Meta-Analysis of Time-Series Studies of Air Pollution and Mortality: Update in Relation to the Use of Generalized Additive Models

In an earlier paper, we reported the results of a metaanalysis of the association between air pollution and mortality based on the results of time-series studies published since 1985.1 In the earlier analysis, estimates of effect size were extracted from 109 studies, from single and multipollutant models, and by cause of death, age, and season. PM10, CO, NO2, O3, and SO2 were all positively and significantly associated with allcause mortality. Effect sizes generally were reduced in multipollutant models but remained significantly different from zero for PM10 and SO2. Larger effect sizes were observed for respiratory mortality for all pollutants except O3. Heterogeneity among studies was partially accounted for by differences in variability of pollutant concentration, and results were robust to alternative approaches to selecting estimates from the pool of available candidates. Generalized additive models (GAMs) evolved as the preferred approach to time-series analysis in this area because, compared with fully parametric methods, they permitted greater flexibility in modeling nonlinear relationships, they were better able to deal with missing data, and they were perhaps less prone to investigator bias in selecting the optimum multivariate model. However, it has recently been observed that some estimates of the association between air pollution and acute health effects derived from time-series studies may be incorrect because of previously unrecognized problems with GAMs.2 The principal issues that have been identified are that the default convergence criterion for the estimation procedure was not sufficiently stringent and that results differed when fully parametric versus nonparametric smoothing functions were used to control for effects of time and weather. The problem appears to have a particularly important impact when adjustments for both temporal cycles and weather are made using nonparametric smoothing functions. An additional issue is that the standard error associated with regression parameters is underestimated when the default approximate method is used to estimate this value, although in the context of a random effects model employed in meta-analyses, standard errors associated with pooled estimates of effect size appear to be only slightly affected, because greater within-study variance is offset by reduced betweenstudy variance.3 In light of these recent revelations, we revisited our original analysis and classified estimates of effect size from primary studies according to whether they were GAM-based. Any estimate that was based on nonparametric smoothing functions of time or weather was considered to be potentially affected. Figure 1 shows the prevalence of use of GAMs based on the 272 effectsize estimates for all-cause mortality from single and multipollutant models, which served as the basis of pooled estimates in our original paper. The prevalence of GAM-based estimates has clearly increased dramatically since these methods were first applied in this area in 1996. However, the frequency varies significantly among the pollutants and geographic regions considered in the original analysis. The percentage of GAMbased primary estimates ranged from 42% for SO2 (28 of 67 estimates) to 85% for CO (29 of 34), and from 33% for Australia and New Zealand (4 of 12) to 100% for Canada (27 of 27). Table 1 presents pooled estimates of effect size according to whether primary estimates were GAM-based. Effect sizes were calculated based on the same changes in pollutant concentrations as reported in the original paper. Based on single-pollutant models, all pollutants were positively and significantly associated with mortality. For all pollutants, pooled estimates from single-pollutant models were greater than those from multipollutant models. As reported in the earlier paper, pooled estimates from multipollutant models remained significantly different from zero for PM10 and SO2, based on both GAMand non-GAM-based estimates. Based on single-pollutant models, the largest effect sizes were observed for CO (non-GAM-based) and NO2 (GAM-based), while for multipollutant models, PM10 NOTEBOOK PAPER ISSN 1047-3289 J. Air & Waste Manage. Assoc. 53:258–261