Increasing the power of the Mann‐Whitney test in randomized experiments through flexible covariate adjustment

Abstract

The Mann-Whitney U test is frequently used to evaluate treatment effects in randomized experiments with skewed outcome distributions or small sample sizes. It may lack power, however, because it ignores the auxiliary baseline covariate information that is routinely collected. Wald and score tests in so-called probabilistic index models generalize the Mann-Whitney U test to enable adjustment for covariates, but these may lack robustness by demanding correct model specification and do not lend themselves to small sample inference. Using semiparametric efficiency theory, we here propose an alternative extension of the Mann-Whitney U test, which increases its power by exploiting covariate information in an objective way and which lends itself to permutation inference. Simulation studies and an application to an HIV clinical trial show that the proposed permutation test attains the nominal Type I error rate and can be drastically more powerful than the classical Mann-Whitney U test.