On the Bayesian Index of Superiority and the p-Value of the Fisher Exact Test for Binomial Proportions

Abstract

Proportions based on the binominal distribution are often compared in clinical tests. Biostatisticians often use the Fisher exact test in order to show the superiority of the binominal proportions of a test drug. Kawasaki and Miyaoka (2012) derived an accurate expression for a new index: θ = P (π1,post > π2,post | X1, X2) within a Bayesian framework. In this paper, we investigate the relationship between θ proposed by Kawasaki and Miyaoka (2012) and the p-value of Fisher’s exact test (Fisher (1934)). We show that these two indicators are equivalent under certain conditions.