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

Analyzing dental fluorosis data using a novel Bayesian model for clustered longitudinal ordinal outcomes with an inflated category

We propose a Bayesian hurdle mixed-effects model to analyze longitudinal ordinal data under a complex multilevel structure. This research was motivated by the dataset gathered from the Iowa Fluoride Study (IFS) in order to establish the relationships between fluorosis status and potential risk/protective factors. Dental fluorosis is characterized by spots on tooth enamel and is due to ingestion of excessive fluoride intake during enamel formation. Observations are collected from multiple surface zones on each tooth and on all available teeth of children from the studied cohort, which are longitudinally observed at ages 9, 13, and 17. The data not only exhibit a complex hierarchical structure, but also have a large proportion of zero values that are likely to follow different statistical patterns from non-zero categories. Therefore, we develop a hurdle model to consider the zero category separately, while a proportional odds model is used for the positive categories. The estimated parameters are obtained from a Gibbs sampler implemented by the OpenBUGS software. Our model is compared with two popular methods for ordinal data: the proportional odds model and the partial proportional odds model. We perform a comprehensive analysis of the IFS data and evaluate the accuracy and effectiveness of our methodology through simulation studies. Our discoveries provide novel insights to statisticians and dental practitioners about the associations between patient and clinical characteristics and dental fluorosis.