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Semiparametric estimation and inference for distributional and general treatment effects


  • Jing Cheng
  • Jing Qin
  • Biao Zhang


There is a large literature on methods of analysis for randomized trials with noncompliance which focuses on the effect of treatment on the average outcome. The paper considers evaluating the effect of treatment on the entire distribution and general functions of this effect. For distributional treatment effects, fully non-parametric and fully parametric approaches have been proposed. The fully non-parametric approach could be inefficient but the fully parametric approach is not robust to the violation of distribution assumptions. We develop a semiparametric instrumental variable method based on the empirical likelihood approach. Our method can be applied to general outcomes and general functions of outcome distributions and allows us to predict a subject's latent compliance class on the basis of an observed outcome value in observed assignment and treatment received groups. Asymptotic results for the estimators and likelihood ratio statistic are derived. A simulation study shows that our estimators of various treatment effects are substantially more efficient than the currently used fully non-parametric estimators. The method is illustrated by an analysis of data from a randomized trial of an encouragement intervention to improve adherence to prescribed depression treatments among depressed elderly patients in primary care practices. Copyright (c) 2009 Royal Statistical Society.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssb:v:71:y:2009:i:4:p:881-904

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    References listed on IDEAS

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    Cited by:

    1. Ertefaie Ashkan & Small Dylan & Flory James & Hennessy Sean, 2016. "Selection Bias When Using Instrumental Variable Methods to Compare Two Treatments But More Than Two Treatments Are Available," The International Journal of Biostatistics, De Gruyter, vol. 12(1), pages 219-232, May.
    2. Jing Cheng, 2011. "The authors replied as follows:," Biometrics, The International Biometric Society, vol. 67(1), pages 323-325, March.
    3. 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.
    4. Michael E. Sobel & Bengt Muthén, 2012. "Compliance Mixture Modelling with a Zero-Effect Complier Class and Missing Data," Biometrics, The International Biometric Society, vol. 68(4), pages 1037-1045, December.

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