Sensitivity Analysis for the Adjusted Mann-Whitney Test with Observational Studies

Abstract

The Mann-Whitney test is a popular nonparametric test for comparing two samples. It has been recently extended by Satten et al. (2018) to allow testing for the existence of treatment effects in observational studies. Their proposed adjusted Mann-Whitney test relies on the unconfoundedness assumption which is untestable in practice. It hence becomes important to assess the impact of violating this assumption on the degree to which causal conclusions remain valid. In this paper, we consider a marginal sensitivity analysis framework to address this problem by utilizing a bootstrap approach that provides a sensitivity interval for the estimand with a guaranteed coverage probability as long as the data generating mechanism is included in the set of pre-specified sensitivity models. We develop efficient optimization algorithms for computing the sensitivity interval and further extend our approach to a general class of adjusted multi-sample U-statistics. Simulation studies and two real data applications are discussed to demonstrate the utility of our proposed methodology.