A Doubly Robust and Powerful Adaptation of the Mann-Whitney Test with Application to Randomized Experiments

• Activity Number: 69
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section
• Author(s): Karel Vermeulen*+ and Stijn Vansteelandt
• Companies: Ghent University and Ghent University
• Keywords: Causal inference ; Double robustness ; Nonparametric test ; Semi-parametric estimation ; Covariate adjustment ; Randomized experiments

Abstract

We propose a novel doubly robust adaptation of the Mann-Whitney (MW) test statistic for comparing treatments using the marginal probabilistic index (MPI, the probability that the outcome of a randomly chosen treated subject is higher than that of a randomly chosen untreated subject) to adjust for measured confounding in observational studies. The adaptation requires specification of a propensity score model and a so called probabilistic index model. The adaptation is efficient for the MPI and doubly robust: valid as soon as at least one of these working models is correctly specified. We apply this adaptation to the setting of randomized experiments. The double robustness and efficiency properties enable increasing the power of the MW test by adjusting for auxiliary covariates without the risk of bias due to model misspecification by relying on the known randomisation probabilities. Considering that the MW test is often indicated in small sample settings, we propose a permutation test based on this test statistic. Simulation studies show that the proposed permutation test attains the nominal Type I error rate and illustrate the increase in power, compared to the classical MW test.