Effects of Treatment on the Treated: Identification and Generalization

TL;DR

This paper investigates the conditions under which the effect of treatment on the treated (ETT) can be identified from experimental and observational data, providing graphical criteria and methods for estimation.

Contribution

It offers a comprehensive graphical framework for identifying ETT with single and multiple treatments, extending causal inference capabilities.

Findings

Simple graphical conditions for ETT identification with single treatments

Graphical criteria for multiple treatments on the treated

Methods to construct ETT estimands from observational and interventional data

Abstract

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.