Potential outcome approach to causal inference in assessing the short   term impact of air pollution on mortality
  The opportunity to assess short term impact of air pollution relies on the causal interpretation of the exposure-outcome association, but up to now few studies explicitly faced this issue within a causal inference framework. In this paper, we reformulated the problem of assessing the short term impact of air pollution on health using the potential outcome approach to causal inference. We focused on the impact of high daily levels of PM10 on mortality within two days from the exposure in the metropolitan area of Milan (Italy), during the period 2003-2006. After defining the number of attributable deaths in terms of difference between potential outcomes, we used the estimated propensity score to match each high exposure-day with a day with similar background characteristics but lower PM10 level. Then, we estimated the impact by comparing mortality between matched days. We found that during the study period daily exposures larger than 40 microgram per cubic meter were responsible of 1079 deaths (116; 2042). The impact was more evident among the elderly than in the younger classes of age. The propensity score matching turned out to be an appealing method to assess historical impacts in this field. 
Michela Baccini, Alessandra Mattei, Fabrizia Mealli, Pier Alberto   Bertazzi, Michele Carugno
stat.AP stat.ME