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Bounds on causal effects in three‐arm trials with non‐compliance

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  • Jing Cheng
  • Dylan S. Small

Abstract

Summary. The paper considers the analysis of three‐arm randomized trials with non‐compliance. In these trials, the average causal effects of treatments within principal strata of compliance behaviour are of interest for better understanding the effect of the treatment. Unfortunately, even with the usual assumptions, the average causal effects of treatments within principal strata are not point identified. However, the observable data do provide useful information on the bounds of the identification regions of the parameters of interest. Under two sets of assumptions, we derive sharp bounds for the causal effects within principal strata for binary outcomes and construct confidence intervals to cover the identification regions. The methods are illustrated by an analysis of data from a randomized study of treatments for alcohol dependence.

Suggested Citation

  • Jing Cheng & Dylan S. Small, 2006. "Bounds on causal effects in three‐arm trials with non‐compliance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 815-836, November.
    • Handle: RePEc:bla:jorssb:v:68:y:2006:i:5:p:815-836
    DOI: 10.1111/j.1467-9868.2006.00568.x
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    Cited by:

    1. Peter Z. Schochet, 2020. "The Complier Average Causal Effect Parameter for Multiarmed RCTs," Evaluation Review, , vol. 44(5-6), pages 410-436, October.
    2. Jiannan Lu & Peng Ding & Tirthankar Dasgupta, 2018. "Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds," Journal of Educational and Behavioral Statistics, , vol. 43(5), pages 540-567, October.
    3. Zhichao Jiang & Peng Ding & Zhi Geng, 2016. "Principal causal effect identification and surrogate end point evaluation by multiple trials," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 829-848, September.
    4. Chiba, Yasutaka, 2012. "A note on bounds for the causal infectiousness effect in vaccine trials," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1422-1429.
    5. Julia Y. Lin & Thomas R. Ten Have & Michael R. Elliott, 2009. "Nested Markov Compliance Class Model in the Presence of Time-Varying Noncompliance," Biometrics, The International Biometric Society, vol. 65(2), pages 505-513, June.
    6. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    7. Qi Long & Roderick J. A. Little & Xihong Lin, 2010. "Estimating causal effects in trials involving multitreatment arms subject to non‐compliance: a Bayesian framework," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(3), pages 513-531, May.
    8. VanderWeele Tyler J, 2011. "Principal Stratification -- Uses and Limitations," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-14, July.
    9. Dustin M. Long & Michael G. Hudgens, 2013. "Sharpening Bounds on Principal Effects with Covariates," Biometrics, The International Biometric Society, vol. 69(4), pages 812-819, December.
    10. Hong, Kai & Dragan, Kacie & Glied, Sherry, 2019. "Seeing and hearing: The impacts of New York City’s universal pre-kindergarten program on the health of low-income children," Journal of Health Economics, Elsevier, vol. 64(C), pages 93-107.
    11. Linbo Wang & Thomas S. Richardson & Xiao-Hua Zhou, 2017. "Causal analysis of ordinal treatments and binary outcomes under truncation by death," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 719-735, June.
    12. Jing Cheng, 2009. "Estimation and Inference for the Causal Effect of Receiving Treatment on a Multinomial Outcome," Biometrics, The International Biometric Society, vol. 65(1), pages 96-103, March.
    13. Peng Ding & Jiannan Lu, 2017. "Principal stratification analysis using principal scores," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 757-777, June.
    14. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    15. 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.
    16. Martin Huber & Giovanni Mellace, 2010. "Sharp IV bounds on average treatment effects under endogeneity and noncompliance," University of St. Gallen Department of Economics working paper series 2010 2010-31, Department of Economics, University of St. Gallen.
    17. VanderWeele, Tyler J., 2008. "Simple relations between principal stratification and direct and indirect effects," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2957-2962, December.
    18. Peter Z. Schochet, "undated". "Multi-Armed RCTs: A Design-Based Framework," Mathematica Policy Research Reports eedf2eac4d4c4d8e869052c1d, Mathematica Policy Research.
    19. Chiba, Yasutaka, 2012. "Bounds on the complier average causal effect in randomized trials with noncompliance," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1352-1357.
    20. 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.
    21. Imai, Kosuke, 2008. "Sharp bounds on the causal effects in randomized experiments with "truncation-by-death"," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 144-149, February.

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