A flexible hierarchical framework for improving inference in area-referenced environmental health studies - Pirani,M; Mason,A; Hansell,A; Richardson,S; Blangiardo,M (Biometrical Journal: journal of mathematical methods in biosciences, 2020)
Study designs where data have been aggregated by geographical areas are popular in environmental epi-demiology. These studies are commonly based on administrative databases and, providing a completespatial coverage, are particularly appealing to make inference on the entire population. However, the re-sulting estimates are often biased and difficult to interpret due to unmeasured confounders, which typicallyare not available from routinely collected data. We propose a framework to improve inference drawn fromsuch studies exploiting information derived from individual-level survey data. The latter are summarized inan 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 studiesand assumes a binary exposure variable. Here we generalize its use to cope with area-referenced stud-ies characterized by a continuous exposure. Our approach is based upon Bayesian hierarchical structuresspecified into a two-stage design: (i) geolocated individual-level data from survey samples are up-scaled atecological-level, then the latter are used to estimate a generalizedecological propensity score(EPS) in thein-sample areas; (ii) the generalized EPS is imputed in the out-of-sample areas under different assumptionsabout the missingness mechanisms, then it is included into the ecological regression, linking the exposureof interest to the health outcome. This delivers area-level risk estimates which allow a fuller adjustment forconfounding than traditional areal studies. The methodology is illustrated by using simulations and a casestudy investigating the risk of lung cancer mortality associated with nitrogen dioxide in England (UK).