A Doubly Robust Adaptation of the Mann-Whitney Test to Adjust for Measured Confounding

• Activity Number: 456
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Stijn Vansteelandt*+ and Karel Vermeulen
• Companies: Ghent University and Ghent University
• Keywords: Causal inference ; Double robustness ; Nonparametric test ; Nuisance parameter ; Semi-parametric estimation

Abstract

We propose an adaptation of the Mann-Whitney test for comparing treatment effects, which enables adjustment for measured confounding. The proposed adaptation requires the specification of a propensity score model and a so-called probabilistic index model, but is doubly robust: valid as soon as at least one of these working models is correctly specified. Because the choice of estimators of the nuisance parameters indexing these working models can be very influential under model misspecification, we here propose a focussed estimation strategy. Considering that the Mann-Whitney test is often indicated in small sample settings, we design this focussed estimation strategy so that it improves the finite-sample performance of the doubly robust analysis. Asymptotic properties are evaluated. Simulation studies are used to assess the procedure's finite-sample performance, as well as its ability to improve power in randomized experiments, relative to the use of the conventional Mann-Whitney test.