How low can you go? Air pollution affects mortality at very low levels

Abstract

The World Health Organization (WHO) recently released new guidelines for outdoor fine particulate air pollution (PM2.5) recommending an annual average concentration of 5 μg/m3. Yet, our understanding of the concentration-response relationship between outdoor PM2.5 and mortality in this range of near-background concentrations remains incomplete. To address this uncertainty, we conducted a population-based cohort study of 7.1 million adults in one of the world's lowest exposure environments. Our findings reveal a supralinear concentration-response relationship between outdoor PM2.5 and mortality at very low (<5 μg/m3) concentrations. Our updated global concentration-response function incorporating this new information suggests an additional 1.5 million deaths globally attributable to outdoor PM2.5 annually compared to previous estimates. The global health benefits of meeting the new WHO guideline for outdoor PM2.5 are greater than previously assumed and indicate a need for continued reductions in outdoor air pollution around the world.

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Weichenthal et al., Sci. Adv. 8, eabo3381 (2022) 28 September 2022
SCIENCE ADVANCES | RESEARCH ARTICLE
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SOCIAL SCIENCES
How low can you go? Air pollution affects mortality at
very low levels
Scott Weichenthal1,2*†, Lauren Pinault3†, Tanya Christidis3, Richard T. Burnett4, Jeffrey R. Brook5,
Yen Chu6, Dan L. Crouse7, Anders C. Erickson6, Perry Hystad8, Chi Li9, Randall V. Martin9,10,
Jun Meng10,11, Amanda J. Pappin2, Michael Tjepkema3, Aaron van Donkelaar9,10,
Crystal L. Weagle9, Michael Brauer4,6
The World Health Organization (WHO) recently released new guidelines for outdoor fine particulate air pollution
(PM2.5) recommending an annual average concentration of 5 g/m3. Yet, our understanding of the concentration-
response relationship between outdoor PM2.5 and mortality in this range of near-background concentrations
remains incomplete. To address this uncertainty, we conducted a population-based cohort study of 7.1 million
adults in one of the world’s lowest exposure environments. Our findings reveal a supralinear concentration-
response relationship between outdoor PM2.5 and mortality at very low (<5 g/m3) concentrations. Our updated
global concentration-response function incorporating this new information suggests an additional 1.5 million
deaths globally attributable to outdoor PM2.5 annually compared to previous estimates. The global health bene-
fits of meeting the new WHO guideline for outdoor PM2.5 are greater than previously assumed and indicate a need
for continued reductions in outdoor air pollution around the world.
INTRODUCTION
In September 2021, the World Health Organization (WHO) released
new guidelines for annual average outdoor concentrations of fine
particulate air pollution (PM2.5, <2.5 m) and cut its previous guide-
line value in half from 10 to 5 g/m3 (1). The current United States
Environmental Protection Agency (U.S. EPA) standard of 12 g/m3
is now more than double the value recommended by the WHO (2).
This ambitious new guideline is based on a large body of epidemio-
logical evidence supporting a causal relationship between long-term
exposure to outdoor PM2.5 and premature mortality, which has been
demonstrated around the world (1,3–5). Nevertheless, few cohort
studies to date provide a detailed characterization of the shape of
the concentration-response relationship between outdoor PM2.5 and
mortality in the low range of global PM2.5 concentrations, the space
now occupied by the new WHO guideline (6). It is crucial to quantify
this relationship to accurately characterize the global health benefits
of meeting the ambitious new level set by the WHO.
Numerous challenges must be addressed in estimating the rela-
tionship between long-term exposures (i.e., annual average) to out-
door PM2.5 and mortality including (i) identifying and enumerating
a large population-based cohort that adequately reflects the popula-
tion of interest and also includes detailed information on the timing
and types of mortality outcomes; (ii) accurately and reliably assign-
ing cohort members’ exposures to outdoor PM2.5 concentrations on
a fine spatial scale (i.e., residential location) over broad geographic
areas with exposures updated over time for residential mobility and
including back-casted exposure to capture historical variations in
pollutant concentrations; (iii) collecting detailed information on
important confounding factors that may distort the observed rela-
tionship between PM2.5 and mortality; and (iv) combining this
information in a flexible statistical framework to estimate the rela-
tionship between outdoor PM2.5 and mortality risk to inform future
regulatory interventions. The functional form of the PM2.5-mortality
relationship can be modeled as linear (i.e., a linear relationship be-
tween outdoor PM2.5 concentrations and logarithm of the mortality
rate) or more complex nonlinear functional forms as needed. The
Canadian Census Health and Environment Cohort (CanCHEC)
was developed to address these challenges. Specifically, this national
population-representative cohort was created by linking people who
completed the mandatory Long-Form Census questionnaire (in-
cluding multiple cycles in the years 1991, 1996, and 2001) to income
tax files and mortality records across Canada combined with state-
of-the-art predictions for outdoor PM2.5 concentrations developed
and refined using satellite remote sensing, ground-level measure-
ments of PM2.5 and aerosol optical depth (AOD), and chemical
transport models (7).
Here, we use CanCHEC to characterize the shape of the PM2.5-
mortality function (and associated uncertainty) at PM2.5 concentra-
tions < 20 g/m3 including values below the latest WHO guideline.
Using this new information, we first develop a refined concentration-
response function for outdoor PM2.5 and mortality to capture health
risks on the low end of the global exposure distribution. Next, we
apply this revised function to derive updated annual global mortality
estimates given this improved understanding of the PM2.5-morality
relationship. The analysis used to refine the global concentration-
response function is based on 7.1 million adults followed between
1991 and 2016 and adjusting for numerous individual-level and
neighborhood-level covariates. We also verified these results in an
ancillary cohort [the Canadian Community Health Survey (CCHS)
cohort, including 450,000 adults] which allowed for additional ad-
justment for individual-level behavioral factors such as smoking,
diet, and obesity on observed relationships between PM2.5 and mor-
tality. Our analysis focusses on nonaccidental mortality as this
1McGill University, Montreal, QC, Canada. 2Health Canada, Ottawa, ON, Canada.
3Statistics Canada, Ottawa, ON, Canada. 4Institute for Health Metrics and Evaluation,
University of Washington, Seattle, WA, USA. 5University of Toronto, Toronto, ON,
Canada. 6University of British Columbia, Vancouver, BC, Canada. 7Health Effects
Institute, Boston, MA, USA. 8Oregon State University, Corvallis, OR, USA. 9Dalhousie
University, Halifax, NS, Canada. 10Washington University, Saint Louis, WA, USA.
11Air Quality Research Division, Environment and Climate Change Canada, Toronto,
ON, Canada.
*Corresponding author. Email: scott.weichenthal@mcgill.ca
†These authors contributed equally to this work.
Copyright © 2022
The Authors, some
rights reserved;
exclusive licensee
American Association
for the Advancement
of Science. No claim to
original U.S. Government
Works. Distributed
under a Creative
Commons Attribution
NonCommercial
License 4.0 (CC BY-NC).

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outcome is most influential in terms of guiding regulatory interven-
tions and associated cost-benefit analyses (8). Note that our refined
PM2.5-mortality function at low concentrations was not used in de-
veloping the most recent WHO guideline as our study was completed
after this guideline was released.
The main purpose of this study was to (i) derive a new global
exposure-response function for outdoor PM2.5 and mortality cap-
turing the shape of this relationship at low levels and (ii) to update
estimates of annual global mortality attributable to outdoor PM2.5
incorporating new knowledge of the shape of this relationship at
low PM2.5 levels, including values at or below the new WHO guide-
line. The cohort populations used to support this analysis are the
same as recently described (9); however, for this application, we
combined unique participants from the three CanCHEC cohorts
for increased statistical power at low PM2.5 concentrations (10).
Moreover, this analysis uses updated estimates of long-term expo-
sures to outdoor PM2.5 concentrations across Canada, which were
previously refined using colocated measurements of ground-level
PM2.5, aerosol scatter, and AOD (V4.NA.02.MAPLE) (10,11).
RESULTS AND DISCUSSION
In total, our analyses included more than 128 million person-years
of follow-up time with 1.2 million nonaccidental deaths observed
between 1991 and 2016 (table S1). The mean outdoor PM2.5 con-
centration during follow-up (assigned as a 10-year moving average
at 1-km2 resolution with a 1-year lag) was 8.5 g/m3 (SD=3.1 g/
m3) with values ranging from 2.5 to 17.7 g /m3. In total, 13.3% of
person-years in the cohort had outdoor PM2.5 concentrations below
5 g/m3. Each 10 g/m3 increase in long-term average outdoor
Fig. 1. Fully adjusted restricted cubic spline relative risk predictions for non-
accidental mortality over the CanCHEC PM2.5 concentration range (red dashed
line, mean; red shaded area, 95% CIs) with associated eSCHIF predictions (blue
solid line, mean; gray shaded area, 95% CIs). The green x-axis tick marks indicate the
nine restricted cubic spline (RCS) knot locations that reflect percentiles of PM2.5 (2, 14,
26, 50, 62, 74, 86, and 98%) for person-years of during follow-up (13.3% of person-years
had PM2.5 values below 5 g/m3, which is indicated by the vertical dotted line).
Fig. 2. Concentration-response functions describing the relationship between outdoor PM2.5 concentrations and nonaccidental mortality. (A) Concentration-
response functions on the low end of the global exposure distribution (0 to 20 g/m3). The blue line (and shaded 95% CI) indicates the shape of the refined global function
that incorporates the supralinear relationship between PM2.5 and mortality at low concentrations as characterized by the CanCHEC cohort. The red line (and shaded 95%
CI) indicates the shape of the current global concentration-response function for PM2.5 and mortality at low concentrations which uses a random counterfactual concen-
tration selected from a uniform distribution between 2.5 and 5 g/m3. (B) Current (red) and refined (blue) concentration-response functions for PM2.5 and mortality over
the global PM2.5 exposure distribution.

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PM2.5 concentration was associated with an 8.0% [95% confidence
interval (CI): 7.0, 10.0] increased risk of nonaccidental mortality
after adjusting for numerous potential confounding factors includ-
ing age (5-year categories), sex, recent immigrant status, income,
visible minority status, indigenous identity, educational attainment,
labor force status, marital status, community size, airshed, urban
form, and four dimensions of the Canadian Marginalization Index
(CAN-Marg). This estimate is based on a model that assumes a lin-
ear relationship between PM2.5 and the logarithm of the mortality
rate and is equal in magnitude to the estimate obtained from a meta-
analysis of cohort studies conducted globally by the WHO [8.0%
(95% CI: 6.0, 9.0)] (12), thus suggesting that the PM2.5-mortality
association observed in CanCHEC is similar to that based on the
large body of epidemiological evidence globally. Analyses replicated
in the ancillary CCHS cohort with additional detailed adjustment
for individual-level behavioral covariates including smoking, alco-
hol consumption, body mass index (BMI), exercise, and fruit and
vegetable intake confirmed these results (9.0% increase; 95% CI: 2.0,
16) (table S2).
Using our population-based cohort, we characterized the shape
of the concentration-response relationship between outdoor PM2.5
and nonaccidental mortality at the low end of the global exposure
distribution (down to 2.5 g/m3) and refined the global concentra-
tion-response function over the concentration range from 2.5 to
5 g/m3 to incorporate this improved understanding of PM2.5 health
risks at low concentrations. Next, we updated global estimates
of annual deaths attributable to outdoor PM2.5 using this refined
concentration-response relationship which explicitly models the non-
linear relationship (and uncertainty) between PM2.5 and nonaccidental
mortality at levels below the current WHO guideline (i.e., 5 g/m3)
while also incorporating existing epidemiological evidence across the
global exposure distribution (table S3).
We observed strong evidence of a supralinear concentration-
response relationship between outdoor PM2.5 concentrations and
mortality in CanCHEC (Fig.1), resulting in a refined global con-
centration-response function (Fig.2). This refined understanding
of the concentration-response relationship between outdoor PM2.5
and mortality at low concentrations suggests a large increase in the
Fig. 3. Percent increase in annual mortality attributable to outdoor PM2.5 on a global scale and global variations in annual average outdoor PM2.5. (A) Percent
increase in annual attributable mortality comparing deaths predicted using our refined global exposure-response function for outdoor PM2.5 and mortality to a function
which uses a random counterfactual concentration selected from a uniform distribution between 2.5 and 5 g/m3. (B) Global distribution of annual average outdoor PM2.5
concentrations.

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number of annual global deaths attributable to outdoor PM2.5, par-
ticularly in “low pollution” settings (Figs.3 and 4). Specifically, we
estimate an additional 1.55 million deaths (95% CI: 1.53 million,
1.57 million) annually on a global scale [i.e., 10.8 million (95% CI:
10.7 million, 10.9 million) compared to 9.24 million (95% CI:
9.17 million, 9.31 million)], with larger underestimation of attributable
mortality occurring in countries with lower PM2.5 concentrations
and higher incomes (Fig.4). This pattern is illustrated in Fig.5 for
attributable mortality estimates inlocations above (i.e., >12 g/m3)
and below (≤12 g/m3) the current U.S. EPA standard for annual
average outdoor PM2.5. On an absolute scale, the number of deaths
underestimated in regions above 12 g/m3 was larger [i.e., 1.15 mil-
lion (95% CI: 1.14 million, 1.17 million) compared to 403,000 (95%
CI: 407,500, 398,500)] as most of the world’s population lives in ar-
eas above the current EPA standard.
The supralinear concentration-response relationship identified
between outdoor PM2.5 and mortality at low concentrations has a
marked impact on global estimates of annual mortality attributable
to PM2.5 compared to models using a random counterfactual con-
centration selected from a uniform distribution between 2.5 and
5 g/m3 (1). While the reason for this supralinear shape at low con-
centrations has yet to be fully elucidated, other studies examining
the impact of outdoor PM2.5 on mortality risk have reported similar
shapes including both time series studies and cohort studies (5,12–14).
Recent evidence related to PM2.5 chemical composition suggests one
possible explanation for the observed pattern of steeper slopes at
lower PM2.5 concentrations. Specifically, a recent study of PM2.5 and
acute cardiovascular events reported an interaction between the tran-
sition metal and sulfur content of PM2.5, with stronger associations
observed when the mass fractions of both these components are
elevated (15). Since the mass fraction of sulfur increases as PM2.5
decreases (15), the biological availability of metals in PM2.5 may be
higher at lower PM2.5 mass concentrations, thus increasing the slope
of concentration-response functions in this range. The validity of
our results depends on the global generalizability of risk estimates
from Canada, which is supported by the fact that the hazard ratio
observed in CanCHEC was nearly identical to the estimate obtained
in a meta-analysis of global studies of outdoor PM2.5 (12). More-
over, other large cohort studies conducted in the United States (4)
and Europe (5) also reported clear and consistent relationships be-
tween outdoor PM2.5 and mortality at low concentrations, support-
ing the notion that this relationship is not limited to Canada. In the
United States, Di etal. (4) also conducted analyses separately for
person-years above and below the current U.S. EPA standard for
annual average outdoor PM2.5 (12 g/m3) and reported stronger
associations at lower PM2.5 mass concentrations, which is again
consistent with a supralinear concentration response relationship.
Likewise, Strak etal. (5) performed a similar analysis in Europe
by removing person-years above various PM2.5 concentrations
between 10 and 25 g/m3 and reported stronger associations at lower
concentrations. Collectively, recent evidence from large cohort studies
of outdoor PM2.5 and mortality suggests important health risks be-
low existing standards for annual average PM2.5.
In summary, refining the shape of the global concentration-
response function for outdoor PM2.5 and mortality at the low end of
the exposure distribution results in more than 1.5 million addition-
al attributable deaths each year globally. This finding may be used
to strengthen support for air quality management globally as our
results suggest that country-specific burden estimates vary substantially
depending on how the PM2.5-mortality association is characterized.
Fig. 4. Percent increase in annual mortality attributable to outdoor PM2.5 by income group and annual average outdoor PM2.5. OECD, Organization for Economic
Co-operation and Development.

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Refinement of this function comes at a crucial time given that in-
creasing evidence of PM2.5 health affects below existing regula-
tory standards. The results of this analysis suggest that global efforts
to meet the new WHO guideline of 5 g/m3 for annual average out-
door PM2.5 mass concentrations will have much larger benefits than
previously anticipated, even in regions of the world with relatively
low outdoor air pollution concentrations.
MATERIALS AND METHODS
Cohort study populations
Our primary study cohort pooled all individuals from three waves
(1991, 1996, and 2001) of CanCHEC which comprises subjects re-
sponding to the long-form Census questionnaire, capturing indi-
vidual and household sociodemographic data on census day, and
linking them to longitudinal vital statistics and tax records (16). To
create the cohorts, respondents were linked to death records and
residential history through Statistics Canada’s Social Data Linkage
Environment. Linkage was approved by Statistics Canada and is
governed by the Directive on Microdata Linkage. A list of linked
unique individuals was created through linkages that were either
deterministic (matching records based on unique identifiers) or
probabilistic (matching records based on nonunique identifiers
such as names, sex, date of birth, and postal code and estimating the
likelihood that records are referring to the same entity).
Minimum ages in the original CanCHECs differed between
waves but were standardized for this study to include adults older
than 25 years, including 2.5 million individuals from the 1991 Census
(4 June 1991), 3 million individuals from the 1996 Census (14 May 1996),
and 3 million individuals from the 2001 Census (15 May 2001). Af-
ter pooling the three waves and removing duplicate subjects across
waves, we applied additional exclusion criteria to person-years to
obtain the final pooled cohort. First, since postal code history was
not available for each person in every year of follow-up (e.g., be-
cause respondents did not file a tax return), missing postal codes
were imputed (using the Statistic Canada Postal Code Conversion
File Plus) (17) fully or partially based on postal codes reported in
adjacent years using a method where the probability of imputation
varied depending on the number of adjacent years missing (18). In
Canadian urban areas, six-digit postal codes typically represent one
side of a city block or the center of an apartment building with a
positional accuracy of approximately 150m. Location uncertainty
is greater for rural postal codes that are typically accurate to within
1 to 5km (19). In total, 89.9% of all person-years had a valid postal
code after imputation. Additional person-years were excluded if
respondents immigrated to Canada less than 10 years before the survey
Fig. 5. Density plots comparing estimated annual global mortality attributable to outdoor PM2.5. (A) Distributions of attributable mortality per year predicted by
the current global exposure-response function [random counterfactual distribution (RCF)] and our new refined function incorporating the supralinear relationship be-
tween PM2.5 and mortality at low concentrations (CanCHEC). (B) Distributions of attributable mortality per year predicted above [>12 g/m3 (high PM2.5)] and below
[≤12 g/m3 (low PM2.5)] the current U.S. EPA standard by the RCF model and our new CanCHEC model. Percent underestimation of attributable deaths by the RCF model
is greater at lower PM2.5 concentrations.

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date (9,364,400 person-years excluded), age during the follow-up
exceeded 89 years (7,357,200 person-years excluded), or postal codes
could not be matched to an air pollution estimate (17,814,400 person-
years excluded), a CAN-Marg value (25,613,100 person-years ex-
cluded), or airshed (25,545,500 person-years excluded) (note that
these exclusion numbers overlapped for many person-years so per-
centages are not informative as they are not mutually exclusive).
Last, since air pollution exposures were based on a 10-year moving
average with a 1-year lag, person-years were excluded if fewer than
7 of 10 years of data were available (21,751,800 person-years excluded).
After applying these criteria, a total of 128,371,800 person-years
(7.1 million subjects) were available for analysis.
We used a secondary cohort to estimate possible confounding
by health behaviors and health status: the CCHS—mortality cohort.
The CCHS includes 540,900 subjects over the age of 25 years who
completed one of the CCHS panels between 2001 and 2012, linked
to longitudinal vital statistics and tax records from the date of survey
to 31 December 2016 (20). We applied the same exclusion criteria as
with the CanCHEC; the total available person-years for analyses
were 4,405,000 (450,000 subjects) after all exclusions.
Individual-level covariates captured at baseline in both the
CanCHEC and CCHS included income, educational attainment,
marital status, indigenous identity, employment status, occupational
class, and visible minority status. Furthermore, CCHS analyses
included additional covariates describing fruit and vegetable con-
sumption, leisure exercise frequency, alcohol consumption behavior,
smoking behavior, and BMI categories. We also considered area-
based contextual measures to capture neighborhood characteristics
in both cohorts including community size, urban form (a designa-
tion of population density and transportation characteristics) (21),
and airshed (large geographic areas with similar air quality charac-
teristics and dispersion patterns) (22). We used the CAN-Marg to
describe inequalities across four dimensions of marginalization:
material deprivation, residential instability, dependency, and ethnic
concentration (23). Additional details on cohort composition and
methodology are available elsewhere (10).
Outdoor PM2.5 concentrations
Our epidemiological analysis applied the most recent estimates of
outdoor PM2.5 mass concentrations across Canada over the follow-
up period (V4.NA.02.MAPLE) (7,11,24–26). Briefly, daily satellite
retrievals of AOD at 1-km2 resolution were combined with simula-
tions of the daily AOD-to-PM2.5 relationship using GEOS-Chem (a
chemical transport model) to produce ground-level estimates of PM2.5
mass concentrations (24). This most recent model incorporates im-
provements based on collocated measurements of aerosol scatter and
PM2.5 mass across North America and uses geographically weighted
regression to fuse monthly mean measurements from PM2.5 moni-
tors with the geophysical PM2.5 estimates (7,24–25).
Statistical analysis
We first used Cox proportional hazards models to estimate the lin-
ear relationship between outdoor PM2.5 concentrations and the log-
arithm of the mortality rate. Individuals were followed from census
or survey date until either the age of 89 years, the year of death, or
the end of follow-up in 2016. We considered nonaccidental mortality
as the primary outcome, and all models were stratified by age (5-year
age groups), sex, immigrant status, and CanCHEC/CCHS cycle. All Cox
models were adjusted for the individual and contextual variables
listed in table S1 (fig. S1). CCHS analyses were additionally adjusted
for the behavioral covariates of fruit and vegetable consumption, exer-
cise frequency, alcohol consumption, smoking, and BMI. Smoking
was defined as never/former/occasional smokers and, for regular smok ers,
by the number of cigarettes smoked per day. All PM2.5 exposures
were assigned as a 10-year moving average with a 1-year lag. The
10-year moving average exposure used in our analyses was selected
on the basis of a previous evaluation of the impact of exposure time
window on PM2.5-mortality associations (27).
Shape of the association between outdoor PM2.5
and mortality in CanCHEC
We developed a two-stage method to characterize the shape (non-
linear) of the association between outdoor PM2.5 concentrations and
mortality in CanCHEC. In the first stage, a spline of PM2.5 is fit
within the Cox survival model. We selected restricted cubic splines
(RCS) to flexibly model the association between outdoor concentra-
tions of PM2.5 and mortality (28). These regression-based splines
require fewer computing resources compared with smoothing splines,
a restriction that is necessary within the computing environment at
Statistics Canada. The RCS has the form
RCS(z) =  0 (z −
_
z ) + ∑
l=1
K−2
 l ( s l (z) − s l (
_
z ))
for K ≥ 3 with
s l (z) =
(
max
(
0, z −  l
─
(  K −  1 ) 2/3
)
)
3
−
(
 K −  l
─
 K −  K−1
)
(
max
(
0, z −  K−1
─
(  K −  1 ) 2/3
)
)
3
+
(
 K−1 −  l
─
 k −  k−1
)
(
max
(
0, z −  K
─
(  K −  1 ) 2/3
)
)
3
and K knot concentrations (1, …, K). The RCS is linear below 1
and above K with continuous second derivatives at the K knots.
The K−1 unknown parameters (0, …, K−2) are estimated within
the Cox survival model framework by including (z, s1(z), …, sK(z))
as K −1 variables in the survival model. The analyst must specify
the number and location of the knots. Knot locations were based on
percentiles of the PM2.5 person-year distribution.
Let
ˆ
 = (
ˆ
 0 , …
ˆ
 K−2 ) ′ be a K−1 by 1 vector of parameter esti-
mates with corresponding covariance matrix
ˆ
V and let s(z)=
(z, s1(z), …, sK−2(z))′. The estimate of the lnRCS(z) prediction is given
by ln
ˆ
RCS (z) =
ˆ
 ′ (s(z) − s(
_
z )), where
_
z is the person-year–based
mean concentration, with uncertainty in the estimate given by
ˆ
 (z) = (s(z) − s(
ˆ
z ) ) ′
ˆ
V (s(z) − s(
ˆ
z ) ) . We summarize the information
obtained from the fitted RCS model by its mean prediction at any
concentration z,
ˆ
RCS (z) , and its 95% CI: exp( ln
ˆ
RCS (z) ∓ 1.96 ×
ˆ
 (z)
)
.
For all nonaccidental causes of death, we fit 16 RCS models based on
3 to 18 knots and selected the model that minimized the BIC (Bayes-
ian Information Criterion) (the best fitting model included nine
knots). We then incorporated a counterfactual concentration, zcf,
such that our prediction of relative risk at zcf is equal to one by cal-
culating
ˆ
RCS (z) /
ˆ
RCS ( z cf ) . As described below, zcf was set to the
minimum observed concentration (2.5g/m3).

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In some cases, RCS predictions may not be suitable for health benefits
analysis as they may not be monotonically increasing in concentration
or may have “wiggles” in the predictions. Therefore, to ensure a relative
risk function that is suitable for benefits analysis, in the second stage, we
fit an algebraic function specifically designed for benefits analysis to
the RCS predictions. Our aim was to estimate a function that can
take a variety of shapes including linear, sub/supralinear, and sig-
modal. We also require a function whose statistical certainty is such
that prediction uncertainty limits increa se as conce ntrations deviat e
from their mean, a property of spline predictions.
The shape constrained health impact function (SCHIF) (29) has
been proposed to model concentration-mortality associations
within a cohort using an algebraic from suitable for benefits analysis:
SCHIF(z) = exp
{
 ln
(
(z −
z cf )
_
 + 1
)
/ (1 + exp
(
− z − z cf−
_
v
)
}
, with param-
eters (, , , andv) estimated from the cohort data. Although this
function can take near linear, sub/supralinear, and sigmodal forms,
it cannot capture the property of spline predictions with uncertainty
limits increasing as concentrations deviate from their mean. To in-
corporate this property, we added a term to the SCHIF(z) of the form
exp
{
ln
(
(z − z cf )
_
 + 1
)
}
with two additional parameters ( and) and
denote our new model as eSCHIF(z) for our extension of the SCHIF.
To fit the eSCHIF, we first generate 1000 sets of RCS predictions
over the concentration range by simulating 1000 sets of RCS regression
coefficients
ˆ
r i = MVN(
ˆ
 ,
ˆ
V ) , where MVN is the multivariate normal
distribution and calculating
ˆ
RCS i (z) = exp {
ˆ
r i ′ s(z)} over a sequence of
J concentrations (zcf, z1, …, zJ) with zJ defined as the maximum concen-
tration and i = 1, …,1000. These 1000 sets of predictions capture both the
shape and uncertainty of splines over the concentration range. We then
fit the eSCHIF functional form to each of the 1000 sets of predictions
ˆ
RCS i ( z j ) /
ˆ
RCS i ( z cf ) . We denote our relative risk model as CanCHEC(z).
It has been defined such that CanCHEC(zcf) = 1, where zcf is the
minimum observed concentration in the cohort (2.5g/m3).
Relative risk model covering the global concentration range
WHO identified a set of cohort studies examining the association
between long-term average outdoor PM2.5 concentrations and mor-
tality from all nonaccidental causes (12). Burnett and colleagues
(30) used these studies to develop a new model, Fusion, to charac-
terize the magnitude and shape of the association over the global
concentration range. We note that the Fusion model was developed
as an alternative to the Global Exposure Mortality Model (GEMM)
(14). Both these models characterize the potentially nonlinear rela-
tionship between outdoor PM2.5 concentrations and nonaccidental
mortality over the range of exposures reported by cohort studies.
However, the GEMM requires a detailed examination of the con-
centration response within each cohort, while the Fusion model only
relies on meta-data from each cohort to fit the model parameters,
such as that provided by Chen and Hoek (12). A detailed comparison
between the global burden estimates provided by these two models
suggests that the mean burden estimates are similar; however, the
Fusion model has less uncertainty at high global concentrations (30).
The algebraic form of the Fusion model is given by
F(z) = exp
{
 × (min(z, ) + ∫
 z
(
1 + 1 − 
─

(
x − 
─
 − 
)
−
_
(1−)
)
−1
dx +
ln(max(z, )/))
}
Estimates of the parameters (, , , and) were derived from
results reported in the literature for each cohort, including the slope
estimate based on a linear association between the logarithm of the
mortality and PM2.5, its standard error, and the 5th and 95th per-
centiles of the PM2.5 exposure distribution. Hence, the model cannot
identify the shape of the association at very low concentrations (i.e.,
below the fifth percentile of PM2.5 concentrations from available
cohorts). To address this limitation, we considered two different
characterizations of the shape and uncertainty of the PM2.5-mortality
relationship at these low concentrations. The first function, FRCF,
incorporates guidance from WHO that a positive association exists
between outdoor concentrations of PM2.5 and mortality when con-
centrations are greater than 5.0g/m3. However, it is uncertain whether
such associations exist below 5.0g/m3. We incorporate this guidance
mathematically into the Fusion model by creating a random counter-
factual distribution (RCF), defined as a uniform distribution be-
tween 2.5 and 5.0g/m3. Then, FRCF is defined such that
F RCF (z) = 1
if
z < 2.5g / m 3
F RCF (z) = 1 if z ≤ RCF~U(2.5g / m 3 , 5.0g / m 3 )
F RCF (z) = F(z) / F(CF)
if
z > RCF~U(2.5g / m 3 , 5.0g / m 3 )
This formulation stochastically models uncertainty regarding the
value of the true counterfactual concentration in this range. Such
RCFs have also been used by GBD (Global Burden of Disease) (3).
Alternatively, we define the function FCanCHEC by directly modeling
the shape and uncertainty over this concentration interval (2.5,5.0g/m3)
based on the CanCHEC(z) model identified using the CanCHEC
cohort. Under FCanCHEC, the shape of the PM2.5-mortality function
is defined by CanCHEC(z) when PM2.5 concentrations are below
5 g/m3 and by F when PM2.5 concentrations are ≥5 g/m3. This is
represented as
F CanCHEC (z) = 1
if
z ≤ 2.5g / m 3
F CanCHEC (z) = CanCHEC(z) if 2.5g / m 3 < z < 5.0g / m 3
F CanCHEC (z) = F(z) / CanCHEC(z)
if
z ≥ 5.0g / m 3
To calculate excess deaths (i.e., all nonaccidental causes of death)
attributable to outdoor PM2.5 mass concentrations, the total num-
ber of country-specific deaths for population greater than 25 years
of age (31) was multiplied by the population attributable fraction,
defined by one minus the inverse of the relative risk evaluated at the
population-weighted country-specific average. Counterfactual concen-
trations (i.e., when RR=1) for FCanCHEC and FRCF are defined above.
All country-specific data for nonaccidental mortality were obtained
from the Institute of Health Metrics and Evaluation (IHME) at the
University of Washington (https://vizhub.healthdata.org/gbd-compar e/).
Country-level PM2.5 data were also obtained from IHME (https://
ghdx.healthdata.org/record/global-burden-disease-study-2019-
gbd-2019-air-pollution-exposure-estimates-1990-2019) (32). Data and
code needed to replicate the burden estimates are available in the
Supplementary Materials.
SUPPLEMENTARY MATERIALS
Supplementary materials for this article is available at https://science.org/doi/10.1126/
sciadv.abo3381

Weichenthal et al., Sci. Adv. 8, eabo3381 (2022) 28 September 2022
SCIENCE ADVANCES | RESEARCH ARTICLE
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Acknowledgments
Funding: United States Health Effects Institute: Research described in this article was
conducted under contract to the Health Effects Institute (HEI), an organization jointly funded
by the U.S. Environmental Protection Agency (EPA; assistance award no. R-82811201) and
certain motor vehicle and engine manufacturers. The contents of this article do not necessarily

Weichenthal et al., Sci. Adv. 8, eabo3381 (2022) 28 September 2022
SCIENCE ADVANCES | RESEARCH ARTICLE
9 of 9
reflect the views of HEI or its sponsors nor do they necessarily reflect the views and policies of
the EPA or motor vehicle and engine manufacturers. S.W. is supported by a Research Scholar
Award provided by FRQS (Fonds de Rescherche Santé). Author contributions:
Conceptualization: S.W., R.T.B., and M.B. Methodology and statistical analyses: R.T.B., L.P., and
T.C. Data visualization: S.W. and R.T.B. Writing—original draft: S.W. and R.T.B. Writing—review
and editing: S.W., L.P., T.C., R.T.B., J.R.B., Y.C., D.L.C., A.C.E., P.H., C.L., R.V.M., J.M., A.J.P., M.T.,
A.v.D., C.L.W., and M.B. Competing interests: M.B. served on the WHO Guideline Development
Group (no remuneration was provided but travel costs to meetings were covered). All other
authors declare that they have no competing interests. Data and materials availability:
Outdoor PM2.5 data used for epidemiological analysis are available at https://zenodo.org/
record/6557778. Annual average outdoor PM2.5 data used for burden estimates are available
at https://ghdx.healthdata.org/record/global-burden-disease-study-2019-gbd-2019-air-
pollution-exposure-estimates-1990-2019. CanCHEC cohort data are held in secure facilities
managed by Statistics Canada. These can be accessed through the microdata access portal
application process (the application process and procedures are available online: www.
statcan.gc.ca/en/microdata/data-centres/access). Application forms are available online: www.
statcan.gc.ca/en/microdata/data-centres/forms. Briefly, users must create an account and
provide the following information: (i) information on the type of project (e.g., government
funded, academic, and other); (ii) a project proposal including timelines and other necessary
information specified in the application procedure; and (iii) investigator profiles. Statistics
Canada then reviews the application and communicates with the principal investigator to
complete the remaining administrative procedures before data access is granted through
Research Data Centers located across Canada. Data and code used for burden estimates are
available in the Supplementary Materials.
Submitted 27 January 2022
Accepted 11 August 2022
Published 28 September 2022
10.1126/sciadv.abo3381