Simple Bayesian analysis in clinical trials: a tutorial

Abstract

In this tutorial paper we give a simple Bayesian analysis of data that arise in clinical trials. We consider the case when there are two treatment groups and the response in each group can be assumed to be binomially distributed. We also assume that prior beliefs about the rate parameter in each group can be adequately expressed by a Beta distribution. Using such a model approximate posterior inferences can then be made about the odds ratio between the two groups. We illustrate this methodology by analyzing a randomized trial to assess the benefits of treating patients with carcinoma of the pelvic region (rectum, bladder, colon, cervix) using high-energy fast neutrons as opposed to conventional megavoltage x-rays (photons). In this trial there was prior information about the relative efficacy of neutron therapy based on the beliefs of 10 clinicians. Some of the deficiencies of this simple approach are high-lighted and other approaches to analysis indicated. The paper facilitates practical consideration of a Bayesian approach without the complexities that a fuller analysis necessitates.