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：在过去二十多年中，考虑暴露测量误差一直被视为环境流行病学的一个关键问题。贝叶斯层次模型提供了一种连贯的概率框架，用于评估环境暴露与健康效应之间的关联，该模型同时考虑了由估计暴露量的不确定性以及暴露与健康结局数据之间的空间错位所引入的暴露测量误差。尽管当联合估计不可行时，两阶段贝叶斯分析通常被视为全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恰当地传播至第二阶段健康模型的研究却极少，尤其是在参与者位置数量庞大且暴露空间相关的情况下。我们提出了一种可扩展的两阶段贝叶斯方法，称为稀疏多元正态（sparse MVN）先验方法，该方法基于Vecchia近似，用于评估环境流行病学中暴露与健康结局之间的关联。我们通过模拟将其性能与现有方法进行比较。我们的稀疏MVN先验方法表现出与全贝叶斯方法（一种黄金标准，但在某些情况下无法实施）相当的性能。我们采用包括新开发方法在内的几种方法，研究了2012年德克萨斯州哈里斯县特定来源暴露源与污染物（二氧化氮（NO$_2$））特异性暴露源与出生结局之间的关联。