Bayesian hierarchical spatial model for small-area estimation with non-ignorable nonresponses and its application to the NHANES dental caries data

The National Health and Nutrition Examination Survey (NHANES) is a major program of the National Center for Health Statistics, designed to assess the health and nutritional status of adults and children in the United States. The analysis of NHANES dental caries data faces several challenges, including (1) the data were collected using a complex, multistage, stratified, unequal-probability sampling design; (2) the sample size of some primary sampling units (PSU), e.g., counties, is very small; (3) the measures of dental caries have complicated structure and correlation, and (4) there is a substantial percentage of nonresponses, which are expected not to be missing at random or non-ignorable. We propose a Bayesian hierarchical spatial model to address these analysis challenges. We develop a two-level Potts model that closely resembles the caries evolution process, and captures complicated spatial correlations between teeth and surfaces of the teeth. By adding Bayesian hierarchies to the Potts model, we account for the multistage survey sampling design, while also enabling information borrowing across PSUs for small-area estimation. We incorporate sampling weights by including them as a covariate in the model and adopt flexible B-splines to achieve robust inference. We account for non-ignorable missing outcomes and covariates using the selection model. We use data augmentation coupled with the noisy Monte Carlo algorithm to overcome the numerical difficulty caused by doubly-intractable normalizing constants and sample posteriors. Our analysis results show strong spatial associations between teeth and tooth surfaces, including that dental hygienic factors, such as fluorosis and sealant, reduce dental disease risks.