A Bayesian hierarchical spatial model for dental caries assessment using non-Gaussian Markov random fields

Ick Hoon Jin, Ying Yuan, Dipankar Bandyopadhyay

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)884-905
Number of pages22
JournalAnnals of Applied Statistics
Issue number2
Publication statusPublished - 2016 Jun

Bibliographical note

Funding Information:
Supported in part by the National Institutes of Health (NIH) Grants R01CA154591, National Institutes of Health (NIH) R03DE020114 and National Institutes of Health (NIH)R03DE021762.

Publisher Copyright:
© Institute of Mathematical Statistics, 2016.

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Statistics, Probability and Uncertainty


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