Open Access
June 2016 A Bayesian hierarchical spatial model for dental caries assessment using non-Gaussian Markov random fields
Ick Hoon Jin, Ying Yuan, Dipankar Bandyopadhyay
Ann. Appl. Stat. 10(2): 884-905 (June 2016). DOI: 10.1214/16-AOAS917


Research in dental caries generates data with two levels of hierarchy: that of a tooth overall and that of the different surfaces of the tooth. The outcomes often exhibit spatial referencing among neighboring teeth and surfaces, that is, the disease status of a tooth or surface might be influenced by the status of a set of proximal teeth/surfaces. Assessments of dental caries (tooth decay) at the tooth level yield binary outcomes indicating the presence/absence of teeth, and trinary outcomes at the surface level indicating healthy, decayed or filled surfaces. The presence of these mixed discrete responses complicates the data analysis under a unified framework. To mitigate complications, we develop a Bayesian two-level hierarchical model under suitable (spatial) Markov random field assumptions that accommodates the natural hierarchy within the mixed responses. At the first level, we utilize an autologistic model to accommodate the spatial dependence for the tooth-level binary outcomes. For the second level and conditioned on a tooth being nonmissing, we utilize a Potts model to accommodate the spatial referencing for the surface-level trinary outcomes. The regression models at both levels were controlled for plausible covariates (risk factors) of caries and remain connected through shared parameters. To tackle the computational challenges in our Bayesian estimation scheme caused due to the doubly-intractable normalizing constant, we employ a double Metropolis–Hastings sampler. We compare and contrast our model performances to the standard nonspatial (naive) model using a small simulation study, and illustrate via an application to a clinical dataset on dental caries.


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Ick Hoon Jin. Ying Yuan. Dipankar Bandyopadhyay. "A Bayesian hierarchical spatial model for dental caries assessment using non-Gaussian Markov random fields." Ann. Appl. Stat. 10 (2) 884 - 905, June 2016.


Received: 1 May 2014; Revised: 1 November 2015; Published: June 2016
First available in Project Euclid: 22 July 2016

zbMATH: 06625673
MathSciNet: MR3528364
Digital Object Identifier: 10.1214/16-AOAS917

Keywords: Autologistic model , Bayesian inference , dental caries , Markov chain Monte Carlo , Potts model , spatial data analysis

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.10 • No. 2 • June 2016
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