Group-Sequential Three-Arm Non-inferiority Clinical Trials

  • Toshimitsu HamasakiEmail author
  • Koko Asakura
  • Scott R. Evans
  • Toshimitsu Ochiai
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)


We discuss group-sequential three-arm non-inferiority (NI) clinical trials, i.e., trials that include a test intervention as well as active and placebo controls for evaluating both assay sensitivity and NI. We extend two existing approaches, the fixed margin and fraction approaches, to a group-sequential setting with two decision-making frameworks. We provide an example to illustrate the methods.


Assay sensitivity Average sample number Constancy Fixed margin approach Fraction approach Maximum sample size Non-inferiority Type I error 


  1. Committee for Medicinal Products for Human Use (CHMP) (2005) Guideline on the choice of the non-inferiority margin. Available at: Accessed 25 Nov 2015
  2. D’Agostino RB, Massaro JM, Sullivan LM (2003) Non-inferiority trials: design concepts and issues—the encounters of academic consultants in statistics. Stat Med 22:169–186CrossRefGoogle Scholar
  3. Evans SR, Follmann D (2015) Fundamentals and innovation in antibiotic trials. Stat Biopharm Res 7:331–336CrossRefGoogle Scholar
  4. Fishbane S, Schiller B, Locatelli F, Covic AC, Provenzano R, Wiecek A, Levin NW, Kaplan M, Macdougall IC, Francisco C, Mayo MR, Polu KR, Duliege AM, Besarab A, for the EMERALD Study Groups (2013) Peginesatide in patients with anemia undergoing hemodialysis. New Engl J Med 368:307–319Google Scholar
  5. Food and Drug Administration (FDA) (2010) Guidance for industry non-inferiority trials. U.S. Department of health and human services food and drug administration. Rockville, MD, USA. Available at: Accessed 25 Nov 2015
  6. Gao P, Ware JH (2008) Assessing non-inferiority: a combination approach. Stat Med 27:392–406MathSciNetCrossRefGoogle Scholar
  7. Genz A (1992) Numerical computation of multivariate normal probabilities. J Comput Graph Stat 1:141–149Google Scholar
  8. Hauschke D, Pigeot I (2005a) Establishing efficacy of a new experimental treatment in the ‘gold standard’ design. Biometrical J 47:782–786MathSciNetCrossRefGoogle Scholar
  9. Hauschke D, Pigeot I (2005b) Rejoinder to “establishing efficacy of a new experimental treatment in the ‘gold standard’ design”. Biometrical J 47:797–798MathSciNetCrossRefGoogle Scholar
  10. Hasler M, Vonk R, Hothorn LA (2008) Assessing non-inferiority of a new treatment in a three-arm trial in the presence of heteroscedasticity. Stat Med 27:490–503MathSciNetCrossRefGoogle Scholar
  11. Hamasaki T, Sugimoto T, Evans SR, Sozu T (2013) Sample size determination for clinical trials with co-primary outcomes: exponential event times. Pharm Stat 12:28–34CrossRefGoogle Scholar
  12. Hida E, Tango T (2011a) On the three-arm non-inferiority trial including a placebo with a prespecified margin. Stat Med 30:224–231MathSciNetCrossRefGoogle Scholar
  13. Hida E, Tango T (2011b) Response to Joachim Röhmel and Iris Pigeot. Stat Med 30:3165MathSciNetCrossRefGoogle Scholar
  14. Hida E, Tango T (2013) Three-arm noninferiority trials with a prespecified margin for inference of the difference in the proportions of binary endpoints. J Biopharm Stat 23:774–789MathSciNetCrossRefGoogle Scholar
  15. International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use (ICH) (2000) ICH harmonised tripartite guideline E10: Choice of control group and related issues in clinical trials. July 2000. Available at: Accessed 25 Nov 2015
  16. Kieser M, Friede T (2007) Planning and analysis of three-arm non-inferiority trials with binary endpoints. Stat Med 26:253–273MathSciNetCrossRefGoogle Scholar
  17. Koch A, Röhmel J (2004) Hypothesis testing in the ‘gold standard’ design for proving the efficacy of an experimental treatment. J Biopharm Stat 14:315–325CrossRefGoogle Scholar
  18. Kombrink K, Munk A, Friede T (2013) Design and semiparametric analysis of non-inferiority trials with active and placebo control for censored time-to-event data. Stat Med 32:3055–3066MathSciNetCrossRefGoogle Scholar
  19. Lan KKG, DeMets DL (1983) Discrete sequential boundaries for clinical trials. Biometrika 70:659–663MathSciNetCrossRefzbMATHGoogle Scholar
  20. Li G, Gao S (2010) A group sequential type design for three-arm non-inferiority trials with binary endpoints. Biometrical J 52:504–518MathSciNetCrossRefzbMATHGoogle Scholar
  21. Mielke M, Munk A, Schacht A (2008) The assessment of non-inferiority in a gold standard design with censored, exponentially distributed endpoints. Stat Med 27:5093–5110MathSciNetCrossRefGoogle Scholar
  22. Mizuno Y, Nomoto M, Hasegawa K, Hattori N, Kondo T, Murata M, Takeuchi M, Takahashi M, Tomida T, on behalf of the Rotigotine Trial Group (2014) Rotigotine vs ropinirole in advanced stage Parkinson’s disease: a double-blind study. Parkinsonism and Related Disorders 20:1388–1393Google Scholar
  23. O’Brien PC, Fleming TR (1979) A multiple testing procedure for clinical trials. Biometrics 35:549–556CrossRefGoogle Scholar
  24. Ochiai T, Hamasaki T, Evans SR, Asakura K, Ohno Y (2016) Group-sequential three-arm noninferiority clinical trial designs. J Biopharm Stat (First published online: 18 Feb 2016 as doi: 10.1080/10543406.2016.1148710)
  25. Pigeot I, Schäfer J, Röhmel J, Hauschke D (2003) Assessing non-inferiority of a new treatment in a three-arm clinical trial including a placebo. Stat Med 22:883–899CrossRefGoogle Scholar
  26. Pocock SJ (1977) Group sequential methods in the design and analysis of clinical trials. Biometrika 64:191–199CrossRefGoogle Scholar
  27. Röhmel J, Pigeot I (2011) Statistical strategies for the analysis of clinical trials with an experimental treatment, an active control and placebo, and a prespecified fixed non-inferiority margin for the difference in means. Stat Med 30:3162–3164MathSciNetCrossRefGoogle Scholar
  28. Rothmann MD, Wiens BL, Chan ISF (2011) Design and analysis of non-inferiority trials. Chapman and Hall/CRC Press, Boca RatonzbMATHGoogle Scholar
  29. Schlömer P, Brannath W (2013) Group sequential designs for three-arm ‘gold standard’ non-inferiority trials with fixed margin. Stat Med 32:4875–4899MathSciNetCrossRefGoogle Scholar
  30. Stucke K, Kieser M (2012) A general approach for sample size calculation for the three-arm ‘gold standard’ non-inferiority design. Stat Med 31:3579–3596MathSciNetCrossRefGoogle Scholar
  31. Sugimoto T, Sozu T, Hamasaki T (2012) A convenient formula for sample size calculations in clinical trials with multiple co-primary continuous endpoints. Pharm Stat 11:118–128CrossRefzbMATHGoogle Scholar
  32. Tang ML, Tang NS (2004) Test of noninferiority via rate difference for three-arm clinical trials with placebo. J Biopharm Stat 14:337–347CrossRefGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Toshimitsu Hamasaki
    • 1
    Email author
  • Koko Asakura
    • 2
  • Scott R. Evans
    • 3
  • Toshimitsu Ochiai
    • 4
  1. 1.Department of Data ScienceNational Cerebral and Cardiovascular CenterSuitaJapan
  2. 2.Department of Data ScienceNational Cerebral and Cardiovascular CenterSuitaJapan
  3. 3.Department of Biostatistics and the Center for Biostatistics in AIDS ResearchHarvard T.H. Chan School of Public HealthBostonUSA
  4. 4.Biostatistics DepartmentShionogi & Co., Ltd.OsakaJapan

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