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 like-lihood 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 em-pirical 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 examin-ing 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 test-ing method can also be more powerful than previously developed procedures. Statistical software is available in an R package ‘emplik’