Name: Westfall

Firstname: Peter

Title: Professor

Institution: Texas Tech University

Street: 15th and Flint

City: Lubbock, TX

Zip-Code: 79409-2101

Country: USA

Phone: 806-742-2174

Fax: 806-742-2099


Authors: Mithat Gon\"en, Peter H. Westfall, Wesley O. Johnson

Title: Bayesian Multiple Testing for Two-Sample Multivariate Endpoints

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 a 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 two examples.

References: Berger, J. O. and Delampady, M. (1987), Testing precise hypothesis. Statistical Science, 2, 317--352.

Gopalan, R. and Berry D. A. (1998). Bayesian multiple comparisons using Dirichlet process priors. Journal of the American Statistical Association, 93, 1130--1139.

Westfall, P. H., Johnson, W. O., and Utts, J. M. (1997). A Bayesian perspective on the Bonferroni adjustment. Biometrika, 84, 419--427.