On the Validity of Covariate Adjustment for Estimating Causal Effects

Ilya Shpitser, Tyler Vander Weele, James Robins
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:526-535, 2010.

Abstract

Identifying effects of actions (treatments) on outcome variables from observational data and causal assumptions is a fundamental problem in causal inference. This identification is made difficult by the presence of confounders which can be related to both treatment and outcome variables. Confounders are often handled, both in theory and in practice, by adjusting for covariates, in other words considering outcomes conditioned on treatment and covariate values, weighed by probability of observing those covariate values. In this paper, we give a complete graphical criterion for covariate adjustment, which we term the adjustment criterion, and derive some interesting corollaries of the completeness of this criterion.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-shpitser10a, title = {On the Validity of Covariate Adjustment for Estimating Causal Effects}, author = {Shpitser, Ilya and Weele, Tyler Vander and Robins, James}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {526--535}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/shpitser10a/shpitser10a.pdf}, url = {https://proceedings.mlr.press/r8/shpitser10a.html}, abstract = {Identifying effects of actions (treatments) on outcome variables from observational data and causal assumptions is a fundamental problem in causal inference. This identification is made difficult by the presence of confounders which can be related to both treatment and outcome variables. Confounders are often handled, both in theory and in practice, by adjusting for covariates, in other words considering outcomes conditioned on treatment and covariate values, weighed by probability of observing those covariate values. In this paper, we give a complete graphical criterion for covariate adjustment, which we term the adjustment criterion, and derive some interesting corollaries of the completeness of this criterion.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T On the Validity of Covariate Adjustment for Estimating Causal Effects %A Ilya Shpitser %A Tyler Vander Weele %A James Robins %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-shpitser10a %I PMLR %P 526--535 %U https://proceedings.mlr.press/r8/shpitser10a.html %V R8 %X Identifying effects of actions (treatments) on outcome variables from observational data and causal assumptions is a fundamental problem in causal inference. This identification is made difficult by the presence of confounders which can be related to both treatment and outcome variables. Confounders are often handled, both in theory and in practice, by adjusting for covariates, in other words considering outcomes conditioned on treatment and covariate values, weighed by probability of observing those covariate values. In this paper, we give a complete graphical criterion for covariate adjustment, which we term the adjustment criterion, and derive some interesting corollaries of the completeness of this criterion. %Z Reissued by PMLR on 04 October 2026.
APA
Shpitser, I., Weele, T.V. & Robins, J.. (2010). On the Validity of Covariate Adjustment for Estimating Causal Effects. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:526-535 Available from https://proceedings.mlr.press/r8/shpitser10a.html. Reissued by PMLR on 04 October 2026.

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