Partitioning evidence of association between air pollution and mortality

We thank Drs. Pope and Burnett for their insightful commentary and for emphasizing the key point of our paper: in studies of air pollution and health, it is useful to quantify the evidence of the association between air pollution and health at distinct temporal and spatial scales of variation in the data because the estimated association at some of these scales might be more subject to confounding bias than others. In this paper, we estimate the association between month-tomonth variation in average PM2.5 in the previous year and month-to-month variation in mortality rates in 113 U.S. counties from 2000 to 2002. Our approach decomposes evidence for this association into three components: comparisons across counties of average PM2.5 levels and mortality rates (spatial); comparisons across time of national levels in PM2.5 and mortality rates (temporal); and comparisons across counties of deviations in county-specific trends in PM2.5 and mortality from their respective national trends (space-by-time interaction). In this paper, we set aside the spatial component of association, and we estimate the association at the remaining two scales (temporal and space-by-time interaction). We report the associations at each of these scales separately. The spatial variability is the key information used to estimate the health effects of long-term exposure in the ACS and Six-Cities studies. Note that these studies rely on time-invariant measures of exposure common to all individuals residing in a community and incorporate only individual-level covariates collected at baseline. Therefore, although they use prospectively collected health data, they are based on cross-sectional comparisons. Because the many factors that vary across populations in distant communities may be associated with both air pollution and mortality, the spatial information may be subject to confounding bias from unmeasured factors. For this reason, the analysis presented in this paper sets this component of variation aside by including county-specific intercepts in the regression models. The two remaining components of variation (the temporal and spaceby-time components) have not previously been studied in detail. The question we address is whether this information provides results similar to previous studies of the spatial component. In our analysis, we compare mortality rates over time within a county, thereby using each county as its own control and avoiding biases from cross-sectional comparisons. Our simplest model (model 1) combines the temporal and spaceby-time interaction information and estimates a large positive association between monthly variation in annual average PM2.5 and monthly variation in mortality rates, similar in magnitude to that estimated in previous spatial analyses. We note that the standard error of the PM2.5 effect from this model is only twice the standard error of the PM2.5 coefficient in the American Cancer Society’s prospective study and one-quarter the size of the standard error of the PM2.5 coefficient from the Six-Cities Study. Therefore, there is considerable information left for estimating the long-term effect of PM2.5 in model 1 after the cross-sectional component is set aside. We further partition the variation used in model 1 into its two constituents: temporal variation and the space-by-time interaction. If there is no residual confounding in the withincity comparisons over time, so that model 1 is correctly specified, the association between PM2.5 and mortality should be the same at the two scales. However, we find very different associations at the two scales. Both nationally averaged PM2.5 and mortality are trending down over time, producing a large positive association at this scale. However, counties with the steepest downward trends in PM2.5 do not have correspondingly steep declines in mortality, producing no association at the local scale. We agree with Drs. Pope and Burnett that the association between the national trends is more likely to be confounded. There are a multitude of factors that cause trends in PM2.5 and mortality at the national scale. We believe that there is less potential for confounding bias at the local scale. Note that there is sufficient information to estimate the PM2.5 effect at both scales; the space-by-time interaction accounts for 57% of the temporal variability in these data (see Table 1 of our paper). In summary, our paper introduces an approach that decomposes information from an observational epidemiologic study into distinct temporal and spatial components which might experience different degrees of confounding bias. Most previous studies of long-term air pollution exposure have focused on the cross-sectional comparison; here, we look exclusively at comparisons over time, using each city as its own control. We find a substantial difference in the estimated PM2.5-mortality association when we look at nationally averaged trends versus local trends. Although both PM2.5 and mortality are trending downward nationally, counties with steeper reductions in PM2.5 do not tend to have steeper reductions in mortality. These results, together with the fact that our findings differ from previously published studies, emphasize the importance of investigating the potenFrom the Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland. Copyright © 2007 by Lippincott Williams & Wilkins ISSN: 1044-3983/07/1804-0427 DOI: 10.1097/EDE.0b013e318068647b