Multivariate Spatial-Temporal Modeling of Environmental-Health Processes

Abstract

In many applications in environmental sciences and epidemiology, data are often collected over space and time. In some cases, the spatial-temporal data of interest are multivariate, and these multivariate spatial-temporal processes often have a complicated dependency structure. Hence, multivariate spatial-temporal modeling is a very challenging task. In this study, we develop statistical models to effectively account for multivariate spatial-temporal dependency structures of air pollution concentrations and human health outcomes.

Fine particulate matter (PM2.5) is an atmospheric pollutant that has been linked to serious health problems, including mortality. PM2.5 has five main components: sulfate, nitrate, total carbonaceous mass, ammonium, and crustal material. These components have complex spatial-temporal dependency and cross dependency structures. It is important to gain better understanding about the spatial-temporal distribution of each component of the total PM2.5 mass, and also to estimate how the composition of PM2.5 changes with space and time. We introduce a multivariate spatial-temporal model for speciated PM2.5. Our hierarchical framework combines different sources of data and accounts for potential bias. In addition, a spatiotemporal extension of the linear model of coregionalization is developed to account for spatial and temporal dependency structures for each component as well as the associations among the components. We apply our framework to speciated PM2.5 data in the United States for the year 2004.

In addition, the chemical composition of PM2.5 varies across space and time so the association between PM2.5 and mortality could change with space and season. Thus, we develop and implement a multi-stage Bayesian framework that provides a very broad and flexible approach to studying the spatial-temporal associations between mortality and population exposure to daily PM2.5 mass, while accounting for different sources of uncertainty. In the first stage, we map ambient PM2.5 air concentrations using all available monitoring data and an air quality model (CMAQ) at different spatial and temporal scales. In the second stage, we examine the spatial-temporal relationships between the health end-points and the exposures to PM2.5 by introducing a spatial-temporal generalized Poisson regression model. We adjust for time-varying confounders, such as seasonal trends. A common seasonal trends model uses a fixed number of basis functions to account for these confounders, but the results can be sensitive to the number of basis functions. Thus, instead the number of the basis functions is treated as an unknown parameter in our Bayesian model, and we use a space-time stochastic search variable selection method. The framework is illustrated using a data set in North Carolina for the year 2001.