## Effects of treatment on the treated: Identification and generalization (2009)

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Venue: | In Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence |

Citations: | 14 - 5 self |

### BibTeX

@INPROCEEDINGS{Shpitser09effectsof,

author = {Ilya Shpitser},

title = {Effects of treatment on the treated: Identification and generalization},

booktitle = {In Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence},

year = {2009},

publisher = {AUAI Press}

}

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### 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. 1

### Citations

1247 |
Causality: models, reasoning, and inference
- Pearl
(Show Context)
Citation Context ...on which, nevertheless, yields a simple way of constructing the ETT estimand. 2 Preliminaries In this paper, we formalize counterfactual expressions using the Structural Causal Model (SCM) defined in =-=[4]-=-, Chapter 7. Such models have a marked advantage over the potential-outcome approach of [2] and [7] in that they permit background knowledge to be expressed in the ordinary scientific language of caus... |

650 |
Estimating Causal Effects of Treatments in Randomized and Non-randomized Studies
- Rubin
- 1974
(Show Context)
Citation Context ...is paper, we formalize counterfactual expressions using the Structural Causal Model (SCM) defined in [4], Chapter 7. Such models have a marked advantage over the potential-outcome approach of [2] and =-=[7]-=- in that they permit background knowledge to be expressed in the ordinary scientific language of cause-effect relationships instead of the artificial language of counterfactual independencies require... |

222 | Equivalence and synthesis of causal models - Verma, Pearl - 1991 |

79 | Ancestral graph Markov models - Richardson, Spirtes |

63 | A general identification condition for causal effects
- Tian, Pearl
- 2002
(Show Context)
Citation Context ...elpful terminology. A C-component [11] of a latent projection is a maximal set of nodes pairwise connected by bidirected paths. Each causal diagram has a unique partition into Ccomponents. A Q-factor =-=[12]-=- for a C-component in G consisting of a set Y, denoted by Q[Y] G v , is defined as P(y|do(v \ y)), where V is the set of all observable nodes. Note that in this notation, v denotes the set of values t... |

45 | Identification of conditional interventional distributions
- Shpitser, Pearl
- 2006
(Show Context)
Citation Context ...le by considering P(y|w, do(x)) in the graph G ′ shown in Fig. 1 (b), while the counterfactual graph for P(Yx = y|x ′ ) is shown in Fig. 1 (c). Identifying P(y|w, do(x)) in G ′ using the algorithm in =-=[8]-=-, we get ∑ z P(z|x)∑ x P(y|z, w, x)P(w, x)/P(w). Replacing w by x ′ ∑ yields the expression z P(z|x)∑ x P(y|z, x′ , x)P(x ′, x)/P(x ′). Note that P(y|z, x ′, x) equals 0 for any value of x other than ... |

37 | Identification of joint interventional distributions in recursive semi-Markovian causal models
- Shpitser, Pearl
- 2006
(Show Context)
Citation Context ...ot identifiable, then P(Yx|x ′) isn’t either. This is because results in [10] imply P(Yx = y|x ′) is identifiable iff either P(y|do(x)) or P(Yx = y, X = x ′) is. In the latter case there is a hedge H =-=[9]-=- for P(y, w|do(x)) in G ′ . In this case, it is possible to convert two counterexample models witnessing nonidentification of P(y, w|do(x)) into two counterexample models witnessing non-identification... |

14 |
Randomization and social policy evaluation. In Evaluating welfare and training programs
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- 1992
(Show Context)
Citation Context ...riable representing the behavior of Y after X is set to value x, each of the two queries can be represented by the expression P(Yx = y|x ′ ), often called the effect of treatment on the treated (ETT) =-=[1]-=-. Modeling and identification issues which arise in these queries have received some attention in the literature [6]. In subsequent sections, we introduce the machinery of causal inference necessary t... |

11 |
Studies in causal reasoning and learning
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- 2002
(Show Context)
Citation Context ...plicates by Theorem 4, in which case its existence is ruled out by the second condition of Theorem 3. □ Identification of γ in terms of P(v) can be ensured by using existing identification algorithms =-=[11]-=- to check that each Q-factor in the expression in Theorem 5 is identifiable from P(v). In fact, since Theorem 5 ensures there are no conflicts among variable assignments in the Q-factors, it is possib... |

9 |
Discussion of ”causal effects in the presence of non compliance a latent variable interpretation” by forcina, a
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(Show Context)
Citation Context ...xpression P(Yx = y|x ′ ), often called the effect of treatment on the treated (ETT) [1]. Modeling and identification issues which arise in these queries have received some attention in the literature =-=[6]-=-. In subsequent sections, we introduce the machinery of causal inference necessary to define such expressions precisely using causal diagrams as carriers of background knowledge, and show that, if X i... |

4 |
les applications de la thar des probabilities aux experiences Agaricales: Essay des principle. Excerpts reprinted
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(Show Context)
Citation Context ...es In this paper, we formalize counterfactual expressions using the Structural Causal Model (SCM) defined in [4], Chapter 7. Such models have a marked advantage over the potential-outcome approach of =-=[2]-=- and [7] in that they permit background knowledge to be expressed in the ordinary scientific language of cause-effect relationships instead of the artificial language of counterfactual independencies... |