Abstract
Studies of the relationships between environmental exposures and adverse health outcomes often rely on a two-stage statistical modeling approach, where exposure is modeled/predicted in the first stage and used as input to a separately fit health outcome analysis in the second stage. Uncertainty in these predictions is frequently ignored, or accounted for in an overly simplistic manner when estimating the associations of interest. Working in the Bayesian setting, we propose a flexible kernel density estimation (KDE) approach for fully utilizing posterior output from the first stage modeling/prediction to make accurate inference on the association between exposure and health in the second stage, derive the full conditional distributions needed for efficient model fitting, detail its connections with existing approaches, and compare its performance through simulation. Our KDE approach is shown to generally have improved performance across several settings and model comparison metrics. Using competing approaches, we investigate the association between lagged daily ambient fine particulate matter levels and stillbirth counts in New Jersey (2011-2015), observing an increase in risk with elevated exposure 3 days prior to delivery. The newly developed methods are available in the R package KDExp.