Bayesian Modeling of Multivariate Spatial Discrete Data, with Applications to Dental Caries

• Activity Number: 505
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: International Indian Statistical Association
• Author(s): Dipankar Bandyopadhyay*+ and Ick Hoon Jin and Ying Yuan
• Companies: University of Minnesota and The University of Texas MD Anderson Cancer Center and UT MD Anderson Cancer Center
• Keywords: Bayesian ; discrete ; autologistic ; Potts ; spatial ; caries

Abstract

Dental data consist of two levels of hierarchy, a tooth level and a surface level, and outcomes often exhibit spatial structures among neighboring teeth and surfaces (i.e. the disease/decay status of a tooth or surface might be influenced by the decay status of a group of neighboring teeth/surfaces). Assessments of dental caries at the tooth level yield binary outcomes (presence/absence of teeth) and assessments at the surface level yield trinary outcomes, indicating the healthy, decayed, or filled surfaces. We develop a Bayesian two-stage spatial model to analyze these data. At the first stage, we focus on estimating the degree of spatial association between existing and missing teeth using an autologistic model. At the second stage, we quantify spatial associations among surfaces on the existing teeth using a Potts model. Both models include random effects term to adjust for the data hierarchy involved. Computational difficulty due to the intractable normalizing constant is tackled using an approximate exchange sampler. We apply our methodology to a sample of subjects from a clinical study on dental caries conducted at the Medical University of South Carolina.