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Studies of the relationships between environmental exposures and adversehealth outcomes often rely on a two-stage statistical modeling approach, whereexposure is modeled/predicted in the first stage and used as input to aseparately fit health outcome analysis in the second stage. Uncertainty inthese predictions is frequently ignored, or accounted for in an overlysimplistic manner, when estimating the associations of interest. Working in theBayesian setting, we propose a flexible kernel density estimation (KDE)approach for fully utilizing posterior output from the first stagemodeling/prediction to make accurate inference on the association betweenexposure and health in the second stage, derive the full conditionaldistributions needed for efficient model fitting, detail its connections withexisting approaches, and compare its performance through simulation. Our KDEapproach is shown to generally have improved performance across severalsettings and model comparison metrics. Using competing approaches, weinvestigate the association between lagged daily ambient fine particulatematter levels and stillbirth counts in New Jersey (2011-2015), observing anincrease in risk with elevated exposure three days prior to delivery. The newlydeveloped methods are available in the R package KDExp.

A Bayesian framework for incorporating exposure uncertainty into health analyses with application to air pollution and stillbirth