Estimating treatment effects with observed confounders and mediators

Shantanu Gupta, Zachary C. Lipton, David Childers
Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:982-991, 2021.

Abstract

Given a causal graph, the do-calculus can express treatment effects as functionals of the observational joint distribution that can be estimated empirically. Sometimes the do-calculus identifies multiple valid formulae, prompting us to compare the statistical properties of the corresponding estimators. For example, the backdoor formula applies when all confounders are observed and the frontdoor formula applies when an observed mediator transmits the causal effect. In this paper, we investigate the over-identified scenario where both confounders and mediators are observed, rendering both estimators valid. Addressing the linear Gaussian causal model, we demonstrate that either estimator can dominate the other by an unbounded constant factor. Next, we derive an optimal estimator, which leverages all observed variables, and bound its finite-sample variance. We show that it strictly outperforms the backdoor and frontdoor estimators and that this improvement can be unbounded. We also present a procedure for combining two datasets, one with observed confounders and another with observed mediators. Finally, we evaluate our methods on both simulated data and the IHDP and JTPA datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v161-gupta21b, title = {Estimating treatment effects with observed confounders and mediators}, author = {Gupta, Shantanu and Lipton, Zachary C. and Childers, David}, booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence}, pages = {982--991}, year = {2021}, editor = {de Campos, Cassio and Maathuis, Marloes H.}, volume = {161}, series = {Proceedings of Machine Learning Research}, month = {27--30 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v161/gupta21b/gupta21b.pdf}, url = {https://proceedings.mlr.press/v161/gupta21b.html}, abstract = {Given a causal graph, the do-calculus can express treatment effects as functionals of the observational joint distribution that can be estimated empirically. Sometimes the do-calculus identifies multiple valid formulae, prompting us to compare the statistical properties of the corresponding estimators. For example, the backdoor formula applies when all confounders are observed and the frontdoor formula applies when an observed mediator transmits the causal effect. In this paper, we investigate the over-identified scenario where both confounders and mediators are observed, rendering both estimators valid. Addressing the linear Gaussian causal model, we demonstrate that either estimator can dominate the other by an unbounded constant factor. Next, we derive an optimal estimator, which leverages all observed variables, and bound its finite-sample variance. We show that it strictly outperforms the backdoor and frontdoor estimators and that this improvement can be unbounded. We also present a procedure for combining two datasets, one with observed confounders and another with observed mediators. Finally, we evaluate our methods on both simulated data and the IHDP and JTPA datasets.} }
Endnote
%0 Conference Paper %T Estimating treatment effects with observed confounders and mediators %A Shantanu Gupta %A Zachary C. Lipton %A David Childers %B Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2021 %E Cassio de Campos %E Marloes H. Maathuis %F pmlr-v161-gupta21b %I PMLR %P 982--991 %U https://proceedings.mlr.press/v161/gupta21b.html %V 161 %X Given a causal graph, the do-calculus can express treatment effects as functionals of the observational joint distribution that can be estimated empirically. Sometimes the do-calculus identifies multiple valid formulae, prompting us to compare the statistical properties of the corresponding estimators. For example, the backdoor formula applies when all confounders are observed and the frontdoor formula applies when an observed mediator transmits the causal effect. In this paper, we investigate the over-identified scenario where both confounders and mediators are observed, rendering both estimators valid. Addressing the linear Gaussian causal model, we demonstrate that either estimator can dominate the other by an unbounded constant factor. Next, we derive an optimal estimator, which leverages all observed variables, and bound its finite-sample variance. We show that it strictly outperforms the backdoor and frontdoor estimators and that this improvement can be unbounded. We also present a procedure for combining two datasets, one with observed confounders and another with observed mediators. Finally, we evaluate our methods on both simulated data and the IHDP and JTPA datasets.
APA
Gupta, S., Lipton, Z.C. & Childers, D.. (2021). Estimating treatment effects with observed confounders and mediators. Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 161:982-991 Available from https://proceedings.mlr.press/v161/gupta21b.html.

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