A Conditionally Autoregressive-Spatial Model for Clustered Count Data Controlling for Two Classes of Neighbor Relations

• Activity Number: 355 - Contributed Poster Presentations: Section on Bayesian Statistical Science
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jason Clague* and Thomas Belin and Vivek Shetty
• Companies: University of California Los Angeles and University of California, Los Angeles and University of California Los Angeles
• Keywords: CAR Prior ; Dentistry ; Overdispersion ; Count Data ; Beta-Binomial

Abstract

Dental caries data contain unique and complex correlation structures stemming from the spatial structure of the mouth. Overdispersion can occur due to the dependent variable in this setting being a count variable, namely the total number of decayed, missing, or filled surfaces for each tooth. Using a sample of 571 methamphetamine users from Los Angeles, we model the dental decay process with beta-binomial and beta-negative binomial models to account for possible overdispersion in the data, and we incorporate conditionally autoregressive (CAR) prior distributions to account for the unique correlation structure of dental data. To allow for more flexibility in modeling this correlation structure, the CAR portion of the model reflects two neighbor relations: nearest-neighbor teeth on the same jaw that are adjacent to each other, and teeth that are directly across from one another on the other side of the mouth. The model includes separate smoothing parameters for each neighbor relation. By utilizing this more flexible CAR structure, spatial smoothing can yield greater precision and a better understanding of the underlying mechanisms of dental decay in methamphetamine users.