Bayesian Hierarchical Spatial Model for Small Area Estimation with Non-ignorable Nonresponses and Its Applications to the NHANES Dental Caries Assessments
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In order to identify the demographic or dental hygienic factors that related to the dental caries outcomes, we analyze dental cavity data collected in the National Health and Nutrition Examination Survey (NHANES) with a newly proposed model. Our model consists of four components; (1) we use a Bayesian hierarchical spatial model that closely resembles the caries evolution process in humans to model dental caries outcomes for each primary sampling units (PSU), (2) we apply B-spline in incorporating the sampling weights in the measurement models to model relationship between probability sampling design and outcome variables flexibly, (3) we add an additional hierarchical modeling framework for small area estimation that allows borrowing information across PSUs in the survey and help to estimate parameters with sparse information, and (4) we adapt the selection model to handle the non-ignorable missingness both in the covariates and in the outcome variables. We use data augmentation to impute missing values and the noisy exchange sampler to generate samples from our measurement model that involves doubly-intractable normalizing constants. Our analysis results show that there exist strong spatial associations between teeth and tooth surfaces and dental hygienic factors, fluorosis and sealant reduce the risks of having dental diseases.
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