Bayesian Multilevel Modeling in Dental Research

Abstract

Clinical designs in dentistry collect measurements of the teeth of each subject, forming complex data structures; however, standard statistical methods (Student’s t-test, ANOVA, and regression models) do not treat the data as a grouped data type; that is, the measurements are treated as independent despite not being the case. A disadvantage of not considering the dependence on multilevel data is that if there is a significant correlation between the observations, it is ignored by the researcher and consequently finds statistically significant results when in fact they are not. Bayesian methods have the advantage of not assuming normality, unlike maximum likelihood estimation, and Bayesian methods are appropriate when you have small samples. We showed the minimum statistical theory for the use of multilevel models in dental research when the response variable is numerical. In this regard, it was proposed to carry out a Bayesian multilevel analysis to determine the clinical factors associated with the depth of periodontal probing. We adapted the bottom-up strategy to specify a multilevel model in the frequentist approach to the Bayesian approach. We checked the adequacy of the fit of the postulated model using posterior predictive density.