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Robust estimation of causal effects via a high-dimensional covariate balancing propensity score

Author

Listed:
  • Yang Ning
  • Peng Sida
  • Kosuke Imai

Abstract

SummaryWe propose a robust method to estimate the average treatment effects in observational studies when the number of potential confounders is possibly much greater than the sample size. Our method consists of three steps. We first use a class of penalized $M$-estimators for the propensity score and outcome models. We then calibrate the initial estimate of the propensity score by balancing a carefully selected subset of covariates that are predictive of the outcome. Finally, the estimated propensity score is used to construct the inverse probability weighting estimator. We prove that the proposed estimator, which we call the high-dimensional covariate balancing propensity score, has the sample boundedness property, is root-$n$ consistent, asymptotically normal, and semiparametrically efficient when the propensity score model is correctly specified and the outcome model is linear in covariates. More importantly, we show that our estimator remains root-$n$ consistent and asymptotically normal so long as either the propensity score model or the outcome model is correctly specified. We provide valid confidence intervals in both cases and further extend these results to the case where the outcome model is a generalized linear model. In simulation studies, we find that the proposed methodology often estimates the average treatment effect more accurately than existing methods. We also present an empirical application, in which we estimate the average causal effect of college attendance on adulthood political participation. An open-source software package is available for implementing the proposed methodology.

Suggested Citation

  • Yang Ning & Peng Sida & Kosuke Imai, 2020. "Robust estimation of causal effects via a high-dimensional covariate balancing propensity score," Biometrika, Biometrika Trust, vol. 107(3), pages 533-554.
  • Handle: RePEc:oup:biomet:v:107:y:2020:i:3:p:533-554.
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    File URL: http://hdl.handle.net/10.1093/biomet/asaa020
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    Citations

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    Cited by:

    1. He, Xin & Mao, Xiaojun & Wang, Zhonglei, 2024. "Nonparametric augmented probability weighting with sparsity," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    2. Kuanhao Jiang & Rajarshi Mukherjee & Subhabrata Sen & Pragya Sur, 2022. "A New Central Limit Theorem for the Augmented IPW Estimator: Variance Inflation, Cross-Fit Covariance and Beyond," Papers 2205.10198, arXiv.org, revised Oct 2022.
    3. Shixiao Zhang & Peisong Han & Changbao Wu, 2023. "Calibration Techniques Encompassing Survey Sampling, Missing Data Analysis and Causal Inference," International Statistical Review, International Statistical Institute, vol. 91(2), pages 165-192, August.
    4. Maciej Berk{e}sewicz, 2023. "Survey calibration for causal inference: a simple method to balance covariate distributions," Papers 2310.11969, arXiv.org, revised Mar 2024.
    5. Joseph Antonelli & Georgia Papadogeorgou & Francesca Dominici, 2022. "Causal inference in high dimensions: A marriage between Bayesian modeling and good frequentist properties," Biometrics, The International Biometric Society, vol. 78(1), pages 100-114, March.
    6. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    7. Dasom Lee & Shu Yang & Lin Dong & Xiaofei Wang & Donglin Zeng & Jianwen Cai, 2023. "Improving trial generalizability using observational studies," Biometrics, The International Biometric Society, vol. 79(2), pages 1213-1225, June.
    8. Zulj, Valentin & Jin, Shaobo, 2024. "Can model averaging improve propensity score based estimation of average treatment effects?," Working Paper Series 2024:1, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    9. Sandro Heiniger, 2024. "Data-driven model selection within the matrix completion method for causal panel data models," Papers 2402.01069, arXiv.org.
    10. Heejun Shin & Joseph Antonelli, 2023. "Improved inference for doubly robust estimators of heterogeneous treatment effects," Biometrics, The International Biometric Society, vol. 79(4), pages 3140-3152, December.

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