Effects of Treatment on the Treated: Identification and Generalization
This work addresses a fundamental problem in causal inference for researchers and practitioners evaluating programs, policies, and decisions, though it is incremental as it builds on existing graphical methods.
The paper tackles the problem of estimating the counterfactual effect of withholding an action that has been implemented, known as the effect of treatment on the treated (ETT), by exploring conditions for its identification from experimental and observational data. It provides graphical characterizations for identifying ETT with singleton variables and extends this to multiple treatments, along with methods for constructing ETT estimands from interventional and observational distributions.
Many applications of causal analysis call for assessing, retrospectively, the effect of withholding an action that has in fact been implemented. This counterfactual quantity, sometimes called "effect of treatment on the treated," (ETT) have been used to to evaluate educational programs, critic public policies, and justify individual decision making. In this paper we explore the conditions under which ETT can be estimated from (i.e., identified in) experimental and/or observational studies. We show that, when the action invokes a singleton variable, the conditions for ETT identification have simple characterizations in terms of causal diagrams. We further give a graphical characterization of the conditions under which the effects of multiple treatments on the treated can be identified, as well as ways in which the ETT estimand can be constructed from both interventional and observational distributions.