Bayesian Construction of Improved Nonrandomized Tests for One-sided Hypotheses about Discrete Distributions

• Activity Number: 140
• Type: Contributed
• Date/Time: Monday, August 8, 2005 : 10:30 AM to 12:20 PM
• Sponsor: General Methodology
• Author(s): Stefan Wellek*+
• Companies: CIMH/University of Heidelberg
• Keywords: Conditional test ; Exact power computation ; Frequentist properties of Bayesian tests ; Noninferiority ; Raised nominal significance level

Abstract

The best-known example of the type of problem to be considered here arises in the two-sample setting with binary data. When the odds ratio is the parameter of interest, there is an optimal conditional test irrespective of whether the problem is formulated in the conventional way or as a so-called noninferiority (one-sided equivalence) problem. Unfortunately, the nonrandomized version of such an optimal test often is conservative. A conceptually simple way of removing this effect, at least partially, is Boschloo's (1970) technique of raising the nominal significance level as far as possible without increasing the size beyond the target level. As an alternative, we propose using Bayesian tests with noninformative specification of the prior and adjustment for size. A major advantage of this approach is its flexibility with respect to the choice of the target parameter, in terms of which the equivalence region shall be defined in the noninferiority case. In cases where a UMPU test exists, the power properties of the Bayesian procedure turn out to be similar to those of the nonrandomized version of the optimal conditional test at a maximally increased nominal level.