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High-dimensional Inference for Dynamic Treatment Effects

Author

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  • Jelena Bradic
  • Weijie Ji
  • Yuqian Zhang

Abstract

Estimating dynamic treatment effects is a crucial endeavor in causal inference, particularly when confronted with high-dimensional confounders. Doubly robust (DR) approaches have emerged as promising tools for estimating treatment effects due to their flexibility. However, we showcase that the traditional DR approaches that only focus on the DR representation of the expected outcomes may fall short of delivering optimal results. In this paper, we propose a novel DR representation for intermediate conditional outcome models that leads to superior robustness guarantees. The proposed method achieves consistency even with high-dimensional confounders, as long as at least one nuisance function is appropriately parametrized for each exposure time and treatment path. Our results represent a significant step forward as they provide new robustness guarantees. The key to achieving these results is our new DR representation, which offers superior inferential performance while requiring weaker assumptions. Lastly, we confirm our findings in practice through simulations and a real data application.

Suggested Citation

  • Jelena Bradic & Weijie Ji & Yuqian Zhang, 2021. "High-dimensional Inference for Dynamic Treatment Effects," Papers 2110.04924, arXiv.org, revised May 2023.
    • Handle: RePEc:arx:papers:2110.04924
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    References listed on IDEAS

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    1. Max H. Farrell & Tengyuan Liang & Sanjog Misra, 2021. "Deep Neural Networks for Estimation and Inference," Econometrica, Econometric Society, vol. 89(1), pages 181-213, January.
    2. S. Vansteelandt & E. Goetghebeur, 2003. "Causal inference with generalized structural mean models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 817-835, November.
    3. Yinchu Zhu & Jelena Bradic, 2018. "Linear Hypothesis Testing in Dense High-Dimensional Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1583-1600, October.
    4. Lucia Babino & Andrea Rotnitzky & James Robins, 2019. "Multiple robust estimation of marginal structural mean models for unconstrained outcomes," Biometrics, The International Biometric Society, vol. 75(1), pages 90-99, March.
    5. 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.
    6. Yuan Chen & Donglin Zeng & Yuanjia Wang, 2021. "Learning Individualized Treatment Rules for Multiple-Domain Latent Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 269-282, January.
    7. Murphy S.A. & van der Laan M.J. & Robins J.M., 2001. "Marginal Mean Models for Dynamic Regimes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1410-1423, December.
    8. Wensheng Zhu & Donglin Zeng & Rui Song, 2019. "Proper Inference for Value Function in High-Dimensional Q-Learning for Dynamic Treatment Regimes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1404-1417, July.
    9. Cain Lauren E. & Robins James M. & Lanoy Emilie & Logan Roger & Costagliola Dominique & Hernán Miguel A., 2010. "When to Start Treatment? A Systematic Approach to the Comparison of Dynamic Regimes Using Observational Data," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-26, April.
    10. Kosuke Imai & Marc Ratkovic, 2015. "Robust Estimation of Inverse Probability Weights for Marginal Structural Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1013-1023, September.
    11. Iavor Bojinov & Neil Shephard, 2019. "Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1665-1682, October.
    12. 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.
    13. Jelena Bradic & Stefan Wager & Yinchu Zhu, 2019. "Sparsity Double Robust Inference of Average Treatment Effects," Papers 1905.00744, arXiv.org.
    14. Joffe Marshall M. & Yang Wei Peter & Feldman Harold I., 2010. "Selective Ignorability Assumptions in Causal Inference," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-25, March.
    15. Xinkun Nie & Emma Brunskill & Stefan Wager, 2021. "Learning When-to-Treat Policies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 392-409, January.
    16. S. A. Murphy, 2003. "Optimal dynamic treatment regimes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 331-355, May.
    17. Zhou, Xiang & Wodtke, Geoffrey T., 2020. "Residual Balancing: A Method of Constructing Weights for Marginal Structural Models," Political Analysis, Cambridge University Press, vol. 28(4), pages 487-506, October.
    18. A. Belloni & V. Chernozhukov & K. Kato, 2015. "Uniform post-selection inference for least absolute deviation regression and other Z-estimation problems," Biometrika, Biometrika Trust, vol. 102(1), pages 77-94.
    19. Oliver Dukes & Vahe Avagyan & Stijn Vansteelandt, 2020. "Doubly robust tests of exposure effects under high‐dimensional confounding," Biometrics, The International Biometric Society, vol. 76(4), pages 1190-1200, December.
    20. Tran Linh & Yiannoutsos Constantin & Wools-Kaloustian Kara & Siika Abraham & van der Laan Mark & Petersen Maya, 2019. "Double Robust Efficient Estimators of Longitudinal Treatment Effects: Comparative Performance in Simulations and a Case Study," The International Journal of Biostatistics, De Gruyter, vol. 15(2), pages 1-27, November.
    21. Davide Viviano & Jelena Bradic, 2021. "Dynamic covariate balancing: estimating treatment effects over time with potential local projections," Papers 2103.01280, arXiv.org, revised Jan 2024.
    22. Michael Lechner & Ruth Miquel, 2010. "Identification of the effects of dynamic treatments by sequential conditional independence assumptions," Empirical Economics, Springer, vol. 39(1), pages 111-137, August.
    23. Orellana Liliana & Rotnitzky Andrea & Robins James M., 2010. "Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part II: Proofs of Results," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-19, March.
    24. Orellana Liliana & Rotnitzky Andrea & Robins James M., 2010. "Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part I: Main Content," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-49, March.
    25. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
    26. van der Laan Mark J. & Petersen Maya L & Joffe Marshall M, 2005. "History-Adjusted Marginal Structural Models and Statically-Optimal Dynamic Treatment Regimens," The International Journal of Biostatistics, De Gruyter, vol. 1(1), pages 1-41, November.
    27. Tran Linh & Yiannoutsos Constantin & Wools-Kaloustian Kara & Siika Abraham & van der Laan Mark & Petersen Maya, 2019. "Double Robust Efficient Estimators of Longitudinal Treatment Effects: Comparative Performance in Simulations and a Case Study," The International Journal of Biostatistics, De Gruyter, vol. 15(2), pages 1-27, November.
    28. Shi, Chengchun & Fan, Ailin & Song, Rui & Lu, Wenbin, 2018. "High-dimensional A-learning for optimal dynamic treatment regimes," LSE Research Online Documents on Economics 102113, London School of Economics and Political Science, LSE Library.
    29. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
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    Cited by:

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    3. Isaac Meza & Rahul Singh, 2021. "Nested Nonparametric Instrumental Variable Regression: Long Term, Mediated, and Time Varying Treatment Effects," Papers 2112.14249, arXiv.org, revised Mar 2024.

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