Causal Inference Under Multiple Versions of Treatment

By Tyler J. VanderWeele, Miguel A. Hern'an. 2013

251 citations recorded by the source corpus.

Abstract: In this article, we discuss causal inference when there are multiple versions of treatment. The potential outcomes framework, as articulated by Rubin, makes an assumption of no multiple versions of treatment, and here we discuss an extension of this potential outcomes framework to accommodate causal inference under violations of this assumption. A variety of examples are discussed in which the assumption may be violated. Identification results are provided for the overall treatment effect and the effect of treatment on the treated when multiple versions of treatment are present and also for the causal effect comparing a version of one treatment to some other version of the same or a different treatment. Further identification and interpretative results are given for cases in which the version precedes the treatment as when an underlying treatment variable is coarsened or dichotomized to create a new treatment variable for which there are effectively “multiple versions”. Results are also given for effects defined by setting the version of treatment to a prespecified distribution. Some of the identification results bear resemblance to identification results in the literature on direct and indirect effects. We describe some settings in which ignoring multiple versions of treatment, even when present, will not lead to incorrect inferences.

Subfields: Economics and Econometrics, Statistics and Probability

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Citations in the corpus

An introduction to g methods. (2016, background): “Rather, this assumption’s validity depends on the nature of the exposure assignment mechanism.(4) Under counterfactual consistency, we partially identify our average causal effect.”
Counterfactual risk assessments, evaluation, and fairness (2019, methodology): “We note, however, that DR estimation methods can be used in any treatment setting, including for continuous treatments such as dosing [24, 52].”
Multivariate Regression Analysis for the Item Count Technique (2011, background): “Addressing these design effects is beyond the scope of this article, but interested readers may refer to Blair and Imai (2010b) who develop several methods to address these potential violations of the identification assumptions (see also VanderWeele and Hernán 2010).”
Causal diagrams for interference (2014, background): “Under the assumptions of no interference and a single version of treatment (we will not discuss the latter assumption here; see VanderWeele and Hernan, 2013, for discussion), Yi(a), a = 0,1 is defined as the counterfactual outcome we would have observed if, possibly contrary to fact, subject i had…”
Why Propensity Scores Should Not Be Used for Matching (2019, methodology): “…score matching (PSM) (Rosenbaum and Rubin, 1983) is the most common matching method, possibly even “the most developed and popular strategy for causal analysis in observational studies” (Pearl, 2010); it is used or referenced in over 47,300 scholarly articles.1 We show here that PSM, as it…”