A spatial augmented beta regression model for periodontal proportion data

Abstract

Clinical dental research generates large amounts of data with a potentially complex correlation structure from measurements recorded at several sites throughout the mouth. Clinical attachment level (CAL) is one such measure popularly used to assess the periodontal disease (PD) status. We model the proportion of sites for each tooth-type (i.e., incisor, canine, pre-molar and molar) per subject that exhibit moderate to severe PD. Disease free and highly diseased tooth-sites cause these proportion responses to lie in the closed interval [0, 1]. In addition, PD may be spatially referenced, i.e., the disease status of a site is influenced by its neighbours. While beta regression can assess the covariate-response relationship for proportion data, its support in the interval (0, 1) impairs its ability to account for the observed proportions at zero and one. In contrast to ad hoc transformations that confine responses to (0, 1), we develop a framework that augments the beta density with non-zero masses at zero and one while also controlling for spatial referencing. Our approach is Bayesian and is computationally amenable to available software. A simulation study evaluates estimation of regression effects in scenarios of varying sample size, degree of spatial dependence and response transformations. Application to real PD data provide insights into assessing covariate effects on proportion responses.

Bootstrap Bartlett correction in inflated beta regression

“…The mean response is related to a linear predictor through a link function and the linear predictor involves known covariates and unknown regression parameters (Ospina et al, 2006;Bayer and Cribari-Neto, 2013). In Parker et al (2014) the authors present a discussion about the origins of beta regression models.…”