LAUSR

The potential outcomes framework1 allows epidemiologists to mathematically define causal effects of interest as a contrast between two potential (or counterfactual) outcomes.2 This, in turn, has allowed the use of observational data in efforts to answer questions relating to hypothetical interventions. The causal interpretation of contrasting potential outcomes relies on assumptions that the potential outcomes framework also allows investigators to explicitly state. Whether or not those assumptions actually hold, however, will typically not be entirely testable or ultimately known. Nevertheless, the appeal of using observational data for causal inference, especially in an area where experimental data are limited, has generated excitement in air pollution epidemiology and has spurred the adoption of methodology from this framework in recent years.3 In one such example, Chen et al. report in this issue of Environmental Health Perspectives on an application of the parametric g-formula to assess the effect of hypothetical interventions on fine particulate matter [particulate matter ≤2:5 lm in aerodynamic diameter (PM2:5)] exposures in a Canadian cohort.4 They report findings of reduced mortality outcomes associated with hypothetical reductions in exposure while identifying several advantages of the approach compared with a more traditional analysis approach using a survival framework, the Cox proportional hazards model. The parametric g-formula approach is indeed advantageous because it can address situations of exposure–confounder feedback in time-varying settings and does not suffer from the built-in selection bias of the Cox model.5 However, these are not likely to be major sources of bias in the study by Chen et al.4 Exposure–confounder feedback is not generally a feature in air pollution epidemiology settings and, in the current example, depletion of susceptible individuals leading to crossing of hazards also is not expected to be a major source of bias, with ∼ 90% of participants still alive at the end of followup. Overall, this is confirmed by the sensitivity analysis results fitting a Cox model and yielding qualitatively similar (though not directly comparable) effect estimates as the parametric g-formula. The use of this method is, therefore, not likely to greatly improve upon the internal validity of effect estimates and, as previously stated, we should be cautious about attributing causal interpretations of findings owing simply to the statistical method in any particular study.6,7 The parametric g-formula, nevertheless, is still advantageous in this setting compared with more traditional regression approaches. Unlike the Cox model, which yields target parameters based on the hazard, the parametric g-formula reports findings based on risk (cumulative incidence) and carries advantages over the hazard, such as collapsibility and the increased applicability with respect to public health relevance, especially when focusing on the risk difference.5,8 The approach further yields marginal effect estimates as opposed to conditional. However, in my opinion, the major advantage of the approach is the framing of the parameters of interest in terms of the dynamic interventions considered. Rather than focus target parameters based simply on exposure–response relationships, such as associations for a particular increase in exposure from level A to level B, these hypothetical interventions essentially compare the effect as a contrast of two counterfactual distributions of exposure in the same population. This is far more representative of how an intervention or policy could actually affect exposure and, by extension, health outcomes on the population level in a real-world setting. Despite this advantage, hypothetical interventions of the type that Chen at al.4 considered do have some perhaps fewer obvious limitations relating to key assumptions required for causal interpretation of these findings. Among these are the assumption of consistency and the “no multiple versions of treatment” assumption, part of Rubin’s stable unit treatment value assumption.9,10 Briefly, the assumptions require that a well-defined intervention is contrasted in the counterfactual effect estimate, and that there do not exist multiple versions of the treatment of interest (here, exposure to PM2:5). It is arguable that neither holds here. Depending on the intervention or policy change that would lead to a reduction in exposure levels, we may expect different sources of pollution (e.g., transportation, energy, agriculture) to be affected to varying degrees. That, in turn, may affect who experiences a greater change in pollution levels. However, even if we somehow achieved reductions according to some threshold or percentage-based intervention on the individual level, the differing composition of individual-level PM2:5 exposuresmaymean that the same concentration could have different effects in otherwise perfectly exchangeable individuals.11 This would constitute a violation of “no multiple versions of treatment” and would also lead to bias if unmeasured common causes exist between particle composition (version of treatment) and the outcome.10 Along the same lines, an intervention to reduce PM2:5 will likely lead to differential changes in other pollutants as well, given the common sources many air pollutants share. In that regard, the true intervention effect would be higher than estimated simply by considering PM2:5 alone. As the health burden of air pollution is, in essence, a result of joint effects of multiple pollutants, the solution maximizing potential health benefits should be one of joint interventions. On the other hand, because individual pollutants are regulated separately, it could be argued that reporting of individual effects is still useful for policy purposes. However, those, too,would probably be more accurate if the effect of other pollutants was also taken into account. One application of an exposure mixture approach has been proposed within the g-formula framework,12 although combining some of the work involving multipollutant models and causal inference is an area that requiresmore applied examples. Address correspondence to Andreas Neophytou, 1681 CampusDelivery, Fort Collins, CO 80523-1681USA. Email: [email protected] The author declares he has no conflicts of interest. Received 28 September 2022; Revised 11 February 2023; Accepted 14 February 2023; Published 15 March 2023. Note to readers with disabilities: EHP strives to ensure that all journal content is accessible to all readers. 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