iv: Initial Value Calculation for Deriving an Exact Nonparametric Confidence Band for the Survivor Function

Description

This function computes an initial value that very roughly approximates the 0.95-quantile from the exact null distribution of the modified B-J statistic from which a nonparametric confidence band for the population survivor function, based on its one-sample Kaplan-Meier estimate, can be derived.

Usage

iv(sobj)

Arguments

sobj

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

Value

An approximate 0.95-quantile from the sample-specific exact null distribution of the modified B-J statistic derived from the single-sample Kaplan-Meier estimate.

Details

The initial value approximation uses the 0.95-quantile formula from Jager, L. and Wellner, J.A. (2005) “A new goodness of fit test: the reversed Berk-Jones statistic.” Technical report 443. University of Washington, Department of Statistics. The accuracy of the approximation depends on the presence and location of right-censored responses in the original dataset, since the Jager-Wellner formulae were developed for deriving a confidence band for the cumulative distribution function, based on the single-sample ecdf estimator.

Examples

Run this code

## Calculate an initial value from the exact null distribution of the 
## modified Berk-Jones statistic leading to an exact confidence band for 
## leukemia patient remission experience based on data from 20 patients 
## receiving Treatment B
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)
iv(fit)