row for each cell in the arrays.} \item{offtable}{ the number of person-years of exposure in the cohort that was not part of any cell in the \code{pyears} array. This is often useful as an error check; if there is a mismatch of units between two variables, nearly all the person years may be off table. } \item{tcut}{whether the call included any time-dependent cutpoints.} \item{summary}{ a summary of the rate-table matching. This is also useful as an error check. } \item{call}{ an image of the call to the function. } \item{observations}{the number of observations in the input data set, after any missings were removed.} \item{na.action}{ the \code{na.action} attribute contributed by an \code{na.action} routine, if any. } } \details{ Because \code{pyears} may have several time variables, it is necessary that all of them be in the same units. For instance, in the call \preformatted{ py <- pyears(futime ~ rx, rmap=list(age=age, sex=sex, year=entry.dt), ratetable=survexp.us) } the natural unit of the ratetable is hazard per day, it is important that \code{futime}, \code{age} and \code{entry.dt} all be in days. Given the wide range of possible inputs, it is difficult for the routine to do sanity checks of this aspect. The ratetable being used may have different variable names than the user's data set, this is dealt with by the \code{rmap} argument. The rate table for the above calculation was \code{survexp.us}, a call to \code{summary{survexp.us}} reveals that it expects to have variables \code{age} = age in days, \code{sex}, and \code{year} = the date of study entry, we create them in the \code{rmap} line. The sex variable is not mapped, therefore the code assumes that it exists in \code{mydata} in the correct format. (Note: for factors such as sex, the program will match on any unique abbreviation, ignoring case.) A special function \code{tcut} is needed to specify time-dependent cutpoints. For instance, assume that age is in years, and that the desired final arrays have as one of their margins the age groups 0-2, 2-10, 10-25, and 25+. A subject who enters the study at age 4 and remains under observation for 10 years will contribute follow-up time to both the 2-10 and 10-25 subsets. If \code{cut(age, c(0,2,10,25,100))} were used in the formula, the subject would be classified according to his starting age only. The \code{tcut} function has the same arguments as \code{cut}, but produces a different output object which allows the \code{pyears} function to correctly track the subject. The results of \code{pyears} are normally used as input to further calculations. The \code{print} routine, therefore, is designed to give only a summary of the table. } \seealso{ \code{\link{ratetable}}, \code{\link{survexp}}, \code{\link{Surv}}. } \examples{ # Look at progression rates jointly by calendar date and age # temp.yr <- tcut(mgus$dxyr, 55:92, labels=as.character(55:91)) temp.age <- tcut(mgus$age, 34:101, labels=as.character(34:100)) ptime <- ifelse(is.na(mgus$pctime), mgus$futime, mgus$pctime) pstat <- ifelse(is.na(mgus$pctime), 0, 1) pfit <- pyears(Surv(ptime/365.25, pstat) ~ temp.yr + temp.age + sex, mgus, data.frame=TRUE) # Turn the factor back into numerics for regression tdata <- pfit$data tdata$age <- as.numeric(as.character(tdata$temp.age)) tdata$year<- as.numeric(as.character(tdata$temp.yr)) fit1 <- glm(event ~ year + age+ sex +offset(log(pyears)), data=tdata, family=poisson) \dontrun{ # fit a gam model gfit.m <- gam(y ~ s(age) + s(year) + offset(log(time)), family = poisson, data = tdata) } # Example #2 Create the hearta data frame: hearta <- by(heart, heart$id, function(x)x[x$stop == max(x$stop),]) hearta <- do.call("rbind", hearta) # Produce pyears table of death rates on the surgical arm # The first is by age at randomization, the second by current age fit1 <- pyears(Surv(stop/365.25, event) ~ cut(age + 48, c(0,50,60,70,100)) + surgery, data = hearta, scale = 1) fit2 <- pyears(Surv(stop/365.25, event) ~ tcut(age + 48, c(0,50,60,70,100)) + surgery, data = hearta, scale = 1) fit1$event/fit1$pyears #death rates on the surgery and non-surg arm fit2$event/fit2$pyears #death rates on the surgery and non-surg arm } \keyword{survival} survival/man/genfan.Rd0000644000175100001440000000146412657107650014461 0ustar hornikusers\name{genfan} \alias{genfan} \docType{data} \title{Generator fans} \description{ The data come from a field engineering study of the time to failure of diesel generator fans. The ultimate goal was to decide whether or not to replace the working fans with a higher quality fan to prevent future failures. Seventy generators were studied. For each one, the number of hours of running time from its first being put into service until fan failure or until the end of the study(whichever came first) was recorded. } \usage{data("genfan")} \format{ A data frame with 70 observations on the following 2 variables. \describe{ \item{\code{hours}}{hours of service} \item{\code{status}}{1=failure, 0=censored} } } \references{ Nelson, Journal of Quality Technology, 1:27-52, 1969 } \keyword{datasets, survival} survival/man/nwtco.Rd0000644000175100001440000000225312760114003014333 0ustar hornikusers\name{nwtco} \alias{nwtco} \docType{data} \title{Data from the National Wilm's Tumor Study} \description{ Measurement error example. Tumor histology predicts survival, but prediction is stronger with central lab histology than with the local institution determination. } \usage{nwtco} \format{ A data frame with 4028 observations on the following 9 variables. \describe{ \item{\code{seqno}}{id number} \item{\code{instit}}{Histology from local institution} \item{\code{histol}}{Histology from central lab} \item{\code{stage}}{Disease stage} \item{\code{study}}{study} \item{\code{rel}}{indicator for relapse} \item{\code{edrel}}{time to relapse} \item{\code{age}}{age in months} \item{\code{in.subcohort}}{Included in the subcohort for the example in the paper} } } \references{ NE Breslow and N Chatterjee (1999), Design and analysis of two-phase studies with binary outcome applied to Wilms tumour prognosis. \emph{Applied Statistics} \bold{48}, 457--68. } \examples{ with(nwtco, table(instit,histol)) anova(coxph(Surv(edrel,rel)~histol+instit,data=nwtco)) anova(coxph(Surv(edrel,rel)~instit+histol,data=nwtco)) } \keyword{datasets} survival/man/survfit.Rd0000644000175100001440000000452413013633731014714 0ustar hornikusers\name{survfit} \alias{survfit} \title{Create survival curves} \description{ This function creates survival curves from either a formula (e.g. the Kaplan-Meier), a previously fitted Cox model, or a previously fitted accelerated failure time model. } \usage{ survfit(formula, ...) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{formula}{either a formula or a previously fitted model} \item{\dots}{other arguments to the specific method} } \details{ A survival curve is based on a tabulation of the number at risk and number of events at each unique death time. When time is a floating point number the definition of "unique" is subject to interpretation. The code uses factor() to define the set. For further details see the documentation for the appropriate method, i.e., \code{?survfit.formula} or \code{?survfit.coxph}. A survfit object may contain a single curve, a set of curves, or a matrix curves. Predicted curves from a \code{coxph} model have one row for each stratum in the Cox model fit and one column for each specified covariate set. Curves from a multi-state model have one row for each stratum and a column for each state, the strata correspond to predictors on the right hand side of the equation. The default printing and plotting order for curves is by column, as with other matrices. Curves can be subscripted using either a single or double subscript. If the set of curves is a matrix, as in the above, and one of the dimensions is 1 then the code allows a single subscript to be used. (That is, it is not quite as general as using a single subscript for a numeric matrix.) } \value{ An object of class \code{survfit} containing one or more survival curves. } \author{Terry Therneau} \note{Older releases of the code also allowed the specification for a single curve to omit the right hand of the formula, i.e., \code{survfit(Surv(time, status))}, in which case the formula argument is not actually a formula. Handling this case required some non-standard and fairly fragile manipulations, and this case is no longer supported. } \seealso{\code{\link{survfit.formula}}, \code{\link{survfit.coxph}}, \code{\link{survfit.object}}, \code{\link{print.survfit}}, \code{\link{plot.survfit}}, \code{\link{quantile.survfit}}, \code{\link{summary.survfit}}} \keyword{ survival} survival/man/model.matrix.coxph.Rd0000644000175100001440000000263313013633731016734 0ustar hornikusers\name{model.matrix.coxph} \Rdversion{1.1} \alias{model.matrix.coxph} \title{ Model.matrix method for coxph models } \description{ Reconstruct the model matrix for a cox model. } \usage{ \method{model.matrix}{coxph}(object, data=NULL, contrast.arg = object$contrasts, ...) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{object}{the result of a \code{coxph} model} \item{data}{optional, a data frame from which to obtain the data} \item{contrast.arg}{optional, a contrasts object describing how factors should be coded} \item{\dots}{other possible argument to \code{model.frame}} } \details{ When there is a \code{data} argument this function differs from most of the other \code{model.matrix} methods in that the response variable for the original formula is \emph{not} required to be in the data. If the data frame contains a \code{terms} attribute then it is assumed to be the result of a call to \code{model.frame}, otherwise a call to \code{model.frame} is applied with the data as an argument. } \value{ The model matrix for the fit } \author{Terry Therneau} \seealso{\code{\link{model.matrix}}} \examples{ fit1 <- coxph(Surv(time, status) ~ age + factor(ph.ecog), data=lung) xfit <- model.matrix(fit1) fit2 <- coxph(Surv(time, status) ~ age + factor(ph.ecog), data=lung, x=TRUE) all.equal(model.matrix(fit1), fit2$x) } \keyword{ survival } survival/man/plot.aareg.Rd0000644000175100001440000000155111732700061015240 0ustar hornikusers\name{plot.aareg} \alias{plot.aareg} \title{ Plot an aareg object. } \description{ Plot the estimated coefficient function(s) from a fit of Aalen's additive regression model. } \usage{ \method{plot}{aareg}(x, se=TRUE, maxtime, type='s', ...) } \arguments{ \item{x}{ the result of a call to the \code{aareg} function } \item{se}{ if TRUE, standard error bands are included on the plot } \item{maxtime}{ upper limit for the x-axis. } \item{type}{ graphical parameter for the type of line, default is "steps". } \item{\dots }{ other graphical parameters such as line type, color, or axis labels. } } \section{Side Effects}{ A plot is produced on the current graphical device. } \section{References}{ Aalen, O.O. (1989). A linear regression model for the analysis of life times. Statistics in Medicine, 8:907-925. } \seealso{ aareg } survival/man/coxph.Rd0000644000175100001440000002465513013633731014342 0ustar hornikusers\name{coxph} \alias{coxph} \alias{vcov.coxph} \alias{print.coxph.null} \alias{print.coxph.penal} \alias{coxph.penalty} \alias{[.coxph.penalty} \alias{coxph.getdata} \alias{summary.coxph.penal} \title{ Fit Proportional Hazards Regression Model } \description{ Fits a Cox proportional hazards regression model. Time dependent variables, time dependent strata, multiple events per subject, and other extensions are incorporated using the counting process formulation of Andersen and Gill. } \usage{ coxph(formula, data=, weights, subset, na.action, init, control, ties=c("efron","breslow","exact"), singular.ok=TRUE, robust=FALSE, model=FALSE, x=FALSE, y=TRUE, tt, method, ...) } \arguments{ \item{formula}{ a formula object, with the response on the left of a \code{~} operator, and the terms on the right. The response must be a survival object as returned by the \code{Surv} function. } \item{data}{ a data.frame in which to interpret the variables named in the \code{formula}, or in the \code{subset} and the \code{weights} argument. } \item{weights}{ vector of case weights. For a thorough discussion of these see the book by Therneau and Grambsch. } \item{subset}{ expression indicating which subset of the rows of data should be used in the fit. All observations are included by default. } \item{na.action}{ a missing-data filter function. This is applied to the model.frame after any subset argument has been used. Default is \code{options()\$na.action}. } \item{init}{ vector of initial values of the iteration. Default initial value is zero for all variables. } \item{control}{ Object of class \code{\link{coxph.control}} specifying iteration limit and other control options. Default is \code{coxph.control(...)}. } \item{ties}{ a character string specifying the method for tie handling. If there are no tied death times all the methods are equivalent. Nearly all Cox regression programs use the Breslow method by default, but not this one. The Efron approximation is used as the default here, it is more accurate when dealing with tied death times, and is as efficient computationally. The ``exact partial likelihood'' is equivalent to a conditional logistic model, and is appropriate when the times are a small set of discrete values. See further below. } \item{singular.ok}{ logical value indicating how to handle collinearity in the model matrix. If \code{TRUE}, the program will automatically skip over columns of the X matrix that are linear combinations of earlier columns. In this case the coefficients for such columns will be NA, and the variance matrix will contain zeros. For ancillary calculations, such as the linear predictor, the missing coefficients are treated as zeros. } \item{robust}{ this argument has been deprecated, use a cluster term in the model instead. (The two options accomplish the same goal -- creation of a robust variance -- but the second is more flexible). } \item{model}{ logical value: if \code{TRUE}, the model frame is returned in component \code{model}. } \item{x}{ logical value: if \code{TRUE}, the x matrix is returned in component \code{x}. } \item{y}{ logical value: if \code{TRUE}, the response vector is returned in component \code{y}. } \item{tt}{optional list of time-transform functions.} \item{method}{alternate name for the \code{ties} argument.} \item{...}{Other arguments will be passed to \code{\link{coxph.control}} } } \value{ an object of class \code{coxph} representing the fit. See \code{coxph.object} for details. } \section{Side Effects}{ Depending on the call, the \code{predict}, \code{residuals}, and \code{survfit} routines may need to reconstruct the x matrix created by \code{coxph}. It is possible for this to fail, as in the example below in which the predict function is unable to find \code{tform}. \preformatted{ tfun <- function(tform) coxph(tform, data=lung) fit <- tfun(Surv(time, status) ~ age) predict(fit)} In such a case add the \code{model=TRUE} option to the \code{coxph} call to obviate the need for reconstruction, at the expense of a larger \code{fit} object. } \details{ The proportional hazards model is usually expressed in terms of a single survival time value for each person, with possible censoring. Andersen and Gill reformulated the same problem as a counting process; as time marches onward we observe the events for a subject, rather like watching a Geiger counter. The data for a subject is presented as multiple rows or "observations", each of which applies to an interval of observation (start, stop]. The routine internally scales and centers data to avoid overflow in the argument to the exponential function. These actions do not change the result, but lead to more numerical stability. However, arguments to offset are not scaled since there are situations where a large offset value is a purposefully used. Users should not use normally allow large numeric offset values. } \section{Special terms}{ There are three special terms that may be used in the model equation. A \code{strata} term identifies a stratified Cox model; separate baseline hazard functions are fit for each strata. The \code{cluster} term is used to compute a robust variance for the model. The term \code{+ cluster(id)} where each value of \code{id} is unique is equivalent to specifying the \code{robust=T} argument. If the \code{id} variable is not unique, it is assumed that it identifies clusters of correlated observations. The robust estimate arises from many different arguments and thus has had many labels. It is variously known as the Huber sandwich estimator, White's estimate (linear models/econometrics), the Horvitz-Thompson estimate (survey sampling), the working independence variance (generalized estimating equations), the infinitesimal jackknife, and the Wei, Lin, Weissfeld (WLW) estimate. A time-transform term allows variables to vary dynamically in time. In this case the \code{tt} argument will be a function or a list of functions (if there are more than one tt() term in the model) giving the appropriate transform. See the examples below. } \section{Convergence}{ In certain data cases the actual MLE estimate of a coefficient is infinity, e.g., a dichotomous variable where one of the groups has no events. When this happens the associated coefficient grows at a steady pace and a race condition will exist in the fitting routine: either the log likelihood converges, the information matrix becomes effectively singular, an argument to exp becomes too large for the computer hardware, or the maximum number of interactions is exceeded. (Nearly always the first occurs.) The routine attempts to detect when this has happened, not always successfully. The primary consequence for he user is that the Wald statistic = coefficient/se(coefficient) is not valid in this case and should be ignored; the likelihood ratio and score tests remain valid however. } \section{Ties}{ There are three possible choices for handling tied event times. The Breslow approximation is the easiest to program and hence became the first option coded for almost all computer routines. It then ended up as the default option when other options were added in order to "maintain backwards compatability". The Efron option is more accurate if there are a large number of ties, and it is the default option here. In practice the number of ties is usually small, in which case all the methods are statistically indistinguishable. Using the "exact partial likelihood" approach the Cox partial likelihood is equivalent to that for matched logistic regression. (The \code{clogit} function uses the \code{coxph} code to do the fit.) It is technically appropriate when the time scale is discrete and has only a few unique values, and some packages refer to this as the "discrete" option. There is also an "exact marginal likelihood" due to Prentice which is not implemented here. The calculation of the exact partial likelihood is numerically intense. Say for instance 15 of 180 subjects at risk had an event on day 7; then the code needs to compute sums over all 180-choose-15 > 10^43 different possible subsets of size 15. There is an efficient recursive algorithm for this task, but even with this the computation can be insufferably long. With (start, stop) data it is much worse since the recursion needs to start anew for each unique start time. } \section{Penalized regression}{ \code{coxph} can now maximise a penalised partial likelihood with arbitrary user-defined penalty. Supplied penalty functions include ridge regression (\link{ridge}), smoothing splines (\link{pspline}), and frailty models (\link{frailty}). } \references{ Andersen, P. and Gill, R. (1982). Cox's regression model for counting processes, a large sample study. \emph{Annals of Statistics} \bold{10}, 1100-1120. Therneau, T., Grambsch, P., Modeling Survival Data: Extending the Cox Model. Springer-Verlag, 2000. } \seealso{ \code{\link{cluster}}, \code{\link{strata}}, \code{\link{Surv}}, \code{\link{survfit}}, \code{\link{pspline}}, \code{\link{frailty}}, \code{\link{ridge}}. } \examples{ # Create the simplest test data set test1 <- list(time=c(4,3,1,1,2,2,3), status=c(1,1,1,0,1,1,0), x=c(0,2,1,1,1,0,0), sex=c(0,0,0,0,1,1,1)) # Fit a stratified model coxph(Surv(time, status) ~ x + strata(sex), test1) # Create a simple data set for a time-dependent model test2 <- list(start=c(1,2,5,2,1,7,3,4,8,8), stop=c(2,3,6,7,8,9,9,9,14,17), event=c(1,1,1,1,1,1,1,0,0,0), x=c(1,0,0,1,0,1,1,1,0,0)) summary(coxph(Surv(start, stop, event) ~ x, test2)) # # Create a simple data set for a time-dependent model # test2 <- list(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8), stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17), event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0), x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) ) summary( coxph( Surv(start, stop, event) ~ x, test2)) # Fit a stratified model, clustered on patients bladder1 <- bladder[bladder$enum < 5, ] coxph(Surv(stop, event) ~ (rx + size + number) * strata(enum) + cluster(id), bladder1) # Fit a time transform model using current age coxph(Surv(time, status) ~ ph.ecog + tt(age), data=lung, tt=function(x,t,...) pspline(x + t/365.25)) } \keyword{survival} survival/man/logLik.coxph.Rd0000644000175100001440000000275212534312154015554 0ustar hornikusers\name{logLik.coxph} \alias{logLik.coxph} \alias{logLik.survreg} \title{logLik method for a Cox model} \description{The logLik function for survival models} \usage{ \method{logLik}{coxph}(object, ...) \method{logLik}{survreg}(object, ...) } \arguments{ \item{object}{the result of a \code{coxph} or \code{survreg} fit} \item{\dots}{optional arguments for other instances of the method} } \details{ The logLik function is used by summary functions in R such as \code{AIC}. For a Cox model, this method returns the partial likelihood. The number of degrees of freedom (df) used by the fit and the effective number of observations (nobs) are added as attributes. Per Raftery and others, the effective number of observations is the taken to be the number of events in the data set. For a \code{survreg} model the proper value for the effective number of observations is still an open question (at least to this author). For right censored data the approach of \code{logLik.coxph} is the possible the most sensible, but for interval censored observations the result is unclear. The code currently does not add a \emph{nobs} attribute. } \value{an object of class \code{logLik}} \references{ Robert E. Kass and Adrian E. Raftery (1995). "Bayes Factors". J. American Statistical Assoc. 90 (430): 791. Raftery A.E. (1995), "Bayesian Model Selection in Social Research", Sociological methodology, 111-196. } \seealso{\code{\link{logLik}}} \author{Terry Therneau} \keyword{ survival} survival/man/statefig.Rd0000644000175100001440000000663712776705563015051 0ustar hornikusers\name{statefig} \alias{statefig} \title{Draw a state space figure.} \description{ For multi-state survival models it is useful to have a figure that shows the states and the possible transitions between them. This function creates a simple "box and arrows" figure. It's goal was simplicity. } \usage{ statefig(layout, connect, margin = 0.03, box = TRUE, cex = 1, col = 1, lwd=1, lty=1, bcol=col, acol=col, alwd=lwd, alty=lty) } \arguments{ \item{layout}{describes the layout of the boxes on the page. See the detailed description below. } \item{connect}{a square matrix with one row for each state. If \code{connect[i,j] !=0} then an arrow is drawn from state i to state j. The row names of the matrix are used as the labels for the states. } \item{margin}{the fraction of white space between the label and the surrounding box, and between the box and the arrows, as a function of the plot region size. } \item{box}{should boxes be drawn? TRUE or FALSE. } \item{cex, col, lty, lwd}{default graphical parameters used for the text and boxes. The last 3 can be a vector of values. } \item{bcol}{color for the box, if it differs from that used for the text.} \item{acol, alwd, alty}{color, line type and line width for the arrows. Only the first element is used.} } \details{ The \code{layout} argument is normally a vector of integers, e.g., the vector (1, 3, 2) describes a layout with 3 columns. The first has a single state, the second column has 3 states and the third has 2. The coordinates of the plotting region are 0 to 1 for both x and y. Within a column the centers of the boxes are evenly spaced, with 1/2 a space between the boxes and the margin, e.g., 4 boxes would be at 1/8, 3/8, 5/8 and 7/8. If \code{layout} were a 1 column matrix with values of (1, 3, 2) then the layout will have three rows with 1, 3, and 2 boxes per row, respectively. Alternatively, the user can supply a 2 column matrix that directly gives the centers. The values of the connect matrix should be 0 for pairs of states that do not have a transition and values between 0 and 2 for those that do. States are connected by an arc that passes through the centers of the two boxes and a third point that is between them. Specifically, consider a line segment joining the two centers and erect a second segment at right angles to the midpoint of length d times the distance from center to midpoint. The arc passes through this point. A value of d=0 gives a straight line, d=1 a right hand half circle centered on the midpoint and d= -1 a left hand half circle. The \code{connect} matrix contains values of d+1 with -1 < d < 1. } \value{a matrix containing the centers of the boxes, with the invisible attribute set.} \author{Terry Therneau} \note{ The goal of this function is to make ``good enough'' figures as simply as possible, and thereby to encourage users to draw them. The \code{layout} argument was inspired by the \code{diagram} package, which can draw more complex and well decorated figures, e.g., many different shapes, shading, multiple types of connecting lines, etc., but at the price of greater complexity. } \examples{ # Draw a simple competing risks figure states <- c("Entry", "Complete response", "Relapse", "Death") connect <- matrix(0, 4, 4, dimnames=list(states, states)) connect[1, -1] <- c(1.1, 1, 0.9) statefig(c(1, 3), connect) } \keyword{survival} \keyword{hplot} survival/man/survfit.coxph.Rd0000644000175100001440000002524413017617770016047 0ustar hornikusers\name{survfit.coxph} \alias{survfit.coxph} \title{ Compute a Survival Curve from a Cox model } \description{ Computes the predicted survivor function for a Cox proportional hazards model. } \usage{ \method{survfit}{coxph}(formula, newdata, se.fit=TRUE, conf.int=.95, individual=FALSE, type,vartype, conf.type=c("log","log-log","plain","none"), censor=TRUE, id, start.time, na.action=na.pass, ...) } \arguments{ \item{formula}{ A \code{coxph} object. } \item{newdata}{ a data frame with the same variable names as those that appear in the \code{coxph} formula. It is also valid to use a vector, if the data frame would consist of a single row. The curve(s) produced will be representative of a cohort whose covariates correspond to the values in \code{newdata}. Default is the mean of the covariates used in the \code{coxph} fit. } \item{individual}{ This argument has been superseded by the \code{id} argument and is present only for backwards compatability. A logical value indicating whether each row of \code{newdata} represents a distinct individual (FALSE, the default), or if each row of the data frame represents different time epochs for only one individual (TRUE). In the former case the result will have one curve for each row in \code{newdata}, in the latter only a single curve will be produced. } \item{conf.int}{ the level for a two-sided confidence interval on the survival curve(s). Default is 0.95. } \item{se.fit}{ a logical value indicating whether standard errors should be computed. Default is \code{TRUE}. } \item{type,vartype}{ a character string specifying the type of survival curve. Possible values are \code{"aalen"}, \code{"efron"}, or \code{"kalbfleisch-prentice"} (only the first two characters are necessary). The default is to match the computation used in the Cox model. The Nelson-Aalen-Breslow estimate for \code{ties='breslow'}, the Efron estimate for \code{ties='efron'} and the Kalbfleisch-Prentice estimate for a discrete time model \code{ties='exact'}. Variance estimates are the Aalen-Link-Tsiatis, Efron, and Greenwood. The default will be the Efron estimate for \code{ties='efron'} and the Aalen estimate otherwise. } \item{conf.type}{ One of \code{"none"}, \code{"plain"}, \code{"log"} (the default), or \code{"log-log"}. Only enough of the string to uniquely identify it is necessary. The first option causes confidence intervals not to be generated. The second causes the standard intervals \code{curve +- k *se(curve)}, where k is determined from \code{conf.int}. The log option calculates intervals based on the cumulative hazard or log(survival). The last option bases intervals on the log hazard or log(-log(survival)). } \item{censor}{if FALSE time points at which there are no events (only censoring) are not included in the result.} \item{id}{optional variable name of subject identifiers. If this is present, then each group of rows with the same subject id represents the covariate path through time of a single subject, and the result will contain one curve per subject. If the \code{coxph} fit had strata then that must also be specified in \code{newdata}. If missing, then each individual row of \code{newdata} is presumed to represent a distinct subject and there will be \code{nrow(newdata)} times the number of strata curves in the result (one for each strata/subject combination). result.} \item{start.time}{optional starting time, a single numeric value. If present the returned curve contains survival after \code{start.time} conditional on surviving to \code{start.time}. } \item{na.action}{the na.action to be used on the newdata argument} \item{\dots}{for future methods} } \value{ an object of class \code{"survfit"}. See \code{survfit.object} for details. Methods defined for survfit objects are \code{print}, \code{plot}, \code{lines}, and \code{points}. } \details{ Serious thought has been given to removing the default value for \code{newdata}, which is to use a single "pseudo" subject with covariate values equal to the means of the data set, since the resulting curve(s) almost never make sense. It remains due to an unwarranted attachment to the option shown by some users and by other packages. Two particularly egregious examples are factor variables and interactions. Suppose one were studying interspecies transmission of a virus, and the data set has a factor variable with levels ("pig", "chicken") and about equal numbers of observations for each. The ``mean'' covariate level will be 1/2 -- is this a flying pig? As to interactions assume data with sex coded as 0/1, ages ranging from 50 to 80, and a model with age*sex. The ``mean'' value for the age:sex interaction term will be about 30, a value that does not occur in the data. Users are strongly advised to use the newdata argument. When the original model contains time-dependent covariates, then the path of that covariate through time needs to be specified in order to obtain a predicted curve. This requires \code{newdata} to contain multiple lines for each hypothetical subject which gives the covariate values, time interval, and strata for each line (a subject can change strata), along with an \code{id} variable which demarks which rows belong to each subject. The time interval must have the same (start, stop, status) variables as the original model: although the status variable is not used and thus can be set to a dummy value of 0 or 1, it is necessary for the variables to be recognized as a \code{Surv} object. Last, although predictions with a time-dependent covariate path can be useful, it is very easy to create a prediction that is senseless. Users are encouraged to seek out a text that discusses the issue in detail. When a model contains strata but no time-dependent covariates the user of this routine has a choice. If newdata argument does not contain strata variables then the returned object will be a matrix of survival curves with one row for each strata in the model and one column for each row in newdata. (This is the historical behavior of the routine.) If newdata does contain strata variables, then the result will contain one curve per row of newdata, based on the indicated stratum of the original model. In the rare case of a model with strata by covariate interactions the strata variable must be included in newdata, the routine does not allow it to be omitted (predictions become too confusing). (Note that the model Surv(time, status) ~ age*strata(sex) expands internally to strata(sex) + age:sex; the sex variable is needed for the second term of the model.) When all the coefficients are zero, the Kalbfleisch-Prentice estimator reduces to the Kaplan-Meier, the Aalen estimate to the exponential of Nelson's cumulative hazard estimate, and the Efron estimate to the Fleming-Harrington estimate of survival. The variances of the curves from a Cox model are larger than these non-parametric estimates, however, due to the variance of the coefficients. See \code{\link{survfit}} for more details about the counts (number of events, number at risk, etc.) The censor argument was fixed at FALSE in earlier versions of the code and not made available to the user. The default argument is sensible in most instances --- and causes the familiar + sign to appear on plots --- it is not sensible for time dependent covariates since it may lead to a large number of spurious marks. } \section{Notes}{ If the following pair of lines is used inside of another function then the \code{model=TRUE} argument must be added to the coxph call: \code{fit <- coxph(...); survfit(fit)}. This is a consequence of the non-standard evaluation process used by the \code{model.frame} function when a formula is involved. } \section{References}{ Fleming, T. H. and Harrington, D. P. (1984). Nonparametric estimation of the survival distribution in censored data. \emph{Comm. in Statistics} \bold{13}, 2469-86. Kalbfleisch, J. D. and Prentice, R. L. (1980). \emph{The Statistical Analysis of Failure Time Data.} New York:Wiley. Link, C. L. (1984). Confidence intervals for the survival function using Cox's proportional hazards model with covariates. \emph{Biometrics} \bold{40}, 601-610. Therneau T and Grambsch P (2000), Modeling Survival Data: Extending the Cox Model, Springer-Verlag. Tsiatis, A. (1981). A large sample study of the estimate for the integrated hazard function in Cox's regression model for survival data. \emph{Annals of Statistics} \bold{9}, 93-108. } \seealso{ \code{\link{print.survfit}}, \code{\link{plot.survfit}}, \code{\link{lines.survfit}}, \code{\link{coxph}}, \code{\link{Surv}}, \code{\link{strata}}. } \examples{ #fit a Kaplan-Meier and plot it fit <- survfit(Surv(time, status) ~ x, data = aml) plot(fit, lty = 2:3) legend(100, .8, c("Maintained", "Nonmaintained"), lty = 2:3) #fit a Cox proportional hazards model and plot the #predicted survival for a 60 year old fit <- coxph(Surv(futime, fustat) ~ age, data = ovarian) plot(survfit(fit, newdata=data.frame(age=60)), xscale=365.25, xlab = "Years", ylab="Survival") # Here is the data set from Turnbull # There are no interval censored subjects, only left-censored (status=3), # right-censored (status 0) and observed events (status 1) # # Time # 1 2 3 4 # Type of observation # death 12 6 2 3 # losses 3 2 0 3 # late entry 2 4 2 5 # tdata <- data.frame(time =c(1,1,1,2,2,2,3,3,3,4,4,4), status=rep(c(1,0,2),4), n =c(12,3,2,6,2,4,2,0,2,3,3,5)) fit <- survfit(Surv(time, time, status, type='interval') ~1, data=tdata, weight=n) # # Time to progression/death for patients with monoclonal gammopathy # Competing risk curves (cumulative incidence) fit1 <- survfit(Surv(stop, event=='progression') ~1, data=mgus1, subset=(start==0)) fit2 <- survfit(Surv(stop, status) ~1, data=mgus1, subset=(start==0), etype=event) #competing risks # CI curves are always plotted from 0 upwards, rather than 1 down plot(fit2, fun='event', xscale=365.25, xmax=7300, mark.time=FALSE, col=2:3, xlab="Years post diagnosis of MGUS") lines(fit1, fun='event', xscale=365.25, xmax=7300, mark.time=FALSE, conf.int=FALSE) text(10, .4, "Competing Risk: death", col=3) text(16, .15,"Competing Risk: progression", col=2) text(15, .30,"KM:prog") } \keyword{survival} survival/man/residuals.coxph.Rd0000644000175100001440000000606311732700061016322 0ustar hornikusers\name{residuals.coxph} \alias{residuals.coxph.penal} \alias{residuals.coxph.null} \alias{residuals.coxph} \title{ Calculate Residuals for a `coxph' Fit } \description{ Calculates martingale, deviance, score or Schoenfeld residuals for a Cox proportional hazards model. } \usage{ \method{residuals}{coxph}(object, type=c("martingale", "deviance", "score", "schoenfeld", "dfbeta", "dfbetas", "scaledsch","partial"), collapse=FALSE, weighted=FALSE, ...) \method{residuals}{coxph.null}(object, type=c("martingale", "deviance","score","schoenfeld"), collapse=FALSE, weighted=FALSE, ...) } \arguments{ \item{object}{ an object inheriting from class \code{coxph}, representing a fitted Cox regression model. Typically this is the output from the \code{coxph} function. } \item{type}{ character string indicating the type of residual desired. Possible values are \code{"martingale"}, \code{"deviance"}, \code{"score"}, \code{"schoenfeld"}, "dfbeta"', \code{"dfbetas"}, and \code{"scaledsch"}. Only enough of the string to determine a unique match is required. } \item{collapse}{ vector indicating which rows to collapse (sum) over. In time-dependent models more than one row data can pertain to a single individual. If there were 4 individuals represented by 3, 1, 2 and 4 rows of data respectively, then \code{collapse=c(1,1,1, 2, 3,3, 4,4,4,4)} could be used to obtain per subject rather than per observation residuals. } \item{weighted}{ if \code{TRUE} and the model was fit with case weights, then the weighted residuals are returned. }\item{...}{other unused arguments}} \value{ For martingale and deviance residuals, the returned object is a vector with one element for each subject (without \code{collapse}). For score residuals it is a matrix with one row per subject and one column per variable. The row order will match the input data for the original fit. For Schoenfeld residuals, the returned object is a matrix with one row for each event and one column per variable. The rows are ordered by time within strata, and an attribute \code{strata} is attached that contains the number of observations in each strata. The scaled Schoenfeld residuals are used in the \code{cox.zph} function. The score residuals are each individual's contribution to the score vector. Two transformations of this are often more useful: \code{dfbeta} is the approximate change in the coefficient vector if that observation were dropped, and \code{dfbetas} is the approximate change in the coefficients, scaled by the standard error for the coefficients. } \section{NOTE}{ For deviance residuals, the status variable may need to be reconstructed. For score and Schoenfeld residuals, the X matrix will need to be reconstructed. } \references{ T. Therneau, P. Grambsch, and T. Fleming. "Martingale based residuals for survival models", \emph{Biometrika}, March 1990. } \seealso{ \code{\link{coxph}}} \examples{ fit <- coxph(Surv(start, stop, event) ~ (age + surgery)* transplant, data=heart) mresid <- resid(fit, collapse=heart$id) } \keyword{survival} % Converted by Sd2Rd version 0.3-2. survival/man/coxph.control.Rd0000644000175100001440000000254713017617770016026 0ustar hornikusers\name{coxph.control} \alias{coxph.control} \title{Ancillary arguments for controlling coxph fits} \description{ This is used to set various numeric parameters controlling a Cox model fit. Typically it would only be used in a call to \code{coxph}. } \usage{ coxph.control(eps = 1e-09, toler.chol = .Machine$double.eps^0.75, iter.max = 20, toler.inf = sqrt(eps), outer.max = 10, timefix=TRUE) } \arguments{ \item{eps}{Iteration continues until the relative change in the log partial likelihood is less than eps. Must be positive.} \item{toler.chol}{Tolerance for detection of singularity during a Cholesky decomposition of the variance matrix, i.e., for detecting a redundant predictor variable.} \item{iter.max}{Maximum number of iterations to attempt for convergence.} \item{toler.inf}{Tolerance criteria for the warning message about a possible infinite coefficient value.} \item{outer.max}{For a penalized coxph model, e.g. with pspline terms, there is an outer loop of iteration to determine the penalty parameters; maximum number of iterations for this outer loop.} \item{timefix}{Resolve any near ties in the time variables. (Floating point representation error can cause actual tied times to appear distinct.)} } \value{ a list containing the values of each of the above constants } \author{Terry Therneau } \seealso{\code{\link{coxph}} } \keyword{survival} survival/man/cox.zph.Rd0000644000175100001440000000464411732700061014603 0ustar hornikusers\name{cox.zph} \alias{cox.zph} \alias{[.cox.zph} \alias{print.cox.zph} \title{ Test the Proportional Hazards Assumption of a Cox Regression } \description{ Test the proportional hazards assumption for a Cox regression model fit (\code{coxph}). } \usage{ cox.zph(fit, transform="km", global=TRUE) } \arguments{ \item{fit}{ the result of fitting a Cox regression model, using the \code{coxph} function. } \item{transform}{ a character string specifying how the survival times should be transformed before the test is performed. Possible values are \code{"km"}, \code{"rank"}, \code{"identity"} or a function of one argument. } \item{global}{ should a global chi-square test be done, in addition to the per-variable tests. } } \value{ an object of class \code{"cox.zph"}, with components: \item{table}{ a matrix with one row for each variable, and optionally a last row for the global test. Columns of the matrix contain the correlation coefficient between transformed survival time and the scaled Schoenfeld residuals, a chi-square, and the two-sided p-value. For the global test there is no appropriate correlation, so an NA is entered into the matrix as a placeholder. } \item{x}{ the transformed time axis. } \item{y}{ the matrix of scaled Schoenfeld residuals. There will be one column per variable and one row per event. The row labels contain the original event times (for the identity transform, these will be the same as \code{x}). } \item{call}{ the calling sequence for the routine. The computations require the original \code{x} matrix of the Cox model fit. Thus it saves time if the \code{x=TRUE} option is used in \code{coxph}. This function would usually be followed by both a plot and a print of the result. The plot gives an estimate of the time-dependent coefficient \code{beta(t)}. If the proportional hazards assumption is true, \code{beta(t)} will be a horizontal line. The printout gives a test for \code{slope=0}. } } \references{ P. Grambsch and T. Therneau (1994), Proportional hazards tests and diagnostics based on weighted residuals. \emph{Biometrika,} \bold{81}, 515-26. } \seealso{ \code{\link{coxph}}, \code{\link{Surv}}. } \examples{ fit <- coxph(Surv(futime, fustat) ~ age + ecog.ps, data=ovarian) temp <- cox.zph(fit) print(temp) # display the results plot(temp) # plot curves } \keyword{survival} survival/man/print.summary.survexp.Rd0000644000175100001440000000113211732700061017542 0ustar hornikusers\name{print.summary.survexp} \alias{print.summary.survexp} \title{Print Survexp Summary} \description{ Prints the results of \code{summary.survexp} } \usage{ \method{print}{summary.survexp}(x, digits = max(options()$digits - 4, 3), ...) } \arguments{ \item{x}{ an object of class \code{summary.survexp}. } \item{digits}{ the number of digits to use in printing the result. } \item{\dots}{for future methods} } \value{ \code{x}, with the invisible flag set to prevent further printing. } \author{Terry Therneau} \seealso{\code{link{summary.survexp}}, \code{\link{survexp}}} \keyword{ survival } survival/man/tcut.Rd0000644000175100001440000000225112265342777014203 0ustar hornikusers\name{tcut} \alias{tcut} \alias{[.tcut} \alias{levels.tcut} \title{Factors for person-year calculations} \description{ Attaches categories for person-year calculations to a variable without losing the underlying continuous representation } \usage{ tcut(x, breaks, labels, scale=1) \method{levels}{tcut}(x) } %- maybe also `usage' for other objects documented here. \arguments{ \item{x}{numeric/date variable } \item{breaks}{breaks between categories, which are right-continuous } \item{labels}{labels for categories } \item{scale}{Multiply \code{x} and \code{breaks} by this.} } \value{ An object of class \code{tcut} } \seealso{ \code{\link{cut}}, \code{\link{pyears}} } \examples{ mdy.date <- function(m,d,y) as.Date(paste(ifelse(y<100, y+1900, y), m, d, sep='/')) temp1 <- mdy.date(6,6,36) temp2 <- mdy.date(6,6,55)# Now compare the results from person-years # temp.age <- tcut(temp2-temp1, floor(c(-1, (18:31 * 365.24))), labels=c('0-18', paste(18:30, 19:31, sep='-'))) temp.yr <- tcut(temp2, mdy.date(1,1,1954:1965), labels=1954:1964) temp.time <- 3700 #total days of fu py1 <- pyears(temp.time ~ temp.age + temp.yr, scale=1) #output in days py1 } \keyword{survival} survival/man/aml.Rd0000644000175100001440000000116111732700061013752 0ustar hornikusers\name{aml} \docType{data} \alias{aml} \alias{leukemia} \title{Acute Myelogenous Leukemia survival data} \description{Survival in patients with Acute Myelogenous Leukemia. The question at the time was whether the standard course of chemotherapy should be extended ('maintainance') for additional cycles.} \usage{ aml leukemia } \format{ \tabular{ll}{ time:\tab survival or censoring time\cr status:\tab censoring status\cr x: \tab maintenance chemotherapy given? (factor)\cr } } \source{ Rupert G. Miller (1997), \emph{Survival Analysis}. John Wiley & Sons. ISBN: 0-471-25218-2. } \keyword{datasets} survival/man/pbc.Rd0000644000175100001440000000434611732700061013755 0ustar hornikusers\name{pbc} \alias{pbc} \docType{data} \title{Mayo Clinic Primary Biliary Cirrhosis Data} \description{D This data is from the Mayo Clinic trial in primary biliary cirrhosis (PBC) of the liver conducted between 1974 and 1984. A total of 424 PBC patients, referred to Mayo Clinic during that ten-year interval, met eligibility criteria for the randomized placebo controlled trial of the drug D-penicillamine. The first 312 cases in the data set participated in the randomized trial and contain largely complete data. The additional 112 cases did not participate in the clinical trial, but consented to have basic measurements recorded and to be followed for survival. Six of those cases were lost to follow-up shortly after diagnosis, so the data here are on an additional 106 cases as well as the 312 randomized participants. A nearly identical data set found in appendix D of Fleming and Harrington; this version has fewer missing values. } \usage{pbc} \format{ \tabular{ll}{ age:\tab in years\cr albumin:\tab serum albumin (g/dl)\cr alk.phos:\tab alkaline phosphotase (U/liter)\cr ascites:\tab presence of ascites \cr ast:\tab aspartate aminotransferase, once called SGOT (U/ml)\cr bili:\tab serum bilirunbin (mg/dl)\cr chol:\tab serum cholesterol (mg/dl)\cr copper:\tab urine copper (ug/day)\cr edema:\tab 0 no edema, 0.5 untreated or successfully treated\cr \tab 1 edema despite diuretic therapy\cr hepato:\tab presence of hepatomegaly or enlarged liver\cr id:\tab case number\cr platelet:\tab platelet count\cr protime:\tab standardised blood clotting time\cr sex:\tab m/f\cr spiders:\tab blood vessel malformations in the skin\cr stage:\tab histologic stage of disease (needs biopsy)\cr status:\tab status at endpoint, 0/1/2 for censored, transplant, dead\cr time: \tab number of days between registration and the earlier of death,\cr \tab transplantion, or study analysis in July, 1986\cr trt:\tab 1/2/NA for D-penicillmain, placebo, not randomised\cr trig:\tab triglycerides (mg/dl)\cr } } \source{ T Therneau and P Grambsch (2000), \emph{Modeling Survival Data: Extending the Cox Model}, Springer-Verlag, New York. ISBN: 0-387-98784-3. } \keyword{datasets} survival/man/Surv.Rd0000644000175100001440000001334613013633731014153 0ustar hornikusers\name{Surv} \alias{Surv} \alias{is.Surv} \alias{print.Surv} \alias{Math.Surv} \alias{Summary.Surv} \alias{[.Surv} \alias{format.Surv} \alias{as.data.frame.Surv} \alias{as.character.Surv} \alias{as.matrix.Surv} \alias{is.na.Surv} \alias{Ops.Surv} \title{ Create a Survival Object } \description{ Create a survival object, usually used as a response variable in a model formula. Argument matching is special for this function, see Details below. } \usage{ Surv(time, time2, event, type=c('right', 'left', 'interval', 'counting', 'interval2', 'mstate'), origin=0) is.Surv(x) } \arguments{ \item{time}{ for right censored data, this is the follow up time. For interval data, the first argument is the starting time for the interval. } \item{event}{ The status indicator, normally 0=alive, 1=dead. Other choices are \code{TRUE}/\code{FALSE} (\code{TRUE} = death) or 1/2 (2=death). For interval censored data, the status indicator is 0=right censored, 1=event at \code{time}, 2=left censored, 3=interval censored. Although unusual, the event indicator can be omitted, in which case all subjects are assumed to have an event. } \item{time2}{ ending time of the interval for interval censored or counting process data only. Intervals are assumed to be open on the left and closed on the right, \code{(start, end]}. For counting process data, \code{event} indicates whether an event occurred at the end of the interval. } \item{type}{ character string specifying the type of censoring. Possible values are \code{"right"}, \code{"left"}, \code{"counting"}, \code{"interval"}, \code{"interval2"} or \code{"mstate"}. } \item{origin}{ for counting process data, the hazard function origin. This option was intended to be used in conjunction with a model containing time dependent strata in order to align the subjects properly when they cross over from one strata to another, but it has rarely proven useful.} \item{x}{ any R object. } } \value{ An object of class \code{Surv}. There are methods for \code{print}, \code{is.na}, and subscripting survival objects. \code{Surv} objects are implemented as a matrix of 2 or 3 columns that has further attributes. These include the type (left censored, right censored, counting process, etc.) and labels for the states for multi-state objects. Any attributes of the input arguments are also preserved in \code{inputAttributes}. This may be useful for other packages that have attached further information to data items such as labels; none of the routines in the survival package make use of these values, however. In the case of \code{is.Surv}, a logical value \code{TRUE} if \code{x} inherits from class \code{"Surv"}, otherwise an \code{FALSE}. } \details{ When the \code{type} argument is missing the code assumes a type based on the following rules: \itemize{ \item If there are two unnamed arguments, they will match \code{time} and \code{event} in that order. If there are three unnamed arguments they match \code{time}, \code{time2} and \code{event}. \item If the event variable is a factor then type \code{mstate} is assumed. Otherwise type \code{right} if there is no \code{time2} argument, and type \code{counting} if there is. } As a consequence the \code{type} argument will normally be omitted. When the survival type is "mstate" then the status variable will be treated as a factor. The first level of the factor is taken to represent censoring and remaining ones a transition to the given state. Interval censored data can be represented in two ways. For the first use \code{type = "interval"} and the codes shown above. In that usage the value of the \code{time2} argument is ignored unless event=3. The second approach is to think of each observation as a time interval with (-infinity, t) for left censored, (t, infinity) for right censored, (t,t) for exact and (t1, t2) for an interval. This is the approach used for type = interval2. Infinite values can be represented either by actual infinity (Inf) or NA. The second form has proven to be the more useful one. Presently, the only methods allowing interval censored data are the parametric models computed by \code{survreg} and survival curves computed by \code{survfit}; for both of these, the distinction between open and closed intervals is unimportant. The distinction is important for counting process data and the Cox model. The function tries to distinguish between the use of 0/1 and 1/2 coding for censored data via the condition \code{if (max(status)==2)}. If 1/2 coding is used and all the subjects are censored, it will guess wrong. In any questionable case it is safer to use logical coding, e.g., \code{Surv(time, status==3)} would indicate that a \code{3} is the code for an event. For multi-state survival (type= "mstate") the status variable can have multiple levels. The first of these will stand for censoring, and the others for various event types, e.g., causes of death. Surv objects can be subscripted either as a vector, e.g. \code{x[1:3]} using a single subscript, in which case the \code{drop} argument is ignored and the result will be a survival object; or as a matrix by using two subscripts. If the second subscript is missing and \code{drop=F} (the default), the result of the subscripting will be a Surv object, e.g., \code{x[1:3,,drop=F]}, otherwise the result will be a matrix (or vector), in accordance with the default behavior for subscripting matrices. } \seealso{ \code{\link{coxph}}, \code{\link{survfit}}, \code{\link{survreg}}. } \examples{ with(lung, Surv(time, status)) Surv(heart$start, heart$stop, heart$event) } \keyword{survival} survival/man/coxph.object.Rd0000644000175100001440000000531712703256650015607 0ustar hornikusers\name{coxph.object} \alias{coxph.object} \alias{extractAIC.coxph.penal} \alias{print.coxph} \title{ Proportional Hazards Regression Object } \description{ This class of objects is returned by the \code{coxph} class of functions to represent a fitted proportional hazards model. Objects of this class have methods for the functions \code{print}, \code{summary}, \code{residuals}, \code{predict} and \code{survfit}. } \section{Components}{ The following components must be included in a legitimate \code{coxph} object. } \arguments{ \item{coefficients}{ the vector of coefficients. If the model is over-determined there will be missing values in the vector corresponding to the redundant columns in the model matrix. } \item{var}{ the variance matrix of the coefficients. Rows and columns corresponding to any missing coefficients are set to zero. } \item{naive.var}{ this component will be present only if the \code{robust} option was true. If so, the \code{var} component will contain the robust estimate of variance, and this component will contain the ordinary estimate. } \item{loglik}{ a vector of length 2 containing the log-likelihood with the initial values and with the final values of the coefficients. } \item{score}{ value of the efficient score test, at the initial value of the coefficients. } \item{rscore}{ the robust log-rank statistic, if a robust variance was requested. } \item{wald.test}{ the Wald test of whether the final coefficients differ from the initial values. } \item{iter}{ number of iterations used. } \item{linear.predictors}{ the vector of linear predictors, one per subject. Note that this vector has been centered, see \code{predict.coxph} for more details. } \item{residuals}{ the martingale residuals. } \item{means}{ vector of column means of the X matrix. Subsequent survival curves are adjusted to this value. } \item{n}{ the number of observations used in the fit. } \item{nevent}{ the number of events (usually deaths) used in the fit. } \item{concordance}{the concordance, as computed by survConcordance.} \item{first}{the first derivative vector at the solution.} \item{weights}{ the vector of case weights, if one was used. } \item{method}{ the computation method used. } \item{na.action}{ the na.action attribute, if any, that was returned by the \code{na.action} routine. The object will also contain the following, for documentation see the \code{lm} object: \code{terms}, \code{assign}, \code{formula}, \code{call}, and, optionally, \code{x}, \code{y}, and/or \code{frame}. } } \seealso{ \code{\link{coxph}}, \code{\link{coxph.detail}}, \code{\link{cox.zph}}, \code{\link{residuals.coxph}}, \code{\link{survfit}}, \code{\link{survreg}}. } \keyword{survival} survival/man/veteran.Rd0000644000175100001440000000137713067454773014701 0ustar hornikusers\name{veteran} \alias{veteran} \docType{data} \title{Veterans' Administration Lung Cancer study} \description{Randomised trial of two treatment regimens for lung cancer. This is a standard survival analysis data set.} \usage{veteran} \format{ \tabular{ll}{ trt:\tab 1=standard 2=test\cr celltype:\tab 1=squamous, 2=smallcell, 3=adeno, 4=large\cr time:\tab survival time\cr status:\tab censoring status\cr karno:\tab Karnofsky performance score (100=good)\cr diagtime:\tab months from diagnosis to randomisation\cr age:\tab in years\cr prior:\tab prior therapy 0=no, 10=yes\cr } } \source{ D Kalbfleisch and RL Prentice (1980), \emph{The Statistical Analysis of Failure Time Data}. Wiley, New York. } \keyword{datasets} survival/man/coxph.wtest.Rd0000644000175100001440000000123013017617770015500 0ustar hornikusers\name{coxph.wtest} \alias{coxph.wtest} \title{Compute a quadratic form} \description{ This function is used internally by several survival routines. It computes a simple quadratic form, while properly dealing with missings. } \usage{ coxph.wtest(var, b, toler.chol = 1e-09) } \arguments{ \item{var}{variance matrix} \item{b}{vector} \item{toler.chol}{tolerance for the internal cholesky decomposition} } \details{ Compute b' V-inverse b. Equivalent to sum(b * solve(V,b)), except for the case of redundant covariates in the original model, which lead to NA values in V and b. } \value{a real number} \author{Terry Therneau} \keyword{ survival } survival/man/survobrien.Rd0000644000175100001440000000567211732700061015412 0ustar hornikusers\name{survobrien} \alias{survobrien} \title{ O'Brien's Test for Association of a Single Variable with Survival } \description{ Peter O'Brien's test for association of a single variable with survival This test is proposed in Biometrics, June 1978. } \usage{ survobrien(formula, data, subset, na.action, transform) } \arguments{ \item{formula}{ a valid formula for a cox model. } \item{data}{ a data.frame in which to interpret the variables named in the \code{formula}, or in the \code{subset} and the \code{weights} argument. } \item{subset}{ expression indicating which subset of the rows of data should be used in the fit. All observations are included by default. } \item{na.action}{ a missing-data filter function. This is applied to the model.frame after any subset argument has been used. Default is \code{options()\$na.action}. } \item{transform}{the transformation function to be applied at each time point. The default is O'Brien's suggestion logit(tr) where tr = (rank(x)- 1/2)/ length(x) is the rank shifted to the range 0-1 and logit(x) = log(x/(1-x)) is the logit transform. }} \value{ a new data frame. The response variables will be column names returned by the \code{Surv} function, i.e., "time" and "status" for simple survival data, or "start", "stop", "status" for counting process data. Each individual event time is identified by the value of the variable \code{.strata.}. Other variables retain their original names. If a predictor variable is a factor or is protected with \code{I()}, it is retained as is. Other predictor variables have been replaced with time-dependent logit scores. The new data frame will have many more rows that the original data, approximately the original number of rows * number of deaths/2. } \section{Method}{ A time-dependent cox model can now be fit to the new data. The univariate statistic, as originally proposed, is equivalent to single variable score tests from the time-dependent model. This equivalence is the rationale for using the time dependent model as a multivariate extension of the original paper. In O'Brien's method, the x variables are re-ranked at each death time. A simpler method, proposed by Prentice, ranks the data only once at the start. The results are usually similar. } \references{ O'Brien, Peter, "A Nonparametric Test for Association with Censored Data", \emph{Biometrics} 34: 243-250, 1978. } \note{ A prior version of the routine returned new time variables rather than a strata. Unfortunately, that strategy does not work if the original formula has a strata statement. This new data set will be the same size, but the \code{coxph} routine will process it slightly faster. } \seealso{ \code{\link{survdiff}} } \keyword{survival} \examples{ xx <- survobrien(Surv(futime, fustat) ~ age + factor(rx) + I(ecog.ps), data=ovarian) coxph(Surv(time, status) ~ age + strata(.strata.), data=xx) } survival/man/basehaz.Rd0000644000175100001440000000263413013633731014627 0ustar hornikusers\name{basehaz} \alias{basehaz} \title{Alias for the survfit function} \description{ Compute the predicted survival curve for a Cox model. } \usage{ basehaz(fit, centered=TRUE) } \arguments{ \item{fit}{a coxph fit} \item{centered}{if TRUE return data from a predicted survival curve at the mean values of the covariates \code{fit$mean}, if FALSE return a prediction for all covariates equal to zero.} } \details{ This function is simply an alias for \code{survfit}, which is the actual function that does all the computations. See the manual page for that function for the preferred use. This function survives only for backwards support of prior usage. The function returns a data frame containing the \code{time}, \code{cumhaz} and optionally the strata (if the fitted Cox model used a strata statement), which are copied the \code{survfit} result. If there are factor variables in the model, then the default predictions at the "mean" are meaningless since they do not correspond to any possible subject; correct results require use of the \code{newdata} argument of survfit. Results for all covariates =0 are normally only of use as a building block for further calculations. } \value{ a data frame with variable names of \code{hazard}, \code{time} and optionally \code{strata}. The first is actually the cumulative hazard. } \seealso{\code{\link{survfit.coxph}}} \keyword{survival } survival/man/aareg.Rd0000644000175100001440000001712713017617770014305 0ustar hornikusers\name{aareg} \alias{aareg} \title{ Aalen's additive regression model for censored data } \description{ Returns an object of class \code{"aareg"} that represents an Aalen model. } \usage{ aareg(formula, data, weights, subset, na.action, qrtol=1e-07, nmin, dfbeta=FALSE, taper=1, test = c('aalen', 'variance', 'nrisk'), model=FALSE, x=FALSE, y=FALSE) } \arguments{ \item{formula}{ a formula object, with the response on the left of a `~' operator and the terms, separated by \code{+} operators, on the right. The response must be a \code{Surv} object. Due to a particular computational approach that is used, the model MUST include an intercept term. If "-1" is used in the model formula the program will ignore it. } \item{data}{ data frame in which to interpret the variables named in the \code{formula}, \code{subset}, and \code{weights} arguments. This may also be a single number to handle some speci al cases -- see below for details. If \code{data} is missing, the variables in the model formula should be in the search path. } \item{weights}{ vector of observation weights. If supplied, the fitting algorithm minimizes the sum of the weights multiplied by the squared residuals (see below for additional technical details). The length of \code{weights} must be the same as the number of observations. The weights must be nonnegative and it i s recommended that they be strictly positive, since zero weights are ambiguous. To exclude particular observations from the model, use the \code{subset} argument instead of zero weights. } \item{subset}{ expression specifying which subset of observations should be used in the fit. Th is can be a logical vector (which is replicated to have length equal to the numb er of observations), a numeric vector indicating the observation numbers to be included, or a character vector of the observation names that should be included. All observations are included by default. } \item{na.action}{ a function to filter missing data. This is applied to the \code{model.fr ame} after any \code{subset} argument has be en applied. The default is \code{na.fail}, which returns a n error if any missing values are found. An alternative is \code{na.excl ude}, which deletes observations that contain one or more missing values. } \item{qrtol}{ tolerance for detection of singularity in the QR decomposition } \item{nmin}{ minimum number of observations for an estimate; defaults to 3 times the number of covariates. This essentially truncates the computations near the tail of the data set, when n is small and the calculations can become numerically unstable. } \item{dfbeta}{ should the array of dfbeta residuals be computed. This implies computation of the sandwich variance estimate. The residuals will always be computed if there is a \code{cluster} term in the model formula. } \item{taper}{ allows for a smoothed variance estimate. Var(x), where x is the set of covariates, is an important component of the calculations for the Aalen regression model. At any given time point t, it is computed over all subjects who are still at risk at time t. The tape argument allows smoothing these estimates, for example \code{taper=(1:4)/4} would cause the variance estimate used at any event time to be a weighted average of the estimated variance matrices at the last 4 death times, with a weight of 1 for the current death time and decreasing to 1/4 for prior event times. The default value gives the standard Aalen model. } \item{test}{ selects the weighting to be used, for computing an overall ``average'' coefficient vector over time and the subsequent test for equality to zero. } \item{model, x, y }{ should copies of the model frame, the x matrix of predictors, or the response vector y be included in the saved result. } } \value{ an object of class \code{"aareg"} representing the fit, with the following components: \item{n}{vector containing the number of observations in the data set, the number of event times, and the number of event times used in the computation} \item{times}{vector of sorted event times, which may contain duplicates} \item{nrisk}{vector containing the number of subjects at risk, of the same length as \code{times}} \item{coefficient}{matrix of coefficients, with one row per event and one column per covariate} \item{test.statistic}{the value of the test statistic, a vector with one element per covariate} \item{test.var}{variance-covariance matrix for the test} \item{test}{the type of test; a copy of the \code{test} argument above} \item{tweight}{matrix of weights used in the computation, one row per event} \item{call}{a copy of the call that produced this result} } \details{ The Aalen model assumes that the cumulative hazard H(t) for a subject can be expressed as a(t) + X B(t), where a(t) is a time-dependent intercept term, X is the vector of covariates for the subject (possibly time-dependent), and B(t) is a time-dependent matrix of coefficients. The estimates are inherently non-parametric; a fit of the model will normally be followed by one or more plots of the estimates. The estimates may become unstable near the tail of a data set, since the increment to B at time t is based on the subjects still at risk at time t. The tolerance and/or nmin parameters may act to truncate the estimate before the last death. The \code{taper} argument can also be used to smooth out the tail of the curve. In practice, the addition of a taper such as 1:10 appears to have little effect on death times when n is still reasonably large, but can considerably dampen wild occilations in the tail of the plot. } \section{References}{ Aalen, O.O. (1989). A linear regression model for the analysis of life times. Statistics in Medicine, 8:907-925. Aalen, O.O (1993). Further results on the non-parametric linear model in survival analysis. Statistics in Medicine. 12:1569-1588. } \seealso{ print.aareg, summary.aareg, plot.aareg } \examples{ # Fit a model to the lung cancer data set lfit <- aareg(Surv(time, status) ~ age + sex + ph.ecog, data=lung, nmin=1) \dontrun{ lfit Call: aareg(formula = Surv(time, status) ~ age + sex + ph.ecog, data = lung, nmin = 1 ) n=227 (1 observations deleted due to missing values) 138 out of 138 unique event times used slope coef se(coef) z p Intercept 5.26e-03 5.99e-03 4.74e-03 1.26 0.207000 age 4.26e-05 7.02e-05 7.23e-05 0.97 0.332000 sex -3.29e-03 -4.02e-03 1.22e-03 -3.30 0.000976 ph.ecog 3.14e-03 3.80e-03 1.03e-03 3.70 0.000214 Chisq=26.73 on 3 df, p=6.7e-06; test weights=aalen plot(lfit[4], ylim=c(-4,4)) # Draw a plot of the function for ph.ecog } lfit2 <- aareg(Surv(time, status) ~ age + sex + ph.ecog, data=lung, nmin=1, taper=1:10) \dontrun{lines(lfit2[4], col=2) # Nearly the same, until the last point} # A fit to the mulitple-infection data set of children with # Chronic Granuomatous Disease. See section 8.5 of Therneau and Grambsch. fita2 <- aareg(Surv(tstart, tstop, status) ~ treat + age + inherit + steroids + cluster(id), data=cgd) \dontrun{ n= 203 69 out of 70 unique event times used slope coef se(coef) robust se z p Intercept 0.004670 0.017800 0.002780 0.003910 4.55 5.30e-06 treatrIFN-g -0.002520 -0.010100 0.002290 0.003020 -3.36 7.87e-04 age -0.000101 -0.000317 0.000115 0.000117 -2.70 6.84e-03 inheritautosomal 0.001330 0.003830 0.002800 0.002420 1.58 1.14e-01 steroids 0.004620 0.013200 0.010600 0.009700 1.36 1.73e-01 Chisq=16.74 on 4 df, p=0.0022; test weights=aalen } } \keyword{survival} % docclass is function survival/man/plot.cox.zph.Rd0000644000175100001440000000412112656741055015564 0ustar hornikusers\name{plot.cox.zph} \alias{plot.cox.zph} \title{ Graphical Test of Proportional Hazards } \description{ Displays a graph of the scaled Schoenfeld residuals, along with a smooth curve. } \usage{ \method{plot}{cox.zph}(x, resid=TRUE, se=TRUE, df=4, nsmo=40, var, xlab="Time", ylab, lty=1:2, col=1, lwd=1, ...) } \arguments{ \item{x}{ result of the \code{cox.zph} function. } \item{resid}{ a logical value, if \code{TRUE} the residuals are included on the plot, as well as the smooth fit. } \item{se}{ a logical value, if \code{TRUE}, confidence bands at two standard errors will be added. } \item{df}{ the degrees of freedom for the fitted natural spline, \code{df=2} leads to a linear fit. } \item{nsmo}{number of points to use for the lines} \item{var}{ the set of variables for which plots are desired. By default, plots are produced in turn for each variable of a model. Selection of a single variable allows other features to be added to the plot, e.g., a horizontal line at zero or a main title. This has been superseded by a subscripting method; see the example below. } \item{xlab}{label for the x-axis of the plot} \item{ylab}{optional label for the y-axis of the plot. If missing a default label is provided. This can be a vector of labels.} \item{lty, col, lwd}{line type, color, and line width for the overlaid curve. Each of these can be vector of length 2, in which case the second element is used for the confidence interval.} \item{\dots}{ additional graphical arguments passed to the \code{plot} function. } } \section{Side Effects}{ a plot is produced on the current graphics device. } \seealso{ \code{\link{coxph}}, \code{\link{cox.zph}}. } \examples{ vfit <- coxph(Surv(time,status) ~ trt + factor(celltype) + karno + age, data=veteran, x=TRUE) temp <- cox.zph(vfit) plot(temp, var=5) # Look at Karnofsy score, old way of doing plot plot(temp[5]) # New way with subscripting abline(0, 0, lty=3) # Add the linear fit as well abline(lm(temp$y[,5] ~ temp$x)$coefficients, lty=4, col=3) title(main="VA Lung Study") } \keyword{survival} survival/man/dsurvreg.Rd0000644000175100001440000000630413013633731015051 0ustar hornikusers\name{dsurvreg} \alias{dsurvreg} \alias{psurvreg} \alias{qsurvreg} \alias{rsurvreg} \title{ Distributions available in survreg. } \description{ Density, cumulative distribution function, quantile function and random generation for the set of distributions supported by the \code{survreg} function. } \usage{ dsurvreg(x, mean, scale=1, distribution='weibull', parms) psurvreg(q, mean, scale=1, distribution='weibull', parms) qsurvreg(p, mean, scale=1, distribution='weibull', parms) rsurvreg(n, mean, scale=1, distribution='weibull', parms) } \arguments{ \item{x}{ vector of quantiles. Missing values (\code{NA}s) are allowed. } \item{q}{ vector of quantiles. Missing values (\code{NA}s) are allowed. } \item{p}{ vector of probabilities. Missing values (\code{NA}s) are allowed. } \item{n}{number of random deviates to produce} \item{mean}{vector of linear predictors for the model. This is replicated to be the same length as \code{p}, \code{q} or \code{n}. } \item{scale}{ vector of (positive) scale factors. This is replicated to be the same length as \code{p}, \code{q} or \code{n}. } \item{distribution}{ character string giving the name of the distribution. This must be one of the elements of \code{survreg.distributions} } \item{parms}{ optional parameters, if any, of the distribution. For the t-distribution this is the degrees of freedom. } } \value{ density (\code{dsurvreg}), probability (\code{psurvreg}), quantile (\code{qsurvreg}), or for the requested distribution with mean and scale parameters \code{mean} and \code{sd}. } \details{ Elements of \code{q} or \code{p} that are missing will cause the corresponding elements of the result to be missing. The \code{location} and \code{scale} values are as they would be for \code{survreg}. The label "mean" was an unfortunate choice (made in mimicry of qnorm); since almost none of these distributions are symmetric it will not actually be a mean, but corresponds instead to the linear predictor of a fitted model. Translation to the usual parameterization found in a textbook is not always obvious. For example, the Weibull distribution is fit using the Extreme value distribution along with a log transformation. Letting \eqn{F(t) = 1 - \exp[-(at)^p]}{F(t) = 1 - exp(-(at)^p)} be the cumulative distribution of the Weibull using a standard parameterization in terms of \eqn{a} and \eqn{p}, the survreg location corresponds to \eqn{-\log(a)}{-log(a)} and the scale to \eqn{1/p} (Kalbfleisch and Prentice, section 2.2.2). } \section{References}{ Kalbfleisch, J. D. and Prentice, R. L. (1970). \emph{The Statistical Analysis of Failure Time Data} Wiley, New York. } \seealso{ \code{\link{survreg}}, \code{\link{Normal}} } \examples{ # List of distributions available names(survreg.distributions) \dontrun{ [1] "extreme" "logistic" "gaussian" "weibull" "exponential" [6] "rayleigh" "loggaussian" "lognormal" "loglogistic" "t" } # Compare results all.equal(dsurvreg(1:10, 2, 5, dist='lognormal'), dlnorm(1:10, 2, 5)) # Hazard function for a Weibull distribution x <- seq(.1, 3, length=30) haz <- dsurvreg(x, 2, 3)/ (1-psurvreg(x, 2, 3)) \dontrun{ plot(x, haz, log='xy', ylab="Hazard") #line with slope (1/scale -1) } } \keyword{distribution} survival/man/survSplit.Rd0000644000175100001440000000747312756625242015246 0ustar hornikusers\name{survSplit} \alias{survSplit} \title{Split a survival data set at specified times } \description{ Given a survival data set and a set of specified cut times, split each record into multiple subrecords at each cut time. The new data set will be in `counting process' format, with a start time, stop time, and event status for each record. } \usage{ survSplit(formula, data, subset, na.action=na.pass, cut, start="tstart", id, zero=0, episode, end="tstop", event="event") } %- maybe also `usage' for other objects documented here. \arguments{ \item{formula}{a model formula} \item{data}{a data frame} \item{subset, na.action}{rows of the data to be retained} \item{cut}{the vector of timepoints to cut at} \item{start}{character string with the name of a start time variable (will be created if needed) } \item{id}{character string with the name of new id variable to create (optional). This can be useful if the data set does not already contain an identifier.} \item{zero}{If \code{start} doesn't already exist, this is the time that the original records start.} \item{episode}{character string with the name of new episode variable (optional)} \item{end}{character string with the name of event time variable } \item{event}{character string with the name of censoring indicator } } \value{ New, longer, data frame. } \details{ Each interval in the original data is cut at the given points; if an original row were (15, 60] with a cut vector of (10,30, 40) the resulting data set would have intervals of (15,30], (30,40] and (40, 60]. Each row in the final data set will lie completely within one of the cut intervals. Which interval for each row of the output is shown by the \code{episode} variable, where 1= less than the first cutpoint, 2= between the first and the second, etc. For the example above the values would be 2, 3, and 4. The routine will normally be called with a formula as the first argument. The right hand side of the formula can be used to delimit variables that should be retained; normally one will use \code{ ~ .} as a shorthand to retain them all. When called in this way the routine will try to retain variable names, e.g. \code{Surv(adam, joe, fred)~.} will result in a data set with those same variable names for \code{tstart}, \code{end}, and \code{event} options rather than the defaults. Any user specified values for these options will be used if they are present, of course. However, the routine is not sophisticated; it only does this substitution for simple names. A call of \code{Surv(time, stat==2)} for instance will result in use of the 'event' argument for that variable name. The \code{end} and \code{event} arguments are required if there is no formula. Rows of data with a missing time or status are copied across unchanged, unless the na.action argument is changed from its default value of \code{na.pass}. But in the latter case any row that is missing for any variable will be removed, which is rarely what is desired. } \seealso{\code{\link{Surv}}, \code{\link{cut}}, \code{\link{reshape}} } \examples{ fit1 <- coxph(Surv(time, status) ~ karno + age + trt, veteran) plot(cox.zph(fit1)[1]) # a cox.zph plot of the data suggests that the effect of Karnofsky score # begins to diminish by 60 days and has faded away by 120 days. # Fit a model with separate coefficients for the three intervals. # vet2 <- survSplit(Surv(time, status) ~., veteran, cut=c(60, 120), episode ="timegroup") fit2 <- coxph(Surv(tstart, time, status) ~ karno* strata(timegroup) + age + trt, data= vet2) c(overall= coef(fit1)[1], t0_60 = coef(fit2)[1], t60_120= sum(coef(fit2)[c(1,4)]), t120 = sum(coef(fit2)[c(1,5)])) } \keyword{survival } \keyword{utilities} survival/man/clogit.Rd0000644000175100001440000001076413013633731014476 0ustar hornikusers\name{clogit} \alias{clogit} \title{Conditional logistic regression } \description{ Estimates a logistic regression model by maximising the conditional likelihood. Uses a model formula of the form \code{case.status~exposure+strata(matched.set)}. The default is to use the exact conditional likelihood, a commonly used approximate conditional likelihood is provided for compatibility with older software. } \usage{ clogit(formula, data, weights, subset, na.action, method=c("exact", "approximate", "efron", "breslow"), \dots) } \arguments{ \item{formula}{Model formula} \item{data}{data frame } \item{weights}{optional, names the variable containing case weights} \item{subset}{optional, subset the data} \item{na.action}{optional na.action argument. By default the global option \code{na.action} is used.} \item{method}{use the correct (exact) calculation in the conditional likelihood or one of the approximations} \item{\dots}{optional arguments, which will be passed to \code{coxph.control}} } \value{ An object of class \code{"clogit"}, which is a wrapper for a \code{"coxph"} object. } \author{Thomas Lumley} \details{ It turns out that the loglikelihood for a conditional logistic regression model = loglik from a Cox model with a particular data structure. Proving this is a nice homework exercise for a PhD statistics class; not too hard, but the fact that it is true is surprising. When a well tested Cox model routine is available many packages use this `trick' rather than writing a new software routine from scratch, and this is what the clogit routine does. In detail, a stratified Cox model with each case/control group assigned to its own stratum, time set to a constant, status of 1=case 0=control, and using the exact partial likelihood has the same likelihood formula as a conditional logistic regression. The clogit routine creates the necessary dummy variable of times (all 1) and the strata, then calls coxph. The computation of the exact partial likelihood can be very slow, however. If a particular strata had say 10 events out of 20 subjects we have to add up a denominator that involves all possible ways of choosing 10 out of 20, which is 20!/(10! 10!) = 184756 terms. Gail et al describe a fast recursion method which partly ameliorates this; it was incorporated into version 2.36-11 of the survival package. The computation remains infeasible for very large groups of ties, say 100 ties out of 500 subjects, and may even lead to integer overflow for the subscripts -- in this latter case the routine will refuse to undertake the task. The Efron approximation is normally a sufficiently accurate substitute. Most of the time conditional logistic modeling is applied data with 1 case + k controls per set, in which case all of the approximations for ties lead to exactly the same result. The 'approximate' option maps to the Breslow approximation for the Cox model, for historical reasons. Case weights are not allowed when the exact option is used, as the likelihood is not defined for fractional weights. Even with integer case weights it is not clear how they should be handled. For instance if there are two deaths in a strata, one with weight=1 and one with weight=2, should the likelihood calculation consider all subsets of size 2 or all subsets of size 3? Consequently, case weights are ignored by the routine in this case. } \seealso{\code{\link{strata}},\code{\link{coxph}},\code{\link{glm}} } \examples{ \dontrun{clogit(case ~ spontaneous + induced + strata(stratum), data=infert)} # A multinomial response recoded to use clogit # The revised data set has one copy per possible outcome level, with new # variable tocc = target occupation for this copy, and case = whether # that is the actual outcome for each subject. # See the reference below for the data. resp <- levels(logan$occupation) n <- nrow(logan) indx <- rep(1:n, length(resp)) logan2 <- data.frame(logan[indx,], id = indx, tocc = factor(rep(resp, each=n))) logan2$case <- (logan2$occupation == logan2$tocc) clogit(case ~ tocc + tocc:education + strata(id), logan2) } \section{References}{ Michell H Gail, Jay H Lubin and Lawrence V Rubinstein. Likelihood calculations for matched case-control studies and survival studies with tied death times. Biometrika 68:703-707, 1980. John A. Logan. A multivariate model for mobility tables. Am J Sociology 89:324-349, 1983. } \keyword{survival} \keyword{models} survival/man/print.aareg.Rd0000644000175100001440000000276211732700061015423 0ustar hornikusers\name{print.aareg} \alias{print.aareg} \title{ Print an aareg object } \description{ Print out a fit of Aalen's additive regression model } \usage{ \method{print}{aareg}(x, maxtime, test=c("aalen", "nrisk"),scale=1,...) } \arguments{ \item{x}{ the result of a call to the \code{aareg} function } \item{maxtime}{ the upper time point to be used in the test for non-zero slope } \item{test}{ the weighting to be used in the test for non-zero slope. The default weights are based on the variance of each coefficient, as a function of time. The alternative weight is proportional to the number of subjects still at risk at each time point. } \item{scale}{scales the coefficients. For some data sets, the coefficients of the Aalen model will be very small (10-4); this simply multiplies the printed values by a constant, say 1e6, to make the printout easier to read.} \item{\dots}{for future methods} } \value{ the calling argument is returned. } \section{Side Effects}{ the results of the fit are displayed. } \details{ The estimated increments in the coefficient estimates can become quite unstable near the end of follow-up, due to the small number of observations still at risk in a data set. Thus, the test for slope will sometimes be more powerful if this last `tail' is excluded. } \section{References}{ Aalen, O.O. (1989). A linear regression model for the analysis of life times. Statistics in Medicine, 8:907-925. } \seealso{ aareg } \keyword{survival} % docclass is function % Converted by Sd2Rd version 37351. survival/man/logan.Rd0000644000175100001440000000164611732700061014311 0ustar hornikusers\name{logan} \docType{data} \alias{logan} \title{Data from the 1972-78 GSS data used by Logan} \usage{data(logan)} \description{ Intergenerational occupational mobility data with covariates. } \format{ A data frame with 838 observations on the following 4 variables. \describe{ \item{occupation}{subject's occupation, a factor with levels \code{farm}, \code{operatives}, \code{craftsmen}, \code{sales}, and \code{professional}} \item{focc}{father's occupation} \item{education}{total years of schooling, 0 to 20} \item{race}{levels of \code{non-black} and \code{black}} } } \source{ General Social Survey data, see the web site for detailed information on the variables. \url{http://www3.norc.org/GSS+Website}. } \references{ Logan, John A. (1983). A Multivariate Model for Mobility Tables. \cite{American Journal of Sociology} 89: 324-349.} \keyword{datasets} survival/man/cch.Rd0000644000175100001440000001206213013633731013743 0ustar hornikusers\alias{cch} \name{cch} \title{Fits proportional hazards regression model to case-cohort data} \description{ Returns estimates and standard errors from relative risk regression fit to data from case-cohort studies. A choice is available among the Prentice, Self-Prentice and Lin-Ying methods for unstratified data. For stratified data the choice is between Borgan I, a generalization of the Self-Prentice estimator for unstratified case-cohort data, and Borgan II, a generalization of the Lin-Ying estimator. } \usage{ cch(formula, data = sys.parent(), subcoh, id, stratum=NULL, cohort.size, method =c("Prentice","SelfPrentice","LinYing","I.Borgan","II.Borgan"), robust=FALSE) } \arguments{ \item{formula}{ A formula object that must have a \code{\link{Surv}} object as the response. The Surv object must be of type \code{"right"}, or of type \code{"counting"}. } \item{subcoh}{ Vector of indicators for subjects sampled as part of the sub-cohort. Code \code{1} or \code{TRUE} for members of the sub-cohort, \code{0} or \code{FALSE} for others. If \code{data} is a data frame then \code{subcoh} may be a one-sided formula. } \item{id}{ Vector of unique identifiers, or formula specifying such a vector. } \item{stratum}{A vector of stratum indicators or a formula specifying such a vector} \item{cohort.size}{ Vector with size of each stratum original cohort from which subcohort was sampled } \item{data}{ An optional data frame in which to interpret the variables occurring in the formula. } \item{method}{ Three procedures are available. The default method is "Prentice", with options for "SelfPrentice" or "LinYing". } \item{robust}{For \code{"LinYing"} only, if \code{robust=TRUE}, use design-based standard errors even for phase I} } \value{ An object of class "cch" incorporating a list of estimated regression coefficients and two estimates of their asymptotic variance-covariance matrix. \item{coef}{ regression coefficients. } \item{naive.var}{ Self-Prentice model based variance-covariance matrix. } \item{var}{ Lin-Ying empirical variance-covariance matrix. }} \details{ Implements methods for case-cohort data analysis described by Therneau and Li (1999). The three methods differ in the choice of "risk sets" used to compare the covariate values of the failure with those of others at risk at the time of failure. "Prentice" uses the sub-cohort members "at risk" plus the failure if that occurs outside the sub-cohort and is score unbiased. "SelfPren" (Self-Prentice) uses just the sub-cohort members "at risk". These two have the same asymptotic variance-covariance matrix. "LinYing" (Lin-Ying) uses the all members of the sub-cohort and all failures outside the sub-cohort who are "at risk". The methods also differ in the weights given to different score contributions. The \code{data} argument must not have missing values for any variables in the model. There must not be any censored observations outside the subcohort. } \author{Norman Breslow, modified by Thomas Lumley} \references{ Prentice, RL (1986). A case-cohort design for epidemiologic cohort studies and disease prevention trials. Biometrika 73: 1--11. Self, S and Prentice, RL (1988). Asymptotic distribution theory and efficiency results for case-cohort studies. Annals of Statistics 16: 64--81. Lin, DY and Ying, Z (1993). Cox regression with incomplete covariate measurements. Journal of the American Statistical Association 88: 1341--1349. Barlow, WE (1994). Robust variance estimation for the case-cohort design. Biometrics 50: 1064--1072 Therneau, TM and Li, H (1999). Computing the Cox model for case-cohort designs. Lifetime Data Analysis 5: 99--112. Borgan, \eqn{O}{O}, Langholz, B, Samuelsen, SO, Goldstein, L and Pogoda, J (2000) Exposure stratified case-cohort designs. Lifetime Data Analysis 6, 39-58. } \seealso{ \code{twophase} and \code{svycoxph} in the "survey" package for more general two-phase designs. \url{http://faculty.washington.edu/tlumley/survey/} } \examples{ ## The complete Wilms Tumor Data ## (Breslow and Chatterjee, Applied Statistics, 1999) ## subcohort selected by simple random sampling. ## subcoh <- nwtco$in.subcohort selccoh <- with(nwtco, rel==1|subcoh==1) ccoh.data <- nwtco[selccoh,] ccoh.data$subcohort <- subcoh[selccoh] ## central-lab histology ccoh.data$histol <- factor(ccoh.data$histol,labels=c("FH","UH")) ## tumour stage ccoh.data$stage <- factor(ccoh.data$stage,labels=c("I","II","III","IV")) ccoh.data$age <- ccoh.data$age/12 # Age in years ## ## Standard case-cohort analysis: simple random subcohort ## fit.ccP <- cch(Surv(edrel, rel) ~ stage + histol + age, data =ccoh.data, subcoh = ~subcohort, id=~seqno, cohort.size=4028) fit.ccP fit.ccSP <- cch(Surv(edrel, rel) ~ stage + histol + age, data =ccoh.data, subcoh = ~subcohort, id=~seqno, cohort.size=4028, method="SelfPren") summary(fit.ccSP) ## ## (post-)stratified on instit ## stratsizes<-table(nwtco$instit) fit.BI<- cch(Surv(edrel, rel) ~ stage + histol + age, data =ccoh.data, subcoh = ~subcohort, id=~seqno, stratum=~instit, cohort.size=stratsizes, method="I.Borgan") summary(fit.BI) } \keyword{survival} survival/man/neardate.Rd0000644000175100001440000000774112652730256015011 0ustar hornikusers\name{neardate} \alias{neardate} \title{ Find the index of the closest value in data set 2, for each entry in data set one. } \description{ A common task in medical work is to find the closest lab value to some index date, for each subject. } \usage{ neardate(id1, id2, y1, y2, best = c("after", "prior"), nomatch = NA_integer_) } \arguments{ \item{id1}{vector of subject identifiers for the index group} \item{id2}{vector of identifiers for the reference group} \item{y1}{normally a vector of dates for the index group, but any orderable data type is allowed} \item{y2}{reference set of dates} \item{best}{if \code{best='prior'} find the index of the first y2 value less than or equal to the target y1 value, for each subject. If \code{best='after'} find the first y2 value which is greater than or equal to the target y1 value, for each subject.} \item{nomatch}{the value to return for items without a match} } \details{ This routine is closely related to \code{match} and to \code{findInterval}, the first of which finds exact matches and the second closest matches. This finds the closest matching date within sets of exactly matching identifiers. Closest date matching is often needed in clinical studies. For example data set 1 might contain the subject identifier and the date of some procedure and data set set 2 has the dates and values for laboratory tests, and the query is to find the first test value after the intervention but no closer than 7 days. The \code{id1} and \code{id2} arguments are similar to \code{match} in that we are searching for instances of \code{id1} that will be found in \code{id2}, and the result is the same length as \code{id1}. However, instead of returning the first match with \code{id2} this routine returns the one that best matches with respect to \code{y1}. The \code{y1} and \code{y2} arguments need not be dates, the function works for any data type such that the expression \code{c(y1, y2)} gives a sensible, sortable result. Be careful about matching Date and DateTime values and the impact of time zones, however, see \code{\link{as.POSIXct}}. If \code{y1} and \code{y2} are not of the same class the user is on their own. Since there exist pairs of unmatched data types where the result could be sensible, the routine will in this case proceed under the assumption that "the user knows what they are doing". Caveat emptor. } \value{the index of the matching observations in the second data set, or the \code{nomatch} value for no successful match} \author{Terry Therneau} \examples{ data1 <- data.frame(id = 1:10, entry.dt = as.Date(paste("2011", 1:10, "5", sep='-'))) temp1 <- c(1,4,5,1,3,6,9, 2,7,8,12,4,6,7,10,12,3) data2 <- data.frame(id = c(1,1,1,2,2,4,4,5,5,5,6,8,8,9,10,10,12), lab.dt = as.Date(paste("2011", temp1, "1", sep='-')), chol = round(runif(17, 130, 280))) #first cholesterol on or after enrollment indx1 <- neardate(data1$id, data2$id, data1$entry.dt, data2$lab.dt) data2[indx1, "chol"] # Closest one, either before or after. # indx2 <- neardate(data1$id, data2$id, data1$entry.dt, data2$lab.dt, best="prior") ifelse(is.na(indx1), indx2, # none after, take before ifelse(is.na(indx2), indx1, #none before ifelse(abs(data2$lab.dt[indx2]- data1$entry.dt) < abs(data2$lab.dt[indx1]- data1$entry.dt), indx2, indx1))) # closest date before or after, but no more than 21 days prior to index indx2 <- ifelse((data1$entry.dt - data2$lab.dt[indx2]) >21, NA, indx2) ifelse(is.na(indx1), indx2, # none after, take before ifelse(is.na(indx2), indx1, #none before ifelse(abs(data2$lab.dt[indx2]- data1$entry.dt) < abs(data2$lab.dt[indx1]- data1$entry.dt), indx2, indx1))) } \seealso{\code{\link{match}}, \code{\link{findInterval}}} \keyword{ manip } \keyword{ utilities } survival/man/heart.Rd0000644000175100001440000000261712647160734014330 0ustar hornikusers\name{heart} \docType{data} \alias{jasa1} \alias{jasa} \alias{heart} \title{Stanford Heart Transplant data} \description{Survival of patients on the waiting list for the Stanford heart transplant program.} \usage{ heart jasa jasa1 } \format{ jasa: original data \tabular{ll}{ birth.dt:\tab birth date \cr accept.dt:\tab acceptance into program \cr tx.date:\tab transplant date \cr fu.date:\tab end of followup \cr fustat:\tab dead or alive \cr surgery:\tab prior bypass surgery\cr age: \tab age (in years)\cr futime:\tab followup time\cr wait.time:\tab time before transplant\cr transplant:\tab transplant indicator\cr mismatch:\tab mismatch score\cr hla.a2:\tab particular type of mismatch\cr mscore:\tab another mismatch score\cr reject:\tab rejection occurred\cr } jasa1, heart: processed data \tabular{ll}{ start, stop, event: \tab Entry and exit time and status for this interval of time\cr age:\tab age-48 years\cr year:\tab year of acceptance (in years after 1 Nov 1967)\cr surgery:\tab prior bypass surgery 1=yes\cr transplant: \tab received transplant 1=yes\cr id:\tab patient id\cr } } \seealso{\code{\link{stanford2}}} \source{ J Crowley and M Hu (1977), Covariance analysis of heart transplant survival data. \emph{Journal of the American Statistical Association}, \bold{72}, 27--36. } \keyword{datasets} \keyword{survival} survival/cleanup0000755000175100001440000000007112334226223013515 0ustar hornikusers#!/bin/sh (cd noweb; make clean) (cd tests; rm plot1.pdf)survival/.Rinstignore0000755000175100001440000000002611741354632014456 0ustar hornikusersinst/doc/validate.tex survival/cleanup.win0000644000175100001440000000004111732700061014301 0ustar hornikusers#!/bin/sh (cd noweb; make clean)