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R/cindex.R
In pec: Prediction Error Curves for Risk Prediction Models in Survival Analysis
Defines functions
cindex
Documented in
cindex
#' Concordance index for right censored survival time data
#'
#' In survival analysis, a pair of patients is called concordant if the risk of
#' the event predicted by a model is lower for the patient who experiences the
#' event at a later timepoint. The concordance probability (C-index) is the
#' frequency of concordant pairs among all pairs of subjects. It can be used to
#' measure and compare the discriminative power of a risk prediction models.
#' The function provides an inverse of the probability of censoring weigthed
#' estimate of the concordance probability to adjust for right censoring.
#' Cross-validation based on bootstrap resampling or bootstrap subsampling can
#' be applied to assess and compare the discriminative power of various
#' regression modelling strategies on the same set of data.
#'
#' Pairs with identical observed times, where one is uncensored and one is
#' censored, are always considered usuable (independent of the value of
#' \code{tiedOutcomeIn}), as it can be assumed that the event occurs at a later
#' timepoint for the censored observation.
#'
#' For uncensored response the result equals the one obtained with the
#' functions \code{rcorr.cens} and \code{rcorrcens} from the \code{Hmisc}
#' package (see examples).
#'
#' @aliases cindex
#' @param object A named list of prediction models, where allowed entries are
#' (1) R-objects for which a \link{predictSurvProb} method exists (see
#' details), (2) a \code{call} that evaluates to such an R-object (see
#' examples), (3) a matrix with predicted probabilities having as many rows as
#' \code{data} and as many columns as \code{times}. For cross-validation all
#' objects in this list must include their \code{call}.
#' @param formula A survival formula. The left hand side is used to finde the
#' status response variable in \code{data}. For right censored data, the right
#' hand side of the formula is used to specify conditional censoring models.
#' For example, set \code{Surv(time,status)~x1+x2} and \code{cens.model="cox"}.
#' Then the weights are based on a Cox regression model for the censoring times
#' with predictors x1 and x2. Note that the usual coding is assumed:
#' \code{status=0} for censored times and that each variable name that appears
#' in \code{formula} must be the column name in \code{data}. If there are no
#' covariates, i.e. \code{formula=Surv(time,status)~1} the \code{cens.model} is
#' coerced to \code{"marginal"} and the Kaplan-Meier estimator for the
#' censoring times is used to calculate the weights. If \code{formula} is
#' \code{missing}, try to extract a formula from the first element in object.
#' @param data A data frame in which to validate the prediction models and to
#' fit the censoring model. If \code{data} is missing, try to extract a data
#' set from the first element in object.
#' @param eval.times A vector of timepoints for evaluating the discriminative
#' ability. At each timepoint the c-index is computed using only those pairs
#' where one of the event times is known to be earlier than this timepoint. If
#' \code{eval.times} is \code{missing} then the largest
#' uncensored event time is used.
#' @param pred.times A vector of timepoints for evaluating the prediction
#' models. This should either be exactly one timepoint used for all
#' \code{eval.times}, or be as long as \code{eval.times}, in which case the
#' predicted order of risk for the jth entry of \code{eval.times} is based on
#' the jth entry of \code{pred.times} corresponding
#' @param cause For competing risks, the event of interest. Defaults to the
#' first state of the response, which is obtained by evaluating the left hand
#' side of \code{formula} in \code{data}.
#' @param lyl If \code{TRUE} rank subjects accoring to predicted
#' life-years-lost (See Andersen due to this cause instead of predicted risk.
#' @param cens.model Method for estimating inverse probability of censoring
#' weigths:
#'
#' \code{cox}: A semi-parametric Cox proportional hazard model is fitted to the
#' censoring times
#'
#' \code{marginal}: The Kaplan-Meier estimator for the censoring times
#'
#' \code{nonpar}: Nonparametric extension of the Kaplan-Meier for the censoring
#' times using symmetric nearest neighborhoods -- available for arbitrary many
#' strata variables on the right hand side of argument \code{formula} but at
#' most one continuous variable. See the documentation of the functions
#' \code{prodlim} and \code{neighborhood} from the prodlim package.
#'
#' \code{aalen}: The nonparametric Aalen additive model fitted to the censoring
#' times. Requires the timereg package maintained by Thomas Scheike.
#' @param ipcw.refit If \code{TRUE} the inverse probability of censoring
#' weigths are estimated separately in each training set during
#' cross-validation.
#' @param ipcw.args List of arguments passed to function specified by argument \code{cens.model}.
#' @param ipcw.limit Value between 0 and 1 (but no equal to 0!) used to cut for
#' small weights in order to stabilize the estimate at late times were few
#' individuals are observed.
#' @param tiedPredictionsIn If \code{FALSE} pairs with identical predictions
#' are excluded, unless also the event times are identical and uncensored and
#' \code{tiedMatchIn} is set to \code{TRUE}.
#' @param tiedOutcomeIn If \code{TRUE} pairs with identical and uncensored
#' event times are excluded, unless also the predictions are identical and
#' \code{tiedMatchIn} is set to \code{TRUE}.
#' @param tiedMatchIn If \code{TRUE} then pairs with identical predictions and
#' identical and uncensored event times are counted as concordant pairs.
#' @param splitMethod Defines the internal validation design:
#'
#' \code{none/noPlan}: Assess the models in the give \code{data}, usually
#' either in the same data where they are fitted, or in independent test data.
#'
#' \code{BootCv}: Bootstrap cross validation. The prediction models are trained
#' on \code{B} bootstrap samples, that are either drawn with replacement of the
#' same size as the original data or without replacement from \code{data} of
#' the size \code{M}. The models are assessed in the observations that are NOT
#' in the bootstrap sample.
#'
#' \code{Boot632}: Linear combination of AppCindex and OutOfBagCindex using the
#' constant weight .632.
#'
#' @param B Number of bootstrap samples. The default depends on argument
#' \code{splitMethod}. When \code{splitMethod} in c("BootCv","Boot632") the
#' default is 100. For \code{splitMethod="none"} \code{B} is the number of
#' bootstrap simulations e.g. to obtain bootstrap confidence limits -- default
#' is 0.
#' @param M The size of the bootstrap samples for resampling without
#' replacement. Ignored for resampling with replacement.
#' @param model.args List of extra arguments that can be passed to the
#' \code{predictSurvProb} methods. The list must have an entry for each entry
#' in \code{object}.
#' @param model.parms Experimental. List of with exactly one entry for each
#' entry in \code{object}. Each entry names parts of the value of the fitted
#' models that should be extracted and added to the value.
#' @param keep.index Logical. If \code{FALSE} remove the bootstrap or
#' cross-validation index from the output list which otherwise is included in
#' the method part of the output list.
#' @param keep.matrix Logical. If \code{TRUE} add all \code{B} prediction error
#' curves from bootstrapping or cross-validation to the output.
#' @param keep.models Logical. If \code{TRUE} keep the models in object. Since
#' fitted models can be large objects the default is \code{FALSE}.
#' @param keep.residuals Experimental.
#' @param keep.pvalues Experimental.
#' @param keep.weights Experimental.
#' @param multiSplitTest Experimental.
#' @param testTimes A vector of time points for testing differences between
#' models in the time-point specific Brier scores.
#' @param confInt Experimental.
#' @param confLevel Experimental.
#' @param verbose if \code{TRUE} report details of the progress, e.g. count the
#' steps in cross-validation.
#' @param savePath Place in your filesystem (directory) where training models
#' fitted during cross-validation are saved. If \code{missing} training models
#' are not saved.
#' @param slaveseed Vector of seeds, as long as \code{B}, to be given to the
#' slaves in parallel computing.
#' @param na.action Passed immediately to model.frame. Defaults to na.fail. If
#' set otherwise most prediction models will not work.
#' @param ... Not used.
#' @return Estimates of the C-index.
#' @author Thomas A Gerds \email{tag@@biostat.ku.dk}
#' @references
#'
#' TA Gerds, MW Kattan, M Schumacher, and C Yu. Estimating a time-dependent
#' concordance index for survival prediction models with covariate dependent
#' censoring. Statistics in Medicine, Ahead of print:to appear, 2013. DOI =
#' 10.1002/sim.5681
#'
#' Wolbers, M and Koller, MT and Witteman, JCM and Gerds, TA (2013) Concordance
#' for prognostic models with competing risks Research report 13/3. Department
#' of Biostatistics, University of Copenhagen
#'
#' Andersen, PK (2012) A note on the decomposition of number of life years lost
#' according to causes of death Research report 12/2. Department of
#' Biostatistics, University of Copenhagen
#'
#' Paul Blanche, Michael W Kattan, and Thomas A Gerds. The c-index is not
#' proper for the evaluation of-year predicted risks. Biostatistics, 20(2):
#' 347--357, 2018.
#' @keywords survival
#' @examples
#'
#' # simulate data based on Weibull regression
#' library(prodlim)
#' set.seed(13)
#' dat <- SimSurv(100)
#' # fit three different Cox models and a random survival forest
#' # note: low number of trees for the purpose of illustration
#' library(survival)
#' cox12 <- coxph(Surv(time,status)~X1+X2,data=dat,x=TRUE,y=TRUE)
#' cox1 <- coxph(Surv(time,status)~X1,data=dat,x=TRUE,y=TRUE)
#' cox2 <- coxph(Surv(time,status)~X2,data=dat,x=TRUE,y=TRUE)
#' #
#' # compute the apparent estimate of the C-index at a single time point
#' #
#' A1 <- pec::cindex(list("Cox X1"=cox1),
#' formula=Surv(time,status)~X1+X2,
#' data=dat,
#' eval.times=10)
#' #
#' # compute the apparent estimate of the C-index at different time points
#' #
#' ApparrentCindex <- pec::cindex(list("Cox X1"=cox1,
#' "Cox X2"=cox2,
#' "Cox X1+X2"=cox12),
#' formula=Surv(time,status)~X1+X2,
#' data=dat,
#' eval.times=seq(1,15,1))
#' print(ApparrentCindex)
#' plot(ApparrentCindex)
#' #
#' # compute the bootstrap-crossvalidation estimate of
#' # the C-index at different time points
#' #
#' set.seed(142)
#' bcvCindex <- pec::cindex(list("Cox X1"=cox1,
#' "Cox X2"=cox2,
#' "Cox X1+X2"=cox12),
#' formula=Surv(time,status)~X1+X2,
#' data=dat,
#' splitMethod="bootcv",
#' B=5,
#' eval.times=seq(1,15,1))
#' print(bcvCindex)
#' plot(bcvCindex)
#' # for uncensored data the results are the same
#' # as those obtained with the function rcorr.cens from Hmisc
#'
#' set.seed(16)
#' dat <- SimSurv(30)
#' dat$staus=1
#' fit12 <- coxph(Surv(time,status)~X1+X2,data=dat,x=TRUE,y=TRUE)
#' fit1 <- coxph(Surv(time,status)~X1,data=dat,x=TRUE,y=TRUE)
#' fit2 <- coxph(Surv(time,status)~X2,data=dat,x=TRUE,y=TRUE)
#' Cpec <- pec::cindex(list("Cox X1+X2"=fit12,"Cox X1"=fit1,"Cox X2"=fit2),
#' formula=Surv(time,status)~1,
#' data=dat)
#' p1 <- predictSurvProb(fit1,newdata=dat,times=10)
#' p2 <- predictSurvProb(fit2,newdata=dat,times=10)
#' p12 <- predictSurvProb(fit12,newdata=dat,times=10)
#' if (requireNamespace("Hmisc",quietly=TRUE)){
#' library(Hmisc)
#' harrelC1 <- rcorr.cens(p1,with(dat,Surv(time,status)))
#' harrelC2 <- rcorr.cens(p2,with(dat,Surv(time,status)))
#' harrelC12 <- rcorr.cens(p12,with(dat,Surv(time,status)))
#' harrelC1[["C Index"]]==Cpec$AppCindex[["Cox.X1"]]
#' harrelC2[["C Index"]]==Cpec$AppCindex[["Cox.X2"]]
#' harrelC12[["C Index"]]==Cpec$AppCindex[["Cox.X1.X2"]]
#' }
#' #
#' # competing risks
#' #
#' library(riskRegression)
#' library(prodlim)
#' set.seed(30)
#' dcr.learn <- SimCompRisk(30)
#' dcr.val <- SimCompRisk(30)
#' pec::cindex(CSC(Hist(time,event)~X1+X2,data=dcr.learn),data=dcr.val)
#' fit <- CSC(Hist(time,event)~X1+X2,data=dcr.learn)
#' cif <- predictRisk(fit,newdata=dcr.val,times=3,cause=1)
#' pec::cindex(list(fit),data=dcr.val,times=3)
#' @export
# {{{ header cindex.list
cindex <- function(object,
formula,
data,
eval.times,
pred.times,
cause,
lyl=FALSE,
cens.model="marginal",
ipcw.refit=FALSE,
ipcw.args=NULL,
ipcw.limit,
tiedPredictionsIn=TRUE,
tiedOutcomeIn=TRUE,
tiedMatchIn=TRUE,
splitMethod="noPlan",
B,
M,
model.args=NULL,
model.parms=NULL,
keep.models=FALSE,
keep.residuals=FALSE,
keep.pvalues=FALSE,
keep.weights=FALSE,
keep.index=FALSE,
keep.matrix=FALSE,
multiSplitTest=FALSE,
testTimes,
confInt=FALSE,
confLevel=0.95,
verbose=TRUE,
savePath=NULL,
slaveseed=NULL,
na.action=na.fail,
...){
# }}}
# {{{ checking integrity some arguments
theCall=match.call()
if (match("replan",names(theCall),nomatch=FALSE))
stop("Argument name 'replan' has been replaced by 'splitMethod'.")
if (keep.residuals && missing(testTimes))
stop("To keep.residuals please specify testTimes.")
if (missing(splitMethod) && multiSplitTest==TRUE){
stop("Need data splitting to compute van de Wiel's test")
}
if (missing(M) && multiSplitTest) M <- NA
stopifnot(as.numeric(tiedPredictionsIn) %in% c(0,1))
stopifnot(as.numeric(tiedOutcomeIn) %in% c(0,1))
stopifnot(as.numeric(tiedMatchIn) %in% c(0,1))
# }}}
# {{{ check and convert object
if (!(inherits(x = object,what = "list"))) {
object <- list(object)
}
# }}}
# {{{ formula
if (missing(formula)){
if (length(grep("~",as.character(object[[1]]$call$formula)))==0){
stop(paste("Argument formula is missing and first model has no usable formula:",as.character(object[[1]]$call$formula)))
} else{
ftry <- try(formula <- eval(object[[1]]$call$formula),silent=TRUE)
if (inherits(x=ftry,what="try-error") || !inherits(x = formula,what = "formula"))
stop("Argument formula is missing and first model has no usable formula.")
else if (verbose)
warning("Formula missing. Using formula from first model")
}
}
formula.names <- try(all.names(formula),silent=TRUE)
if (!(formula.names[1]=="~")
||
(match("$",formula.names,nomatch=0)+match("[",formula.names,nomatch=0)>0)){
stop("Invalid specification of formula. Perhaps forgotten right hand side?\nNote that any subsetting, ie data$var or data[,\"var\"], is invalid for this function.")
}
else{
if (!(formula.names[2] %in% c("Surv","Hist")))
survp <- FALSE
else
survp <- TRUE
}
# }}}
# {{{ data
if (missing(data)){
if (match("call",names(object[[1]]),nomatch=0)==0||is.null(object[[1]]$call$data)){
stop("Data missing and cannot borrow data from the first object :(")
}
data <- eval(object[[1]]$call$data)
if (!inherits(x = data,what = "data.frame"))
stop("Argument data is missing.")
else
if (verbose)
warning("Argument data is missing. I use the data from the call to the first model instead.")
}
# }}}
# {{{ censoring model
cens.model <- match.arg(cens.model,c("cox","marginal","nonpar","aalen","none"))
# }}}
# {{{ response
histformula <- formula
if (histformula[[2]][[1]]==as.name("Surv")){
histformula[[2]][[1]] <- as.name("Hist")
}
m <- model.frame(histformula,data,na.action=na.action)
response <- model.response(m)
if (inherits(x = response,what = "Surv")){
attr(response,"model") <- "survival"
attr(response,"cens.type") <- "rightCensored"
model.type <- "survival"
}
censType <- attr(response,"cens.type")
model.type <- attr(response,"model")
if (model.type=="competing.risks"){
if (lyl==TRUE)
predictHandlerFun <- "predictLifeYearsLost"
else
predictHandlerFun <- "predictEventProb"
if (missing(cause))
cause <- attr(response,"state")[1]
}
else{
if (survp==FALSE && NCOL(response)!=1) stop("Response must be one-dimensional.")
if (survp==TRUE && NCOL(response)!=2) stop("Survival response must have two columns: time and status.")
predictHandlerFun <- "predictSurvProb"
}
if (model.type=="competing.risks")
if (verbose==TRUE) message("Cindex for competing risks")
# }}}
# {{{ prediction models
NF <- length(object)
if (is.null(names(object))){
names(object) <- sapply(object,function(o)class(o)[1])
names(object) <- make.names(names(object),unique=TRUE)
}
else{ # fix missing names
if (any(names(object)=="")){
names(object)[(names(object)=="")] <- sapply(object[(names(object)=="")],function(o)class(o)[1])
names(object) <- make.names(names(object),unique=TRUE)
}else{
# leave names as they were given
}
}
# }}}
# {{{ sort the data
if (survp){
neworder <- order(response[,"time"],-response[,"status"])
if (model.type=="competing.risks"){
event <- prodlim::getEvent(response,mode="character")
event <- event[neworder]
}
response <- response[neworder,,drop=FALSE]
Y <- response[,"time"]
if (censType=="uncensored"){
status <- rep(1,length(Y))
cens.model <- "none"
}
else{
status <- response[,"status"]
}
}
else{
cens.model <- "none"
neworder <- order(response)
Y <- response[neworder]
status <- rep(1,length(Y))
}
## for competing risks find the cause of interest.
if (model.type=="competing.risks"){
availableCauses <- unique(event)
if (!match(cause, availableCauses,nomatch=FALSE))
stop("Cause ",cause," is not among the available causes: ",paste(availableCauses,collapse=", "))
event <- event==cause
}
else{
event <- NULL
}
data <- data[neworder,]
unique.Y <- unique(Y)
N <- length(Y)
NU <- length(unique.Y)
# }}}
# {{{ splitMethod
splitMethod <- resolvesplitMethod(splitMethod=splitMethod,B=B,N=N,M=M)
if (splitMethod$internal.name %in% c("Boot632plus")) stop(".632+ method not implemented for c-index.")
B <- splitMethod$B
ResampleIndex <- splitMethod$index
k <- splitMethod$k
do.resample <- !(is.null(ResampleIndex))
if (keep.matrix==TRUE & !do.resample){
warning("Argument keep.matrix set to FALSE, since no resampling/crossvalidation is requested.")
keep.matrix <- FALSE
}
# }}}
# {{{ define the prediction time(s) and the evaluation time(s)
maxtime <- unique.Y[NU]
if (missing(eval.times)){
## eval.times <- max(Y) ## maybe less efficient
eval.times <- max(Y[status==1])
}
else{
if (any(is.infinite(eval.times))) stop("Infinite eval.times are not allowed.")
tooLate <- sum(eval.times>maxtime)
if (tooLate>0){
if (verbose)
warning(tooLate," eval.times beyond the maximal evaluation time: ",ifelse(maxtime>1,round(maxtime,1),round(maxtime,3)))
## eval.times <- c(eval.times[eval.times<maxtime],maxtime)
}
}
if (missing(pred.times))
## pred.times <- median(unique.Y)
pred.times <- eval.times
## FIXME: if the model changes the risk order over time, then we need to care about pred.times
NT <- length(eval.times)
tindex <- match(Y,unique.Y)
# }}}
# {{{ IPCW (all equal to 1 without censoring)
if((cens.model %in% c("aalen","cox","nonpar"))){
if (all(as.numeric(status)==1) || sum(status)==N){
message("No censored observations: cens.model coerced to \"none\".")
cens.model <- "none"
}
if (length(attr(terms(formula),"factors"))==0){
if (verbose==TRUE)
message("No covariates specified: cens.model coerced to \"marginal\".\n")
cens.model <- "marginal"}
}
if (model.type=="competing.risks"){
iFormula <- as.formula(paste("Surv(itime,istatus)","~",as.character(formula)[[3]]))
iData <- data
iData$itime <- response[,"time"]
iData$istatus <- response[,"status"]
weight.i <- ipcw(formula=iFormula,data=iData,method=cens.model,times=NULL,subjectTimes=Y,subjectTimesLag=1,what="IPCW.subjectTimes")$IPCW.subjectTimes
weight.j <- ipcw(formula=iFormula,data=iData,method=cens.model,times=unique.Y,subjectTimes=NULL,subjectTimesLag=0,what="IPCW.times")$IPCW.times
ipcw.call <- NULL
}
else{
# weights for T_i<=T_j
# FIXED: the correct weights are G(T_i|X_j) and G(T_i-|X_i)
weight.i <- ipcw(formula=formula,data=data,method=cens.model,times=NULL,subjectTimes=Y,subjectTimesLag=1,what="IPCW.subjectTimes")$IPCW.subjectTimes
weight.j <- ipcw(formula=formula,data=data,method=cens.model,times=unique.Y,subjectTimes=NULL,subjectTimesLag=0,what="IPCW.times")$IPCW.times
}
if (ipcw.refit==TRUE)
stop("pec: internal refitting of censoring distribution not (not yet) supported for competing risks")
## if (ipcw.refit==TRUE && splitMethod$internal.name %in% c("Boot632plus","BootCv","Boot632"))
## ipcw.call <- list(weight.i=list(formula=formula,data=data,method=cens.model,times=NULL,subjectTimes=Y,subjectTimesLag=1,what="IPCW.subjectTimes"),
## weight.j=list(formula=formula,data=data,method=cens.model,times=unique.Y,subjectTimes=NULL,subjectTimesLag=0,what="IPCW.times"))
## else
ipcw.call <- NULL
## print(weight.j)
# truncate the weights
if (!missing(ipcw.limit) && ipcw.limit!=0){
pfit <- prodlim::prodlim(update(formula,".~1"),data=data)
limit.i <- 1/(1+c(0,cumsum(pfit$n.lost))[1+prodlim::sindex(jump.times=pfit$time,eval.times=Y-min(diff(Y))/2)])
limit.times <- 1/(1+c(0,cumsum(pfit$n.lost))[1+prodlim::sindex(jump.times=pfit$time,eval.times=unique.Y)])
if (ipcw.limit<1 && ipcw.limit>0){
limit.i <- pmax(ipcw.limit,limit.i)
limit.times <- pmax(ipcw.limit,limit.times)
}
weight.i <- pmax(weight.i,limit.i)
if (is.null(dim(weight.j))){
weight.j <- pmax(weight.j,limit.times)
}
else{
weight.j <- t(apply(weight.j,1,function(wj){
pmax(limit.times,wj)
}))
}
}
weights <- list(weight.i=weight.i,weight.j=weight.j)
# }}}
# {{{ checking the models for compatibility with resampling
if (do.resample){
cm <- checkModels(object=object,model.args=model.args,model.parms=model.parms,splitMethod=splitMethod$internal.name)
model.args <- cm$model.args
model.parms <- cm$model.parms
}
# }}}
# {{{ -------------------Apparent or test sample cindex----------------------
AppCindexList <- lapply(1:NF,function(f){
fit <- object[[f]]
extraArgs <- model.args[[f]]
if (model.type=="competing.risks"){
pred <- do.call(predictHandlerFun,c(list(object=fit,newdata=data,times=pred.times,cause=cause),extraArgs))
if ((inherits(x = fit,what = "prodlim")||inherits(x = fit,what = "survfit")) && is.null(dim(pred)) && length(pred)==length(pred.times))
pred <- rep(pred,N)
if (inherits(x = fit,what = "matrix")||inherits(x = fit,what = "numeric")) pred <- pred[neworder,]
if (length(pred.times)==1 && length(pred.times)<length(eval.times))
pred <- rep(pred,length(eval.times))
if (length(pred)!=N*NT) stop(paste0("Prediction of model ",names(object)[f]," has wrong dimension: ",NROW(pred)," rows and ",NCOL(pred), " columns. Should have ",N, "rows and ",NT," columns."))
## if (any(is.na(pred))) stop(paste0("Missing values in prediction of model: ", names(object)[f]))
AppCindexResult <- .C("ccr",
cindex=double(NT),
concA=double(NT),
pairsA=double(NT),
concB=double(NT),
pairsB=double(NT),
as.integer(tindex),
as.double(Y),
as.integer(status),
as.integer(event),
as.double(eval.times),
as.double(weight.i),
as.double(weight.j),
as.double(pred),
as.integer(N),
as.integer(NT),
as.integer(tiedPredictionsIn),
as.integer(tiedOutcomeIn),
as.integer(tiedMatchIn),
as.integer(!is.null(dim(weight.j))),
NAOK=TRUE,
PACKAGE="pec")
AppCindex <- AppCindexResult$cindex
AppPairsA <- AppCindexResult$pairsA
AppConcordantA <- AppCindexResult$concA
AppPairsB <- AppCindexResult$pairsB
AppConcordantB <- AppCindexResult$concB
list(AppCindex=AppCindex,
AppPairs=list(A=AppPairsA,B=AppPairsB),
AppConcordant=list(A=AppConcordantA,B=AppConcordantB))
}
else{
pred <- do.call(predictHandlerFun,c(list(object=fit,newdata=data,times=pred.times),extraArgs))
if ((inherits(x = fit,what = "prodlim")||inherits(x = fit,what = "survfit")) && is.null(dim(pred)) && length(pred)==length(pred.times))
pred <- rep(pred,N)
if (inherits(x = fit,what = "matrix")||inherits(x = fit,what = "numeric")) pred <- pred[neworder,]
if (length(pred.times)==1 && length(pred.times)<length(eval.times))
pred <- rep(pred,length(eval.times))
if (length(pred)!=N*NT) stop(paste0("Prediction of model ",names(object)[f]," has wrong dimension: ",NROW(pred)," rows and ",NCOL(pred), " columns. Should have ",N, "rows and ",NT," columns."))
## if (any(is.na(pred))) stop(paste0("Missing values in prediction of model: ", names(object)[f]))
AppCindexResult <- .C("cindexSRC",cindex=double(NT),conc=double(NT),pairs=double(NT),as.integer(tindex),as.double(Y),as.integer(status),as.double(eval.times),as.double(weight.i),as.double(weight.j),as.double(pred),as.integer(N),as.integer(NT),as.integer(tiedPredictionsIn),as.integer(tiedOutcomeIn),as.integer(tiedMatchIn),as.integer(!is.null(dim(weight.j))),NAOK=TRUE,PACKAGE="pec")
AppCindex <- AppCindexResult$cindex
AppPairs <- AppCindexResult$pairs
AppConcordant <- AppCindexResult$conc
list(AppCindex=AppCindex,
AppPairs=AppPairs,
AppConcordant=AppConcordant)
}
})
AppCindex <- lapply(AppCindexList,function(x){
x$AppCindex
})
if (predictHandlerFun=="predictSurvProb"){
AppPairs <- lapply(AppCindexList,function(x){
2*x$AppPairs
})
AppConcordant <- lapply(AppCindexList,function(x){
2*x$AppConcordant
})
}else{
AppPairs <- lapply(AppCindexList,function(x){
x$AppPairs
})
AppConcordant <- lapply(AppCindexList,function(x){
x$AppConcordant
})
}
names(AppCindex) <- names(object)
names(AppPairs) <- names(object)
names(AppConcordant) <- names(object)
# }}}
# {{{--------------k-fold and leave-one-out CrossValidation-----------------------
if (splitMethod$internal.name %in% c("crossval","loocv")){
kCV <- CindexKFoldCrossValidation(object=object,
data=data,
Y=Y,
status=status,
event=event,
tindex=tindex,
eval.times=eval.times,
pred.times=pred.times,
cause=cause,
weights=weights,
ipcw.refit=ipcw.refit,
ipcw.call=ipcw.call,
tiedPredictionsIn=tiedPredictionsIn,
tiedOutcomeIn=tiedOutcomeIn,
tiedMatchIn=tiedMatchIn,
splitMethod=splitMethod,
multiSplitTest=multiSplitTest,
keepResiduals=keep.residuals,
testTimes=testTimes,
confInt=confInt,
confLevel=confLevel,
getFromModel=model.parms,
giveToModel=model.args,
predictHandlerFun=predictHandlerFun,
keepMatrix=keep.matrix,
verbose=verbose,
savePath=savePath,
slaveseed=slaveseed)
CrossValErr <- kCV$CrossValErr
if (keep.matrix && B>1)
CrossValErrMat <- kCV$CrossValErrMat
}
# }}}
# {{{ ----------------------BootstrapCrossValidation----------------------
if (splitMethod$internal.name %in% c("Boot632plus","BootCv","Boot632")){
if (missing(testTimes)){
testTimes <- NULL
}
BootCv <- CindexBootstrapCrossValidation(object=object,data=data,Y=Y,status=status,event=event,eval.times=eval.times,pred.times=pred.times,cause=cause,weights=weights,ipcw.refit=ipcw.refit,ipcw.call=ipcw.call,splitMethod=splitMethod,multiSplitTest=multiSplitTest,testTimes=testTimes,confInt=confInt,confLevel=confLevel,getFromModel=model.parms,giveToModel=model.args,predictHandlerFun=predictHandlerFun,tiedPredictionsIn=tiedPredictionsIn,tiedOutcomeIn=tiedOutcomeIn,tiedMatchIn=tiedMatchIn,keepMatrix=keep.matrix,keepResiduals=keep.residuals,verbose=verbose,savePath=savePath,slaveseed=slaveseed)
BootstrapCrossValCindex <- BootCv$BootstrapCrossValCindex
Residuals <- BootCv$Residuals
names(BootstrapCrossValCindex) <- names(object)
if (multiSplitTest==TRUE){
comparisons <- allComparisons(names(object))
multiSplitTest <- list(B=B,M=M,N=N,testTimes=testTimes)
multiSplitTest$Comparisons <- lapply(1:length(comparisons),function(cc){
if (length(testTimes)>0){
allPairwisePvaluesTimes <- do.call("rbind",lapply(BootCv$testedResid,function(b){
b$pValue[[cc]]}))
out <- list(pValueTimes=apply(allPairwisePvaluesTimes,2,median))
if (keep.pvalues==TRUE){
out$allPairwisePvaluesTimes <- allPairwisePvaluesTimes
}
}
else out <- NULL
## if (keep.pvalues==TRUE){
## out$allPairwisePvaluesIBS <- allPairwisePvaluesIBS}
out
})
names(multiSplitTest$Comparisons) <- names(comparisons)
class(multiSplitTest) <- "multiSplitTest"
}
if (keep.matrix==TRUE){
BootstrapCrossValCindexMat <- BootCv$BootstrapCrossValCindexMat
names(BootstrapCrossValCindex) <- names(object)
}
}
# }}}
# {{{ Bootstrap .632
if (splitMethod$internal.name=="Boot632"){
B632Cindex <- lapply(1:NF,function(f){
.368 * AppCindex[[f]] + .632 * BootstrapCrossValCindex[[f]]
})
names(B632Cindex) <- names(object)
}
# }}}
# {{{ prepare output
out <- switch(splitMethod$internal.name,
"noPlan"=list("AppCindex"=AppCindex,
"Pairs"=AppPairs,
"Concordant"=AppConcordant),
"Boot632"=list("AppCindex"=AppCindex,
## "Pairs"=AppPairs,
## "Concordant"=AppConcordant,
"BootCvCindex"= BootstrapCrossValCindex,
"Boot632Cindex"=B632Cindex),
"BootCv"=list("AppCindex"=AppCindex,
## "Pairs"=AppPairs,
## "Concordant"=AppConcordant,
"BootCvCindex"=BootstrapCrossValCindex
## "BootCvConcordant"=BootCvConcordant,
## "BootCvPairs"=BootCvPairs
))
observed.maxtime <- sapply(out,function(x){
lapply(x,function(y){
eval.times[length(y)-sum(is.na(y))]
})
})
minmaxtime <- min(unlist(observed.maxtime))
if (multiSplitTest==TRUE){
out <- c(out,list(multiSplitTest=multiSplitTest))
}
if (keep.residuals==TRUE){
out <- c(out,list(Residuals=Residuals))
}
if (keep.matrix==TRUE && splitMethod$internal.name!="noPlan"){
if (splitMethod$internal.name %in% c("crossval","loocv")){
if (B>1)
out <- c(out,list("BootstrapCrossValCindexMat"=BootstrapCrossValCindexMat))
}
else{
if (splitMethod$internal.name!="noinf")
out <- c(out,list("BootstrapCrossValCindexMat"=BootstrapCrossValCindexMat))
}
}
if (!is.null(model.parms)) out <- c(out,list("ModelParameters"=BootCv$ModelParameters))
if (!keep.index) splitMethod$index <- NULL
if(keep.models==TRUE){
outmodels <- object
} else{
outmodels <- names(object)
names(outmodels) <- names(object)
}
out <- c(out,list(call=theCall,
time=eval.times,
pred.time=pred.times,
response=model.response(m),
models=outmodels,
splitMethod=splitMethod,
weights=weights,
cens.model=cens.model,
minmaxtime=minmaxtime,
maxtime=maxtime))
## if (verbose==TRUE && do.resample==TRUE) cat("\n")
# }}}
class(out) <- "Cindex"
out
}
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Defines functions cindex
Documented in cindex
#' Concordance index for right censored survival time data
#'
#' In survival analysis, a pair of patients is called concordant if the risk of
#' the event predicted by a model is lower for the patient who experiences the
#' event at a later timepoint. The concordance probability (C-index) is the
#' frequency of concordant pairs among all pairs of subjects. It can be used to
#' measure and compare the discriminative power of a risk prediction models.
#' The function provides an inverse of the probability of censoring weigthed
#' estimate of the concordance probability to adjust for right censoring.
#' Cross-validation based on bootstrap resampling or bootstrap subsampling can
#' be applied to assess and compare the discriminative power of various
#' regression modelling strategies on the same set of data.
#'
#' Pairs with identical observed times, where one is uncensored and one is
#' censored, are always considered usuable (independent of the value of
#' \code{tiedOutcomeIn}), as it can be assumed that the event occurs at a later
#' timepoint for the censored observation.
#'
#' For uncensored response the result equals the one obtained with the
#' functions \code{rcorr.cens} and \code{rcorrcens} from the \code{Hmisc}
#' package (see examples).
#'
#' @aliases cindex
#' @param object A named list of prediction models, where allowed entries are
#' (1) R-objects for which a \link{predictSurvProb} method exists (see
#' details), (2) a \code{call} that evaluates to such an R-object (see
#' examples), (3) a matrix with predicted probabilities having as many rows as
#' \code{data} and as many columns as \code{times}. For cross-validation all
#' objects in this list must include their \code{call}.
#' @param formula A survival formula. The left hand side is used to finde the
#' status response variable in \code{data}. For right censored data, the right
#' hand side of the formula is used to specify conditional censoring models.
#' For example, set \code{Surv(time,status)~x1+x2} and \code{cens.model="cox"}.
#' Then the weights are based on a Cox regression model for the censoring times
#' with predictors x1 and x2. Note that the usual coding is assumed:
#' \code{status=0} for censored times and that each variable name that appears
#' in \code{formula} must be the column name in \code{data}. If there are no
#' covariates, i.e. \code{formula=Surv(time,status)~1} the \code{cens.model} is
#' coerced to \code{"marginal"} and the Kaplan-Meier estimator for the
#' censoring times is used to calculate the weights. If \code{formula} is
#' \code{missing}, try to extract a formula from the first element in object.
#' @param data A data frame in which to validate the prediction models and to
#' fit the censoring model. If \code{data} is missing, try to extract a data
#' set from the first element in object.
#' @param eval.times A vector of timepoints for evaluating the discriminative
#' ability. At each timepoint the c-index is computed using only those pairs
#' where one of the event times is known to be earlier than this timepoint. If
#' \code{eval.times} is \code{missing} then the largest
#' uncensored event time is used.
#' @param pred.times A vector of timepoints for evaluating the prediction
#' models. This should either be exactly one timepoint used for all
#' \code{eval.times}, or be as long as \code{eval.times}, in which case the
#' predicted order of risk for the jth entry of \code{eval.times} is based on
#' the jth entry of \code{pred.times} corresponding
#' @param cause For competing risks, the event of interest. Defaults to the
#' first state of the response, which is obtained by evaluating the left hand
#' side of \code{formula} in \code{data}.
#' @param lyl If \code{TRUE} rank subjects accoring to predicted
#' life-years-lost (See Andersen due to this cause instead of predicted risk.
#' @param cens.model Method for estimating inverse probability of censoring
#' weigths:
#'
#' \code{cox}: A semi-parametric Cox proportional hazard model is fitted to the
#' censoring times
#'
#' \code{marginal}: The Kaplan-Meier estimator for the censoring times
#'
#' \code{nonpar}: Nonparametric extension of the Kaplan-Meier for the censoring
#' times using symmetric nearest neighborhoods -- available for arbitrary many
#' strata variables on the right hand side of argument \code{formula} but at
#' most one continuous variable. See the documentation of the functions
#' \code{prodlim} and \code{neighborhood} from the prodlim package.
#'
#' \code{aalen}: The nonparametric Aalen additive model fitted to the censoring
#' times. Requires the timereg package maintained by Thomas Scheike.
#' @param ipcw.refit If \code{TRUE} the inverse probability of censoring
#' weigths are estimated separately in each training set during
#' cross-validation.
#' @param ipcw.args List of arguments passed to function specified by argument \code{cens.model}.
#' @param ipcw.limit Value between 0 and 1 (but no equal to 0!) used to cut for
#' small weights in order to stabilize the estimate at late times were few
#' individuals are observed.
#' @param tiedPredictionsIn If \code{FALSE} pairs with identical predictions
#' are excluded, unless also the event times are identical and uncensored and
#' \code{tiedMatchIn} is set to \code{TRUE}.
#' @param tiedOutcomeIn If \code{TRUE} pairs with identical and uncensored
#' event times are excluded, unless also the predictions are identical and
#' \code{tiedMatchIn} is set to \code{TRUE}.
#' @param tiedMatchIn If \code{TRUE} then pairs with identical predictions and
#' identical and uncensored event times are counted as concordant pairs.
#' @param splitMethod Defines the internal validation design:
#'
#' \code{none/noPlan}: Assess the models in the give \code{data}, usually
#' either in the same data where they are fitted, or in independent test data.
#'
#' \code{BootCv}: Bootstrap cross validation. The prediction models are trained
#' on \code{B} bootstrap samples, that are either drawn with replacement of the
#' same size as the original data or without replacement from \code{data} of
#' the size \code{M}. The models are assessed in the observations that are NOT
#' in the bootstrap sample.
#'
#' \code{Boot632}: Linear combination of AppCindex and OutOfBagCindex using the
#' constant weight .632.
#'
#' @param B Number of bootstrap samples. The default depends on argument
#' \code{splitMethod}. When \code{splitMethod} in c("BootCv","Boot632") the
#' default is 100. For \code{splitMethod="none"} \code{B} is the number of
#' bootstrap simulations e.g. to obtain bootstrap confidence limits -- default
#' is 0.
#' @param M The size of the bootstrap samples for resampling without
#' replacement. Ignored for resampling with replacement.
#' @param model.args List of extra arguments that can be passed to the
#' \code{predictSurvProb} methods. The list must have an entry for each entry
#' in \code{object}.
#' @param model.parms Experimental. List of with exactly one entry for each
#' entry in \code{object}. Each entry names parts of the value of the fitted
#' models that should be extracted and added to the value.
#' @param keep.index Logical. If \code{FALSE} remove the bootstrap or
#' cross-validation index from the output list which otherwise is included in
#' the method part of the output list.
#' @param keep.matrix Logical. If \code{TRUE} add all \code{B} prediction error
#' curves from bootstrapping or cross-validation to the output.
#' @param keep.models Logical. If \code{TRUE} keep the models in object. Since
#' fitted models can be large objects the default is \code{FALSE}.
#' @param keep.residuals Experimental.
#' @param keep.pvalues Experimental.
#' @param keep.weights Experimental.
#' @param multiSplitTest Experimental.
#' @param testTimes A vector of time points for testing differences between
#' models in the time-point specific Brier scores.
#' @param confInt Experimental.
#' @param confLevel Experimental.
#' @param verbose if \code{TRUE} report details of the progress, e.g. count the
#' steps in cross-validation.
#' @param savePath Place in your filesystem (directory) where training models
#' fitted during cross-validation are saved. If \code{missing} training models
#' are not saved.
#' @param slaveseed Vector of seeds, as long as \code{B}, to be given to the
#' slaves in parallel computing.
#' @param na.action Passed immediately to model.frame. Defaults to na.fail. If
#' set otherwise most prediction models will not work.
#' @param ... Not used.
#' @return Estimates of the C-index.
#' @author Thomas A Gerds \email{tag@@biostat.ku.dk}
#' @references
#'
#' TA Gerds, MW Kattan, M Schumacher, and C Yu. Estimating a time-dependent
#' concordance index for survival prediction models with covariate dependent
#' censoring. Statistics in Medicine, Ahead of print:to appear, 2013. DOI =
#' 10.1002/sim.5681
#'
#' Wolbers, M and Koller, MT and Witteman, JCM and Gerds, TA (2013) Concordance
#' for prognostic models with competing risks Research report 13/3. Department
#' of Biostatistics, University of Copenhagen
#'
#' Andersen, PK (2012) A note on the decomposition of number of life years lost
#' according to causes of death Research report 12/2. Department of
#' Biostatistics, University of Copenhagen
#'
#' Paul Blanche, Michael W Kattan, and Thomas A Gerds. The c-index is not
#' proper for the evaluation of-year predicted risks. Biostatistics, 20(2):
#' 347--357, 2018.
#' @keywords survival
#' @examples
#'
#' # simulate data based on Weibull regression
#' library(prodlim)
#' set.seed(13)
#' dat <- SimSurv(100)
#' # fit three different Cox models and a random survival forest
#' # note: low number of trees for the purpose of illustration
#' library(survival)
#' cox12 <- coxph(Surv(time,status)~X1+X2,data=dat,x=TRUE,y=TRUE)
#' cox1 <- coxph(Surv(time,status)~X1,data=dat,x=TRUE,y=TRUE)
#' cox2 <- coxph(Surv(time,status)~X2,data=dat,x=TRUE,y=TRUE)
#' #
#' # compute the apparent estimate of the C-index at a single time point
#' #
#' A1 <- pec::cindex(list("Cox X1"=cox1),
#' formula=Surv(time,status)~X1+X2,
#' data=dat,
#' eval.times=10)
#' #
#' # compute the apparent estimate of the C-index at different time points
#' #
#' ApparrentCindex <- pec::cindex(list("Cox X1"=cox1,
#' "Cox X2"=cox2,
#' "Cox X1+X2"=cox12),
#' formula=Surv(time,status)~X1+X2,
#' data=dat,
#' eval.times=seq(1,15,1))
#' print(ApparrentCindex)
#' plot(ApparrentCindex)
#' #
#' # compute the bootstrap-crossvalidation estimate of
#' # the C-index at different time points
#' #
#' set.seed(142)
#' bcvCindex <- pec::cindex(list("Cox X1"=cox1,
#' "Cox X2"=cox2,
#' "Cox X1+X2"=cox12),
#' formula=Surv(time,status)~X1+X2,
#' data=dat,
#' splitMethod="bootcv",
#' B=5,
#' eval.times=seq(1,15,1))
#' print(bcvCindex)
#' plot(bcvCindex)
#' # for uncensored data the results are the same
#' # as those obtained with the function rcorr.cens from Hmisc
#'
#' set.seed(16)
#' dat <- SimSurv(30)
#' dat$staus=1
#' fit12 <- coxph(Surv(time,status)~X1+X2,data=dat,x=TRUE,y=TRUE)
#' fit1 <- coxph(Surv(time,status)~X1,data=dat,x=TRUE,y=TRUE)
#' fit2 <- coxph(Surv(time,status)~X2,data=dat,x=TRUE,y=TRUE)
#' Cpec <- pec::cindex(list("Cox X1+X2"=fit12,"Cox X1"=fit1,"Cox X2"=fit2),
#' formula=Surv(time,status)~1,
#' data=dat)
#' p1 <- predictSurvProb(fit1,newdata=dat,times=10)
#' p2 <- predictSurvProb(fit2,newdata=dat,times=10)
#' p12 <- predictSurvProb(fit12,newdata=dat,times=10)
#' if (requireNamespace("Hmisc",quietly=TRUE)){
#' library(Hmisc)
#' harrelC1 <- rcorr.cens(p1,with(dat,Surv(time,status)))
#' harrelC2 <- rcorr.cens(p2,with(dat,Surv(time,status)))
#' harrelC12 <- rcorr.cens(p12,with(dat,Surv(time,status)))
#' harrelC1[["C Index"]]==Cpec$AppCindex[["Cox.X1"]]
#' harrelC2[["C Index"]]==Cpec$AppCindex[["Cox.X2"]]
#' harrelC12[["C Index"]]==Cpec$AppCindex[["Cox.X1.X2"]]
#' }
#' #
#' # competing risks
#' #
#' library(riskRegression)
#' library(prodlim)
#' set.seed(30)
#' dcr.learn <- SimCompRisk(30)
#' dcr.val <- SimCompRisk(30)
#' pec::cindex(CSC(Hist(time,event)~X1+X2,data=dcr.learn),data=dcr.val)
#' fit <- CSC(Hist(time,event)~X1+X2,data=dcr.learn)
#' cif <- predictRisk(fit,newdata=dcr.val,times=3,cause=1)
#' pec::cindex(list(fit),data=dcr.val,times=3)
#' @export
# {{{ header cindex.list
cindex <- function(object,
formula,
data,
eval.times,
pred.times,
cause,
lyl=FALSE,
cens.model="marginal",
ipcw.refit=FALSE,
ipcw.args=NULL,
ipcw.limit,
tiedPredictionsIn=TRUE,
tiedOutcomeIn=TRUE,
tiedMatchIn=TRUE,
splitMethod="noPlan",
B,
M,
model.args=NULL,
model.parms=NULL,
keep.models=FALSE,
keep.residuals=FALSE,
keep.pvalues=FALSE,
keep.weights=FALSE,
keep.index=FALSE,
keep.matrix=FALSE,
multiSplitTest=FALSE,
testTimes,
confInt=FALSE,
confLevel=0.95,
verbose=TRUE,
savePath=NULL,
slaveseed=NULL,
na.action=na.fail,
...){
# }}}
# {{{ checking integrity some arguments
theCall=match.call()
if (match("replan",names(theCall),nomatch=FALSE))
stop("Argument name 'replan' has been replaced by 'splitMethod'.")
if (keep.residuals && missing(testTimes))
stop("To keep.residuals please specify testTimes.")
if (missing(splitMethod) && multiSplitTest==TRUE){
stop("Need data splitting to compute van de Wiel's test")
}
if (missing(M) && multiSplitTest) M <- NA
stopifnot(as.numeric(tiedPredictionsIn) %in% c(0,1))
stopifnot(as.numeric(tiedOutcomeIn) %in% c(0,1))
stopifnot(as.numeric(tiedMatchIn) %in% c(0,1))
# }}}
# {{{ check and convert object
if (!(inherits(x = object,what = "list"))) {
object <- list(object)
}
# }}}
# {{{ formula
if (missing(formula)){
if (length(grep("~",as.character(object[[1]]$call$formula)))==0){
stop(paste("Argument formula is missing and first model has no usable formula:",as.character(object[[1]]$call$formula)))
} else{
ftry <- try(formula <- eval(object[[1]]$call$formula),silent=TRUE)
if (inherits(x=ftry,what="try-error") || !inherits(x = formula,what = "formula"))
stop("Argument formula is missing and first model has no usable formula.")
else if (verbose)
warning("Formula missing. Using formula from first model")
}
}
formula.names <- try(all.names(formula),silent=TRUE)
if (!(formula.names[1]=="~")
||
(match("$",formula.names,nomatch=0)+match("[",formula.names,nomatch=0)>0)){
stop("Invalid specification of formula. Perhaps forgotten right hand side?\nNote that any subsetting, ie data$var or data[,\"var\"], is invalid for this function.")
}
else{
if (!(formula.names[2] %in% c("Surv","Hist")))
survp <- FALSE
else
survp <- TRUE
}
# }}}
# {{{ data
if (missing(data)){
if (match("call",names(object[[1]]),nomatch=0)==0||is.null(object[[1]]$call$data)){
stop("Data missing and cannot borrow data from the first object :(")
}
data <- eval(object[[1]]$call$data)
if (!inherits(x = data,what = "data.frame"))
stop("Argument data is missing.")
else
if (verbose)
warning("Argument data is missing. I use the data from the call to the first model instead.")
}
# }}}
# {{{ censoring model
cens.model <- match.arg(cens.model,c("cox","marginal","nonpar","aalen","none"))
# }}}
# {{{ response
histformula <- formula
if (histformula[[2]][[1]]==as.name("Surv")){
histformula[[2]][[1]] <- as.name("Hist")
}
m <- model.frame(histformula,data,na.action=na.action)
response <- model.response(m)
if (inherits(x = response,what = "Surv")){
attr(response,"model") <- "survival"
attr(response,"cens.type") <- "rightCensored"
model.type <- "survival"
}
censType <- attr(response,"cens.type")
model.type <- attr(response,"model")
if (model.type=="competing.risks"){
if (lyl==TRUE)
predictHandlerFun <- "predictLifeYearsLost"
else
predictHandlerFun <- "predictEventProb"
if (missing(cause))
cause <- attr(response,"state")[1]
}
else{
if (survp==FALSE && NCOL(response)!=1) stop("Response must be one-dimensional.")
if (survp==TRUE && NCOL(response)!=2) stop("Survival response must have two columns: time and status.")
predictHandlerFun <- "predictSurvProb"
}
if (model.type=="competing.risks")
if (verbose==TRUE) message("Cindex for competing risks")
# }}}
# {{{ prediction models
NF <- length(object)
if (is.null(names(object))){
names(object) <- sapply(object,function(o)class(o)[1])
names(object) <- make.names(names(object),unique=TRUE)
}
else{ # fix missing names
if (any(names(object)=="")){
names(object)[(names(object)=="")] <- sapply(object[(names(object)=="")],function(o)class(o)[1])
names(object) <- make.names(names(object),unique=TRUE)
}else{
# leave names as they were given
}
}
# }}}
# {{{ sort the data
if (survp){
neworder <- order(response[,"time"],-response[,"status"])
if (model.type=="competing.risks"){
event <- prodlim::getEvent(response,mode="character")
event <- event[neworder]
}
response <- response[neworder,,drop=FALSE]
Y <- response[,"time"]
if (censType=="uncensored"){
status <- rep(1,length(Y))
cens.model <- "none"
}
else{
status <- response[,"status"]
}
}
else{
cens.model <- "none"
neworder <- order(response)
Y <- response[neworder]
status <- rep(1,length(Y))
}
## for competing risks find the cause of interest.
if (model.type=="competing.risks"){
availableCauses <- unique(event)
if (!match(cause, availableCauses,nomatch=FALSE))
stop("Cause ",cause," is not among the available causes: ",paste(availableCauses,collapse=", "))
event <- event==cause
}
else{
event <- NULL
}
data <- data[neworder,]
unique.Y <- unique(Y)
N <- length(Y)
NU <- length(unique.Y)
# }}}
# {{{ splitMethod
splitMethod <- resolvesplitMethod(splitMethod=splitMethod,B=B,N=N,M=M)
if (splitMethod$internal.name %in% c("Boot632plus")) stop(".632+ method not implemented for c-index.")
B <- splitMethod$B
ResampleIndex <- splitMethod$index
k <- splitMethod$k
do.resample <- !(is.null(ResampleIndex))
if (keep.matrix==TRUE & !do.resample){
warning("Argument keep.matrix set to FALSE, since no resampling/crossvalidation is requested.")
keep.matrix <- FALSE
}
# }}}
# {{{ define the prediction time(s) and the evaluation time(s)
maxtime <- unique.Y[NU]
if (missing(eval.times)){
## eval.times <- max(Y) ## maybe less efficient
eval.times <- max(Y[status==1])
}
else{
if (any(is.infinite(eval.times))) stop("Infinite eval.times are not allowed.")
tooLate <- sum(eval.times>maxtime)
if (tooLate>0){
if (verbose)
warning(tooLate," eval.times beyond the maximal evaluation time: ",ifelse(maxtime>1,round(maxtime,1),round(maxtime,3)))
## eval.times <- c(eval.times[eval.times<maxtime],maxtime)
}
}
if (missing(pred.times))
## pred.times <- median(unique.Y)
pred.times <- eval.times
## FIXME: if the model changes the risk order over time, then we need to care about pred.times
NT <- length(eval.times)
tindex <- match(Y,unique.Y)
# }}}
# {{{ IPCW (all equal to 1 without censoring)
if((cens.model %in% c("aalen","cox","nonpar"))){
if (all(as.numeric(status)==1) || sum(status)==N){
message("No censored observations: cens.model coerced to \"none\".")
cens.model <- "none"
}
if (length(attr(terms(formula),"factors"))==0){
if (verbose==TRUE)
message("No covariates specified: cens.model coerced to \"marginal\".\n")
cens.model <- "marginal"}
}
if (model.type=="competing.risks"){
iFormula <- as.formula(paste("Surv(itime,istatus)","~",as.character(formula)[[3]]))
iData <- data
iData$itime <- response[,"time"]
iData$istatus <- response[,"status"]
weight.i <- ipcw(formula=iFormula,data=iData,method=cens.model,times=NULL,subjectTimes=Y,subjectTimesLag=1,what="IPCW.subjectTimes")$IPCW.subjectTimes
weight.j <- ipcw(formula=iFormula,data=iData,method=cens.model,times=unique.Y,subjectTimes=NULL,subjectTimesLag=0,what="IPCW.times")$IPCW.times
ipcw.call <- NULL
}
else{
# weights for T_i<=T_j
# FIXED: the correct weights are G(T_i|X_j) and G(T_i-|X_i)
weight.i <- ipcw(formula=formula,data=data,method=cens.model,times=NULL,subjectTimes=Y,subjectTimesLag=1,what="IPCW.subjectTimes")$IPCW.subjectTimes
weight.j <- ipcw(formula=formula,data=data,method=cens.model,times=unique.Y,subjectTimes=NULL,subjectTimesLag=0,what="IPCW.times")$IPCW.times
}
if (ipcw.refit==TRUE)
stop("pec: internal refitting of censoring distribution not (not yet) supported for competing risks")
## if (ipcw.refit==TRUE && splitMethod$internal.name %in% c("Boot632plus","BootCv","Boot632"))
## ipcw.call <- list(weight.i=list(formula=formula,data=data,method=cens.model,times=NULL,subjectTimes=Y,subjectTimesLag=1,what="IPCW.subjectTimes"),
## weight.j=list(formula=formula,data=data,method=cens.model,times=unique.Y,subjectTimes=NULL,subjectTimesLag=0,what="IPCW.times"))
## else
ipcw.call <- NULL
## print(weight.j)
# truncate the weights
if (!missing(ipcw.limit) && ipcw.limit!=0){
pfit <- prodlim::prodlim(update(formula,".~1"),data=data)
limit.i <- 1/(1+c(0,cumsum(pfit$n.lost))[1+prodlim::sindex(jump.times=pfit$time,eval.times=Y-min(diff(Y))/2)])
limit.times <- 1/(1+c(0,cumsum(pfit$n.lost))[1+prodlim::sindex(jump.times=pfit$time,eval.times=unique.Y)])
if (ipcw.limit<1 && ipcw.limit>0){
limit.i <- pmax(ipcw.limit,limit.i)
limit.times <- pmax(ipcw.limit,limit.times)
}
weight.i <- pmax(weight.i,limit.i)
if (is.null(dim(weight.j))){
weight.j <- pmax(weight.j,limit.times)
}
else{
weight.j <- t(apply(weight.j,1,function(wj){
pmax(limit.times,wj)
}))
}
}
weights <- list(weight.i=weight.i,weight.j=weight.j)
# }}}
# {{{ checking the models for compatibility with resampling
if (do.resample){
cm <- checkModels(object=object,model.args=model.args,model.parms=model.parms,splitMethod=splitMethod$internal.name)
model.args <- cm$model.args
model.parms <- cm$model.parms
}
# }}}
# {{{ -------------------Apparent or test sample cindex----------------------
AppCindexList <- lapply(1:NF,function(f){
fit <- object[[f]]
extraArgs <- model.args[[f]]
if (model.type=="competing.risks"){
pred <- do.call(predictHandlerFun,c(list(object=fit,newdata=data,times=pred.times,cause=cause),extraArgs))
if ((inherits(x = fit,what = "prodlim")||inherits(x = fit,what = "survfit")) && is.null(dim(pred)) && length(pred)==length(pred.times))
pred <- rep(pred,N)
if (inherits(x = fit,what = "matrix")||inherits(x = fit,what = "numeric")) pred <- pred[neworder,]
if (length(pred.times)==1 && length(pred.times)<length(eval.times))
pred <- rep(pred,length(eval.times))
if (length(pred)!=N*NT) stop(paste0("Prediction of model ",names(object)[f]," has wrong dimension: ",NROW(pred)," rows and ",NCOL(pred), " columns. Should have ",N, "rows and ",NT," columns."))
## if (any(is.na(pred))) stop(paste0("Missing values in prediction of model: ", names(object)[f]))
AppCindexResult <- .C("ccr",
cindex=double(NT),
concA=double(NT),
pairsA=double(NT),
concB=double(NT),
pairsB=double(NT),
as.integer(tindex),
as.double(Y),
as.integer(status),
as.integer(event),
as.double(eval.times),
as.double(weight.i),
as.double(weight.j),
as.double(pred),
as.integer(N),
as.integer(NT),
as.integer(tiedPredictionsIn),
as.integer(tiedOutcomeIn),
as.integer(tiedMatchIn),
as.integer(!is.null(dim(weight.j))),
NAOK=TRUE,
PACKAGE="pec")
AppCindex <- AppCindexResult$cindex
AppPairsA <- AppCindexResult$pairsA
AppConcordantA <- AppCindexResult$concA
AppPairsB <- AppCindexResult$pairsB
AppConcordantB <- AppCindexResult$concB
list(AppCindex=AppCindex,
AppPairs=list(A=AppPairsA,B=AppPairsB),
AppConcordant=list(A=AppConcordantA,B=AppConcordantB))
}
else{
pred <- do.call(predictHandlerFun,c(list(object=fit,newdata=data,times=pred.times),extraArgs))
if ((inherits(x = fit,what = "prodlim")||inherits(x = fit,what = "survfit")) && is.null(dim(pred)) && length(pred)==length(pred.times))
pred <- rep(pred,N)
if (inherits(x = fit,what = "matrix")||inherits(x = fit,what = "numeric")) pred <- pred[neworder,]
if (length(pred.times)==1 && length(pred.times)<length(eval.times))
pred <- rep(pred,length(eval.times))
if (length(pred)!=N*NT) stop(paste0("Prediction of model ",names(object)[f]," has wrong dimension: ",NROW(pred)," rows and ",NCOL(pred), " columns. Should have ",N, "rows and ",NT," columns."))
## if (any(is.na(pred))) stop(paste0("Missing values in prediction of model: ", names(object)[f]))
AppCindexResult <- .C("cindexSRC",cindex=double(NT),conc=double(NT),pairs=double(NT),as.integer(tindex),as.double(Y),as.integer(status),as.double(eval.times),as.double(weight.i),as.double(weight.j),as.double(pred),as.integer(N),as.integer(NT),as.integer(tiedPredictionsIn),as.integer(tiedOutcomeIn),as.integer(tiedMatchIn),as.integer(!is.null(dim(weight.j))),NAOK=TRUE,PACKAGE="pec")
AppCindex <- AppCindexResult$cindex
AppPairs <- AppCindexResult$pairs
AppConcordant <- AppCindexResult$conc
list(AppCindex=AppCindex,
AppPairs=AppPairs,
AppConcordant=AppConcordant)
}
})
AppCindex <- lapply(AppCindexList,function(x){
x$AppCindex
})
if (predictHandlerFun=="predictSurvProb"){
AppPairs <- lapply(AppCindexList,function(x){
2*x$AppPairs
})
AppConcordant <- lapply(AppCindexList,function(x){
2*x$AppConcordant
})
}else{
AppPairs <- lapply(AppCindexList,function(x){
x$AppPairs
})
AppConcordant <- lapply(AppCindexList,function(x){
x$AppConcordant
})
}
names(AppCindex) <- names(object)
names(AppPairs) <- names(object)
names(AppConcordant) <- names(object)
# }}}
# {{{--------------k-fold and leave-one-out CrossValidation-----------------------
if (splitMethod$internal.name %in% c("crossval","loocv")){
kCV <- CindexKFoldCrossValidation(object=object,
data=data,
Y=Y,
status=status,
event=event,
tindex=tindex,
eval.times=eval.times,
pred.times=pred.times,
cause=cause,
weights=weights,
ipcw.refit=ipcw.refit,
ipcw.call=ipcw.call,
tiedPredictionsIn=tiedPredictionsIn,
tiedOutcomeIn=tiedOutcomeIn,
tiedMatchIn=tiedMatchIn,
splitMethod=splitMethod,
multiSplitTest=multiSplitTest,
keepResiduals=keep.residuals,
testTimes=testTimes,
confInt=confInt,
confLevel=confLevel,
getFromModel=model.parms,
giveToModel=model.args,
predictHandlerFun=predictHandlerFun,
keepMatrix=keep.matrix,
verbose=verbose,
savePath=savePath,
slaveseed=slaveseed)
CrossValErr <- kCV$CrossValErr
if (keep.matrix && B>1)
CrossValErrMat <- kCV$CrossValErrMat
}
# }}}
# {{{ ----------------------BootstrapCrossValidation----------------------
if (splitMethod$internal.name %in% c("Boot632plus","BootCv","Boot632")){
if (missing(testTimes)){
testTimes <- NULL
}
BootCv <- CindexBootstrapCrossValidation(object=object,data=data,Y=Y,status=status,event=event,eval.times=eval.times,pred.times=pred.times,cause=cause,weights=weights,ipcw.refit=ipcw.refit,ipcw.call=ipcw.call,splitMethod=splitMethod,multiSplitTest=multiSplitTest,testTimes=testTimes,confInt=confInt,confLevel=confLevel,getFromModel=model.parms,giveToModel=model.args,predictHandlerFun=predictHandlerFun,tiedPredictionsIn=tiedPredictionsIn,tiedOutcomeIn=tiedOutcomeIn,tiedMatchIn=tiedMatchIn,keepMatrix=keep.matrix,keepResiduals=keep.residuals,verbose=verbose,savePath=savePath,slaveseed=slaveseed)
BootstrapCrossValCindex <- BootCv$BootstrapCrossValCindex
Residuals <- BootCv$Residuals
names(BootstrapCrossValCindex) <- names(object)
if (multiSplitTest==TRUE){
comparisons <- allComparisons(names(object))
multiSplitTest <- list(B=B,M=M,N=N,testTimes=testTimes)
multiSplitTest$Comparisons <- lapply(1:length(comparisons),function(cc){
if (length(testTimes)>0){
allPairwisePvaluesTimes <- do.call("rbind",lapply(BootCv$testedResid,function(b){
b$pValue[[cc]]}))
out <- list(pValueTimes=apply(allPairwisePvaluesTimes,2,median))
if (keep.pvalues==TRUE){
out$allPairwisePvaluesTimes <- allPairwisePvaluesTimes
}
}
else out <- NULL
## if (keep.pvalues==TRUE){
## out$allPairwisePvaluesIBS <- allPairwisePvaluesIBS}
out
})
names(multiSplitTest$Comparisons) <- names(comparisons)
class(multiSplitTest) <- "multiSplitTest"
}
if (keep.matrix==TRUE){
BootstrapCrossValCindexMat <- BootCv$BootstrapCrossValCindexMat
names(BootstrapCrossValCindex) <- names(object)
}
}
# }}}
# {{{ Bootstrap .632
if (splitMethod$internal.name=="Boot632"){
B632Cindex <- lapply(1:NF,function(f){
.368 * AppCindex[[f]] + .632 * BootstrapCrossValCindex[[f]]
})
names(B632Cindex) <- names(object)
}
# }}}
# {{{ prepare output
out <- switch(splitMethod$internal.name,
"noPlan"=list("AppCindex"=AppCindex,
"Pairs"=AppPairs,
"Concordant"=AppConcordant),
"Boot632"=list("AppCindex"=AppCindex,
## "Pairs"=AppPairs,
## "Concordant"=AppConcordant,
"BootCvCindex"= BootstrapCrossValCindex,
"Boot632Cindex"=B632Cindex),
"BootCv"=list("AppCindex"=AppCindex,
## "Pairs"=AppPairs,
## "Concordant"=AppConcordant,
"BootCvCindex"=BootstrapCrossValCindex
## "BootCvConcordant"=BootCvConcordant,
## "BootCvPairs"=BootCvPairs
))
observed.maxtime <- sapply(out,function(x){
lapply(x,function(y){
eval.times[length(y)-sum(is.na(y))]
})
})
minmaxtime <- min(unlist(observed.maxtime))
if (multiSplitTest==TRUE){
out <- c(out,list(multiSplitTest=multiSplitTest))
}
if (keep.residuals==TRUE){
out <- c(out,list(Residuals=Residuals))
}
if (keep.matrix==TRUE && splitMethod$internal.name!="noPlan"){
if (splitMethod$internal.name %in% c("crossval","loocv")){
if (B>1)
out <- c(out,list("BootstrapCrossValCindexMat"=BootstrapCrossValCindexMat))
}
else{
if (splitMethod$internal.name!="noinf")
out <- c(out,list("BootstrapCrossValCindexMat"=BootstrapCrossValCindexMat))
}
}
if (!is.null(model.parms)) out <- c(out,list("ModelParameters"=BootCv$ModelParameters))
if (!keep.index) splitMethod$index <- NULL
if(keep.models==TRUE){
outmodels <- object
} else{
outmodels <- names(object)
names(outmodels) <- names(object)
}
out <- c(out,list(call=theCall,
time=eval.times,
pred.time=pred.times,
response=model.response(m),
models=outmodels,
splitMethod=splitMethod,
weights=weights,
cens.model=cens.model,
minmaxtime=minmaxtime,
maxtime=maxtime))
## if (verbose==TRUE && do.resample==TRUE) cat("\n")
# }}}
class(out) <- "Cindex"
out
}
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