Marie Abele-Bind’s contribution to the Discussion of ‘Methods for estimating the exposure–response curve to inform the new safety standards for fine particulate matter’ by Cork et al.

Methods for Estimating the Exposure-Response Curve to Inform the New Safety Standards for Fine Particulate Matter' by Cork et al.Although the field of causal inference has primarily focused on dichotomous treatment exposures, this interesting article departs from this simple setting and attempts to assess causal inference methods that estimate the effects of a continuous treatment, namely non-randomized air pollution.Classical work in experimental design has already provided methods to assess the effect of a randomized treatment with many levels, and we believe that transporting successful insights from experimental design is essential, especially in complex settings such as those being considered by the current effort.We also believe that it is crucial to embed any causal observational study into a plausible hypothetical randomized experiment, a point that has been emphasized in recent literature (Bind and Rubin, 2019).To achieve this, we need to first define the treatment and its timing, and then try to convince readers that the underlying assumptions, especially the unconfoundedness assumption, are plausible.For instance, if complete randomization is being assumed, researchers should present extensive diagnostics for covariate balance along the full distribution of the continuous treatment, which is tricky to implement.In the context of environmental exposures, days with high vs. low air pollution concentrations generally differ along many dimensions.Ideally, to study the effect of PM 2.5 concentrations, one needs to contrast outcomes on "similar" days with very low, low, medium, high, and very high PM 2.5 concentrations, i.e., outcomes on days with similar levels of all other pollutants (e.g., NO 2 , O 3 ) and similar meteorological conditions (e.g., temperature, relative humidity).All days of very low, low, medium, high, and very high PM 2.5 concentrations also need to be matched on day of the week, month, and year.The problem therefore requires not only extensive datasets, but also multiple measurements various pollution and meteorological conditions across days of the week, months, and years.