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A longitudinal Bayesian mixed effects model with hurdle Conway‐Maxwell‐Poisson distribution
Journal article   Open access   Peer reviewed

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

Tong Kang, Jeremy Gaskins, Steven Levy and Somnath Datta
Statistics in medicine, Vol.40(6), pp.1336-1356
03/15/2021
DOI: 10.1002/sim.8844
PMCID: PMC9167575
PMID: 33368533
url
https://www.ncbi.nlm.nih.gov/pmc/articles/9167575View
Open Access

Abstract

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.
 Bayesian analysis Conway‐Maxwell‐Poisson distribution Hurdle model longitudinal data mixed effects model

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