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Biological and medical researchers often collect count data in clusters at multiple time points. The data can exhibit excessive zeros and a wide range of dispersion levels. In particular, our research was motivated by a dental dataset with such complex data features: the Iowa Fluoride Study (IFS). The study was designed to investigate the effects of various dietary and nondietary factors on the caries development of a cohort of Iowa school children at the ages of 5, 9, and 13. To analyze the multiyear IFS data, we propose a novel longitudinal method of a generalized estimating equations based marginal regression model. We use a zero‐inflated model with a Conway–Maxwell–Poisson (CMP) distribution, which has the flexibility to account for all levels of dispersion. The parameters of interest are estimated through a modified expectation–solution algorithm to account for the clustered and temporal correlation structure. We fit the proposed zero‐inflated CMP model and perform a comprehensive secondary analysis of the IFS dataset. It resulted in a number of notable conclusions that also make clinical sense. Additionally, we demonstrated the superiority of this modeling approach over two other popular competing models: the zero‐inflated Poisson and negative binomial models. In the simulation studies, we further evaluate the performance of our point estimators, the variance estimators, and that of the large sample confidence intervals for the parameters of interest. It is also demonstrated that our longitudinal CMP model can correctly identify the time‐varying dispersion patterns.

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.

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