# ipcw: Estimation of censoring probabilities In riskRegression: Risk Regression Models and Prediction Scores for Survival Analysis with Competing Risks

 ipcw R Documentation

## Estimation of censoring probabilities

### Description

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

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

### 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")`.

### 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`.

### 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

### Author(s)

Thomas A. Gerds tag@biostat.ku.dk

### 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"))