A doubly robust additive model for the probability of dying from air pollution exposure

Abstract

Introduction: Very few studies on the association between PM2.5 and mortality reported a risk difference. Also the adjustment of confounding in most studies relied on a strong assumption that the model is correctly specified. Methods: We studied a general population (13.4 million Medicare enrollees in seven southeast states in the US during 2000–2013 with 97 million person-years of follow up) and used a novel PM2.5 model with 1 km spatial resolution to predict their long-term exposure to PM2.5. We developed a doubly robust additive model which directly estimates the risk difference of death related to PM2.5 and relaxes the assumption on model specification. This is a two-stage approach. In the first stage, the analysis was done within each follow-up year. First, we split the data by PM2.5 quintiles. Within each PM2.5 quintile, we fitted a doubly robust logistic model regressing the probability of dying against all confounders (without PM2.5) which was also weighted by the inverse probability weights of being exposed to the observed PM2.5 concentration given all confounders. Second, we predicted the counterfactual probability of dying in each PM2.5 quintile for all individual at risk. Third, we regressed the average counterfactual probability against the median PM2.5 in each quintile using an additive model. In the second stage, the coefficients were combined across follow-up year. Results: The risk difference of death was 0.020 (95% Confidence Interval 0.018-0.021) per 10 μg m-3 increase in PM2.5. By comparison, the hazard ratio was 1.34 (1.33-1.35) using a Cox proportional hazards model. Conclusions: We developed a novel causal model and estimated the additive effect of PM2.5 on death in a general population. The estimate is easier to interpret and to use in policymaking and risk assessment studies.