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June 2019 A robust and efficient approach to causal inference based on sparse sufficient dimension reduction
Shujie Ma, Liping Zhu, Zhiwei Zhang, Chih-Ling Tsai, Raymond J. Carroll
Ann. Statist. 47(3): 1505-1535 (June 2019). DOI: 10.1214/18-AOS1722


A fundamental assumption used in causal inference with observational data is that treatment assignment is ignorable given measured confounding variables. This assumption of no missing confounders is plausible if a large number of baseline covariates are included in the analysis, as we often have no prior knowledge of which variables can be important confounders. Thus, estimation of treatment effects with a large number of covariates has received considerable attention in recent years. Most existing methods require specifying certain parametric models involving the outcome, treatment and confounding variables, and employ a variable selection procedure to identify confounders. However, selection of a proper set of confounders depends on correct specification of the working models. The bias due to model misspecification and incorrect selection of confounding variables can yield misleading results. We propose a robust and efficient approach for inference about the average treatment effect via a flexible modeling strategy incorporating penalized variable selection. Specifically, we consider an estimator constructed based on an efficient influence function that involves a propensity score and an outcome regression. We then propose a new sparse sufficient dimension reduction method to estimate these two functions without making restrictive parametric modeling assumptions. The proposed estimator of the average treatment effect is asymptotically normal and semiparametrically efficient without the need for variable selection consistency. The proposed methods are illustrated via simulation studies and a biomedical application.


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Shujie Ma. Liping Zhu. Zhiwei Zhang. Chih-Ling Tsai. Raymond J. Carroll. "A robust and efficient approach to causal inference based on sparse sufficient dimension reduction." Ann. Statist. 47 (3) 1505 - 1535, June 2019.


Received: 1 May 2017; Revised: 1 February 2018; Published: June 2019
First available in Project Euclid: 13 February 2019

zbMATH: 07053516
MathSciNet: MR3911120
Digital Object Identifier: 10.1214/18-AOS1722

Primary: 62G08
Secondary: 62G10, 62G20, 62J07

Rights: Copyright © 2019 Institute of Mathematical Statistics


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Vol.47 • No. 3 • June 2019
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