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Bayesian Multiple Testing for Two‐Sample Multivariate Endpoints
Author(s) -
Gönen Mithat,
Westfall Peter H.,
Johnson Wesley O.
Publication year - 2003
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/1541-0420.00009
Subject(s) - multivariate statistics , statistics , bayesian probability , mathematics , covariance , multivariate analysis , posterior probability , context (archaeology) , econometrics , statistical hypothesis testing , paleontology , biology
Summary . 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, and 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 a clinical example.