A Bayesian Approach to the Analysis of Binary Crossover Data

Abstract

Recent advances in sample-based approaches to Bayesian calculation allow a Bayesian approach to the analysis of data from crossover clinical trials, previously restricted to continuous response data, to be extended to examples in which the response is binary. By expressing the data as a 23 contingency table and considering a log-linear model for the cell probabilities, an informative non-conjugate prior is constructed. Posterior moments and marginal densities for model parameters and predictive probabilities, which provide a key summary of the relative efficacies of the two treatments under consideration, can be efficiently calculated by using Gibbs sampling. The presence of patients for whom only first-period data are available, a common feature of the crossover design, is also easily dealt with. The method is illustrated with data from a trial to compare inhalation devices for asthma sufferers.