A Proportional Odds Beta-Binomial Model for Evaluating the Effect of Treatment in Cross-Over Studies with Baseline Covariates: An Application to Condom Failure Data

Cross-over trials with correlated Bernoulli outcomes are common designs. In condom functionality studies, for example, an indicator of condom failure is reported for each sex act using standard or experimental condoms. Two popular analysis methods for such data are Generalized Estimating Equations and logit-normal random effects models. An alternative random effects model, the beta-binomial, is commonly used in contexts involving only between-cluster effects. The flexibility of the beta distribution and the interpretation of random effects as cluster-specific failure probabilities make it appealing, and we consider an extension of the model to account for within-cluster treatment effects using proportional odds assumptions.