Accounting for exposure measurement errors has been recognized as a crucial problem in environmental epidemiology for over two decades. Bayesian hierarchical models offer a coherent probabilistic framework for evaluating associations between environmental exposures and health effects, which take into account exposure measurement errors introduced by uncertainty in the estimated exposure as well as spatial misalignment between the exposure and health outcome data. While two-stage Bayesian analyses are often regarded as a good alternative to fully Bayesian analyses when joint estimation is not feasible, there has been minimal research on how to properly propagate uncertainty from the first-stage exposure model to the second-stage health model, especially in the case of a large number of participant locations along with spatially correlated exposures. We propose a scalable two-stage Bayesian approach, called a sparse multivariate normal (sparse MVN) prior approach, based on the Vecchia approximation for assessing associations between exposure and health outcomes in environmental epidemiology. We compare its performance with existing approaches through simulation. Our sparse MVN prior approach shows comparable performance with the fully Bayesian approach, which is a gold standard but is impossible to implement in some cases. We investigate the association between source-specific exposures and pollutant (nitrogen dioxide (NO$_2$))-specific exposures and birth outcomes for 2012 in Harris County, Texas, using several approaches, including the newly developed method.

翻译：解决暴露测量误差被认为是环境流行病学领域二十多年来的关键问题。贝叶斯层次模型通过统一的概率框架评估环境暴露与健康效应之间的关联，该框架能够纳入由估计暴露不确定性以及暴露与健康结局数据空间错位所引入的暴露测量误差。当联合估计不可行时，两阶段贝叶斯分析通常被视为完整贝叶斯分析的优良替代方案，但关于如何将第一阶段暴露模型的不确定性正确传播至第二阶段健康模型的研究仍十分有限——尤其在参与者位置数量庞大且暴露存在空间相关性的情况下。我们提出了一种可扩展的两阶段贝叶斯方法，即基于Vecchia近似的稀疏多元正态先验方法，用于评估环境流行病学中暴露与健康结局的关联。通过模拟研究，我们将其性能与现有方法进行对比。结果表明，稀疏多元正态先验方法的性能与完整贝叶斯方法（金标准方法，但某些情况下无法实施）相当。我们运用包括新开发方法在内的多种技术，研究了2012年美国德克萨斯州哈里斯县中源特异性暴露、污染物特异性暴露（二氧化氮(NO₂)）与出生结局之间的关联。