A Bayesian Methods for Analyzing Clustered Exchangeable Binary Data
by
E. Olusegun George
The University of Memphis
Coauthors: Roopa Seshadri

Clinical studies in ophthalmology and otolaryngology typically result in correlated observations. Procedures for analysis of data from these studies include the use of generalized estimating equations and generalized mixed effects models. In ophthalmology and otolaryngology studies, when the outcome of interest occurs bilaterally or when the same treatment is applied to each eye or each ear, the assumption of exchangeability is usually quite reasonable. Under this assumption we construct a Bayesian procedure for analyzing correlated binary data obtained from clinical trials. Under exchangeability, a reparameterization of the joint distribution of the responses lends itself to the choice of a restricted Dirichlet distribution as a prior due to its extended conjugate properties. Markov Chain Monte Carlo and empirical Bayes techniques are used with a modified E-M algorithm to obtain posterior estimates of the response probabilities and the hyperparameters. We apply the procedure to analyze data from a retinitis pigmentosa study and an amoxicillin-cefaclor clinical trial.

Keywords: Clustered binary data; Exchangeability; Empirical Bayes; Metropolis-Hastings algorithm; Ophthalmology and Otolaryngology

Date received: March 18, 2008