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Estimating Treatment Effects with Observed Confounders and Mediators

Shantanu Gupta, Zachary C. Lipton, David Childers

arXiv 26 Mar 2020 · Statistics — Methodology · 3 citations (OpenAlex)

arXiv:2003.11991 · PDF · DOI · OpenAlex · Extracted main text

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.

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33
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45
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Isabel R Fulcher, Ilya Shpitser, Stella Marealle, and Eric J Tchetge… (2020) Robust inference on population indirect causal effects: the generalized front door criterion0.81142100%
2Adam N Glynn and Konstantin Kashin (2018) Front-door versus back-door adjustment with unmeasured confounding: Bias formulas for front-door and hybrid adjustments with app…0.73732100%
3Judea Pearl (2009) Causality0.73732100%
4Xiaohong Chen and Andres Santos (2018) Overidentification in regular models0.64422100%
5Andrea Rotnitzky and Ezequiel Smucler (2019) Efficient adjustment sets for population average treatment effect estimation in non-parametric causal graphical models0.64422100%
6Roger Fletcher (2013) Practical methods of optimization0.5112250%
7Jennifer L Hill (2011) Bayesian nonparametric modeling for causal inference0.51121100%
8Judea Pearl (1995) Causal diagrams for empirical research0.51121100%
9V. Dorie (2016) Non-parametrics for causal inference0.40511100%
10Lars Peter Hansen (1982) Large sample properties of generalized method of moments estimators0.40511100%

Showing the top 10 of 33 scored citations.