Bayesian Crossover Designs for Generalized Linear Models

This article discusses D-optimal Bayesian crossover designs for generalized linear models. Crossover trials with t treatments and p periods, for $t <= p$, are considered. The designs proposed in this paper minimize the log determinant of the variance of the estimated treatment effects over all possible allocation of the n subjects to the treatment sequences. It is assumed that the p observations from each subject are mutually correlated while the observations from different subjects are uncorrelated. Since main interest is in estimating the treatment effects, the subject effect is assumed to be nuisance, and generalized estimating equations are used to estimate the marginal means. To address the issue of parameter dependence a Bayesian approach is employed. Prior distributions are assumed on the model parameters which are then incorporated into the D-optimal design criterion by integrating it over the prior distribution. Three case studies, one with binary outcomes in a 4$\times$4 crossover trial, second one based on count data for a 2$\times$2 trial and a third one with Gamma responses in a 3$times$2 crossover trial are used to illustrate the proposed method. The effect of the choice of prior distributions on the designs is also studied.