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

## Usage:

km.mrl(times,cens)

## 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.

## Arguments:

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

## Value:

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

## Examples:


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


## 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).