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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具有障碍康威-麦克斯韦-泊松分布的纵向贝叶斯混合效应模型

龋齿（即蛀牙）是最常见的慢性儿童疾病之一，并且可能在人的一生中持续恶化。爱荷华州氟化物研究 (IFS) 旨在调查各种氟化物、饮食和非饮食因素对爱荷华州学童中龋齿进展的影响。我们开发了一个混合效应模型，对 5、9、13 和 17 岁的 IFS 纵向聚类数据进行综合分析。我们将贝叶斯障碍框架与康威-麦克斯韦-泊松回归模型相结合，该模型可以同时考虑两者过多的零和不同程度的离散度。分层收缩先验分布用于共享固定效应模型中预测变量的时间信息。每个孩子牙齿之间的依赖性是通过随时间变化的随机效应的稀疏协方差结构来建模的。此外，我们从吉布斯采样器获得参数估计和可信区间。进行模拟研究是为了评估我们统计方法的准确性和有效性。本文的结果为统计从业者提供了新颖的工具，并为牙科研究人员提供了关于各种风险和保护因素对龋齿进展的影响的新见解。