IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v84y2022i2p440-472.html
   My bibliography  Save this article

Efficient learning of optimal individualized treatment rules for heteroscedastic or misspecified treatment‐free effect models

Author

Listed:
  • Weibin Mo
  • Yufeng Liu

Abstract

Recent development in data‐driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, researchers can search for the optimal individualized treatment rule (ITR) that maximizes the expected outcome. Existing methods typically require initial estimation of some nuisance models. The double robustness property that can protect from misspecification of either the treatment‐free effect or the propensity score has been widely advocated. However, when model misspecification exists, a doubly robust estimate can be consistent but may suffer from downgraded efficiency. Other than potential misspecified nuisance models, most existing methods do not account for the potential problem when the variance of outcome is heterogeneous among covariates and treatment. We observe that such heteroscedasticity can greatly affect the estimation efficiency of the optimal ITR. In this paper, we demonstrate that the consequences of misspecified treatment‐free effect and heteroscedasticity can be unified as a covariate‐treatment dependent variance of residuals. To improve efficiency of the estimated ITR, we propose an Efficient Learning (E‐Learning) framework for finding an optimal ITR in the multi‐armed treatment setting. We show that the proposed E‐Learning is optimal among a regular class of semiparametric estimates that can allow treatment‐free effect misspecification. In our simulation study, E‐Learning demonstrates its effectiveness if one of or both misspecified treatment‐free effect and heteroscedasticity exist. Our analysis of a type 2 diabetes mellitus (T2DM) observational study also suggests the improved efficiency of E‐Learning.

Suggested Citation

  • Weibin Mo & Yufeng Liu, 2022. "Efficient learning of optimal individualized treatment rules for heteroscedastic or misspecified treatment‐free effect models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 440-472, April.
    • Handle: RePEc:bla:jorssb:v:84:y:2022:i:2:p:440-472
    DOI: 10.1111/rssb.12474
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssb.12474
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssb.12474?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Baqun Zhang & Anastasios A. Tsiatis & Eric B. Laber & Marie Davidian, 2012. "A Robust Method for Estimating Optimal Treatment Regimes," Biometrics, The International Biometric Society, vol. 68(4), pages 1010-1018, December.
    2. Weihua Cao & Anastasios A. Tsiatis & Marie Davidian, 2009. "Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data," Biometrika, Biometrika Trust, vol. 96(3), pages 723-734.
    3. Shuai Chen & Lu Tian & Tianxi Cai & Menggang Yu, 2017. "A general statistical framework for subgroup identification and comparative treatment scoring," Biometrics, The International Biometric Society, vol. 73(4), pages 1199-1209, December.
    4. Toru Kitagawa & Aleksey Tetenov, 2018. "Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice," Econometrica, Econometric Society, vol. 86(2), pages 591-616, March.
    5. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    6. 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.
    7. Zhengyuan Zhou & Susan Athey & Stefan Wager, 2023. "Offline Multi-Action Policy Learning: Generalization and Optimization," Operations Research, INFORMS, vol. 71(1), pages 148-183, January.
    8. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    10. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    11. Xin Zhou & Nicole Mayer-Hamblett & Umer Khan & Michael R. Kosorok, 2017. "Residual Weighted Learning for Estimating Individualized Treatment Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 169-187, January.
    12. Lu Tian & Ash A. Alizadeh & Andrew J. Gentles & Robert Tibshirani, 2014. "A Simple Method for Estimating Interactions Between a Treatment and a Large Number of Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1517-1532, December.
    13. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    14. Jingxiang Chen & Haoda Fu & Xuanyao He & Michael R. Kosorok & Yufeng Liu, 2018. "Estimating individualized treatment rules for ordinal treatments," Biometrics, The International Biometric Society, vol. 74(3), pages 924-933, September.
    15. Yingqi Zhao & Donglin Zeng & A. John Rush & Michael R. Kosorok, 2012. "Estimating Individualized Treatment Rules Using Outcome Weighted Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1106-1118, September.
    16. Heng Lian & Hua Liang & Raymond J. Carroll, 2015. "Variance function partially linear single-index models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 171-194, January.
    17. Zhiqiang Tan, 2010. "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, Biometrika Trust, vol. 97(3), pages 661-682.
    18. Johnson, Brent A. & Lin, D.Y. & Zeng, Donglin, 2008. "Penalized Estimating Functions and Variable Selection in Semiparametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 672-680, June.
    19. Michael P. Wallace & Erica E. M. Moodie, 2015. "Doubly‐robust dynamic treatment regimen estimation via weighted least squares," Biometrics, The International Biometric Society, vol. 71(3), pages 636-644, September.
    20. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2006. "Moving the Goalposts: Addressing Limited Overlap in the Estimation of Average Treatment Effects by Changing the Estimand," NBER Technical Working Papers 0330, National Bureau of Economic Research, Inc.
    21. Yanyuan Ma & Jeng-Min Chiou & Naisyin Wang, 2006. "Efficient semiparametric estimator for heteroscedastic partially linear models," Biometrika, Biometrika Trust, vol. 93(1), pages 75-84, March.
    22. Zhang, Hao Helen & Cheng, Guang & Liu, Yufeng, 2011. "Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1099-1112.
    23. Yinghao Pan & Ying-Qi Zhao, 2021. "Improved Doubly Robust Estimation in Learning Optimal Individualized Treatment Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 283-294, March.
    24. Andrea Rotnitzky & Quanhong Lei & Mariela Sued & James M. Robins, 2012. "Improved double-robust estimation in missing data and causal inference models," Biometrika, Biometrika Trust, vol. 99(2), pages 439-456.
    Full references (including those not matched with items on IDEAS)

    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. Qingyuan Zhao & Dylan S. Small & Ashkan Ertefaie, 2022. "Selective inference for effect modification via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 382-413, April.
    2. Davide Viviano & Jelena Bradic, 2020. "Fair Policy Targeting," Papers 2005.12395, arXiv.org, revised Jun 2022.
    3. Davide Viviano, 2019. "Policy Targeting under Network Interference," Papers 1906.10258, arXiv.org, revised Apr 2024.
    4. Guanhua Chen & Donglin Zeng & Michael R. Kosorok, 2016. "Personalized Dose Finding Using Outcome Weighted Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1509-1521, October.
    5. 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.
    6. Michael C Knaus & Michael Lechner & Anthony Strittmatter, 2021. "Machine learning estimation of heterogeneous causal effects: Empirical Monte Carlo evidence," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 134-161.
    7. Zhengyuan Zhou & Susan Athey & Stefan Wager, 2023. "Offline Multi-Action Policy Learning: Generalization and Optimization," Operations Research, INFORMS, vol. 71(1), pages 148-183, January.
    8. Crystal T. Nguyen & Daniel J. Luckett & Anna R. Kahkoska & Grace E. Shearrer & Donna Spruijt‐Metz & Jaimie N. Davis & Michael R. Kosorok, 2020. "Estimating individualized treatment regimes from crossover designs," Biometrics, The International Biometric Society, vol. 76(3), pages 778-788, September.
    9. Ruoqing Zhu & Ying-Qi Zhao & Guanhua Chen & Shuangge Ma & Hongyu Zhao, 2017. "Greedy outcome weighted tree learning of optimal personalized treatment rules," Biometrics, The International Biometric Society, vol. 73(2), pages 391-400, June.
    10. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    11. Shosei Sakaguchi, 2021. "Estimation of Optimal Dynamic Treatment Assignment Rules under Policy Constraints," Papers 2106.05031, arXiv.org, revised Aug 2024.
    12. Yizhe Xu & Tom H. Greene & Adam P. Bress & Brian C. Sauer & Brandon K. Bellows & Yue Zhang & William S. Weintraub & Andrew E. Moran & Jincheng Shen, 2022. "Estimating the optimal individualized treatment rule from a cost‐effectiveness perspective," Biometrics, The International Biometric Society, vol. 78(1), pages 337-351, March.
    13. Tobias Cagala & Ulrich Glogowsky & Johannes Rincke & Anthony Strittmatter, 2021. "Optimal Targeting in Fundraising: A Machine-Learning Approach," Economics working papers 2021-08, Department of Economics, Johannes Kepler University Linz, Austria.
    14. Huber, Martin, 2019. "An introduction to flexible methods for policy evaluation," FSES Working Papers 504, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    15. Muxuan Liang & Menggang Yu, 2023. "Relative contrast estimation and inference for treatment recommendation," Biometrics, The International Biometric Society, vol. 79(4), pages 2920-2932, December.
    16. Baqun Zhang & Min Zhang, 2018. "C‐learning: A new classification framework to estimate optimal dynamic treatment regimes," Biometrics, The International Biometric Society, vol. 74(3), pages 891-899, September.
    17. Xinyang Huang & Jin Xu, 2020. "Estimating individualized treatment rules with risk constraint," Biometrics, The International Biometric Society, vol. 76(4), pages 1310-1318, December.
    18. Ruohan Zhan & Zhimei Ren & Susan Athey & Zhengyuan Zhou, 2024. "Policy Learning with Adaptively Collected Data," Management Science, INFORMS, vol. 70(8), pages 5270-5297, August.
    19. Kitagawa, Toru & Wang, Guanyi, 2023. "Who should get vaccinated? Individualized allocation of vaccines over SIR network," Journal of Econometrics, Elsevier, vol. 232(1), pages 109-131.
    20. Tobias Cagala & Ulrich Glogowsky & Johannes Rincke & Anthony Strittmatter, 2021. "Optimal Targeting in Fundraising: A Causal Machine-Learning Approach," Papers 2103.10251, arXiv.org, revised Sep 2021.

    More about this item

    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:bla:jorssb:v:84:y:2022:i:2:p:440-472. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.