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Ultra‐high dimensional variable selection for doubly robust causal inference

Author

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  • Dingke Tang
  • Dehan Kong
  • Wenliang Pan
  • Linbo Wang

Abstract

Causal inference has been increasingly reliant on observational studies with rich covariate information. To build tractable causal procedures, such as the doubly robust estimators, it is imperative to first extract important features from high or even ultra‐high dimensional data. In this paper, we propose causal ball screening for confounder selection from modern ultra‐high dimensional data sets. Unlike the familiar task of variable selection for prediction modeling, our confounder selection procedure aims to control for confounding while improving efficiency in the resulting causal effect estimate. Previous empirical and theoretical studies suggest excluding causes of the treatment that are not confounders. Motivated by these results, our goal is to keep all the predictors of the outcome in both the propensity score and outcome regression models. A distinctive feature of our proposal is that we use an outcome model‐free procedure for propensity score model selection, thereby maintaining double robustness in the resulting causal effect estimator. Our theoretical analyses show that the proposed procedure enjoys a number of properties, including model selection consistency and pointwise normality. Synthetic and real data analysis show that our proposal performs favorably with existing methods in a range of realistic settings. Data used in preparation of this paper were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

Suggested Citation

  • Dingke Tang & Dehan Kong & Wenliang Pan & Linbo Wang, 2023. "Ultra‐high dimensional variable selection for doubly robust causal inference," Biometrics, The International Biometric Society, vol. 79(2), pages 903-914, June.
  • Handle: RePEc:bla:biomet:v:79:y:2023:i:2:p:903-914
    DOI: 10.1111/biom.13625
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    3. Jinyong Hahn, 2004. "Functional Restriction and Efficiency in Causal Inference," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 73-76, February.
    4. Emre Barut & Jianqing Fan & Anneleen Verhasselt, 2016. "Conditional Sure Independence Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1266-1277, July.
    5. Farrell, Max H., 2015. "Robust inference on average treatment effects with possibly more covariates than observations," Journal of Econometrics, Elsevier, vol. 189(1), pages 1-23.
    6. Wenliang Pan & Xueqin Wang & Heping Zhang & Hongtu Zhu & Jin Zhu, 2020. "Ball Covariance: A Generic Measure of Dependence in Banach Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 307-317, January.
    7. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    8. Kosuke Imai & Marc Ratkovic, 2014. "Covariate balancing propensity score," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 243-263, January.
    9. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    10. Xueqin Wang & Wenliang Pan & Wenhao Hu & Yuan Tian & Heping Zhang, 2015. "Conditional Distance Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1726-1734, December.
    11. Xavier De Luna & Ingeborg Waernbaum & Thomas S. Richardson, 2011. "Covariate selection for the nonparametric estimation of an average treatment effect," Biometrika, Biometrika Trust, vol. 98(4), pages 861-875.
    12. Ander Wilson & Brian J. Reich, 2014. "Confounder selection via penalized credible regions," Biometrics, The International Biometric Society, vol. 70(4), pages 852-861, December.
    13. Linbo Wang & Eric Tchetgen Tchetgen, 2018. "Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 531-550, June.
    14. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    15. Corwin Matthew Zigler & Francesca Dominici, 2014. "Uncertainty in Propensity Score Estimation: Bayesian Methods for Variable Selection and Model-Averaged Causal Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 95-107, March.
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