A longitudinal Bayesian mixed effects model with hurdle Conway-Maxwell-Poisson distribution

Dental caries (i.e., cavities) is one of the most common chronic childhood diseases and may continue to progress throughout a person's lifetime. The Iowa Fluoride Study (IFS) was designed to investigate the effects of various fluoride, dietary and nondietary factors on the progression of dental caries among a cohort of Iowa school children. We develop a mixed effects model to perform a comprehensive analysis of the longitudinal clustered data of IFS at ages 5, 9, 13, and 17. We combine a Bayesian hurdle framework with the Conway-Maxwell-Poisson regression model, which can account for both excessive zeros and various levels of dispersion. A hierarchical shrinkage prior distribution is used to share the temporal information for predictors in the fixed-effects model. The dependence among teeth of each individual child is modeled through a sparse covariance structure of the random effects across time. Moreover, we obtain the parameter estimates and credible intervals from a Gibbs sampler. Simulation studies are conducted to assess the accuracy and effectiveness of our statistical methodology. The results of this article provide novel tools to statistical practitioners and offer fresh insights to dental researchers on effects of various risk and protective factors on caries progression.