Title: Empirical likelihood tests for stochastic ordering based on censored and biased data
Description: In the classical two-sample comparison problem, it is often of interest to examine whether the distribution function is uniformly higher in one group than the other. This can be framed in terms of the notion of stochastic ordering. We consider testing for stochastic ordering based on two types of data: (1) right-censored and (2) size-biased data. We derive our procedures using the empirical likelihood method, and the proposed tests are based on maximally selected local empirical likelihood statistics. For (1), the proposed test is shown via a simulation study to have superior power to the commonly-used log-rank test under crossing-hazard alternatives. The approach is illustrated using data from a randomized clinical trial involving the treatment of severe alcoholic hepatitis. As for (2), simulations show that the proposed test outperforms the Wald test and the test overlooking size bias in all the cases considered. The approach is illustrated via a real data example of alcohol concentration in fatal driving accidents.