title: Modeling longitudinal spatial periodontal data: a spatially adaptive model with tools for specifying priors and checking fit.
abstract: Attachment loss (AL), the distance down a tooth's root that is no longer attached to surrounding bone by periodontal ligament, is a common measure of periodontal disease. In this article, we develop a spatiotemporal model to monitor the progression of AL. Our model is an extension of the conditionally autoregressive (CAR) prior, which spatially smooths estimates toward their neighbors. However, because AL often exhibits a burst of large values in space and time, we develop a nonstationary spatiotemporal CAR model that allows the degree of spatial and temporal smoothing to vary in different regions of the mouth. To do this, we assign each AL measurement site its own set of variance parameters and spatially smooth the variances with spatial priors. We propose a heuristic to measure the complexity of the site-specific variances, and use it to select priors that ensure parameters in the model are well identified. In data from a clinical trial, this model improves the fit compared to the usual dynamic CAR model for 90 of 99 patients' AL measurements.
authors.affiliation: Department of Statistics, North Carolina State University, 2501 Founders Drive, Box 8203, Raleigh, North Carolina 27695, U.S.A.
authors.forename: Brian J
authors.initials: BJ
authors.lastname: Reich
authors.affiliation: Division of Biostatistics, School of Public Health, University of Minnesota, 2221 University Avenue SE, Suite 200, Minneapolis, Minnesota 55414, U.S.A.
authors.forename: James S
authors.initials: JS
authors.lastname: Hodges
mesh_terms: D000704:Analysis of Variance; D001699:Biometry / Q000379:methods*; D003430:Cross-Sectional Studies; D006801:Humans; D008137:Longitudinal Studies; D003765:Models, Dental; D015233:Models, Statistical; D017622:Periodontal Attachment Loss / Q000473:pathology; D010510:Periodontal Diseases / Q000175:diagnosis / Q000209:etiology / Q000473:pathology; D010517:Periodontics / Q000706:statistics & numerical data*; D012044:Regression Analysis