BAYESIAN-ANALYSIS FOR A SINGLE 2X2-TABLE

The simple comparison of two binomial populations is frequently of int erest in epidemiology when the domains are large. For small domains, h owever, there are no exact methods except Fisher's exact test. A basic problem, therefore, is to compare two populations by assessing the di fference between the proportions of individuals who possess a characte ristic in the first and second populations. When there is prior inform ation, we take the proportions to have independent conjugate beta dist ributions with known parameters, thereby facilitating a Bayesian analy sis. We consider Bayesian inference on functions of the proportions, a nd the three most common scalar measures used in epidemiology and heal th services research, namely relative risk, odds ratio and attributabl e risk. We develop the highest density regions (both exact and approxi mate) for relative risk, odds ratio and attributable risk. In addition , we consider the Bayes factor for testing whether the model with a co mmon proportion holds rather than one with distinct proportions. Using data from the population-based Worcester Heart Attack Study, we apply our methodology to study gender differences in the therapeutic manage ment of patients with acute myocardial infarction (AMI) by selected de mographic and clinical characteristics. The Bayes factor, the approxim ate and exact intervals generally suggest that there are no substantia l differences in the pharmacologic management of males and females hos pitalized with AMI. (C) 1997 by John Wiley & Sons, Ltd.