Research Article Volume 121  Issue 1  January 2013
TimeSeries Analyses of Air Pollution and Mortality in the United States: A Subsampling Approach
Suresh H. Moolgavkar,^{1}^{,}^{2} Roger O. McClellan,^{3} Anup Dewanji,^{4} Jay Turim,^{1} E. Georg Luebeck,^{2} and Melanie Edwards^{1}

Background: Hierarchical Bayesian methods have been used in previous papers to estimate national mean effects of air pollutants on daily deaths in timeseries analyses.
Objectives: We obtained maximum likelihood estimates of the common national effects of the criteria pollutants on mortality based on timeseries data from ≤ 108 metropolitan areas in the United States.
Methods: We used a subsampling bootstrap procedure to obtain the maximum likelihood estimates and confidence bounds for common national effects of the criteria pollutants, as measured by the percentage increase in daily mortality associated with a unit increase in daily 24hr mean pollutant concentration on the previous day, while controlling for weather and temporal trends. We considered five pollutants [PM_{10}, ozone (O_{3}), carbon monoxide (CO), nitrogen dioxide (NO_{2}), and sulfur dioxide (SO_{2})] in single and multipollutant analyses. Flexible ambient concentration–response models for the pollutant effects were considered as well. We performed limited sensitivity analyses with different degrees of freedom for time trends.
Results: In singlepollutant models, we observed significant associations of daily deaths with all pollutants. The O_{3} coefficient was highly sensitive to the degree of smoothing of time trends. Among the gases, SO_{2} and NO_{2} were most strongly associated with mortality. The flexible ambient concentration–response curve for O_{3} showed evidence of nonlinearity and a threshold at about 30 ppb.
Conclusions: Differences between the results of our analyses and those reported from using the Bayesian approach suggest that estimates of the quantitative impact of pollutants depend on the choice of statistical approach, although results are not directly comparable because they are based on different data. In addition, the estimate of the O_{3}mortality coefficient depends on the amount of smoothing of time trends.

Citation: Moolgavkar SH, McClellan RO, Dewanji A, Turim J, Luebeck EG, Edwards M. 2013. TimeSeries Analyses of Air Pollution and Mortality in the United States: A Subsampling Approach. Environ Health Perspect 121:73–78; http://dx.doi.org/10.1289/ehp.1104507
Address correspondence to S.H. Moolgavkar, Exponent Inc., 15375 SE 30th Place, Suite 250, Bellevue, WA 98007 USA. Telephone: (206) 6183954. Fax: (425) 5198799. Email: Moolgavkar@gmail.com
This work was partially funded by the American Petroleum Institute.
S.H.M., R.O.M., and J.T. have, at various times, been consultants to the U.S. Environmental Protection Agency, the utility industry, and the American Petroleum Institute. S.H.M. and M.E. are employed by Exponent Inc., Bellevue, Washington. J.T. was formerly employed by Exponent Inc., Alexandria, Virginia. The remaining authors declare they have no actual or potential competing financial interests.
Received: 18 September 2011
Accepted: 24 October 2012
Advance Publication: 24 October 2012
Final Publication: 1 January 2013
Timeseries analyses of air pollution and various health end points, including daily mortality, using flexible generalized linear models (GLMs) or generalized additive models (GAMs), have become commonplace in the last decade. The National Morbidity, Mortality and Air Pollution Study (NMMAPS) was an ambitious effort undertaken by scientists at Johns Hopkins University (Baltimore, MD, USA) and Harvard University (Cambridge, MA, USA) to investigate the association between particulate pollution (i.e., particulate matter with an aerodynamic diameter ≤ 10 µm; PM_{10}) and morbidity and mortality in the 90 largest metropolitan areas in the United States over the period 1987–1994 using timeseries methods (Dominici et al. 2003; Samet et al., 2000a, 2000b, 2000c). For the mortality analyses, the investigators used a common approach for analyses of the timeseries data on daily PM_{10} levels and deaths for each city. Specifically, a national mean estimate for the association between PM_{10} and mortality was obtained by combining the individual cityspecific estimates using a hierarchical Bayes procedure, which assumed that the cityspecific effects were normally distributed. Since then the analyses have been extended to include more cities, more years of data, and a second pollutant, ozone (O_{3}) (Bell et al. 2004; Smith et al. 2009). In this article, we propose an approach to analyzing multicity timeseries data that is complementary to the hierarchical Bayes approach.
Arguably, for standard setting, one might want to estimate not a national mean effect, but a common pollutant effect across the country. The most direct way to estimate a common pollutant effect on mortality across multiple cities would be to analyze all cities simultaneously using a GLM or GAM model postulating a common pollutant effect estimate across cities, but with control of confounders specific to each city. A statistical test for the hypothesis that there is a common pollutant effect across cities could then be based on standard likelihoodbased procedures or on the Akaike or Bayes information criterion (AIC or BIC). Alternatively, a computational approach to investigating the distribution of a common estimator of a pollutant effect is to use the bootstrap or the jackknife procedure on the full complement of cities (Efron and Tibshirani 1993). However, with a large number of cities this conceptually simple approach presents formidable computational problems. One way around the computational problems is to use either the “deletek jackknife” followed by the bootstrap procedure (Efron and Tibshirani 1993) or the subsampling procedure (Politis et al. 1999). In this study, we used the subsampling procedure to analyze the timeseries data on all the criteria pollutants, with the exception of lead, and mortality in 108 metropolitan areas in the United States over the 14year period 1987–2000.
Methods
We downloaded the mortality and air pollution timeseries data from the NMMAPS web site maintained by the Johns Hopkins investigators (http://www.ihapss.jhsph.edu/data/data.htm). Using the same database allowed direct comparisons to be made to the previous work of the Johns Hopkins team and others using these data. Daily data on the number of deaths are available for 108 metropolitan areas over the 14year period 1987–2000. Daily concentrations of the criteria pollutants—PM_{10}, O_{3}, carbon monoxide (CO), nitrogen dioxide (NO_{2}), and sulfur dioxide (SO_{2})—are also available; although for each of the pollutants, information is available only for a subset of the days. A limitation, shared with all epidemiologic analyses of air pollution data, is that the data were collected from stationary monitors to determine compliance with air quality regulation. Thus, the data collected are not necessarily ideal for epidemiologic studies. We recognize also that ambient concentrations are imperfect surrogates for personal exposure.
For the usual bootstrap approach, for each bootstrap cycle, 108 cities would be chosen with replacement from the original set of 108 cities, and the maximum likelihood estimate (MLE) of the pollutant effect computed using Poisson regression methods. This procedure would be repeated many times to obtain an estimate of the distribution of the common pollutant effect. However, with the large number of cities considered in these analyses, it is computationally infeasible to derive an MLE using this approach. Therefore, an alternative procedure, such as the deletek jackknife (Efron and Tibshirani 1993) or the closely related subsampling procedure (Politis et al. 1999) must be implemented. For the deletek jackknife followed by the bootstrap procedure, first the set of all possible subsets of size d = 108 – k is constructed from the 108 cities. Each bootstrap cycle then randomly selects a city from this set, and the common pollutant effect is estimated for the specific chosen set of d cities.
We used a closely related method, the subsampling procedure described by Politis et al. (1999). In this procedure, for each bootstrap cycle, we randomly chose d cities without replacement out of the 108 cities with available data, and estimated the common pollutant effect for each sample of d cities. Politis et al. (1999) recommend that d be much smaller than 108, and we chose d = 4. The choice of d is arbitrary; however, the confidence intervals (CIs) for the parameter estimates have to be adjusted for this choice as discussed below. The distribution of the estimator of the common pollutant effect was based on 5,000 bootstrap cycles.
Let X_{1}, X_{2}, …, X_{n} be a sequence of independent observations (i.e., a sequence of realizations of independent random variables). In our case, each observation in the sequence represents the data on daily deaths, pollutant concentrations, and weather variables over the period 1987–2000 in each of the n cities considered in the analyses. The total number of cities, n, depends on the pollutant or combination of pollutants considered. For example, n = 102 for analyses that involve PM_{10} alone, and n = 56 for analyses that involve all pollutants. Let Θ be the parameter representing the common effect of a pollutant, and let Θ_{n} be the MLE for Θ based on n observations and Θ_{d} the MLE for Θ based on d<<n observations (i.e., based on a subset of d cities), then, by general maximum likelihood theory, Θ_{n} and Θ_{d} converge to Θ with rates _{√}n and _{√}d, respectively.
Under standard likelihoodbased procedures, inferences would be based on the distribution of Θ_{n}. However, computation of Θ_{n} and its distribution is infeasible with large n. Therefore, we based our inferences on Θ_{d}, where in our case, d = 4, and based our CIs on the subsampling distribution as described by Politis et al. (1999). The properties of the subsampling procedure hold under rather weak conditions. The sequence of observations is required to satisfy the αmixing condition (Politis et al. 1999, p. 315). This condition is seen to be trivially satisfied by a sequence of independent observations. An anonymous referee suggested that sampling units other than entire cities might be more appropriate. We agree that other sampling schemes need to be explored.
CIs were computed after adjusting for the size of the subsample as follows. If F_{d}* represents the empirical distribution function of [pmath]sqrt{d}[/pmath] (Θ_{d} – Θ), then for any significance level α,
F_{d}^{*–1}(α/2) < [pmath]sqrt{n}[/pmath] (Θ_{n} – Θ) < F_{d}^{*–1}(1 – α/2), [1]
with probability close to 1 – α. It then follows that Θ_{n} – (1/[pmath]sqrt{n}[/pmath])F_{d}^{*–1}(1 – α/2) < Θ < Θ_{n} – (1/[pmath]sqrt{n}[/pmath])F_{d}^{*–1}(α/2) is a 1 – α CI for ∪. In our case, we were unable to estimate ∪_{n} because of computational issues. We therefore approximated Θ_{n} by (ΣΘ_{d})/N, where N = 5,000, the total number of subsamples drawn. That is, we approximated Θ_{n} as the mean of the Θ_{d}.
Thus, for our analyses, for each bootstrap cycle, we drew a random sample of four cities without replacement from among the 108 cities with available data. We then fit an overdispersed Poisson model to the randomly chosen 4 cities to obtain the MLE of the common pollutant effects on mortality in the 4 cities, but with confounders, such as temperature and relative humidity, being separately controlled in each of the 4 cities. Because a number of previous analyses (e.g., Bell et al. 2004; Dominici et al. 2003) have considered the effect of the pollutants with a 1day lag, we have done the same in these analyses. Likewise, the number of degrees of freedom (df) for time trends and weather are also consistent with those used in previous analyses (Bell et al. 2004; Dominici et al. 2003; Moolgavkar 2003). Specifically, for each bootstrap cycle we modeled the number of deaths from all causes (with accidents and suicides removed) in a city on a specific day as a function of the 24hr average pollutant concentration on the previous day, temporal trends (50 or 100 df natural spline), day of the week (categorical variable), mean temperature on the previous day (6 df natural spline), and mean dewpoint temperature on the previous day (6 df natural spline). Note that this model controlled for confounders, day of week effects, and time trends in a cityspecific fashion.
To investigate the shape of the ambient concentration–response relationship, we used the same models with the pollutant effects represented by natural splines with 6 df. Multiple pollutants that have been concurrently measured can be easily added as covariates in these analyses. Because of missing data, the size of the data set from which samples of cities were drawn for analyses depended on the number of pollutants considered.
Clearly, the choice of lags for specific pollutants and for the weather variables—temperature, and relative humidity—should be based on biological considerations whenever possible. Unfortunately, there is little information to guide these choices. In previous publications, a 1day lag has often been used. For example, in the revised NMMAPS analyses, Dominici et al. (2003) used the same lag for each of the pollutants in their multipollutant analyses. Their results indicate that a 1day lag yields close to the maximum impact on daily mortality. It would be possible also to consider other lag structures, such as distributed lag models. However, the purpose of this study was not to be a comprehensive reanalysis of the NMMAPS data, but to provide an approach to the analysis of national data that complements the Bayesian approach. Similarly for the weather covariates, we used a 1day lag because there is little biological information to suggest that any specific lag structure is better than any other.
The model was fit to the data using the R software package (http://www.rproject.org). The means of the 5,000 maximum likelihood estimates of the common pollutant effects were approximately unbiased and consistent estimators of the common national effects of the pollutants.
We conducted simulations to investigate the coverage properties of the CIs constructed as described above. Specifically, we generated 100 observations based on a Poisson variate with an intercept and a slope. From these 100 observations, we drew 5,000 subsamples of size 4 without replacement and computed 90% and 95% CIs as described above in addition to computing the usual likelihoodbased CIs. We repeated this entire procedure 1,000 times to investigate the coverage properties of the CIs. We found that the mean of the 5,000 subsample estimates was an excellent approximation to the MLE (data not shown). While the usual likelihoodbased CIs covered the true values of the parameters with the nominal coverage probabilities, the subsampling CIs were conservative, that is, their coverage probabilities were larger than the nominal coverage probabilities. The 95% CIs covered the true values of the parameters approximately 98% of the time and the 90% CIs covered the true values of the parameters approximately 95% of the time (data not shown). Therefore, because the estimated CIs were highly conservative (i.e., too wide), we present both 95% and 90% CIs in our tables in the present study and note that our tests of significance (i.e., whether the CIs contain 0) are also conservative (i.e., the actual level of significance is smaller than the nominal alpha). The coverage properties of both of the CIs constructed using the subsampling approach and the credible intervals constructed in the hierarchical Bayes approach need to be explored in realistic simulation scenarios.
Results
Bootstrap means and 90% and 95% CIs after smallsample corrections for common nationwide estimates of effects of pollutants represent associations with incremental changes in the 24hr average concentration on the previous day of 10 μg/m^{3} for PM_{10}; 10 ppb for O_{3}, SO_{2}, and NO_{2}; and 1 ppm for CO. The unit measures for the individual pollutants were chosen to facilitate comparisons with previous estimates rather than typical daytoday variations in ambient concentrations, which vary among cities. With time trends smoothed using 100 df natural splines, all pollutants were significantly (at the 0.05 level) associated with mortality in singlepollutant models (Table 1). With 50 df natural splines for time trends, the estimated coefficient for O_{3} was greatly attenuated and statistically insignificant.
The magnitudes of associations with incremental increases in CO, NO_{2}, and SO_{2} were greater than for associations with PM_{10} and O_{3}. When CO, NO_{2}, and SO_{2} were included in the same model with 100 df splines for time trends, all three associations were attenuated and the association of CO with mortality was no longer statistically significant (Table 2).
Twopollutant analyses of PM_{10} and each of the gases with 100 df splines for time trends indicated significant associations for PM_{10} in all four models, although estimated effects were attenuated except in the model adjusted for O_{3} (Table 3). Effect estimates for CO, NO_{2}, and SO_{2} were significant and consistent with estimates that were not adjusted for PM_{10}, but the estimated effect of O_{3} on mortality was attenuated and was not statistically significant based on the 95% CI or even the 90% CI (Table 3).
Bootstrap means for flexible ambient concentration–response relationships, using 6 df natural splines, between pollutant concentrations and deaths on the following day estimated from singlepollutant models suggest nonlinearity and thresholdlike behavior for NO_{2}, PM_{10}, and O_{3} (Figure 1). However, the CIs for NO_{2} and PM_{10} are wide and the concentration–response relationships are consistent with linearity.
Our approach assumes a common national pollutant effect. However, if there is a common national pollutant effect, then for a randomly chosen set of four cities, one would expect a common sharedeffects model to have a lower AIC than a model postulating separate effects. Therefore, for each bootstrap cycle, we computed the AIC for the common pollutant effect model and for the individual models of each sample of four cities selected for each cycle. For all pollutants, the AIC was lower for the separate fourcity fits than for the model postulating common pollutant effects for more than half the cycles (data not shown).
Discussion
In this study, we used a subsampling bootstrap approach to estimating maximum likelihood estimates for common national effects for associations of individual pollutants with mortality. Previous analyses of NMMAPS data have used a hierarchical Bayes approach (e.g., Bell et al. 2004; Samet et al. 2000a, 2000b, 2000c; Smith et al. 2009) to estimate a national mean effect.
The procedure described in this study is one approach to estimating common pollutant effects, if they exist; however, in a vast geographically and climatically diverse country such as the United States, it is not unreasonable to expect heterogeneity of pollutant effects across the country. First, PM is a complex mixture whose composition varies by region and season. O_{3} could also be considered a mixture because it is generally present with other oxidants. Second, for all pollutants, any effects on human health would be expected to be modified by weather and by the circumstances of exposure, which clearly vary by region and season. A comparison of AIC statistics for samplespecific (four city) models and for common estimate models suggests that the fourcity models fit the data better than the common model in most cases, which is consistent with heterogeneous effects among cities. This finding is consistent with the results of the hierarchical Bayes multicity analyses (Bell and Dominici 2008; Dominici et al. 2003; Smith et al. 2009). The heterogeneity of pollutant effects suggests that any single national estimate may not provide a reliable measure of the health benefits that would accrue from a reduction in pollutant concentrations.
An advantage of the Bayesian approach is that it allows for heterogeneity of cityspecific coefficients, albeit with the simplifying assumptions that these are independent and identically distributed. That said, the hierarchical Bayes approach and the subsampling approach described in this study are complementary approaches to estimating a single national pollutant effect. Under both approaches, however, further investigation of heterogeneity requires that regional analyses be performed.
The use of Bayesian methods in multicity analyses was pioneered by the first investigators of NMMAPS (Dominici et al. 2000; Samet et al. 2000a, 2000b, 2000c). Their approach to the analyses of multicity data used a twostage procedure, with analyses of single cities at the first stage, followed by a hierarchical Bayes analysis of the firststage results to arrive at a single estimate of a national mean for the pollutant effect. Once the firststage analyses were completed, the estimated pollutant effects were considered in isolation from the other covariates and combined in a second stage, resulting in a procedure that is operationally similar to a metaanalysis. This procedure assumes that the asymptotic distribution of the pollutant effect estimate has been achieved, and that a simple approximation to a full Bayesian analysis yields valid results in the second stage. The first assumption regarding the asymptotic distribution of parameter estimates is widely made in statistical procedures; in fact, one study (Dominici et al. 2000) reports that the asymptotic properties of the MLE are well approximated in the firststage analyses. Our procedure also relied on asymptotic results.
The assumptions underlying the secondstage procedure may be more problematic. A fully Bayesian analysis would put prior distributions on all the parameters of the model, not just the pollutant coefficients, and allow the parameter estimates along with their covariance structure from the first stage to be carried forward to the secondstage analyses. Although this procedure may be possible in theory, it would be much more computationally intensive and may not be practical. Although it is not clear that a fully Bayesian analysis would make a substantial difference to the results, these issues do not arise with the approach proposed in this study, and common national pollutant–mortality coefficients and their CIs can be estimated in a singlestage analysis even when multiple pollutants are modeled using splines. However, the simple simulation that we performed indicated that the CIs generated using our approach were conservative. The coverage properties of CIs and credible intervals generated, respectively, by the subsampling and the hierarchical Bayes procedures need to be investigated using realistic and comprehensive simulation scenarios.
Smith et al. (2009) observed that the national mean from the hierarchical Bayes analysis approximates the mean (not the inverse variance weighted mean) of the individual cityspecific estimates as the variance of assumed distribution of the cityspecific coefficients goes to infinity. They cautioned against any use of a national statistic, but advocated the use of a populationweighted mean if a national statistic is computed. The mean of the distribution of the bootstrap samples we generated implicitly has a population weight built in because the common estimate for each bootstrap cycle is influenced by the sizes of the populations of the cities in that cycle.
Our CIs for the estimated common national effects of the pollutants are wider than the credible intervals reported in earlier studies using the hierarchical Bayes approach. This could be a consequence of hierarchical Bayes credible intervals that may be too narrow (because the fully Bayesian procedure is replaced by an approximation that ignores estimates of weather and timetrend parameters in the secondstage analyses), in addition to subsampling CIs that are too wide (conservative), as suggested by our simulations.
Previous multicity analyses have focused on PM_{10} or O_{3} (Bell et al. 2004, 2006; Dominici et al. 2003; Katsouyanni and Samet 2009; Smith et al. 2009). Analyses that addressed regional heterogeneity (Bell and Dominici 2008; Dominici et al. 2003; Smith et al. 2009) reported considerable heterogeneity of estimated coefficients for both PM and O_{3}. Dominici et al. (2003) reported the largest PM_{10} coefficients were in the Northeast region among the seven regions they considered, followed by Southern California. The smallest PM_{10} coefficients were reported in the Upper Midwest. The estimated coefficients in the Northeast were twice as high as those reported for the Upper Midwest. Smith et al. (2009) estimated the highest O_{3} coefficients for the Northeast and the Industrial Midwest but did not estimate significant effects for Southern California, where levels of O_{3} have always been high. A similar gradient of O_{3} coefficients, with no associations in Los Angeles, intermediate effect estimates for Chicago, and larger effect estimates for New York have been reported in other studies (Moolgavkar 2003).
Previous timeseries analyses of air pollution and mortality have focused on PM_{10} or O_{3}, with other pollutants addressed as confounders, if at all (Dominici et al. 2003). Our findings suggest that the emphasis on PM and O_{3} may deserve reconsideration because estimated associations were strongest for CO, NO_{2}, and SO_{2}. In addition, coefficients for all three gases remained highly significant in joint pollutant analyses with PM_{10}, and coefficients for NO_{2}, and SO_{2} remained significant in a model that included all three gases.
PM_{10}_{.} The NMMAPS analyses estimated a national mean increase of 0.27% in mortality for a 10μg/m^{3} increase in PM_{10} on the previous day using GAMs, and a 0.22% increase using a GLM. Our estimate of the mean with 50 df natural splines for time trends is 0.4% (95% CI: 0.30, 0.53). This estimate is not directly comparable to the estimates from the hierarchical Bayes analyses because we used somewhat different cityspecific models and had many more cities with more years of data, although it is of interest to note that our estimate is virtually identical to the estimate reported for the Northeast (0.41; 95% posterior interval: 0.04, 0.78) in the NMMAPS reanalyses (Dominici et al. 2003).
In twopollutant analyses of PM_{10} with CO, NO_{2}, or SO_{2}, the PM_{10} coefficients were somewhat attenuated but continued to be significantly associated with mortality. The association with PM_{10} was attenuated most in joint pollutant analyses with NO_{2}. With the exception of the twopollutant model of PM_{10} and O_{3}, which produced a highly insignificant coefficient for O_{3} when a 50 df smoother was used, results were robust to the degree of smoothing of time trends (data not shown). Therefore, we report only 100df timetrend smoothers for joint pollutant analyses in this study.
O_{3}. There are several fairly recent metaanalyses (Bell et al. 2005; Ito et al. 2005; Levy et al. 2005) and multicity analyses (Bell et al. 2004; Katsouyanni and Samet 2009; Smith et al. 2009) of the association between O_{3} and daily deaths. As Smith et al. (2009) point out, there are two kinds of potential biases in metaanalyses: publication bias and model selection bias (in which the investigators test many models and report the results of only those models that show positive and significant associations). Therefore, multicity analyses are preferable to metaanalyses.
The first multicity analyses were conducted by Dominici et al. (2003). These analyses were based on 8 years of data in 90 cities in the United States. For a 10ppb increase in daily O_{3}, Dominici et al. (2003) reported a national mean increase of approximately 0.25% in deaths on the following day, and this estimate was statistically significant. In an update of these analyses in 95 cities and with 14 years of data, Bell et al. (2004) reported a statistically significant national mean of approximately 0.2% (approximate 95% posterior interval: 0.1, 0.3%) for a 1day lag O_{3} effect on mortality. In a reanalysis of data from the NMMAPS (Katsouyanni and Samet 2009), the O_{3} mortality estimates were highly sensitive to the degree and type of smoothing used for seasonality control, and inclusion of PM_{10} markedly reduced the O_{3} mortality estimates. Our estimated mean with 100 df smoothers for time trends is 0.40% (95% CI: 0.27, 0.56). With 50 df smoothers for time trends, the estimated mean for O_{3} is 0.08% (95% CI: –0.16, 0.38). Thus, the estimated O_{3} effect is sensitive to the degree of smoothing of temporal trends, in agreement with the results reported by Katsouyanni and Samet (2009). Because O_{3} is a highly seasonal pollutant, adequate control of seasonality is important, and using only 50 df for time trends may not be sufficient. To investigate this issue more thoroughly, further analyses of the data stratified by season should be undertaken.
In joint pollutant analyses (100 df smoothers for time trends) with PM_{10}, the O_{3} coefficient is substantially attenuated and becomes insignificant, as also reported by Smith et al. (2009) and Katsouyanni and Samet (2009). One possible reason for the widening of CIs for O_{3} effects is the greatly reduced data set used in joint pollutant analyses. If this were the sole reason, however, one would expect to observe the same phenomenon for the PM_{10} effect, which was virtually unchanged and continued to remain highly significant.
In an update to the Bell et al. (2004) study, Bell et al. (2006) examined the ambient concentration–response curve for O_{3} and mortality, where their O_{3} metric was the average of the 24hr mean concentrations on the current and previous days. Among various approaches evaluating ambient concentration–response relationships, Bell et al. (2006) used natural splines followed by a hierarchical Bayes procedure to obtain a national estimate. The results shown in Figure 3 of their article suggest the possibility of a threshold at about 15 ppb. Smith et al. (2009) fit a piecewise linear ambient concentration–response relationship with breaks at 40 ppb and 60 ppb, and they showed that a hockeystick–shaped curve with a break at 40 ppb is consistent with the data. Our analysis shows evidence of a threshold at a little over 30 ppb (Figure 1B). However, the data are too sparse to draw any firm conclusions regarding the shape of the concentration–response curve at low concentrations. We emphasize here that our analyses are based on 24hr average concentrations of O_{3}, whereas regulation is based on the maximum 8hr averages. Pollutant effect estimates cannot easily be converted from one averaging time to another. Smith et al. (2009) showed that a simple scaling procedure is inadequate. It is, therefore, important to repeat these analyses with other measures of exposure.
CO, NO_{2}, SO_{2}. The only previous multicity analyses of these three pollutants were conducted during reanalyses of NMMAPS (Dominici et al. 2003). For increases of 1 ppm for CO and 10 ppb for NO_{2} and SO_{2}, respectively, the NMMAPS investigators reported statistically significant increases in allcause mortality at a 1day lag of approximately 0.5%, 0.25%, and 0.6%. Our singlepollutant estimates of the mean are higher for each of these pollutants (e.g., 1.3%, 1.0%, and 1.5%, respectively, using 100 df splines for time trends). In a multipollutant model including these three gases, CO was no longer significantly associated with mortality (mean 0.64%; 95% CI: –0.20, 1.09), but NO_{2} and SO_{2} remained so (mean 0.62; 95% CI: 0.40, 0.98 and mean 0.82; 95% CI: 0.48, 1.15, respectively). In interpreting this result it should be kept in mind that, because of missing data, multipollutant analyses are based on a smaller set of cities than singlepollutant analyses. Concentration–response relationships for CO and SO_{2} are consistent with linearity. Although there is the suggestion of a threshold at around 20 ppb for NO_{2}, as for PM_{10}, the confidence bounds are too wide to rule out linearity.
Conclusions
We used the subsampling bootstrap procedure to derive maximum likelihood estimators of national effects of exposures to criteria pollutants on deaths the following day. The AIC for the fitted models provided little evidence of a common effect estimate across the United States, however (data not shown). While the focus of much air pollution research for the past couple of decades has been on PM and O_{3}, we find stronger associations between CO, NO_{2}, and SO_{2} and mortality. The ambient concentration–response relationship for O_{3} shows evidence of nonlinearity. Regional and seasonal analyses using the methods described in this study may offer further insight. Previous publications have reported that the results of timeseries analyses of air pollution data in individual cities can be highly sensitive to choice of statistical model (e.g., Clyde 2000; Koop and Tole 2004; Moolgavkar 2003). While our analyses are based on the most recent data available to us (which are not identical to the data used in previous analyses), our results suggest that different statistical approaches to multicity analyses can yield disparate results.
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CEHN November 2015 Article of the Month
“Infant Infections and Respiratory Symptoms in Relation to in Utero Arsenic Exposure in a U.S. Cohort” (DOI:10.1289/ehp.1409282) has been selected by the Children’s Environmental Health Network (CEHN) as its November 2015 Article of the Month. These CEHN summaries discuss the potential policy implications of current children’s environmental health research.Sign Up to Receive Email Alerts
Recent Advance Publications

Residential Road Traffic Noise and High Depressive Symptoms after Five Years of Followup: Results from the Heinz Nixdorf Recall Study

Key Characteristics of Carcinogens as a Basis for Organizing Data on Mechanisms of Carcinogenesis

Arsenic and Environmental Health: State of the Science and Future Research Opportunities

Inorganic Arsenic Related Changes in the Stromal Tumor Microenvironment in a Prostate Cancer Cell–Conditioned Media Model

SoyBased Infant Formula Feeding and UltrasoundDetected Uterine Fibroids among Young AfricanAmerican Women with No Prior Clinical Diagnosis of Fibroids