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

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  • 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
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    References listed on IDEAS

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    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.
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    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).

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