Practical bayesian approaches to the analystcs of a 2×2 contingency table with incompletely categorized data

Abstract

Abstract To assess the efficacy of a treatment, patients are administered a pre-test, the treatment, and a post-test (identical to the pre-test). These patients are then categorized according to their outcomes observed on both tests,e.g., (S,S), (S,F), etc. Also, we observe "incomplete" information on the pre-tests' outcomes for some patients and the results of only the post-test being known for thers, A Bayesian framework is fit to the problem and Bayes factors, posterior odds ratios, and utility functions are given to evaluate th e treatment, A method of assessing the prior distribution is specified and a numerical example is worked. Keywords: bayes factorbayesian statisticscontingency tablehypothesis of symmetrymarginally categorized dataposterior odds ratioutility function