On Well-defined Hypothetical Interventions in the Potential Outcomes Framework

To the Editor: A recent series of articles, commentaries, letters, and responses across numerous journals1–12 has considered the role and limits of the potential outcomes framework within the broader undertaking of causal inference. In one response in that exchange, Broadbent et al7 noted that the potential outcomes framework often makes reference to the notion of a “hypothetical intervention” but typically without formal explication of what this is. Often when the potential outcomes framework is described, the potential outcomes themselves, Y1 and Y0, are understood as the outcomes that would occur under a “hypothetical intervention” to set the exposure or treatment to levels 1 and 0, respectively. The term “hypothetical intervention” is generally taken as a primitive and left undefined. I would like to put forward a proposal here as to how a “hypothetical intervention,” within the potential outcomes framework, is to be understood. I am not suggesting that there is anything new in this proposal, and indeed I think what is here proposed is what is generally implicitly understood by many writers on the potential outcomes framework when using the term. The hope of this letter is thus only to make explicit what I think is often understood implicitly, and thus, to open the proposal to additional comment, refinement, and critique. I will be adapting here some discussion in Chapter 16 of my book,13Explanation in Causal Inference, that relates causation to entailment by the laws of nature. Even in my book, while I certainly had a notion of what constituted a “hypothetical intervention” in mind, and discussed what I took to be the relevant concepts in reference to statements of the form “X had an effect on Y,” I did not explicitly tie this to the notion of a “hypothetical intervention,” which again often seems to be taken as a primitive, left undefined, within the potential outcomes framework. I would propose that a hypothetical intervention to set X to x is simply the specification, possibly contrary to fact, of the event or state X=x, such that we say that a hypothetical intervention is well-defined with respect to outcome Y, exposure X, setting X=x, and population P, if for each individual i in population P, there is a unique value Yx(i) (or distribution of values Yx(i) in the context of stochastic counterfactuals) such that the event or state X=x, along with the state of the universe and the laws of nature, jointly entail Y=Yx(i). Otherwise, the hypothetical intervention is said to be ill-defined or ambiguous. A hypothetical intervention on X is thus essentially just the specification of a potentially counterfactual state of exposure X but one such that such that the state or event X=x is itself sufficiently well-specified so as to fix the value or distribution Yx for each individual in the population under consideration. We might also refer to a “hypothetical intervention” as simply a “hypothetical setting” or, when the setting is contrary to fact, a “counterfactual state.” As discussed in the eAppendix; https://links.lww.com/EDE/B334, the ambiguity of hypothetical intervention potentially arises from failure to sufficiently specify the state of the universe that is in view at least as it pertains to the outcome under consideration. The extent to which a hypothetical intervention is well defined or ambiguous is of course a relative concept. Most specifications of an event or state will be ambiguous to a certain extent, but again for the hypothetical intervention to be well defined, the specification of the state only needs to be sufficiently fixed so as to entail a unique outcome or distribution of outcomes Y. When hypothetical interventions are well defined, then so are the potential outcomes, and thus so are also the quantitative causal effect estimands.4 Discussion is also given in the eAppendix; https://links.lww.com/EDE/B334 as to challenges in conceptualizing the laws of nature themselves, how the proposal here relates to Pearl’s “do” operator, how it relates to multiple versions of treatment, and how it helps clarify that manipulability is helpful, but not necessary, in specifying well-defined hypothetical interventions. I hope that this discussion here and in the eAppendix; https://links.lww.com/EDE/B334 goes some way in addressing the inquiry by Broadbent et al7 concerning the conceptualization of “hypothetical interventions” in the potential outcomes literature, and that it will also allow for further discussion and critique. Tyler J. VanderWeeleDepartments of Epidemiology and BiostatisticsHarvard T.H. Chan School of Public HealthHarvard UniversityBoston, MA