Analyzing zero-inflated clustered longitudinal ordinal outcomes using GEE-type models with an application to dental fluorosis studies

Motivated by the Iowa Fluoride Study (IFS), which tracked fluoride intake and dental outcomes from childhood to young adulthood (ages 9, 13, 17, and 23), we analyze dental fluorosis - a condition caused by excessive fluoride exposure during enamel formation. In this context, fluorosis scores across tooth surfaces present as zero-inflated, clustered, and longitudinal ordinal outcomes, prompting the development of a unified modeling framework. Leveraging generalized estimating equations (GEEs), we construct separate models for the presence and severity of fluorosis and propose a combined model that links these components though shared covariates. To improve estimation efficiency and borrowing strength across timepoints, we incorporate James-Stein shrinkage estimators. We compare several working correlation structures, including a data-driven jackknifed structure, and perform model selection via rank aggregation. Simulation studies validate the finite-sample performance of the proposed models, and a bootstrap-based power analysis further confirms the validity of the testing procedure. In our analysis of the IFS data, early-life total daily fluoride intake, average home water fluoride concentration, and specific teeth and zones emerge as significant risk factors for dental fluorosis. Maxillary lateral incisors and zones closer to the gum show protective effects across different ages. These findings reveal novel age-specific associations between early-life exposures and the progression of dental fluorosis through early adulthood.