Estimating the effect of latent time-varying count exposures using multiple lists

A major challenge in longitudinal built-environment health studies is the accuracy of commercial business databases that are used to characterize dynamic food environments. Different databases often provide conflicting exposure measures on the same subject due to different source credibilities. As on-site verification is not feasible for historical data, we suggest combining multiple databases to correct the bias in health effect estimates due to measurement error in any 1 datasource. We propose a joint model for the time-varying health outcomes, observed count exposures, and latent true count exposures. Our model estimates the time-specific quality of sources and incorporates time dependence of true count exposure by Poisson integer-valued first-order autoregressive process. We take a Bayesian nonparametric approach to flexibly account for location-specific exposures. By resolving the discordance between different databases, our method reduces the bias in the longitudinal health effect of the true exposures. Our method is demonstrated with childhood obesity data in California public schools with respect to convenience store exposures in school neighborhoods from 2001 to 2008.