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Estimating causal effects in trials involving multitreatment arms subject to non-compliance: a Bayesian framework


  • Qi Long
  • Roderick J. A. Little
  • Xihong Lin


Data analysis for randomized trials including multitreatment arms is often complicated by subjects who do not comply with their treatment assignment. We discuss here methods of estimating treatment efficacy for randomized trials involving multitreatment arms subject to non-compliance. One treatment effect of interest in the presence of non-compliance is the complier average causal effect, which is defined as the treatment effect for subjects who would comply regardless of the treatment assigned. Following the idea of principal stratification, we define principal compliance in trials with three treatment arms, extend the complier average causal effect and define causal estimands of interest in this setting. In addition, we discuss structural assumptions that are needed for estimation of causal effects and the identifiability problem that is inherent in this setting from both a Bayesian and a classical statistical perspective. We propose a likelihood-based framework that models potential outcomes in this setting and a Bayes procedure for statistical inference. We compare our method with a method-of-moments approach that was proposed by Cheng and Small in 2006 by using a hypothetical data set, and we further illustrate our approach with an application to a behavioural intervention study. Copyright (c) 2010 Royal Statistical Society.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssc:v:59:y:2010:i:3:p:513-531

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    References listed on IDEAS

    1. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    2. Roderick J. Little & Qi Long & Xihong Lin, 2009. "A Comparison of Methods for Estimating the Causal Effect of a Treatment in Randomized Clinical Trials Subject to Noncompliance," Biometrics, The International Biometric Society, vol. 65(2), pages 640-649, June.
    3. Long, Qi & Little, Roderick J. & Lin, Xihong, 2008. "Causal Inference in Hybrid Intervention Trials Involving Treatment Choice," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 474-484, June.
    4. Marshall M. Joffe, 2001. "Using information on realized effects to determine prospective causal effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 759-774.
    5. Yahong Peng & Roderick J. A. Little & Trivellore E. Raghunathan, 2004. "An Extended General Location Model for Causal Inferences from Data Subject to Noncompliance and Missing Values," Biometrics, The International Biometric Society, vol. 60(3), pages 598-607, September.
    6. Janevic, Mary R. & Janz, Nancy K. & Dodge, Julia A. & Lin, Xihong & Pan, Wenqin & Sinco, Brandy R. & Clark, Noreen M., 2003. "The role of choice in health education intervention trials: a review and case study," Social Science & Medicine, Elsevier, vol. 56(7), pages 1581-1594, April.
    7. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    8. Guido W. Imbens & Donald B. Rubin, 1997. "Estimating Outcome Distributions for Compliers in Instrumental Variables Models," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 555-574.
    9. Jin, Hui & Rubin, Donald B., 2008. "Principal Stratification for Causal Inference With Extended Partial Compliance," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 101-111, March.
    10. 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.
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    Cited by:

    1. repec:bla:jorssb:v:79:y:2017:i:3:p:719-735 is not listed on IDEAS
    2. 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.
    3. Peter Z. Schochet, "undated". "Multi-Armed RCTs: A Design-Based Framework," Mathematica Policy Research Reports eedf2eac4d4c4d8e869052c1d, Mathematica Policy Research.

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