Combined multiple testing of multivariate survival times by censored empirical likelihood

In each study testing the survival experience of one or more populations, one must not only choose an appropriate class of tests, but further an appropriate weight function. As the optimal choice depends on the true shape of the hazard ratio, one is often not capable of getting the best results with respect to a specific dataset. For the univariate case several methods were proposed to conquer this problem. However, most of the interesting datasets contain multivariate observations nowadays. In this work we propose a multivariate version of a method based on multiple constrained censored empirical likelihood where the constraints are formulated as linear functionals of the cumulative hazard functions. By considering the conditional hazards, we take the correlation between the components into account with the goal of obtaining a test that exhibits a high power irrespective of the shape of the hazard ratio under the alternative hypothesis.