riskRegression (version 2022.09.23)

ipcw: Estimation of censoring probabilities

Description

This function is used internally to obtain inverse of the probability of censoring weights.

Usage

ipcw(
  formula,
  data,
  method,
  args,
  times,
  subject.times,
  lag = 1,
  what,
  keep = NULL
)

Value

A list with elements depending on argument keep.

times

The times at which weights are estimated

IPCW.times

Estimated weights at times

IPCW.subject.times

Estimated weights at individual time values subject.times

fit

The fitted censoring model

method

The method for modelling the censoring distribution

call

The call

Arguments

formula

A survival formula like, Surv(time,status)~1, where as usual status=0 means censored. The status variable is internally reversed for estimation of censoring rather than survival probabilities. Some of the available models (see argument model) will use predictors on the right hand side of the formula.

data

The data used for fitting the censoring model

method

Censoring model used for estimation of the (conditional) censoring distribution.

args

A list of arguments which is passed to method

times

For what="IPCW.times" a vector of times at which to compute the probabilities of not being censored.

subject.times

For what="IPCW.subject.times" a vector of individual times at which the probabilities of not being censored are computed.

lag

If equal to 1 then obtain G(T_i-|X_i), if equal to 0 estimate the conditional censoring distribution at the subject.times, i.e. (G(T_i|X_i)).

what

Decide about what to do: If equal to "IPCW.times" then weights are estimated at given times. If equal to "IPCW.subject.times" then weights are estimated at individual subject.times. If missing then produce both.

keep

Which elements to add to the output. Any subset of the vector c("times","fit","call").

Author

Thomas A. Gerds

Details

Inverse of the probability of censoring weights (IPCW) usually refer to the probabilities of not being censored at certain time points. These probabilities are also the values of the conditional survival function of the censoring time given covariates. The function ipcw estimates the conditional survival function of the censoring times and derives the weights.

IMPORTANT: the data set should be ordered, order(time,-status) in order to get the values IPCW.subject.times in the right order for some choices of method.

Examples

library(prodlim)
library(rms)
dat=SimSurv(30)

dat <- dat[order(dat$time),]

# using the marginal Kaplan-Meier for the censoring times

WKM=ipcw(Hist(time,status)~X2,
  data=dat,
  method="marginal",
  times=sort(unique(dat$time)),
  subject.times=dat$time,keep=c("fit"))
plot(WKM$fit)
WKM$fit

# using the Cox model for the censoring times given X2
library(survival)
WCox=ipcw(Hist(time=time,event=status)~X2,
  data=dat,
  method="cox",
  times=sort(unique(dat$time)),
  subject.times=dat$time,keep=c("fit"))
WCox$fit

plot(WKM$fit)
lines(sort(unique(dat$time)),
      1-WCox$IPCW.times[1,],
      type="l",
      col=2,
      lty=3,
      lwd=3)
lines(sort(unique(dat$time)),
      1-WCox$IPCW.times[5,],
      type="l",
      col=3,
      lty=3,
      lwd=3)

# using the stratified Kaplan-Meier
# for the censoring times given X2

WKM2=ipcw(Hist(time,status)~X2,
  data=dat,
  method="nonpar",
  times=sort(unique(dat$time)),
  subject.times=dat$time,keep=c("fit"))
plot(WKM2$fit,add=FALSE)