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#Resampling optimism of reliability of a Cox survival model
#For predicting survival at a fixed time u, getting grouped K-M estimates
#with avg. of m subjects in a group, or using cutpoints cuts if present,
#e.g. cuts=c(0,.2,.4,.6,.8,1).
#B: # reps method=see predab.resample
#bw=T to incorporate backward stepdown (using fastbw) with params rule,type,sls
#pr=T to print results of each rep
#what="observed" to get optimism in observed (Kaplan-Meier) survival for
#groups by predicted survival
#what="observed-predicted" to get optimism in KM - Cox - more suitable if
#distributions of predicted survival vary greatly withing quantile groups
#defined from original sample's predicted survival
calibrate.cph <- function(fit,method="boot",u,m=150,cuts,B=40,
bw=FALSE,rule="aic",
type="residual",sls=.05,aics=0,
pr=FALSE,what="observed-predicted",tol=1e-12, ...) {
call <- match.call()
#.Options$digits <- 3 14Sep00
oldopt <- options(digits=3)
on.exit(options(oldopt))
unit <- fit$units
if(unit=="") unit <- "Day"
ssum <- fit$surv.summary ##14Nov00
if(!length(ssum)) stop('did not use surv=T for cph( )')
cat("Using Cox survival estimates at ", dimnames(ssum)[[1]][2],
" ", unit,"s\n",sep="")
surv.by.strata <- ssum[2,,1] #2nd time= at u, all strata
xb <- fit$linear.predictors
if(length(stra <- Surv.strata(xb)))
surv.by.strata <- surv.by.strata[stra]
survival <- surv.by.strata^exp(xb)
if(missing(cuts)) {
g <- max(1,floor(length(xb)/m))
cuts <- quantile(c(0,1,survival), seq(0,1,length=g+1),na.rm=TRUE)
}
distance <- function(x,y,fit,iter,u,fit.orig,what="observed",
orig.cuts, ...) {
##Assumes y is matrix with 1st col=time, 2nd=event indicator, 3rd=strata
## This is now invalid for Surv objects. strata info stored in attribute.
if(sum(y[,2])<5)return(NA)
surv.by.strata <- fit$surv.summary[2,,1]
##2 means to use estimate at first time past t=0 (i.e., at u)
if(length(stra <- Surv.strata(y)))
surv.by.strata <- surv.by.strata[stra] #Get for each stratum in data
cox <- surv.by.strata^exp(x - fit$center)
##Assumes x really= x * beta
pred.obs <- groupkm(cox,Surv(y[,1],y[,2]),u=u,cuts=orig.cuts)
if(what=="observed") dist <- pred.obs[,"KM"] else
dist <- pred.obs[,"KM"] - pred.obs[,"x"]
if(iter==0) {
print(pred.obs)
## assign("pred.obs", pred.obs, where=1) 18Apr01
storeTemp(pred.obs, "pred.obs") #Store externally for plotting
}
dist
}
coxfit <- function(x,y,u,iter=0, ...) {
etime <- y[,1]
e <- y[,2]
stra <- Surv.strata(y)
## attr(x,"strata") <- strata
if(sum(e)<5)return(list(fail=TRUE))
## f <- coxph(x,etime,e,surv="summary",time.inc=u,pr=F)
x <- x #Get around lazy evaluation creating complex expression
f <- if(length(x)) {
# cph(Surv(etime,e) ~ x + strat(stra), surv=TRUE, time.inc=u)
if(length(stra)) {
cph(Surv(etime,e) ~ x + strat(stra), surv=TRUE, time.inc=u)
} else {
cph(Surv(etime,e) ~ x, surv=TRUE, time.inc=u)
}
}else{
cph(Surv(etime,e) ~ strat(stra), surv=TRUE, time.inc=u)
}
## length(x)==0 case 25apr03
##Get predicted survival at times 0, u, 2u, 3u, ...
attr(f$terms, "Design") <- NULL
## f$non.slopes <- f$assume <- f$assume.code <- f$assign <- f$name <- NULL
##Don't fool fastbw called from predab.resample
f
}
b <- min(10,B)
overall.reps <- max(1,round(B/b)) #Bug in S prevents>10 loops in predab.resample
cat("\nAveraging ", overall.reps," repetitions of B=",b,"\n\n")
rel <- 0
opt <- 0
nrel <- 0
B <- 0
for(i in 1:overall.reps) {
reliability <-
predab.resample(fit, method=method,
fit=coxfit,measure=distance,
pr=pr, B=b, bw=bw, rule=rule, type=type,
u=u, m=m, what=what, sls=sls, aics=aics, strata=TRUE,
orig.cuts=cuts, tol=tol, ...)
n <- reliability[,"n"]
rel <- rel + n * reliability[,"index.corrected"]
opt <- opt + n * reliability[,"optimism"]
nrel <- nrel + n
B <- B + max(n)
## cat("Memory used after ",i," overall reps:",memory.size(),"\n")
}
mean.corrected <- rel/nrel
mean.opt <- opt/nrel
rel <- cbind(mean.optimism=mean.opt,mean.corrected=mean.corrected,n=nrel)
cat("\nMean over ",overall.reps," overall replications\n\n")
print(rel)
pred <- pred.obs[,"x"]
KM <- pred.obs[,"KM"]
obs.corrected <- KM - mean.opt
e <- fit$y[,2]
structure(cbind(reliability[,c("index.orig","training","test"),drop=FALSE],
rel,mean.predicted=pred,KM=KM,
KM.corrected=obs.corrected,std.err=pred.obs[,"std.err",drop=FALSE]),
class="calibrate", u=u, units=unit, n=length(e), d=sum(e),
p=length(fit$coef), m=m, B=B, what=what, call=call)
}
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