An Approach to the Estimation of Chronic Air Pollution Effects Using Spatio-Temporal Information

There is substantial observational evidence that long-term exposure to particulate air pollution is associated with premature death in urban populations. Estimates of the magnitude of these effects derive largely from cross-sectional comparisons of adjusted mortality rates among cities with varying pollution levels. Such estimates are potentially confounded by other differences among the populations correlated with air pollution, for example, socioeconomic factors. An alternative approach is to study covariation of particulate matter and mortality across time within a city, as has been done in investigations of short-term exposures. In either event, observational studies like these are subject to confounding by unmeasured variables. Therefore the ability to detect such confounding and to derive estimates less affected by confounding are a high priority. In this article, we describe and apply a method of decomposing the exposure variable into components with variation at distinct temporal, spatial, and time by space scales, here focusing on the components involving time. Starting from a proportional hazard model, we derive a Poisson regression model and estimate two regression coefficients: the global coefficient that measures the association between national trends in pollution and mortality; and the local coefficient, derived from space by time variation, that measures the association between location-specific trends in pollution and mortality adjusted by the national trends. Absent unmeasured confounders and given valid model assumptions, the scale-specific coefficients should be similar; substantial differences in these coefficients constitute a basis for questioning the model. We derive a backfitting algorithm to fit our model to very large spatio-temporal datasets. We apply our methods to the Medicare Cohort Air Pollution Study (MCAPS), which includes individual-level information on time of death and age on a population of 18.2 million for the period 2000-2006. Results based on the global coefficient indicate a large increase in the national life expectancy for reductions in the yearly national average of PM2.5. However, this coefficient based on national trends in PM2.5 and mortality is likely to be confounded by other variables trending on the national level. Confounding of the local coefficient by unmeasured factors is less likely, although it cannot be ruled out. Based on the local coefficient alone, we are not able to demonstrate any change in life expectancy for a reduction in PM2.5. We use additional survey data available for a subset of the data to investigate sensitivity of results to the inclusion of additional covariates, but both coefficients remain largely unchanged.