A total of 144 estimates from 39 studies were included in the meta-analysis.3–5,7,9,11–15,18,19,27,29,47–71
We considered the following:
- Mortality outcome (total, cardiovascular, or respiratory);
- Location (United States or elsewhere);
- Potential confounding by PM (no adjustment for PM or adjustment by either PM10 or PM2.5; PM with an aerodynamic diameter no more than 10 or 2.5 µm, respectively);
- Cycle of analysis (yearly data or warm periods, eg, summer);
- Lag (0, 1, or 2 days; average of days 0 and 1; or average of days 1 and 2);
- Age (all ages, or the elderly— either 64+ or 65+); and
- Concentration metric (daily average, daily 1-hour maximum, or daily 8-hour maximum).
These same issues were also considered in pooled estimates for NMMAPS.
We performed a chi-squared test for heterogeneity on several subsets of studies, including the United States for total mortality and both the United States and non-United States combined for total mortality. When we rejected the hypothesis of homogeneity, we fitted the 2-stage Bayesian hierarchical model in equation 1
and evaluated the posterior distribution of the pooled effect µ. shows posterior means and 95% posterior intervals (the Bayesian formulation of the 95% confidence interval) of µ under alternative distributional assumptions for the second stage and under alternative prior specifications. Note that a single study can contribute multiple estimates if it includes data from more than one city.
Sensitivity Analysis Results of the Pooled Log-Relative Rates With Respect to the Specification of the Bayesian Hierarchical Model for Pooling*
The pooled estimates are robust to all of these model specifications. Therefore, as a baseline model, we assume at the second stage that βs
| µ, τ2
) with 1/τ2
(0.001,0.001). We also explored the findings with respect to a problem with the default implementation of generalized additive models (GAM) in the commonly used statistical software package, S-Plus.39,72
The pooled estimate was larger for studies without GAM problems such as those that used other modeling techniques or used GAM exact.39
shows the posterior means and 95% posterior regions of the pooled effects for total, cardiovascular, and respiratory causes separately for U.S. cities only and non-U.S. cities, and for all locations. These pooled effects included time-series studies for short-term lags (defined as lags of 0, 1, or 2 days; or average of either days 0 and 1 or days 1 and 2).
Posterior Means and 95% Posterior Intervals of the Pooled Log-Relative Rates for Cause-Specific Mortality*
Overall, we found that a 10-ppb increase in ozone in the few previous days (lags of 0, 1, or 2 days or a 2-day average of lags 0 and 1 or lags 1 and 2) is associated with a 0.87% increase in total mortality (95% posterior interval = 0.55% to 1.18%). Pooled effects were similar for studies within the United States and when studies outside the United States were included. When studies from all locations were considered, we found that the pooled effect for cardiovascular disease mortality is larger than for total mortality, whereas the pooled effect for respiratory mortality was lower ().
The pooled estimate for total mortality in the United States was based on 11 estimates from 9 studies in the following 9 communities: St. Louis; Kingston/Harriman, Tennessee; Santa Clara; Buffalo; Chicago; Philadelphia; Los Angeles; Detroit; and the Coachella Valley, California. Eight of these areas (all but the Coachella Valley) were included in NMMAPS ozone analysis.
We made 2 comparisons between the pooled effects obtained from the meta-analysis and from NMMAPS. First, we compared the pooled effects by including all the cities (9 from the meta-analysis and 95 from NMMAPS). Second, we restricted the comparison to the 8 cities that were included both in the meta-analysis and in NMMAPS.
compares the marginal posterior distributions of the overall effect under the meta-analysis (based on 11 estimates from the 9 cities) and in NMMAPS (95 U.S. cities, all lag 0). When we combined information across the 95 cities, the national average effect of same-day ozone on mortality from NMMAPS was a 0.25% (95% posterior interval = 0.12% to 0.39%) increase in mortality for a 10-ppb increase in the same day’s ozone concentration. compares the marginal posterior distributions of the overall effect under the meta-analysis and in NMMAPS for the 8 cities common to both the approaches (8 U.S. cities, all lag 0). When we combined information across the 8 cities, the NMMAPS pooled effect of same-day ozone concentration was 0.48% (0.03% to 0.92%) as compared with the meta-analysis estimate of 0.83% (0.38% to 1.29%). In both cases (using the 8 cities or using all the estimates), the estimated pooled effects from NMMAPS were lower than estimates from the meta-analysis. This pattern is indicative of possible publication bias.
Posterior distributions of pooled log-relative rates of all-cause mortality associated with 10-ppb increase in ozone in NMMAPS (95 cities) and for the meta-analysis of the United States (11 estimates).
City-specific posterior means and 95% posterior intervals of the log-relative rate of mortality associated with 10-ppb increase in ozone for the 8 cities included in NMMAPS and in the meta-analysis.
The pooled effect from the meta-analysis for cardiovascular and respiratory mortality combined was slightly higher than the overall effect for total mortality. This pattern was also observed in the NMMAPS analyses.
shows the posterior distribution of the heterogeneity parameter τ in log scale for total mortality and for the U.S. and non-U.S. studies combined. The city-specific effects included in the meta-analysis were more heterogeneous than estimates from NMMAPS. In the meta-analysis, there were several sources of heterogeneity in addition to potential differences between cities. These included differences in the specification of the statistical models, in the data quality, and the potential for publication bias, among other factors.
FIGURE 3 Marginal posterior distribution of the log of heterogeneity parameter (τ) for: 1) meta-analysis of 11 U.S estimates; 2) meta-analysis of 41 U.S. and non-U.S. estimates; and 3) for 95 NMMAPS cities in Bell et al.38
In , we summarize the pooled estimates from the meta-analysis with and without adjustment for PM (either PM10
). In the time-series studies, the adjustment for PM was made by including the daily level of PM as a covariate in the Poisson regression model. Pooled effects were robust to the PM adjustment. These results are consistent with the recent NMMAPS analyses.38
Posterior Means and 95% Posterior Intervals of the Pooled Log-Relative Rates With and Without Adjustment for PM*
shows posterior means and 95% posterior regions of the pooled effect for total mortality for lags 0, 1, and 2 from both the meta-analysis (using studies from the United States and elsewhere) and NMMAPS. For both analyses, the pooled effects were largest at lag 0 and smallest at lag 2.
Posterior Means and 95% Posterior Intervals of the Pooled Log-Relative Rates for Total Mortality at Various Single-Day Lags, Percent Increase in Mortality per 10-ppb Increase in Ozone
To further explore publication bias with respect to choice of lag, we calculated a pooled estimate for a variety of single-day lag times and compared the estimates for studies that provided results for only a single lag with those that provided multiple lags in the meta-analysis. More specifically, compares pooled estimates obtained by combining studies that provided a single lag estimate (0 or 1) versus pooled estimates obtained by combining studies that reported estimates for multiple lags, including lags 0 or 1. The pooled effects from the studies that provided a single lag estimate were larger than those obtained from the studies that provided multiple estimates. This indicates that the lag with the highest effect is more likely to have been reported.
Posterior Means and 95% Posterior Intervals of the Pooled Log-Relative Rates by Reported Lags*
Meta-analysis effect estimates are larger for the elderly (ie, 64 years and older or 65 and older). For this age category, a 10-ppb increase in daily ozone is associated with a 1.45% increase in total daily mortality (0.67% to 2.23%), including 10 estimates from 9 studies from both in and outside of the United States. This is higher than the estimate for all ages, at 0.87% (0.55% to 1.18%). The NMMAPS analyses found a slightly larger effect for the elderly.38
shows the pooled effects for total mortality and for cardiovascular disease mortality, as obtained from studies that used the whole year’s data or that analyzed only data in the warmer time periods. Some time-series studies of ozone and mortality explored the relationship during a particular time of year such as May to October or only the summer. These warmer time periods reflect the peak ozone season, because the chemical reactions that form ozone are temperature-dependent.73
In the NMMAPS analysis, no appreciable difference was observed between the ozone and mortality relationship for the whole year and the association during May to October.
Posterior Means and 95% Posterior Intervals of the Pooled Log-Relative Rates for the Warm Time Periods and for the Whole Year*