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.
Bibliographical noteFunding Information:
The authors thank the Center for Oral Health Research at MUSC for providing the motivating data and the context of this work. This work is a component of the first author’s doctoral dissertation at MUSC, and he acknowledges support from an F31 Ruth L. Kirschstein Predoctoral Fellowship from the US National Institutes of Health/National Institutes of Dental and Craniofacial Research (NIH/NIDCR, F31DE022246), as well as prior support from the NIGMS training program T32GM074934. The work of the other two authors is supported by grants R03DE020114 and R03DE021762 from the NIH/NIDCR.
- Augmented beta
- conditionally autoregressive (CAR)
- periodontal disease (PD)
- proportion data