Applications of Circular Distributions and Spatial Point Processes to the Analysis of Periodontal Data.

Abstract

The dissertation focuses on three novel approaches for analyzing data arising from studies of periodontal disease, a common cause of tooth loss in adults, in order to provide periodontists with a better understanding of periodontal disease and improving the prevention and treatment of the disease. Our first two methods focus on identifying regions of the mouth that are most susceptible to periodontal disease and thus determining locations of the mouth where localized treatments for the disease can be best applied. First, we assume the directions of diseased teeth to be observations from a unimodal von Mises distribution, the mean of which is a function of mouth-level covariates. Because multiple teeth from a subject are correlated, we use a bias-corrected generalized estimating equation approach to obtain robust variance estimates for our parameter estimates. Second, we extend our methods to model asymmetry and multimodality by assuming the directions of diseased teeth follow a Generalized von Mises distribution. We use generalized estimating equations to model periodontally diseased locations and use a model selection criterion in order to determine the appropriate number of modes. As applied to our motivating set of data, we find that periodontal disease tends to be located at the back of both sides of the upper jaw, as well as at the middle of the lower jaw. Third, we propose using point pattern data analysis methods to study the association between clinical attachment level (CAL) and bone level (BL) and how the association varies among different types of teeth. Applying these methods to our motivating data, we find that CAL and BL are similar for molars and bicuspids, with the similarity stronger for bicuspids than molars. We also found a substantial similarity between the CAL and BL of molars with the CAL and BL of bicuspids. The results suggest that measurements on a single tooth can be considered to be representative of the measurements obtained from the other teeth. Thus, fewer teeth would need to be part of a periodontal exam, thereby reducing the time and effort devoted to patient exams in future periodontal studies.