km.mrl: Mean Residual Life using Kaplan-Meier estimate

Description

This function computes the mean residual life for censored data using the Kaplan-Meier estimate of the survival function. If \(S(t)\) is the K-M estimate, the MRL for a censored observation is computed as \((\int_t^{\infty} S(u)du)/S(t)\). We take \(S(t)=0\) when \(t\) is greater than the largest observation, regardless of whether that observation was censored.

When there are ties between censored and uncensored observations, for definiteness our ordering places the censored observations before uncensored.

This function is used by locfit.censor to compute censored regression estimates.

Usage

km.mrl(times, cens)

Value

A vector of the estimated mean residual life. For uncensored observations, the corresponding estimate is 0.

Arguments

times: Obsereved survival times.
cens: Logical variable indicating censoring. The coding is 1 or TRUE for censored; 0 or FALSE for uncensored.

References

Buckley, J. and James, I. (1979). Linear Regression with censored data. Biometrika 66, 429-436.

Loader, C. (1999). Local Regression and Likelihood. Springer, NY (Section 7.2).

Examples

Run this code

# censored regression using the Kaplan-Meier estimate.
data(heart, package="locfit")
fit <- locfit.censor(log10(surv+0.5)~age, cens=cens, data=heart, km=TRUE)
plotbyfactor(heart$age, 0.5+heart$surv, heart$cens, ylim=c(0.5,16000), log="y")
lines(fit, tr=function(x)10^x)