Empirical Likelihood Based Tests for Stochastic Ordering Under Right Censorship

Abstract

When comparing survival patterns between two treatment groups in a randomized clinical trial, it is often of interest to examine whether the survival rate is uniformly higher in one group than the other. This can be framed in terms of the classical notion of stochastic ordering. We consider testing for stochastic ordering based on right-censored data, and derive our procedure using the empirical likelihood method. 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. Work done jointly with Dr. Ian McKeague. ?