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Exposure to fine particulate matter ($PM_{2.5}$) poses significant healthrisks and accurately determining the shape of the relationship between$PM_{2.5}$ and health outcomes has crucial policy ramifications. While variousstatistical methods exist to estimate this exposure-response curve (ERC), fewstudies have compared their performance under plausible data-generatingscenarios. This study compares seven commonly used ERC estimators across 72exposure-response and confounding scenarios via simulation. Additionally, weapply these methods to estimate the ERC between long-term $PM_{2.5}$ exposureand all-cause mortality using data from over 68 million Medicare beneficiariesin the United States. Our simulation indicates that regression methods notplaced within a causal inference framework are unsuitable when anticipatingheterogeneous exposure effects. Under the setting of a large sample size andunknown ERC functional form, we recommend utilizing causal inference methodsthat allow for nonlinear ERCs. In our data application, we observe a nonlinearrelationship between annual average $PM_{2.5}$ and all-cause mortality in theMedicare population, with a sharp increase in relative mortality at low PM2.5concentrations. Our findings suggest that stricter $PM_{2.5}$ limits couldavert numerous premature deaths. To facilitate the utilization of our results,we provide publicly available, reproducible code on Github for every step ofthe analysis.

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