Causal effect on a target population: A sensitivity analysis to handle missing covariates

Colnet Bénédicte (), Josse Julie, Varoquaux Gaël and Scornet Erwan ()
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Colnet Bénédicte: Soda Project-team, Premedical Project-team, INRIA, and Centre de Mathémathiques Appliquées, Institut Polytechnique de Paris, Palaiseau, France
Josse Julie: Premedical Project Team, INRIA Sophia-Antipolis, Montpellier, France
Varoquaux Gaël: Soda Project-team, INRIA Saclay, France
Scornet Erwan: Centre de Mathémathiques Appliquées, UMR 7641, École Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, France

Journal of Causal Inference, 2022, vol. 10, issue 1, 372-414

Abstract: Randomized controlled trials (RCTs) are often considered the gold standard for estimating causal effect, but they may lack external validity when the population eligible to the RCT is substantially different from the target population. Having at hand a sample of the target population of interest allows us to generalize the causal effect. Identifying the treatment effect in the target population requires covariates to capture all treatment effect modifiers that are shifted between the two sets. Standard estimators then use either weighting (IPSW), outcome modeling (G-formula), or combine the two in doubly robust approaches (AIPSW). However, such covariates are often not available in both sets. In this article, after proving L 1 {L}^{1} -consistency of these three estimators, we compute the expected bias induced by a missing covariate, assuming a Gaussian distribution, a continuous outcome, and a semi-parametric model. Under this setting, we perform a sensitivity analysis for each missing covariate pattern and compute the sign of the expected bias. We also show that there is no gain in linearly imputing a partially unobserved covariate. Finally, we study the substitution of a missing covariate by a proxy. We illustrate all these results on simulations, as well as semi-synthetic benchmarks using data from the Tennessee student/teacher achievement ratio (STAR), and a real-world example from critical care medicine.

Keywords: average treatment effect; distributional shift; external validity; generalizability; transportability (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:10:y:2022:i:1:p:372-414:n:1

DOI: 10.1515/jci-2021-0059

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