An Empirical Bayes Approach to Estimating the Relation of Mortality to Exposure to Particulate Matter

As part of its assessment of the health risks associated with exposure to particulate matter (PM), the U.S. Environmental Protection Agency analyzed the risks associated with current levels, and the risk reductions that might be achieved by attainment of alternative PM standards, in two locations in the United States, Philadelphia, and Los Angeles. The concentration – response function describing the relation between a health endpoint and ambient PM concentrations is an important component, and a source of substantial uncertainty, in such risk analyses. In the absence of location‐specific estimates, the concentration –r esponse functions necessary for risk assessments in Philadelphia and Los Angeles must be inferred from the available information in other locations. Although the functional form of the concentration – response relations is assumed to be the same everywhere, the value of the PM coefficient in that function may vary from one location to another. Under this model, a distribution describes the probability that the PM coefficient in a randomly selected location will lie in any range of interest. An empirical Bayes estimation technique was used to improve the estimation of location‐specific concentration – response functions relating mortality to short‐term exposure to particles of aerodynamic diameter less than or equal to 2.5 μm (PM‐2.5), for which functions have previously been estimated in several locations. The empirical Bayes‐adjusted parameter values and their SEs were used to derive an estimate of the distribution of PM‐2.5 coefficients for mortality associated with short‐term exposures. From this distribution, distributions of relative risks corresponding to different specified changes in PM‐2.5 concentrations could be derived.