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Efficient nonparametric estimation of causal effects in randomized trials with noncompliance

Author

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  • Jing Cheng
  • Dylan S. Small
  • Zhiqiang Tan
  • Thomas R. Ten Have

Abstract

Causal approaches based on the potential outcome framework provide a useful tool for addressing noncompliance problems in randomized trials. We propose a new estimator of causal treatment effects in randomized clinical trials with noncompliance. We use the empirical likelihood approach to construct a profile random sieve likelihood and take into account the mixture structure in outcome distributions, so that our estimator is robust to parametric distribution assumptions and provides substantial finite-sample efficiency gains over the standard instrumental variable estimator. Our estimator is asymptotically equivalent to the standard instrumental variable estimator, and it can be applied to outcome variables with a continuous, ordinal or binary scale. We apply our method to data from a randomized trial of an intervention to improve the treatment of depression among depressed elderly patients in primary care practices. Copyright 2009, Oxford University Press.

Suggested Citation

  • Jing Cheng & Dylan S. Small & Zhiqiang Tan & Thomas R. Ten Have, 2009. "Efficient nonparametric estimation of causal effects in randomized trials with noncompliance," Biometrika, Biometrika Trust, vol. 96(1), pages 19-36.
  • Handle: RePEc:oup:biomet:v:96:y:2009:i:1:p:19-36
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    File URL: http://hdl.handle.net/10.1093/biomet/asn056
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    Cited by:

    1. Abhinandan Dalal & Patrick Blobaum & Shiva Kasiviswanathan & Aaditya Ramdas, 2024. "Anytime-Valid Inference for Double/Debiased Machine Learning of Causal Parameters," Papers 2408.09598, arXiv.org, revised Sep 2024.
    2. Chunrong Ai & Lukang Huang & Zheng Zhang, 2018. "A Simple and Efficient Estimation of the Average Treatment Effect in the Presence of Unmeasured Confounders," Papers 1807.05678, arXiv.org.
    3. Bo Wei & Limin Peng & Mei‐Jie Zhang & Jason P. Fine, 2021. "Estimation of causal quantile effects with a binary instrumental variable and censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 559-578, July.
    4. Bryan S. Graham & Cristine Campos de Xavier Pinto & Daniel Egel, 2016. "Efficient Estimation of Data Combination Models by the Method of Auxiliary-to-Study Tilting (AST)," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 288-301, April.
    5. Alessandra Mattei & Fabrizia Mealli & Barbara Pacini, 2014. "Identification of causal effects in the presence of nonignorable missing outcome values," Biometrics, The International Biometric Society, vol. 70(2), pages 278-288, June.
    6. Jing Cheng & Jing Qin & Biao Zhang, 2009. "Semiparametric estimation and inference for distributional and general treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 881-904, September.
    7. Jing Cheng, 2011. "The authors replied as follows:," Biometrics, The International Biometric Society, vol. 67(1), pages 323-325, March.
    8. Stuart G. Baker, 2011. "Estimation and Inference for the Causal Effect of Receiving Treatment on a Multinomial Outcome: An Alternative Approach," Biometrics, The International Biometric Society, vol. 67(1), pages 319-323, March.
    9. Shuwei Li & Limin Peng, 2023. "Instrumental variable estimation of complier causal treatment effect with interval‐censored data," Biometrics, The International Biometric Society, vol. 79(1), pages 253-263, March.
    10. Hui Nie & Jing Cheng & Dylan S. Small, 2011. "Inference for the Effect of Treatment on Survival Probability in Randomized Trials with Noncompliance and Administrative Censoring," Biometrics, The International Biometric Society, vol. 67(4), pages 1397-1405, December.

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