A spatial partial differential equation approach to addressing unit misalignments in Bayesian poisson space-time models.

Spatial analyses using data from geographic areas that change shape and location over time, like US ZIP codes, produce biased results to the extent that unit misalignments are related to covariate effects. To address this issue, one method has incorporated a fixed effect measure of population shifts and a spatial structure as a block-diagonal neighborhood adjacency matrix within a Besag-York-Mollié (BYM) model. However, this approach assumes that spatial relationships among units change with time and precludes the assessment of temporal dynamic effects. Here, we assume that a continuous Gaussian random field underlies misaligned data and apply a stochastic partial differential equation (SPDE) approach to modeling area outcomes. We compare SPDE and BYM methods and show that both provide similar estimates of covariate effects. Importantly, we demonstrate that the SPDE approach can additionally identify autoregressive processes underlying the development of problematic health outcomes using data observed across Pennsylvania over 11 years.