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
Email: westfall@ba.ttu.edu
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.