Evaluation of Bayesian spatio-temporal latent models in small area health data

Health outcomes are linked to air pollution, demographic, or socioeconomic factors which vary across space and time. Thus, it is often found that relative risks in space-time health data have locally different temporal patterns. In such cases, latent modeling is useful in the disaggregation of risk profiles. In particular, spatio-temporal mixture models can help to isolate spatial clusters each of which 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 spatio-temporal mixture models with different weight structures in both situations. In addition, spatio-temporal Dirichlet process mixture models are compared to 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 spatio-temporal 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.