IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v178y2021ics0167715221001425.html
   My bibliography  Save this article

On a necessary and sufficient identification condition of optimal treatment regimes with an instrumental variable

Author

Listed:
  • Cui, Yifan
  • Tchetgen Tchetgen, Eric

Abstract

Unmeasured confounding is a threat to causal inference and individualized decision making. Similar to Cui and Tchetgen Tchetgen (2021); Qiu et al. (2021); Han (2021), we consider the problem of identification of optimal individualized treatment regimes with a valid instrumental variable. Han (2021) provided an alternative identifying condition of optimal treatment regimes using the conditional Wald estimand of Cui and Tchetgen Tchetgen (2021); Qiu et al. (2021) when treatment assignment is subject to endogeneity and a valid binary instrumental variable is available. In this note, we provide a necessary and sufficient condition for identification of optimal treatment regimes using the conditional Wald estimand. Our novel condition is necessarily implied by those of Cui and Tchetgen Tchetgen (2021); Qiu et al. (2021); Han (2021) and may continue to hold in a variety of potential settings not covered by prior results.

Suggested Citation

  • Cui, Yifan & Tchetgen Tchetgen, Eric, 2021. "On a necessary and sufficient identification condition of optimal treatment regimes with an instrumental variable," Statistics & Probability Letters, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:stapro:v:178:y:2021:i:c:s0167715221001425
    DOI: 10.1016/j.spl.2021.109180
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715221001425
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2021.109180?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Hongxiang Qiu & Marco Carone & Ekaterina Sadikova & Maria Petukhova & Ronald C. Kessler & Alex Luedtke, 2021. "Optimal Individualized Decision Rules Using Instrumental Variable Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 174-191, March.
    3. Yifan Cui & Eric Tchetgen Tchetgen, 2021. "A Semiparametric Instrumental Variable Approach to Optimal Treatment Regimes Under Endogeneity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 162-173, January.
    4. Hongxiang Qiu & Marco Carone & Ekaterina Sadikova & Maria Petukhova & Ronald C. Kessler & Alex Luedtke, 2021. "Rejoinder: Optimal Individualized Decision Rules Using Instrumental Variable Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 207-209, March.
    5. 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.
    6. 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.
    7. Rubin Daniel B. & van der Laan Mark J., 2012. "Statistical Issues and Limitations in Personalized Medicine Research with Clinical Trials," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-20, July.
    8. 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.
    9. Sukjin Han, 2021. "Comment: Individualized Treatment Rules Under Endogeneity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 192-195, March.
    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. Mao, Lu, 2022. "Identification of the outcome distribution and sensitivity analysis under weak confounder–instrument interaction," Statistics & Probability Letters, Elsevier, vol. 189(C).

    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. Hongming Pu & Bo Zhang, 2021. "Estimating optimal treatment rules with an instrumental variable: A partial identification learning approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 318-345, April.
    2. 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.
    3. Shuxiao Chen & Bo Zhang, 2021. "Estimating and Improving Dynamic Treatment Regimes With a Time-Varying Instrumental Variable," Papers 2104.07822, arXiv.org.
    4. 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.
    5. Xin Qiu & Donglin Zeng & Yuanjia Wang, 2018. "Estimation and evaluation of linear individualized treatment rules to guarantee performance," Biometrics, The International Biometric Society, vol. 74(2), pages 517-528, June.
    6. Michael Lechner, 2023. "Causal Machine Learning and its use for public policy," Swiss Journal of Economics and Statistics, Springer;Swiss Society of Economics and Statistics, vol. 159(1), pages 1-15, December.
    7. 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.
    8. 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.
    9. 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.
    10. Wei Liu & Zhiwei Zhang & Lei Nie & Guoxing Soon, 2017. "A Case Study in Personalized Medicine: Rilpivirine Versus Efavirenz for Treatment-Naive HIV Patients," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1381-1392, October.
    11. Kara E. Rudolph & Iván Díaz, 2022. "When the ends do not justify the means: Learning who is predicted to have harmful indirect effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 573-589, December.
    12. 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.
    13. Yaoyao Xu & Menggang Yu & Ying‐Qi Zhao & Quefeng Li & Sijian Wang & Jun Shao, 2015. "Regularized outcome weighted subgroup identification for differential treatment effects," Biometrics, The International Biometric Society, vol. 71(3), pages 645-653, September.
    14. 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.
    15. Xinyang Huang & Jin Xu, 2020. "Estimating individualized treatment rules with risk constraint," Biometrics, The International Biometric Society, vol. 76(4), pages 1310-1318, December.
    16. Shi, Chengchun & Lu, Wenbin & Song, Rui, 2019. "A sparse random projection-based test for overall qualitative treatment effects," LSE Research Online Documents on Economics 102107, London School of Economics and Political Science, LSE Library.
    17. Xin Chen & Rui Song & Jiajia Zhang & Swann Arp Adams & Liuquan Sun & Wenbin Lu, 2022. "On estimating optimal regime for treatment initiation time based on restricted mean residual lifetime," Biometrics, The International Biometric Society, vol. 78(4), pages 1377-1389, December.
    18. Giorgos Bakoyannis, 2023. "Estimating optimal individualized treatment rules with multistate processes," Biometrics, The International Biometric Society, vol. 79(4), pages 2830-2842, December.
    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. Yunan Wu & Lan Wang, 2021. "Resampling‐based confidence intervals for model‐free robust inference on optimal treatment regimes," Biometrics, The International Biometric Society, vol. 77(2), pages 465-476, June.

    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:eee:stapro:v:178:y:2021:i:c:s0167715221001425. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.