title: 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.
authors.affiliation: Limburgs Universitair Centrum, Center for Statistics, Biostatistics, Universitaire Campus, B-3590 Diepenbeek, Belgium. ziv.shkedy@luc.ac.be
authors.forename: Ziv
authors.initials: Z
authors.lastname: Shkedy
authors.forename: Geert
authors.initials: G
authors.lastname: Molenberghs
authors.forename: Hansfried
authors.initials: H
authors.lastname: Van Craenendonck
authors.forename: Thomas
authors.initials: T
authors.lastname: Steckler
authors.forename: Luc
authors.initials: L
authors.lastname: Bijnens
mesh_terms: D000465:Algorithms; D000818:Animals; D001499:Bayes Theorem; D016000:Cluster Analysis; D003216:Conditioning, Operant / Q000187:drug effects; D018592:Cross-Over Studies; D003627:Data Interpretation, Statistical; D004305:Dose-Response Relationship, Drug; D016014:Linear Models; D015233:Models, Statistical; D016017:Odds Ratio; D016012:Poisson Distribution; D051381:Rats; D012055:Reinforcement Schedule; D012107:Research Design