A hierarchical binomial-poisson model for the analysis of a crossover design for correlated binary data when the number of trials is dose-dependent

Abstract

The differential reinforcement of a low-rate 72-seconds schedule (DRL-72) is a standard behavioral test procedure for screening a potential antidepressant compound. The data analyzed in the article are binary outcomes from a crossover design for such an experiment. Recently, Shkedy et al. ( 2004) proposed to estimate the treatments effect using either generalized linear mixed models (GLMM) or generalized estimating equations ( GEE) for clustered binary data. The models proposed by Shkedy et al. ( 2004) assumed the number of responses at each binomial observation is fixed. This might be an unrealistic assumption for a behavioral experiment such as the DRL-72 because the number of responses ( the number of trials in each binomial observation) is expected to be influenced by the administered dose level. In this article, we extend the model proposed by Shkedy et al. ( 2004) and propose a hierarchical Bayesian binomial-Poisson model, which assumes the number of responses to be a Poisson random variable. The results obtained from the GLMM and the binomial-Poisson models are comparable. However, the latter model allows estimating the correlation between the number of successes and number of trials.