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Background  The shape of the exposure-response curve describing the effects of air pollution on population health has crucial regulatory implications, and it is important in assessing causal impacts of hypothetical policies of air pollution reduction.    Methods  After having reformulated the problem of assessing the short-term impact of air pollution on health within the potential outcome approach to causal inference, we developed a method based on the generalized propensity score (GPS) to estimate the average dose-response function (aDRF) and quantify attributable deaths under different counterfactual scenarios of air pollution reduction. We applied the proposed approach to assess the impact of airborne particles with a diameter less than or equal to 10  μ m (PM 10 ) on deaths from natural, cardiovascular and respiratory causes in the city of Milan, Italy (2003-2006).    Results  As opposed to what is commonly assumed, the estimated aDRFs were not linear, being steeper for low-moderate values of exposure. In the case of natural mortality, the curve became flatter for higher levels; this behavior was less pronounced for cause-specific mortality. The effect was larger in days characterized by higher temperature. According to the curves, we estimated that a hypothetical intervention able to set the daily exposure levels exceeding 40  μ g/m 3  to exactly 40 would have avoided 1157 deaths (90%CI: 689, 1645) in the whole study period, 312 of which for respiratory causes and 771 for cardiovascular causes. These impacts were higher than those obtained previously from regression-based methods.    Conclusion  This novel method based on the GPS allowed estimating the average dose-response function and calculating attributable deaths, without requiring strong assumptions about the shape of the relationship. Its potential as a tool for investigating effect modification by temperature and its use in other environmental epidemiology contexts deserve further investigation.

Assessing short-term impact of PM10 on mortality using a semiparametric generalized propensity score approach