Methods for Estimating the Exposure-Response Curve to Inform the New Safety Standards for Fine Particulate Matter

Exposure to fine particulate matter ($PM_{2.5}$) poses significant health risks and accurately determining the shape of the relationship between $PM_{2.5}$ and health outcomes has crucial policy ramifications. While various statistical methods exist to estimate this exposure-response curve (ERC), few studies have compared their performance under plausible data-generating scenarios. This study compares seven commonly used ERC estimators across 72 exposure-response and confounding scenarios via simulation. Additionally, we apply these methods to estimate the ERC between long-term $PM_{2.5}$ exposure and all-cause mortality using data from over 68 million Medicare beneficiaries in the United States. Our simulation indicates that regression methods not placed within a causal inference framework are unsuitable when anticipating heterogeneous exposure effects. Under the setting of a large sample size and unknown ERC functional form, we recommend utilizing causal inference methods that allow for nonlinear ERCs. In our data application, we observe a nonlinear relationship between annual average $PM_{2.5}$ and all-cause mortality in the Medicare population, with a sharp increase in relative mortality at low PM2.5 concentrations. Our findings suggest that stricter $PM_{2.5}$ limits could avert numerous premature deaths. To facilitate the utilization of our results, we provide publicly available, reproducible code on Github for every step of the analysis.