Effects of Treatment on the Treated: Identification and Generalization

Ilya Shpitser, Judea Pearl
Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, PMLR R7:522-529, 2009.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR7-shpitser09a, title = {Effects of Treatment on the Treated: Identification and Generalization}, author = {Shpitser, Ilya and Pearl, Judea}, booktitle = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence}, pages = {522--529}, year = {2009}, editor = {Bilmes, Jeff and Ng, Andrew Y.}, volume = {R7}, series = {Proceedings of Machine Learning Research}, month = {18--21 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r7/main/assets/shpitser09a/shpitser09a.pdf}, url = {https://proceedings.mlr.press/r7/shpitser09a.html}, 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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Effects of Treatment on the Treated: Identification and Generalization %A Ilya Shpitser %A Judea Pearl %B Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2009 %E Jeff Bilmes %E Andrew Y. Ng %F pmlr-vR7-shpitser09a %I PMLR %P 522--529 %U https://proceedings.mlr.press/r7/shpitser09a.html %V R7 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
Shpitser, I. & Pearl, J.. (2009). Effects of Treatment on the Treated: Identification and Generalization. Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R7:522-529 Available from https://proceedings.mlr.press/r7/shpitser09a.html. Reissued by PMLR on 04 October 2026.

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