Bayesian mkta-analysis of frequentist p-values

Abstract

We develop a fully Bayesian approach to the analysis and combina¬tion of information consisting solely of the p-values and test procedure descriptions from a series of frequentistly analysed research studies involving a common unknown parameter. The approach is illustrated with a number of familiar test procedures. We focus in particular on the t-test and show that the standard noninformative prior specification on the location and scale pa¬rameters leads to a uniform posterior distribution on location. Therefore we demonstrate from a Bayesian perspective that studies whose results consist solely of p-values may not offer any information about the parameters of in¬terest. Wre illustrate our methodology with a meta-analysis of aspirin trials on post-myocardial infarction patients.

Keywords:

• noninformative priors
• Bayesian p-values
• aspirin studies