Fine particulate matter (\(PM_{2.5}\))

For a specific scenario and year, the GAINS model computes mortality related indicators attributed to chronic exposure to ambient PM2.5 for five major diseases: Ischemic heart disease, stroke, chronic obstructive pulmonary disease (COPD), lung cancer, and acute lower respiratory infections (ALRI). The three mortality metrics considered in GAINS are:

The number of premature (attributable) deaths

The shortening of life expectancy

The number of life years lost

Premature (attributable) deaths

Similarly to the Global Burden of Disease (GBD) project, estimations of excess number of deaths associated with ambient fine particulate matter (\(PM_{2.5}\)) in GAINS are based on a Comparative Risk Assessment (CRA) methodology. Within the CRA, the change in population health outcomes are estimated under alternative scenarios based on a counterfactual distribution of exposure to a risk factor over time and using Population Attributable Fractions (PAFs). The CRA of the mortality burden from ambient \(PM_{2.5}\) can be divided into the 5 following components:

Baseline ambient fine particulate matter concentrations: The pollutant concentrations are estimated in GAINS and validated against monitoring data for background concentrations.

Estimates of the distribution of population exposure to ambient fine particulate matter: Population weighted exposure is ascertained by superimposing ambient \(PM_{2.5}\) concentration levels with gridded and total projected population data for each country/region on the same grid. These projections rely on finely gridded population data sourced from the University of Southampton’s WorldPop dataset. To align with scenario years, these projections incorporate trends in both urban and rural population changes from the UN World Urbanization Prospects (2018 revision).

Baseline death rates and population size by cause, age and potentially sex: Baseline age-specific total mortality data in GAINS are derived from the UN World Population Prospects 2017. For regions outside Europe, data on cause-specific shares of disease contributions to total baseline mortality are derived from the GBD 2021 database.

Exposure-Response Functions (ERFs): GAINS uses two different ERFs depending on the region of analysis in Europe and outside Europe. As the latter require regular evaluation and update to incorporate new scientific evidence, ERFs in GAINS have been changing over time following the latest World Health Organization (WHO) or GBD methodology. Typically based on data from pooled cohorts or meta-analyses from cohorts and case-control studies from multiple epidemiological studies in different populations, ERFs are represented by Relative Risk (RR) functions, which show the ratio of the probability of death at a certain age given a specific exposure to the probability of death at that age assuming a counterfactual exposure:

\begin{align} D_{BL,d,a} (PM_{2.5}) = D_0 \cdot RR(PM_{2.5}) \tag{1} \end{align}

where:

BL, d, a	Baseline, disease, age, respectively
\(D_{BL,d,a} (PM_{2.5})\)	Number of deaths under elevated \(PM_{2.5}\) concentrations (baseline total deaths) at age a and disease d
\(D_0\)	Hypothetical number of deaths under a counterfactual level (“clean” level)
\(RR_{d,a}(PM_{2.5})\)	Relative risk for a given level of PM2.5 at age a and disease d

Reference (counterfactual) exposure level: GAINS uses distinct counterfactuals for regions in and outside Europe. Outside Europe, GAINS uses the Theoretical Minimum Risk Exposure Level (TMREL) as the counterfactual. The TMREL is the level of ambient PM2.5 exposure below which its relationship with a disease outcome is not supported by the available evidence, irrespective of whether it is currently attainable in practice. At the TMREL the risk of the exposed population is minimised, and hence maximum population-attributable burden is captured. In Europe, GAINS uses the sum of all natural contributions (dust and sea salt) as counterfactual for ambient \(PM_{2.5}\).

The actual number of additional deaths (“premature” or attributable deaths) caused by \(PM_{2.5}\) exposure is obtained using Population Attributable Fraction (PAF), directly derived from RR functions:

\begin{align} D_{PM,d,a} &= D_{BL,d,a} - D_0 \\ &= D_{BL,d,a} \cdot \frac {RR_{d,a} - 1}{RR_{d,a}} \\ &= D_{BL,d,a} \cdot PAF_{d,a} \tag{2} \end{align}

where:

\(D_{PM,d,a}\)	Number of deaths attributable to \(PM_{2.5}\) concentrations (“premature deaths”) at age a and disease d
\(PAF_{d,a}\)	Population attributable fraction for a given disease d and age a

Years of Life Lost (YLLs)

The YLL metric is a measure for the total loss of human life span in a given region due to the exposure to PM2.5 in a given year. YLLs are calculated by multiplying age-specific attributable deaths with the remaining life expectancy at this age and summing over all ages:

\begin{align} YLL_i = \sum_a pd_{i,a} \cdot lex_{i,a} \tag{3} \end{align}

where:

i, a	Region, age respectively
\(YLL_i\)	Years of life lost in region i
\(pd_{i,a}\)	Premature deaths attributable to \(PM_{2.5}\) at age a in region i
\(lex_{i,a}\)	Remaining life expectancy at age a in region i

The remaining life expectancy is retrieved from life tables from the UN World Population Prospects 2017.

Loss of life expectancy

Loss of life expectancy is calculated from exposure to ambient PM2.5 using a Cox proportional hazards model. [5] Assuming that air pollution only affects natural mortality (about 95% of deaths excluding accidents and suicides) and cohort exposure is being kept constant for the whole lifetime, the age-specific relative risk of dying for adults is expressed as follows using a first-order Taylor expansion with \(\beta << 1\):

\begin{align} RR_{PM} = \exp (\beta \cdot [PM]) \approx 1 + \beta \cdot [PM] \tag{4} \end{align}

where:

\(\beta\)	Coefficient << 1 expressed in \(\mu g/m^3\)
\(RR_{PM}\)	Relative risk function related to the level of \(PM_{2.5}\)

Cohort- and country-specific mortality data extracted from life table statistics from the UN World Population Prospects 2017 are used to calculate for each cohort the baseline survival function over time. When modified by the exposure to ambient \(PM_{2.5}\), the latter can be expressed as follows:

\begin{align} l_{c}(t) = \exp \left( - \sum_{z=c}^{t} \mu_{z,z-c+w_{0}} \right) \tag{5} \end{align}

\begin{align} \bar{l_{c}}(t) = \exp \left( -(1 + \beta [PM]) \sum_{z=c}^{t} \mu_{z,z-c+w_{0}} \right) \tag{6} \end{align}

where:

t, c, \(w_0\)	Time, age of cohort, starting age (30 years) respectively
\(l_c(t)\)	Baseline survival function indicating the percentage of a cohort aged c alive after time t elapsed since starting time \(w_0\)
\(\bar{l_{c}}(t)\)	Baseline survival function modified by the exposure to \(PM_{2.5}\)
\(\mu_{a,b}\)	Mortality rates derived from each country from life tables with a as age and b as calendar time

Following a methodology introduced by Pope et al. [10], it is assumed in GAINS that an increased risk applies only to people older than \(w_0\) = 30 years. The life expectancy \(e_c\) is then calculated as the integral over the remaining life time of the baseline survival function modified by the exposure to \(PM2.5\):

\begin{align} e_{c}(t) = \int_c^{w_1} \bar{l_c}(t) dt \tag{7} \end{align}

where:

\(w_1\)	The maximum age considered (100 years)
\(e_{c}\)	Life expectancy of a cohort c

The change in life expectancy \(\Delta e_c\) in a cohort aged c due to \(PM_{2.5}\) is then calculated as follows:

\begin{align} \Delta e_{c} \approx \beta [PM] \int_c^{w_1} l_c(t) \cdot \log l_c (t) dt \tag{8} \end{align}

where:

\(\Delta e_{c}\)

Change in life expectancy of a cohort c

For all cohorts in a GAINS region i, the change in life expectancy \(\Delta e_i\) is eventually calculated as the averages of the change in life expectancy for the cohorts living in the 7 x 7 \(km^2\) grid cells k of that region i:

\begin{align} \Delta e_{i} = \sum_{c=w_0}^{w_1} \frac {Pop_{c,i}}{Pop_k,i} \Delta e_{c,k} \tag{9} \end{align}

where:

\(\Delta e_{i}\)	Change in life expectancy for all cohorts in region i
\(\Delta e_{c,k}\)	Change in life expectancy in cohorts aged c living in grid cell k of region i
\(Pop_{c,i}\)	Population in cohorts aged c in region i
\(Pop_{k,i}\)	Total population in grid cell k in region i