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Impact of long-term temporal trends in fine particulate matter (PM2.5) on associations of annual PM2.5 exposure and mortality

An analysis of over 20 million Medicare beneficiaries

Eum, Ki-Do*,a; Suh, Helen H.a; Pun, Vivian Chitb; Manjourides, Justinc

Environmental Epidemiology: June 2018 - Volume 2 - Issue 2 - p e009
doi: 10.1097/EE9.0000000000000009
Original Research

Decreasing ambient fine particulate matter (PM2.5) concentrations over time together with increasing life expectancy raise concerns about temporal confounding of associations between PM2.5 and mortality. To address this issue, we examined PM2.5-associated mortality risk ratios (MRRs) estimated for approximately 20,000,000 US Medicare beneficiaries, who lived within six miles of an Environmental Protection Agency air quality monitoring site, between December 2000 and December 2012. We assessed temporal confounding by examining whether PM2.5-associated MRRs vary by study period length. We then evaluated three approaches to control for temporal confounding: (1) assessing exposures using the residual of PM2.5 regressed on time; (2) adding a penalized spline term for time to the health model; and (3) including a term that describes temporal variability in PM2.5 into the health model, with this term estimated using decomposition approaches. We found a 10 μg/m3 increase in PM2.5 exposure to be associated with a 1.20 times (95% confidence interval [CI] = 1.20, 1.21) higher risk of mortality across the 13-year study period, with the magnitude of the association decreasing with shorter study periods. MRRs remained statistically significant but were attenuated when models adjusted for long-term time trends in PM2.5. The residual-based, time-adjusted MRR equaled 1.12 (95% CI = 1.11, 1.12) per 10 μg/m3 for the 13-year study period and did not change when shorter study periods were examined. Spline- and decomposition-based approaches produced similar but less-stable MRRs. Our findings suggest that epidemiological studies of long-term PM2.5 can be confounded by long-term time trends, and this confounding can be controlled using the residuals of PM2.5 regressed on time.

aDepartment of Civil and Environmental Engineering, Tufts University, Medford, MA

bJockey Club School of Public Health and Primary Care, The Chinese University of Hong Kong, Sha Tin, Hong Kong

cDepartment of Health Sciences, Bouvé College of Health Sciences, Northeastern University, Boston, MA.

Received: 27 November 2017; Accepted 6 February 2018

Published online 24 April 2018

Sponsorships or competing interests that may be relevant to content are disclosed at the end of the article.

Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article (

*Corresponding author. Address: Department of Civil and Environmental Engineering, Tufts University, 200 College Avenue, Anderson Hall, Medford, MA. E-mail address: (K.-D. Eum).

This is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License 4.0, where it is permissible to download and share the work provided it is properly cited. The work cannot be changed in any way or used commercially.

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Over the last 2 decades, ambient air pollution concentrations have decreased steadily across the United States primarily as the result of emissions controls instituted as part of the Clean Air Act Amendments. In the United States, PM2.5, annual concentrations have dropped by 24% from 2001 to 2010, with 2010 mean concentrations ranging, by location, between 3 and 18 μg/m3.1 These lower concentrations are projected to result in substantial health benefits. A 2011 US Environmental Protection Agency report, e.g., estimated that the Clean Air Act Amendments will prevent 230,000 early deaths in 2020, with most early deaths attributable to reductions in ambient PM2.5.1

Despite these reductions, PM2.5 concentrations continue to be linked with adverse health impacts.2–6 Numerous multicity studies, including the American Cancer Society, Six Cities, Women’s Health Initiative, Nurses’ Health Study, and National Institutes of Health-American Association of Retired Persons (NIH-AARP) Diet and Health Cohort, have shown positive associations between long-term exposure and mortality.2–7 The observed associations in these studies vary widely, with null associations in Health Professionals Follow-Up Study prospective cohort8 and significant effect estimates ranging from a 3% increase (per 10 μg/m3 in PM2.5) in the NIH-AARP cohort7 to 26% in Nurses’ Health Study.9 Variability in effect sizes has been attributed to differences in cohort characteristics, PM2.5 composition, modeling approaches, and confounding by correlated air pollutants or unmeasured covariates.10–13

Another possible, but little studied, explanation for the variation in PM2.5-associated mortality risks is confounding by long-term time trends in both PM2.5 and mortality, where decline in ambient PM2.5 concentrations is accompanied by increased life expectancy. Several studies provide evidence of the impact of long-term time trends on PM2.5-associated mortality.14 In a simulation study, Griffin et al15 showed that the length of the study period may adversely affect the performance of the Cox proportional hazards model, increasing bias and mean and squared error (MSE) and reducing power as the strength of the linear association between exposure and time increases, as may occur with the temporal trends observed for PM2.5. Similarly, linear models may also produce biased effect estimate, if linear trends exist between both PM2.5 and time, and mortality and time. Consistent with this, Janes et al,16 Greven et al,17 and Pun et al18 found evidence of unmeasured confounding of the association of PM2.5 and all-cause mortality. They did so by decomposing PM2.5 into two orthogonal components describing temporal and spatiotemporal variability, which they term “global” and “local” PM2.5, respectively. When both terms were included in the health model, the coefficient for temporal PM2.5 was larger and statistically significant compared with the spatiotemporal coefficient, which was null. The unequal temporal and spatiotemporal coefficients led the authors to conclude that PM2.5 associations with mortality were confounded by unmeasured variables, such as long-term time trends.

To examine the possibility that temporal confounding is present in the mortality and PM2.5 relationship, we analyzed data for over 20 million Medicare enrollees from 2000 to 2012 to assess the impact of long-term time trends on the association between 1-year–averaged PM2.5 concentrations and mortality.

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The protocol was reviewed and approved by the Institutional Review Boards of Northeastern University.

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Medicare beneficiary and mortality data

We obtained monthly mortality counts for 2000–2012 in the United States (except for Alaska and Hawaii) using data from the Centers for Medicare and Medicaid Services Medicare enrollment file, which provides demographic (age and sex), ZIP code of residence, and survival, including date of death and data for all Medicare enrollees (≥65 years).

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PM2.5 exposure

We compiled daily PM2.5 concentrations from Environmental Protection Agency’s Air Quality System from 2000 to 2012. We did so for monitoring sites (“site”) with daily measurements for at least eight calendar years, with each year having 9+ months with 4+ daily measurements. For the 798 sites that met these criteria, we calculated long-term concentrations following Greven et al.17 Briefly, we smoothed the time series at each site using a linear regression with the daily pollutant values as the response, and thin plate splines of time with four degrees of freedom per year as the predictor. For gaps longer than 90 days, we smoothed the PM2.5 time series before and after each gap separately. We used the predicted daily values to calculate yearly moving averages for PM2.5 each month. Yearly averages were considered valid when 350+ days were available. Sites were classified based on their geographical region: “East” of the Mississippi River, “Center” between the Mississippi River and the Sierra Nevada mountain range, and “West” of the Sierra Nevada mountain range.17

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Data linkage

We linked data for Medicare beneficiaries (65–120 years) to PM2.5 monitors that met the study criteria for each month of the study, which restricted our sample to those beneficiaries living in ZIP codes with centroids within six miles of a valid monitor. We then linked data for beneficiaries living in these ZIP codes to the closest corresponding site’s PM2.5 concentration for the previous 12-month period ending in that study month. We performed the ZIP code identification and linkage by year to reduce exposure error introduced by residential moves and changes in ZIP code boundaries. For each month, we calculated the total number of Medicare beneficiaries at risk and the number of deaths associated with each site.

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Statistical analysis

All analyses were conducted for the entire study population living in the United States as well as separate analyses for Medicare beneficiaries living in each of three US regions (East, Central, and West). In general, we examined the variation in MRR estimates per 10 µg/m3 increase in exposure; although for analyses comparing MRRs for base to those for time-adjusted models, we make comparisons based on an interquartile range (IQR) increase in exposure given their different variabilities. We further present graphical summaries of this variation using linear regression. SAS statistical software package (SAS Institute Inc., Cary, NC, 2003) and R-Studio, Inc., (Boston, MA) were used for all analyses.

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Base models

To examine the association between PM2.5 exposure and monthly rate of all-cause mortality, we fit an age-stratified log-linear model including offset terms for the size of the population at risk as our base model:

where (

) is the number of deaths at time t, in age category a, associated with site C. The exposure measure

is the 1-year average PM2.5 concentration at site C, preceding the month (t) of death. For each age group a and site C, mortality counts are offset by both the baseline hazard of death,

, and the total population at risk at time t,

. The Poisson model was selected (over the quasi-Poisson) as overdispersion parameter values varied from 1.02 to 1.25. To reduce the computational burden of this large dataset, we assumed a constant baseline hazard of death for all age groups above 90 years of age and models were fit via the backfitting algorithm.17–19

To adjust for potential, measured confounders, we performed additional analyses adjusting for county-level behavioral covariates from the Selected Metropolitan/Micropolitan Area Risk Trends of the Behavioral Risk Factor Surveillance System (BRFSS), including proportions of non-whites, current smokers, diabetes, asthma, individuals possessing health care plans, and mean income and body mass index.20

is the vector of BRFSS adjustment variables. Because the BRFSS data are only available for 465 of the 798 sites with PM2.5 monitoring data, we performed these analyses using the corresponding subset of the cohort. As appropriate, we converted results from previous studies into percent change per 10 µg/m3 PM2.5 increase to compare with our results.16–18 Additionally, we assessed whether unmeasured confounding of our base models remained by decomposing PM2.5 into two orthogonal components that capture temporal and spatiotemporal variability, following methods described by Greven et al.17 Briefly,

  • The temporal component describes national trends in exposures by centering the average exposure nationally in month t, , by the average concentration for all sites over the entire study period, :

  • The spatiotemporal component describes site-specific temporal trends in exposure by centering the exposure in month t at site c, , by the average exposure at site c, , and the national trends, ():

We included the temporal and spatiotemporal components jointly in our base models and compared their effect estimates, interpreting a difference in their estimates as evidence of unmeasured confounding.17

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Evaluation of temporal confounding

We evaluated long-term time trends as a potential source of unmeasured confounding. To do so, we ran our base models using data for the entire 13-year study period (2000–2012) and for shorter study periods, ranging between 3 and 12 years in length, with each of these study periods ending in 2012 (e.g., 2001–2012, 2002–2012, 2003–2012, etc., to 2009–2012). We compared mortality risk ratios (MRRs) for the entire 13-year period with those from each of these shorter study periods, assuming that in the absence of temporal confounding, MRRs would be uniform irrespective of the study period length.

In addition to fitting our base model, we also examined three approaches to control for long-term time trends in PM2.5. In our first approach, we adjusted for long-term time trends in PM2.5 using a new exposure measure calculated as the residual

of the linear regression of PM2.5 on time in 4-year intervals December 2000–2004, 2005–2008, and 2009–2012:

The term

was subsequently used as the exposure measure in the log-linear model:

Our second approach adjusted for long-term time trends in PM2.5 by adding a penalized spline term for time,

, modeled as two knots per study year, to our base log-linear model:

For our third approach, we included the temporal component of decomposed PM2.5 into the base model as follows:

where “temporal PM2.5” was calculated by decomposing PM2.5 into its orthogonal temporal and spatiotemporal components as above and in the study by Greven et al.17

For each of these time-adjusted approaches, we ran models using data for study periods ranging between 3 and 13 (2000–2012) years in length and examined whether MRRs varied by length of study period.

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Sensitivity analyses

We ran several sensitivity analyses to examine alternate specifications of our methods to adjust for long-term time trends in PM2.5. Specifically, for the calculation of residuals for our residual-based approach, we adjusted for time as each year rather than for each 4-year interval as in our main analysis:

as well as for years grouped into 2-, 3-, and 6-year intervals:

We subsequently used the residuals from these sensitivity analyses as exposure measures in our log-linear health models and compared their ability to control for confounding by time trends. Additionally, we assessed our ability to account for long-term time trends using penalized splines for time calculated using three, four, or five knots instead of the two knots used in our main analysis.

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We examined 20.7 million Medicare enrollees, observing 5.5 million deaths between December 2000 and December 2012 near 798 sites across the contiguous United States (Table 1). Monthly, our analyses include on average over 9 million enrollees. PM2.5 concentrations varied regionally, with sites located in the East having the highest mean concentrations. Yearly PM2.5 concentrations decreased steadily during our study period (Figure 1), with larger decreases in the East and West as compared to Center. Declines in PM2.5 concentrations were steepest between 2000 and 2009, with yearly concentrations more uniform during 2010–2012. The correlation between PM2.5 and the residual-based exposure measure equaled 0.92, suggesting that this residual-based exposure measure explained most of the variation in PM2.5.

Table 1

Table 1

Figure 1

Figure 1

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Association of PM2.5 and mortality

Base models

We found that a 10 µg/m3 increase in 1-year PM2.5 is significantly associated with a 1.20 times (95% CI = 1.20, 1.21 per 10 μg/m3) higher rate of mortality in our Medicare cohort when data from 2000 to 2012 were analyzed (Table 2). Associations varied by geographic region, with MRRs higher in the Central (1.27; 95% CI = 1.26, 1.28) and Eastern (1.26; 95% CI = 1.25, 1.26) regions compared with the Western United States (1.12; 95% CI = 1.11, 1.12). Associations were similar when models additionally adjust for behavioral covariates (Table S1;, suggesting that behavioral covariates did not confound associations of PM2.5 and mortality.

Table 2

Table 2

Despite this, we showed potential confounding of the association of PM2.5 and mortality by unmeasured variables. When PM2.5 is decomposed into its spatiotemporal and temporal components, we estimated larger MRRs for the temporal as compared to spatiotemporal component of PM2.5 (Table S1; for both base and BRFSS-adjusted models, consistent with the previous study.17 In base models, e.g., a 10 μg/m3 increase in temporal PM2.5 corresponded to a 1.54 times (95% CI = 1.52, 1.56) higher rate of mortality, while spatiotemporal PM2.5 was associated with only a 1.07 times (95% CI = 1.06, 1.09) higher rate.

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Evaluation of temporal confounding

We showed PM2.5-associated MRRs increase with the length of the study, consistent with the hypothesis of confounding by long-term time trends in PM2.5. MRRs were lowest for the 3-year study periods (1.12; 95% CI = 1.11, 1.14) and increase steadily with longer study periods, resulting in a 0.08 higher MRR for the 13-year as compared to 3-year study period (Figure 2). Similar trends between MRRs and length of study period were observed when analyses were performed by geographic region, although these trends were less pronounced in the Central United States, consistent with the more gradual decline in PM2.5 concentrations in the Central Unites States over the 13-year period (Figure S1;

Figure 2

Figure 2

When models were adjusted for long-term time trends, MRRs remain statistically significant (Table 2) but were slightly attenuated (Table S2; For the residual-based approach, we found the MRR to equal 1.04 (95% CI = 1.04, 1.04) per IQR increase in time-adjusted PM2.5, as compared to 1.08 (95% CI = 1.08, 1.08) per IQR increase in the base model. MRRs estimated from the penalized spline- and decomposition-based approaches were also attenuated, with MRRs of 1.01 (95% CI = 1.01, 1.02) and 1.03 (95% CI = 1.02, 1.03) per IQR increase, respectively (Table S2; While consistently lower, MRRs for each of the time-adjusted approaches follow the same regional patterns as with the base models, as time-adjusted MRRs were highest in the Central United States and lowest in the Western United States (Table 2; Figures S2–S4;

When analyses were performed across varying study periods, we demonstrated that the residual-based approach produces MRRs that are nearly uniform (Figure 2). The residual-based MRRs for the 13- and 3-year study periods, e.g., were almost identical, with MRRs of 1.12 (95% CI = 1.11, 1.12) and 1.12 (95% CI = 1.11, 1.14) for a 10 μg/m3 increase in exposure, respectively. In contrast to both the base and residual-based models, MRRs for the spline- and decomposition-based approaches decrease with longer study periods. MRRs from the spline-based approach decrease from 1.09 (95% CI = 1.07, 1.10) for 3-year study period to 1.03 (95% CI = 1.02, 1.04) for 13-year study period. The decomposition-based approach shows a similar decline in MRRs, with MRRs for 3- and 13-year study periods equaling 1.11 (95% CI = 0.10, 1.12) and 1.06 (95% CI = 1.06, 1.07), respectively.

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Sensitivity analyses

Sensitivity analyses demonstrated that alternate calculations of residual-based PM2.5 exposures and of penalized splines produce similar MRRs. Residual-based exposures calculated by regressing PM2.5 concentrations on time as 1-, 2-, or 3-year intervals result in similar MRRs as models controlling for time in 4-year intervals (Figure 3). Residual-based exposure with 6-year intervals showed slightly higher and less-consistent MRRs for longer study periods, suggesting less reliability than with the other intervals. Residual-based exposures calculated using 4-year intervals, however, were more stable, as evidenced by lowest variation in MRRs across study period length. It is also notable that residual-based exposure using 4-year time intervals requires fewer parameters than 1-, 2-, or 3-year intervals, suggesting greater statistical efficiency. For spline-based models, increasing the number of knots per year from two to three or four had little effect on the MRR, thus we selected two knots for better efficiency (results not shown).

Figure 3

Figure 3

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We showed consistent, statistically significant, and positive associations between 1-year PM2.5 exposures and the rate of all-cause mortality among 20.7 million Medicare beneficiaries living across the United States from 2000 to 2012. In our base models, the mortality rate ratio associated with a 10 μg/m3 increase in 1-year average PM2.5 equaled 1.20 (95% CI = 1.20, 1.21). Consistent with our hypothesis that long-term time trends in PM2.5 positively confound the association between PM2.5 and mortality, we found PM2.5-associated rates of mortality to be associated with the length of the study period, with higher MRR per 10 µg/m3 for 13-year as compared to 3-year study periods. Of the three examined approaches, we found the residual-based approach to best control for temporal confounding, as evidenced by its statistically significant and uniform MRRs across all study period lengths, with an MRR for the 3- and 13-year study period of 1.12 (95% CI = 1.11, 1.14) and 1.12 (95% CI = 1.11, 1.12) per 10 µg/m3 increase in exposure, respectively. Note, however, that based on our analysis alone, it is not possible to determine which approach is best suited to control for temporal confounding, indicating the need for further examination, possibly through a simulation study.

Our findings add to the body of evidence showing that long-term PM2.5 exposures are associated with increased mortality,2–7,9–13 lending additional support to findings from the American Cancer Society (ACS) cohort,2 the Nurses’ Health Study,5 and the Medicare cohort.4 Although no studies to date have explicitly examined the possible impact of temporal confounding on these associations, several studies have indirectly examined this possibility. In a study by Lepeule et al,6 e.g., the original21 and initial follow-up22 of the Six Cities Study were extended to include 11 additional years of follow-up, comprising 36 years in total (1974–2009). MRRs were estimated for the entire 36-year study period and for four, equally divided 9-year time periods. While overall PM2.5 concentrations decreased over the 36-year study period, this decrease was uniform neither by city nor over time. PM2.5 concentrations exhibited strong downward trends over time in only the three most polluted cities—Steubenville, Kingston-Harriman, and St. Louis, with these trends steepest and most consistent between 1979 and 1992 and to a lesser extent 2000–2009. The authors found an overall MRR for all-cause mortality of 1.14 (95% CI = 1.07, 1.22) for a 10 µg/m3 increase in 1-year PM2.5. When data for the four 9-year time periods were analyzed, MRRs varied widely, with values of 1.06 (95% CI = 0.96, 1.17) for 1974–1982, 1.32 (95% CI = 1.16, 1.50) for 1983–1991, 1.11 (95% CI = 0.98, 1.27) for 1992–2000, and 1.19 (95% CI = 0.91, 1.55) for 2001–2009. Notably, MRRs were highest during the period when temporal trends in PM2.5 were strongest, providing some, albeit indirect, support for our findings of confounding by long-term temporal trends. The increased MRR for the last 9-year interval compared with the full 36-year MRR may reflect aging of the cohort.

Further support is provided by results from related studies by Janes et al,16 Greven et al,17 and Pun et al18 who decomposed PM2.5 into its temporal and spatiotemporal components and found higher and statistically significant MRRs for temporal as compared to spatiotemporal PM2.5. The authors concluded that differences in the MRRs associated with temporal and spatiotemporal PM2.5 reflected residual confounding by temporally varying covariates. Consistent with Greven et al,17 additional adjustment for county-level BRFSS covariates did not reduce residual confounding, suggesting that the examined behavioral variables do not confound the PM2.5 mortality association. This finding, however, differs from that reported by Pun et al,18 who found that residual confounding decreased after adjustment for BRFSS covariates in models of PM2.5 and mortality. This discrepancy likely results from the fact that the Pun et al18 analysis assessed residual confounding by decomposing both PM2.5 and BRFSS data into their temporal and spatiotemporal components, while we decomposed only PM2.5 since our time-adjusted models already control indirectly for temporal trends in BRFSS data. Together, these results suggest that temporal trends in confounding variables are important to consider as well.

Our findings of increasing MRRs with longer study periods suggest that long-term temporal trends in PM2.5 concentrations may be one source of this unmeasured confounding. We found residual-based exposures to successfully control for these time trends in PM2.5. The ability of residual-based exposures to control for these time trends in PM2.5 is consistent with previous studies.23–25 For example, Mostofsky et al25 used a residual-based approach to estimate the effect of PM2.5 constituents while controlling for confounding by total amount of PM2.5. To do so, they regressed each constituent of interest on the total PM2.5 in a linear model and used the residual to estimate the effect of each individual constituent while holding PM2.5 constant. This approach is similar to our residual-based exposure method, with the only difference being our focus on the effect of PM2.5 while controlling for the unmeasured variables associated with long-term time trends. Because the unmeasured confounders are not perfectly correlated with time, complete control of time (through indicator functions for each month) would have likely over-adjusted for any potential confounding, as observed when the residual model was based on time controlled in 1-, 2-, and 3-year intervals. On the other hand, using a coarser measure of time (such as 6-year intervals) may not sufficiently control for the unmeasured variables, resulting in a lack of independence between time trends and both PM2.5 and mortality. Our results suggest that the residual model controlling for time in 4-year intervals was able to provide MRR estimates that were least affected by study period length.

We found this residual-based method to perform better than the spline and decomposition approaches, both of which showed declining MRRs as study periods increased, suggesting that these methods over-controlled for long-term time trends. Further, by including terms for both PM2.5 and some adjustment for time in the model, the spline- and decomposition-based approaches may result in biased effect estimates, given collinearities of PM2.5 and time.26 In our data, the correlations of PM2.5 with both the spline of PM2.5 and decomposed PM2.5 varied with the length of study period, with correlations for PM2.5 and the spline of PM2.5 equaling 0.15 for 3-year periods and increasing to 0.44 for 12-year periods. Identical correlations were observed for PM2.5 and decomposed PM2.5. These results suggest that the bias in MRRs derived from the spline and decomposed PM2.5 models increases as the study length increases.

Our results are limited by several factors. First, our log-linear models aggregated data by site and limited the number of strata for computational efficiency, thus limiting our ability to control for individual-level covariates. However, when we additionally adjusted for county-level behavioral covariates, we found similar MRRs, suggesting behavioral covariates did not confound associations (Table S1; Second, individual exposure measurement error is unavoidable when using the monitor level air pollution data. This exposure error is likely to be small, given results from studies that show that PM2.5 concentrations to be moderately uniform within a given county and ambient PM2.5 concentrations to be strong surrogates for personal PM2.5 exposure.27 Thus, we expect any exposure error to bias observed associations toward the null and underestimate mortality risk estimates.28 Third, although bias may also be introduced by the “healthy worker effect” where subjects less susceptible to PM2.5 exposures remain in our study population for longer time periods, this bias would be in the opposite direction of the observed changes. Although our study could not examine the impact of temporal variation of PM2.5 composition on MRRs, compositional variability is unlikely to explain our findings given the strong dependence of MRRs on PM2.5 time trends and the inconsistent time trends in PM2.5-associated total carbon concentrations between 2000 and 2010 in the United States.29 Finally, while we found the residual model based on 4-year intervals to best control for temporal trends, further study, such as through a simulation study, is needed to confirm our findings.

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We found significant associations between 1-year PM2.5 exposures and mortality. These associations were likely confounded by long-term temporal trends in PM2.5. We successfully controlled for this confounding by using exposure measures based on the residual of PM2.5 regressed on time in 4-year intervals. Controlling for long-term temporal PM2.5 trends, we found significant 11.7% increase in all-cause mortality among Medicare beneficiaries for a 10 μg/m3 increase in PM2.5. This MRR was reduced compared to the model without controlling for the temporal confounding. These findings demonstrate the importance and need to account for temporal trends in future air pollution health effect studies.

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Conflicts of interest statement

The authors declare that they have no conflicts of interest with regard to the content of this report.

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Medicare beneficiaries; Residual; Temporal confounding; Mortality; Fine particulate matter (PM2.5)

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