Modeling dental disease progression in a longitudinal study
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Periodontal disease is a serious infection of the gums and the bones surrounding the teeth. Its progression in surveillance studies is usually measured using several clinical outcomes on each tooth per patient over time. Statistical models used to analyze the relationship between periodontal disease progression and predictors of disease measured at the patient level need to account for the various correlation structures: the correlation between teeth within each patient and the correlation between temporal observations made on the same tooth of a given patient. Because tooth loss is a complication of periodontal disease, patients more prone to the disease tend to have fewer number of teeth (i.e. smaller cluster) compared to healthier patients. This phenomenon is called informative cluster size. Further, when a patient's periodontal disease progression is monitored over time, the number of observations made on each tooth of the patient tends to decrease due to the patient losing teeth, resulting in another analytical challenge. This dissertation was motivated by the limited availability of statistical methods that properly address informative cluster size in a longitudinal study to model the effect of predictors on one or more outcomes including ordinal variables. Briefly, the three chapters build on an existing method, cluster-weighted generalized estimating equations to: (1) model longitudinal ordinal outcomes; (2) jointly model multiple correlated binary outcomes; and (3) analyze longitudinal binary outcomes, assuming tooth-loss is missing at random. Through extensive simulation studies, we demonstrate the feasibility and consistency of our proposed methods compared to traditional approaches such as unweighted generalized estimating equations. We apply each of our proposed methods to analyze a data set from a real dental longitudinal study and interpret the results.