|
Abstract:
|
The Mann-Whitney 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 test to enable adjustment for baseline 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 propose an alternative (double robust) extension of the Mann-Whitney 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 test. Finally, we also extend these ideas to enable adjustment for confounding in the analysis of observational studies.
|
