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Accounting for exposure measurement errors has been recognized as a crucialproblem in environmental epidemiology for over two decades. Bayesianhierarchical models offer a coherent probabilistic framework for evaluatingassociations between environmental exposures and health effects, which takeinto account exposure measurement errors introduced by uncertainty in theestimated exposure as well as spatial misalignment between the exposure andhealth outcome data. While two-stage Bayesian analyses are often regarded as agood alternative to fully Bayesian analyses when joint estimation is notfeasible, there has been minimal research on how to properly propagateuncertainty from the first-stage exposure model to the second-stage healthmodel, especially in the case of a large number of participant locations alongwith spatially correlated exposures. We propose a scalable two-stage Bayesianapproach, called a sparse multivariate normal (sparse MVN) prior approach,based on the Vecchia approximation for assessing associations between exposureand health outcomes in environmental epidemiology. We compare its performancewith existing approaches through simulation. Our sparse MVN prior approachshows comparable performance with the fully Bayesian approach, which is a goldstandard but is impossible to implement in some cases. We investigate theassociation 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.

A scalable two-stage Bayesian approach accounting for exposure measurement error in environmental epidemiology