Flexibility of Bayesian generalized linear mixed models for oral health research

Many outcome variables in oral research are characterized by positive values and heavy skewness in the right tail. Examples are provided by many distributions of dental variables such as DMF (decayed, missing, filled teeth) scores, oral health impact profile score, gingival index scores, and microbiologic counts. Moreover, heterogeneity in data arises when more than one tooth is studied for each patient, due to the clusterization.Over the past decade, linear mixed models (LMEs) have become a common statistical tool to account for within-subject correlation in data with repeated measures. When a normal error is reasonably assumed, estimates of LMEs are supported by many statistical packages. Such is not the case for skewed data, where generalized linear mixed models (GLMMs) are required. However, the current software available supports only special cases of GLMMs or relies on crude Laplace-type approximation of integrals. In this study, a Bayesian approach is taken to estimate GLMMs for clustered skewed dental data. A Gamma GLMM and a log-normal model are employed to allow for heterogeneity across clusters, deriving from the patient-operator-tooth susceptibility typical of this clinical context. A comparison to the frequentist framework is also provided. In our case, Gamma GLMM fits data better than the log-normal distribution, while providing more precise estimates compared with the likelihood approach. A key advantage of the Bayesian framework is its ability to readily provide a flexible approach for implementation while simultaneously providing a formal procedure for solving inference problems.