emplikCS (version 0.2)

el.CS.prob: Current Status Data Empirical Likellihood Test for the Probability F(t0).

Description

Given n current status data, we may estimate the CDF F(t) by NPMLE (e.g. by isotNEW2() function in this package). This function, el.CS.prob, uses empirical likelihood to test the hypothesis that F(t) at a given location(t0) equal to a given value(Ft0): i.e. H0: F(t0) = Ft0.

Empirical likelihood ratio test returns the Wilks statistics, -2LLR. The -2 log likelihood ratio times (5/3) under H0 is approximately chi square DF=1 distributed. See reference below.

Usage

el.CS.prob(ti, di, t0=0.5, Ft0=0.5)

Value

It returns a list containing

"-2LLR"

The Wilks statistics of the EL test, when multiply by (5/3) has approximate chi SQ DF=1 distribution under null hypothesis.

LogLik0

The log lik value achieved by the un-constrained NPMLE.

LogLik1

The log lik value achieved by the constrained NPMLE.

Arguments

ti

The inspection times, a vector of length n.

di

Either 0 or 1. I[yi <= ti]. length n.

t0

The given time where F() value is tested.

Ft0

The hypothesized value of F(t0). Must be within (0, 1).

Author

Mai Zhou <[e-mail]>.

Details

This function tests the null hypothesis that F(t0) = Ft0 versus not equal. We assume the data given is current status censored data.

We require t0 be equal to one of the inspection times. If not, you have to do something by the right continuity of the NPMLE (change t0 to the closest ti on the left).

The NPMLE F(t) is convergent at cubic root speed and the -2LLR times (5/3) has chi square DF=1 null distribution.

It goes without saying that we assume the NPMLE has finite asymptotic variance (when normalized by cubic root n).

References

Zhou, M. (2026). Empirical Likelihood Method in Survival Analysis 2nd Edition Chapman & Hall/CRC

Sun, J. (2006). The Statistical Analysis of Interval-Censored Failure Time Data Springer, New York.

Examples

N <- 300
set.seed(12345)
itime <- sort(c(rexp(N-1), 0.5) )       #### inspection times      
Stime <- rexp(N)             #### survival times
delta <- as.numeric(Stime <= itime)    ####  current status censoring

el.CS.prob( ti=itime, di=delta, t0=0.5, Ft0=pexp(0.5) ) 

#### You should get 
## $`-2LLR`
## [1] 1.867655     #### and more.