Combined Multiple Testing by Censored Empirical Likelihood

We propose a new procedure for combining multiple tests in samples of right-censored observations. The new method is based on multiple constrained censored empirical likelihood where the constraints are formulated as linear functionals of the cumulative hazard functions. We prove a version of Wilks’ theorem for the multiple constrained censored empirical likelihood ratio, which provides a simple reference distribution for the test statistic of our proposed method. A useful application of the proposed method is found in examining the survival experience of one or more populations by combining different weighted log-rank tests. A real data example is given using the log-rank and Gehan-Wilcoxon tests. In a simulation study, we compare the new method to different weighted log-rank statistics, Renyi-type suprema, and maximin efficiency robust tests. The empirical results demonstrate that, in addition to its computational simplicity, the proposed combined testing method can also be more powerful than previously developed procedures. Statistical software is available in an R package ‘emplik’.