Periodontal disease is a common cause of tooth loss in adults. The severity of periodontal disease is usually quantified based upon the magnitudes of several tooth-level clinical parameters, the most common of which is clinical attachment level (CAL). Re- cent clinical studies have presented data on the distribution of periodontal disease in hopes of providing information for localized treatments that can reduce the prevalence of periodontal disease. However, these findings have been descriptive without consid- eration of statistical modeling for estimation and inference. To this end, we visualize the mouth as a circle and the teeth as points located on the circumference of the circle to allow the use of circular statistical methods to determine the mean location of diseased teeth. We assume the directions of diseased teeth, as determined by their tooth averaged CAL values, to be observations from a 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 (Mancl and DeRouen, 2001, Biometrics 57, 126–134) to obtain robust variance estimates for our parameter estimates. Via simulations of data motivated from an actual study of periodontal disease, we demonstrate that our methods have excellent performance in the moderately small sample sizes common to most periodontal studies.
Maitra, Samopriyo and Braun, Thomas M., "Analysis of Periodontal Data using Circular Statistics" (January 2012). The University of Michigan Department of Biostatistics Working Paper Series. Working Paper 91.