Study designs where data have been aggregated by geographical areas are popular in environmental epidemiology. These studies are commonly based on administrative databases and, providing a complete spatial coverage, are particularly appealing to make inference on the entire population. However, the resulting estimates are often biased and difficult to interpret due to unmeasured confounders, which typically are not available from routinely collected data. We propose a framework to improve inference drawn from such studies exploiting information derived from individual-level survey data. The latter are summarized in an area-level scalar score by mimicking at ecological level the well-known propensity score methodology. The literature on propensity score for confounding adjustment is mainly based on individual-level studies and assumes a binary exposure variable. Here, we generalize its use to cope with area-referenced studies characterized by a continuous exposure. Our approach is based upon Bayesian hierarchical structures specified into a two-stage design: (i) geolocated individual-level data from survey samples are up-scaled at ecological level, then the latter are used to estimate a generalized ecological propensity score (EPS) in the in-sample areas; (ii) the generalized EPS is imputed in the out-of-sample areas under different assumptions about the missingness mechanisms, then it is included into the ecological regression, linking the exposure of interest to the health outcome. This delivers area-level risk estimates, which allow a fuller adjustment for confounding than traditional areal studies. The methodology is illustrated by using simulations and a case study investigating the risk of lung cancer mortality associated with nitrogen dioxide in England (UK).

中文翻译：

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一个灵活的层次框架，用于改进区域参考环境健康研究的推理

按地理区域汇总数据的研究设计在环境流行病学中很流行。这些研究通常基于行政数据库，提供完整的空间覆盖，特别适合对整个人口进行推断。然而，由于未测量的混杂因素，由此产生的估计往往有偏差且难以解释，而这些混杂因素通常无法从常规收集的数据中获得。我们提出了一个框架来改进从此类研究中得出的推论，这些研究利用从个人层面的调查数据中获得的信息。后者通过在生态层面模仿众所周知的倾向得分方法，以区域层面的标量得分进行总结。关于用于混杂调整的倾向得分的文献主要基于个体水平的研究，并假设二元暴露变量。在这里，我们概括了它的用途，以应对以连续暴露为特征的区域参考研究。我们的方法基于指定为两阶段设计的贝叶斯层次结构：（i）来自调查样本的地理定位个体水平数据在生态水平上被放大，然后后者用于估计广义生态倾向得分（EPS）在样本区域内；(ii) 在关于缺失机制的不同假设下，将广义 EPS 归入样本外区域，然后将其纳入生态回归，将兴趣暴露与健康结果联系起来。这提供了区域级风险估计，与传统的区域研究相比，它允许对混杂进行更全面的调整。该方法通过使用模拟和案例研究来说明，该案例研究调查了英格兰（英国）与二氧化氮相关的肺癌死亡率风险。