exact: Calculate an Exact Nonparametric Confidence Band for the Survivor Function

Description

This function computes exact nonparametric confidence limits for the population survivor function, based on its one-sample Kaplan-Meier estimate, when the quantile of the cumulative distribution function, a value of the modified B-J statistic, is x.

Usage

exact(sobj, x)

Arguments

sobj

a one-sample Kaplan-Meier estimate, provided in the form of a survfit.object.

scalar, a quantile of the exact null distribution.

Value

A matrix containing the lower and upper confidence band when the value of the modified B-J statistic is x. The first column of the matrix represents the lower estimate of the population survivor function, and the second column of the matrix provides the corresponding upper estimate.

Details

If the number of times the Kaplan-Meier estimate derived from the sample changes value is $k$, the function returns a matrix of $(k+1) \times 2$ values. These are the lower and upper limits that correspond to the $k+1$ different values for the sample-specific Kaplan-Meier estimate.

For the specified, fixed choice of x, each lower and upper limit is calculated using the Van Wijngaarden-Decker-Brent root-finding algorithm, zbrent. The tolerance required for convergence to each required root/limit is 1.0e-10.

Examples

Run this code

## Calculate the exact, nonparametric lower and upper estimates of
## leukemia patient remission experience based on data from 20 patients 
## receiving Treatment B when the value of x is 0.3
time<-c(1,1,2,2,3,4,5,8,8,9,11,12,14,16,18,21,27,31,38,44)
status<-c(rep(1,16),0,1,0,1)
fit<-survfit(Surv(time,status)~1)
exact(fit,0.3)