Evaluation of Bayesian spatiotemporal latent models in small area health data

Abstract

Health outcomes are linked to air pollution and demographic or socioeconomic factors that vary across space and time. Thus, it is often found that relative risks in spacetime health data have locally different temporal patterns. In such cases, latent modeling is useful in the disaggregation of risk profiles. In particular, spatiotemporal mixture models can help to isolate spatial clusters in which each has a homogeneous temporal pattern in relative risks. In mixture modeling, various weight structures can be used, and two situations can be considered: the number of underlying components is known or unknown. In this paper, we compare spatiotemporal mixture models with different weight structures in both situations. In addition, spatiotemporal Dirichlet process mixture models are compared with them when the number of components is unknown. For comparison, we propose a set of spatial cluster detection diagnostics based on the posterior distribution of the weights. We also develop new accuracy measures to assess the recovery of true relative risks. Based on the simulation study, we examine the performance of various spatiotemporal mixture models in terms of proposed methods and goodness-of-fit measures. We apply our models to a county-level chronic obstructive pulmonary disease data set from the state of Georgia.