Jeremy Gaskins, PhD, Department of Bioinformatics and Biostatistics, University of Louisville

"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, which can progress throughout a person’s lifetime. The Iowa Fluoride Study was designed to investigate the effects of various dietary and non-dietary factors on the progression of dental caries among a cohort of Iowa school children at the ages of 5, 9, 13 and 17. We use a mixed effects model to perform a comprehensive analysis on the longitudinal clustered data of the Iowa Fluoride Study. 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 is used to share the temporal information for predictors in the fixed-effects model. The dependence between 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 approach. The results offer potentially new insights to both statistical practitioners and dental researchers on caries prevention.

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