IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2110.04924.html
   My bibliography  Save this paper

High-dimensional Inference for Dynamic Treatment Effects

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2110.04924
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Jelena Bradic & Stefan Wager & Yinchu Zhu, 2019. "Sparsity Double Robust Inference of Average Treatment Effects," Papers 1905.00744, arXiv.org.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Victor Chernozhukov & Whitney Newey & Rahul Singh & Vasilis Syrgkanis, 2022. "Automatic Debiased Machine Learning for Dynamic Treatment Effects and General Nested Functionals," Papers 2203.13887, arXiv.org, revised Jun 2023.
    2. Yuqian Zhang & Weijie Ji & Jelena Bradic, 2021. "Dynamic treatment effects: high-dimensional inference under model misspecification," Papers 2111.06818, arXiv.org, revised Jun 2023.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yuqian Zhang & Weijie Ji & Jelena Bradic, 2021. "Dynamic treatment effects: high-dimensional inference under model misspecification," Papers 2111.06818, arXiv.org, revised Jun 2023.
    2. 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.
    3. Victor Chernozhukov & Whitney K. Newey & Victor Quintas-Martinez & Vasilis Syrgkanis, 2021. "Automatic Debiased Machine Learning via Riesz Regression," Papers 2104.14737, arXiv.org, revised Mar 2024.
    4. Hugo Bodory & Martin Huber & Lukáš Lafférs, 2022. "Evaluating (weighted) dynamic treatment effects by double machine learning [Identification of causal effects using instrumental variables]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 628-648.
    5. Victor Chernozhukov & Whitney Newey & Rahul Singh & Vasilis Syrgkanis, 2022. "Automatic Debiased Machine Learning for Dynamic Treatment Effects and General Nested Functionals," Papers 2203.13887, arXiv.org, revised Jun 2023.
    6. Shi, Chengchun & Luo, Shikai & Le, Yuan & Zhu, Hongtu & Song, Rui, 2022. "Statistically efficient advantage learning for offline reinforcement learning in infinite horizons," LSE Research Online Documents on Economics 115598, London School of Economics and Political Science, LSE Library.
    7. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Q. Clairon & R. Henderson & N. J. Young & E. D. Wilson & C. J. Taylor, 2021. "Adaptive treatment and robust control," Biometrics, The International Biometric Society, vol. 77(1), pages 223-236, March.
    9. 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.
    10. Jelena Bradic & Victor Chernozhukov & Whitney K. Newey & Yinchu Zhu, 2019. "Minimax Semiparametric Learning With Approximate Sparsity," Papers 1912.12213, arXiv.org, revised Aug 2022.
    11. Philipp Baumann & Enzo Rossi & Michael Schomaker, 2022. "Estimating the effect of central bank independence on inflation using longitudinal targeted maximum likelihood estimation," IFC Bulletins chapters, in: Bank for International Settlements (ed.), Machine learning in central banking, volume 57, Bank for International Settlements.
    12. Lan Wen & Jessica G. Young & James M. Robins & Miguel A. Hernán, 2021. "Parametric g‐formula implementations for causal survival analyses," Biometrics, The International Biometric Society, vol. 77(2), pages 740-753, June.
    13. Victor Chernozhukov & Chen Huang & Weining Wang, 2021. "Uniform Inference on High-dimensional Spatial Panel Networks," Papers 2105.07424, arXiv.org, revised Sep 2023.
    14. Yasuhiro Hagiwara & Tomohiro Shinozaki & Hirofumi Mukai & Yutaka Matsuyama, 2021. "Sensitivity analysis for subsequent treatments in confirmatory oncology clinical trials: A two‐stage stochastic dynamic treatment regime approach," Biometrics, The International Biometric Society, vol. 77(2), pages 702-714, June.
    15. Pan Zhao & Yifan Cui, 2023. "A Semiparametric Instrumented Difference-in-Differences Approach to Policy Learning," Papers 2310.09545, arXiv.org.
    16. Cai, Hengrui & Shi, Chengchun & Song, Rui & Lu, Wenbin, 2023. "Jump interval-learning for individualized decision making with continuous treatments," LSE Research Online Documents on Economics 118231, London School of Economics and Political Science, LSE Library.
    17. Victor Chernozhukov & Whitney K. Newey & Rahul Singh, 2022. "Automatic Debiased Machine Learning of Causal and Structural Effects," Econometrica, Econometric Society, vol. 90(3), pages 967-1027, May.
    18. Ashesh Rambachan & Neil Shephard, 2019. "Econometric analysis of potential outcomes time series: instruments, shocks, linearity and the causal response function," Papers 1903.01637, arXiv.org, revised Feb 2020.
    19. Davide Viviano, 2019. "Policy Targeting under Network Interference," Papers 1906.10258, arXiv.org, revised Apr 2024.
    20. Zhen Li & Jie Chen & Eric Laber & Fang Liu & Richard Baumgartner, 2023. "Optimal Treatment Regimes: A Review and Empirical Comparison," International Statistical Review, International Statistical Institute, vol. 91(3), pages 427-463, December.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2110.04924. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.