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

Pub Date : 2024-06-22 DOI:10.1007/s42952-024-00274-3
Ick Hoon Jin, Fang Liu, Jina Park, Evercita Eugenio, Suyu Liu
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Abstract

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.

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贝叶斯分层空间模型用于具有不可忽略非响应的小区域估算及其在 NHANES 龋齿数据中的应用
美国国家健康与营养调查(NHANES)是美国国家卫生统计中心的一项重要计划,旨在评估美国成人和儿童的健康与营养状况。对 NHANES 龋齿数据的分析面临着一些挑战,其中包括:(1)数据的收集采用了复杂的、多阶段、分层、不等概率抽样设计;(2)一些主要抽样单位(PSU),如县的样本量非常小;(3)龋齿的测量指标具有复杂的结构和相关性;(4)有相当比例的非回复,预计这些非回复不会是随机缺失或不可忽略的。我们提出了一个贝叶斯分层空间模型来解决这些分析难题。我们建立了一个两级 Potts 模型,该模型与龋病演变过程非常相似,并能捕捉牙齿和牙齿表面之间复杂的空间相关性。通过在 Potts 模型中加入贝叶斯层次结构,我们考虑到了多阶段调查抽样设计,同时还实现了在 PSU 之间借用信息进行小区域估算。我们将抽样权重作为协变量纳入模型,并采用灵活的 B 样条来实现稳健推断。我们使用选择模型对不可忽略的缺失结果和协变量进行解释。我们使用数据增强和噪声蒙特卡洛算法来克服双重难以处理的归一化常数和样本后验所带来的数值困难。我们的分析结果表明,牙齿和牙齿表面之间存在很强的空间关联,包括牙齿卫生因素(如氟中毒和密封剂)降低了牙病风险。
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