2.4 Concentration response function

In order to determine an attributable fraction, it is necessary to understand how the response changes with concentration (i.e. does the relative risk increase, decrease, or level off with higher concentrations?). The shape of this concentration response function is an area of ongoing epidemiological research (e.g. Burnett et al., 2014; Pope et al., 2015).

In the simplest form, it might be assumed that the change in relative risk (RR, given as per 10 μg/m³) linearly depends on the surface PM_2.5 concentration (C, in μg/m³) as given in equation 4 (and as presented as an alternate form in Cohen et al., 2004; 2005).

In this equation, C₀ can be considered the “policy relevant (PRB)/target”, “natural background” or “threshold”/ “counterfactual”/ “lowest effect level” surface PM_2.5 concentration. Studies have shown that there is not a concentration level below which there is no adverse health effect for PM (e.g. Pope et al., 2002; Shi et al., 2015) and most experts in health impacts of ambient air quality agree that there is no population-level threshold (although there may be individual-level thresholds, e.g. Roman et al., 2008). However, there are few epidemiological studies in regions with very low annual average concentrations (Crouse et al., 2012 does records a 1.9 μg m⁻³ annual concentration in rural Canada) making it difficult to determine the health risks in relatively clean conditions. How to extrapolate the relationship out of the range of observed measurements is uncertain. Therefore, rather than assuming that the function is linear down to zero, studies often set C₀ to the value of the lowest measured level (LML) observed in the epidemiology study from which the RRs are derived [e.g. Evans et al., 2013 use 5.8 μg/m³ with the RR from Krewski et al. 2009] or use the “policy relevant” background (PRB, generally 0–2 μgm⁻³) concentration. This is the level to which policies might be able to reduce concentration and is generally determined from model simulations in which domestic anthropogenic emissions have been turned off (e.g. Fann et al., 2012). Similarly, some studies have set this value to preindustrial (1850) pollution levels (e.g. Fang et al., 2013; Silva et al., 2013).

Linear response functions are generally a good fit to observed responses at lower concentrations (Pope et al., 2002). However, studies suggest that linear response functions can greatly overestimate RR at high concentrations (e.g. Pope et al., 2015), where responses may start to level off. There is uncertainty at high concentrations because most epidemiology studies of the health effects of air pollution exposure have generally been conducted under lower concentrations (i.e. in the U.S.). In order to determine the shape of this response at higher concentrations, smoking has been used as a proxy (Burnett et al., 2014; Pope et al., 2011, 2009), which does show a diminishing response at higher concentrations. Therefore, both log-linear (Equations 5 and 6, where β = 0.15515/0.23218 for heart disease/lung cancer from Pope et al. (2002) or β = 0.18878/0.21136 for heart disease/lung cancer from Krewski et al., 2009 in Equation 6 and β = 0.01205/0.01328 for heart disease/lung cancer from Krewski et al., 2009 in Equation 5) and power law (Equation 7, where I is the inhalation rate of 18m³day⁻¹, β = 0.2730/0.3195, α = 0.2685/0.7433 for heart disease/lung cancer from Pope et al., 2011 and as used in Marlier et al., 2013) functions have been also been explored in this study.

We note that Cohen et al. (2005) and Anenberg et al. (2010) reference Equation 5 as a log-linear function, while Ostro (2004), Evans et al. (2013), and Giannadaki et al. (2014) use this as their linear function and instead use Equation 6 as their log-linear function, we will refer to these equation numbers for clarity in other sections. Another method to limit the response at high concentrations is to simply use a “ceiling,” “maximum exposure/high-concentration threshold,” or “upper truncation” value in which it is assumed that the response remains the same for any value above it (e.g. Anenberg et al., 2012; Cohen et al., 2005; Evans et al., 2013). This can be a somewhat arbitrary value or the highest observed concentration in the original epidemiological study.

Recently, Burnett et al. (2014) fit an integrated exposure response (IER) model using RRs from a variety of epidemiological studies on ambient and household air pollution, active smoking, and second hand tobacco smoke in order to determine RR functions over all global PM_2.5 exposure ranges for ischemic heart disease, cerebrovascular disease, chronic obstructive pulmonary disease, and lung cancer (Equation 8). Monte Carlo simulations were conducted in order to derive the one thousand sets of coefficients for the IER function (the coefficients are available at http://ghdx.healthdata.org/record/global-burden-disease-study-2010-gbd-2010-ambient-air-pollution-risk-model-1990–2010). for C < C₀, ΔRR= 0

This form is now being widely used (Apte et al., 2015; Lelieveld et al., 2015; Lim et al., 2012) and we use it here for our baseline estimates. In the following sections, we will discuss the uncertainty on the burden of disease associated with the shape of the concentration response function and threshold concentration.