Statistics in Biosciences

, Volume 10, Issue 1, pp 184–201 | Cite as

Optimal Benchmark for Evaluating Drug-Combination Dose-Finding Clinical Trials

  • Beibei GuoEmail author
  • Suyu Liu


Numerous dose-finding methods have been proposed for drug-combination trials. A head-to-head comparison of the performance of these designs is difficult and often not very meaningful because different designs use different models and decision rules that often require judicious calibration to obtain good small-sample performance. It is desirable to have a general benchmark that can be used to evaluate the absolute performance of combination dose-finding designs. In this article, we propose an optimal nonparametric benchmark for evaluating drug-combination dose-finding methods, which provides an upper bound of accuracy beyond which further improvements are generally not achievable without making parametric assumptions of the dose-toxicity relationship. Our method is based on a new concept called critical information, which provides an upper bound on the information that we could possibly learn from patients while explicitly accounting for the partial order of the dose combinations, a fundamental feature of drug-combination trials. Our numerical study shows that the proposed benchmark provides a sharp upper bound that is useful for evaluating the performance of combination dose-finding designs.


Combination trials Dose finding Partial order Optimal benchmark Upper limit 

Supplementary material

12561_2017_9204_MOESM1_ESM.pdf (46 kb)
Supplementary material 1 (pdf 46 KB)


  1. 1.
    Thall P, Millikan R, Mueller P, Lee SJ (2003) Dose-finding with two agents in phase I oncology trials. Biometrics 59:487–496MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Conaway M, Dunbar S, Peddada S (2004) Designs for single- or multiple-agent phase I trials. Biometrics 60:661–669MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Wang K, Ivanova A (2005) Two-dimensional dose finding in discrete dose space. Biostatistics 61:217–222MathSciNetzbMATHGoogle Scholar
  4. 4.
    Yuan Y, Yin G (2008) Sequential continual reassessment method for two-dimensional dose finding. Stat Med 27:5664–5678MathSciNetCrossRefGoogle Scholar
  5. 5.
    Yin G, Yuan Y (2009a) A latent contingency table approach to dose finding for combinations of two agents. Biometrics 65:866–875MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Yin G, Yuan Y (2009) Bayesian dose finding in oncology for drug combinations by copula regression. J R Stat Soc Ser C 58:211–224MathSciNetCrossRefGoogle Scholar
  7. 7.
    Braun TM, Wang S (2010) A hierarchical Bayesian design for phase I trials of novel combinations of cancer therapeutic agents. Biometrics 66:805–812MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Wages NA, Conaway MR, O’Quigley J (2011) Continual reassessment method for partial ordering. Biometrics 67:1555–1563MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Liu S, Ning J (2013) A Bayesian dose-finding design for drug combination trials with delayed toxicities. Bayesian Anal 8:703–722MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Hirakawa A, Hamada C, Matsui S (2013) A dose-finding approach based on shrunken predictive probability for combinations of two agents in phase I trials. Stat Med 32:4515–4525MathSciNetCrossRefGoogle Scholar
  11. 11.
    Riviere MK, Yuan Y, Dubois F, Zohar S (2015) A Bayesian dose finding design for clinical trials combining a cytotoxic agent with a molecularly targeted agent. J R Stat Soc Ser C 64:215–229Google Scholar
  12. 12.
    Lin R, Yin G (2016) Bayesian optimal interval design for dose finding in drug-combination trials. Stat Methods Med Res (In Press)Google Scholar
  13. 13.
    Riviere MK, Dubois F, Zohar S (2014) Competing designs for drug combination in phase I dose-finding clinical trials. Stat Med 34:1–12MathSciNetCrossRefGoogle Scholar
  14. 14.
    Yin G, Lin R (2015) Comments on “Competing designs for drug combination in phase I dose-finding clinical trials” by M-K. Riviere, F. Dubois, and S. Zohar. Stat Med 34:13–17MathSciNetCrossRefGoogle Scholar
  15. 15.
    Wages NA (2015) Comments on “Competing designs for drug combination in phase I dose-finding clinical trials” by M-K. Riviere, F. Dubois, and S. Zohar. Stat Med 34:18–22MathSciNetCrossRefGoogle Scholar
  16. 16.
    O’Quigley J, Paoletti X, Maccario J (2002) Non-parametric optimal design in dose finding studies. Biostatistics 3:51–56CrossRefzbMATHGoogle Scholar
  17. 17.
    Cheung Y (2014) Simple benchmark for complex dose finding studies. Biometrics 70:389–397MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Yuan Y, Zhang L (2017) Designing early-phase drug combination trials, Chapter 6. In: O’Quigley J, Iasonos A, Bornkamp B (eds) Handbook of methods for designing, monitoring, and analyzing dose finding trials. University of California, Oakland, pp 109–126Google Scholar

Copyright information

© International Chinese Statistical Association 2017

Authors and Affiliations

  1. 1.Department of Experimental StatisticsLouisiana State UniversityBaton RougeUSA
  2. 2.Department of BiostatisticsThe University of Texas MD Anderson Cancer CenterHoustonUSA

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