Practical Large-Scale Spatio-Temporal Modeling of Particulate Matter Concentrations

The last two decades have seen intense scientific and regulatory interest in the health effects of particulate matter (PM). Influential epidemiological studies that characterize chronic exposure of individuals rely on monitoring data that are sparse in space and time, so they often assign the same exposure to participants in large geographic areas and across time. We estimate monthly PM during 1988-2002 in a large spatial domain for use in studying health effects in the Nurses' Health Study. We develop a conceptually simple spatio-temporal model that uses a rich set of covariates. The model is used to estimate concentrations of PM10 for the full time period and PM2.5 for a subset of the period. For the earlier part of the period, 1988-1998, few PM2.5 monitors were operating, so we develop a simple extension to the model that represents PM2.5 conditionally on PM10 model predictions. In the epidemiological analysis, model predictions of PM10 are more strongly associated with health effects than when using simpler approaches to estimate exposure. Our modeling approach supports the application in estimating both fine-scale and large-scale spatial heterogeneity and capturing space-time interaction through the use of monthly-varying spatial surfaces. At the same time, the model is computationally feasible, implementable with standard software, and readily understandable to the scientific audience. Despite simplifying assumptions, the model has good predictive performance and uncertainty characterization.

Reduced Bayesian Hierarchical Models: Estimating Health Effects of Simultaneous Exposure to Multiple Pollutants

Quantifying the health effects associated with simultaneous exposure to many air pollutants is now a research priority of the US EPA. Bayesian hierarchical models (BHM) have been extensively used in multisite time series studies of air pollution and health to estimate health effects of a single pollutant adjusted for potential confounding of other pollutants and other time-varying factors. However, when the scientific goal is to estimate the impacts of many pollutants jointly, a straightforward application of BHM is challenged by the need to specify a random-effect distribution on a high-dimensional vector of nuisance parameters, which often do not have an easy interpretation. In this paper we introduce a new BHM formulation, which we call "reduced BHM", aimed at analyzing clustered data sets in the presence of a large number of random effects that are not of primary scientific interest. At the first stage of the reduced BHM, we calculate the integrated likelihood of the parameter of interest (e.g. excess number of deaths attributed to simultaneous exposure to high levels of many pollutants). At the second stage, we specify a flexible random-effect distribution directly on the parameter of interest. The reduced BHM overcomes many of the challenges in the specification and implementation of full BHM in the context of a large number of nuisance parameters. In simulation studies we show that the reduced BHM performs comparably to the full BHM in many scenarios, and even performs better in some cases. Methods are applied to estimate location-specific and overall relative risks of cardiovascular hospital admissions associated with simultaneous exposure to elevated levels of particulate matter and ozone in 51 US counties during the period 1999-2005.

Limitations of Remotely-sensed Aerosol as a Spatial Proxy for Fine Particulate Matter

Recent research highlights the promise of remotely-sensed aerosol optical depth (AOD) as a proxy for ground-level PM2.5. Particular interest lies in the information on spatial heterogeneity potentially provided by AOD, with important application to estimating and monitoring pollution exposure for public health purposes. Given the temporal and spatio-temporal correlations reported between AOD and PM2.5 , it is tempting to interpret the spatial patterns in AOD as reflecting patterns in PM2.5 . Here we find only limited spatial associations of AOD from three satellite retrievals with PM2.5 over the eastern U.S. at the daily and yearly levels in 2004. We then use statistical modeling to show that the patterns in monthly average AOD poorly reflect patterns in PM2.5 because of systematic, spatially-correlated error in AOD as a proxy for PM2.5 . Furthermore, when we include AOD as a predictor of monthly PM2.5 in a statistical prediction model, AOD provides little additional information to improve predictions of PM2.5 when included in a model that already accounts for land use, emission sources, meteorology and regional variability. These results suggest caution in using spatial variation in AOD to stand in for spatial variation in ground-level PM2.5 in epidemiological analyses and indicate that when PM2.5 monitoring is available, careful statistical modeling outperforms the use of AOD.

TRENDS IN PARTICULATE MATTER AND MORTALITY: AN APPROACH TO THE ASSESSMENT OF UNMEASURED CONFOUNDING

We propose a method for diagnosing confounding bias under a model which links a spatially and temporally varying exposure and health outcome. We decompose the association into orthogonal components, corresponding to distinct spatial and temporal scales of variation. If the model fully controls for confounding, the exposure effect estimates should be equal at the different temporal and spatial scales. We show that the overall exposure effect estimate is a weighted average of the scale-specific exposure effect estimates. We use this approach to estimate the association between monthly averages of fine particles (PM2.5) over the preceding 12 months and monthly mortality rates in 113 U.S. counties from 2000-2002. We decompose the association between PM2.5 and mortality into two components: 1) the association between “national trends” in PM2.5 and mortality; and 2) the association between “local trends,” defined as county-specificdeviations from national trends. This second component provides evidence as to whether counties having steeper declines in PM2.5 also have steeper declines in mortality relative to their national trends. We find that the exposure effect estimates are different at these two spatio-temporalscales, which raises concerns about confounding bias. We believe that the association between trends in PM2.5 and mortality at the national scale is more likely to be confounded than is the association between trends in PM2.5 and mortality at the local scale. If the association at the national scale is set aside, there is little evidence of an association between 12-month exposure to PM2.5 and mortality.

The Importance of Scale for Spatial-confounding Bias and Precision of Spatial Regression Estimators

Increasingly, regression models are used when residuals are spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on the bias and precision of regression coefficients, developing a simple framework in which to understand the key issues and derive informative analytic results. When the spatial residual is induced by an unmeasured confounder, regression models with spatial random effects and closely-related models such as kriging and penalized splines are biased, even when the residual variance components are known. Analytic and simulation results show how the bias depends on the spatial scales of the covariate and the residual; bias is reduced only when there is variation in the covariate at a scale smaller than the scale of the unmeasured confounding. I also discuss how the scales of the residual and the covariate affect efficiency and uncertainty estimation when the residuals can be considered independent of the covariate. In an application on the association between black carbon particulate matter air pollution and birth weight, controlling for large-scale spatial variation appears to reduce bias from unmeasured confounders, while increasing uncertainty in the estimated pollution effect.