Bayesian multiple testing for two-sample multivariate endpoints.

Mithat Gonen, Memorial Sloan-Kettering Cancer Center
Peter Westfall
Wesley Johnson

Abstract

In clinical studies involving multiple variables, simultaneous tests are often considered where both the outcomes and hypotheses are correlated. This article proposes a multivariate mixture prior on treatment effects that allows positive probability of zero effect for each hypothesis, correlations among effect sizes, correlations among binary outcomes of zero versus nonzero effect, as well as correlations among the observed test statistics (conditional on the effects). We develop Bayesian multiple testing procedure for the multivariate two-sample situation with unknown covariance structure, and obtain the posterior probabilities of no difference between treatment regimens for specific variables. Prior selection methods and robustness issues are discussed in the context of a clinical example.