Empirical likelihood based tests for stochastic ordering under right censorship

This paper develops an empirical likelihood approach to testing for stochastic ordering between two univariate distributions under right censorship. The proposed test is based on a maximally selected local empirical likelihood statistic. The asymptotic null distribution is expressed in terms of a Brownian bridge. The new procedure is shown via a simulation study to have superior power to the log-rank and weighted Kaplan-Meier tests under crossing hazard alternatives. The approach is illustrated using data from a randomized clinical trial involving the treatment of severe alcoholic hepatitis.