Abstract: We develop a new Bayesian two-stage space-time mixture model to investigate the effects of
air pollution on asthma. The two-stage mixture model proposed allows for the identification
of temporal latent structure as well as the estimation of the effects of covariates on health
outcomes. In the paper, we also consider spatial misalignment of exposure and health data.
A simulation study is conducted to assess the performance of the 2-stage mixture model.
We apply our statistical framework to a county-level ambulatory care asthma data set in the
US state of Georgia for the years 1999-2008.
Key words: Space-time mixture model; air pollution; covariate adjustment; asthma;
Abstract: 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 spatial health data have locally different patterns. In such cases, latent modeling is useful in the disaggregation of risk proﬁles. In particular, spatial-temporal mixture models can help to isolate spatial clusters each of which has a homogeneous temporal pattern in relative risks. Mixture models are assumed as they have various weight structures and considered in two situations: the number of underlying components is known or unknown. In this paper, we compare spatial-temporal mixture models with different weight structures in both situations. For comparison, we propose a set of spatial cluster detection diagnostics which are based on the posterior distribution of weights. We also develop new accuracy measures to assess the recovery of true relative risk. Based on the simulation study, we examine the performance of various spatial-temporal mixture models in terms of proposed methods and goodness-of-ﬁt measures. We examine two real data sets: low birth weight data and chronic obstructive pulmonary disease data.