Design and Statistical Analysis of Multidrug Combinations in Preclinical Studies and Phase I Clinical Trials

  • Ming T. TanEmail author
  • Hong-Bin Fang
  • Hengzhen Huang
  • Yang Yang
Conference paper
Part of the ICSA Book Series in Statistics book series (ICSABSS)


Multidrug combination is an important therapeutic approach for cancer, viral or microbial infections, hypertension and other diseases involving complex biological networks. Synergistic drug combinations, which are more effective than predicted from summing effects of individual drugs, often achieve increased therapeutic index. Because drug-effect is dose-dependent, multiple doses of an individual drug need to be examined, yielding rapidly increasing number of combinations and a challenging high dimensional statistical modeling problem. The lack of proper design and analysis methods for multi-drug combination studies have resulted in many missed therapeutic opportunities. Although systems biology holds the promise to unveil complex interactions within biological systems, the knowledge on network remains predominantly topological until very recently. This article summarizes recent work on efficient maximal power experimental designs on multi-drug combinations, and statistical modeling of the resulting data. The design and analysis of vorinostat and cytarabine combination study is presented to illustrate the approach. We then introduce a model based adaptive Bayesian phase I trial design for drug combinations utilizing the modeling concept. To tackle the challenging problem of combinations of more than three drugs, we present a novel two-stage procedure starting with an initial selection by utilizing an in silico model built upon experimental data of single drugs and current systems biology information to obtain maximum likelihood estimate.


Clinical trial design Biological networks Drug combinations Experimental design Maximal Power design Statistical modeling Synergy analysis 



The research of Drs. Fang, Huang and Tan is partially supported by the National Cancer Institute (NCI) grant R01CA164717. Dr Yang’s research was completed and partially supported by University of Maryland while she was a PhD student there.


  1. Ao, P. Lee, L.W. Lidstrom, M.E. Yin, L. and Zhu, X. Towards kinetic modeling of global metabolic networks: Methylobacterium extorquens AMI growth as validation. Chinese Journal of Biotechnology 24: 980–994, 2008.CrossRefGoogle Scholar
  2. Ashton, J.C. ANOVA and the analysis of drug combination experiments. Nature Methods 12: 1108, 2015.CrossRefGoogle Scholar
  3. Berenbaum, M. C. What is Synergy? Pharmcological Reviews 41: 93–141, 1989.Google Scholar
  4. Bliss, C.I. The toxicity of poison applied jointly. Annals of Applied Biology 18: 585–815, 1939.CrossRefGoogle Scholar
  5. Calzolari, D. et al. Search algorithms as a framework for the optimization of drug combinations. PLoS Computational Biology 4(12): e1000249, 2008.CrossRefGoogle Scholar
  6. Chou, T.C. and Talalay, P. Quantitative analysis of dose–effect relationships: the combined effects of multiple drugs or enzyme inhibitors. Advances in Enzyme Regulation 22: 27–55, 1984.CrossRefGoogle Scholar
  7. Fang, H.B. Chen, X. Pei, X.Y. Grant, S. and Tan, M. Experimental Design and Statistical Analysis for Three-Drug Combination Studies. Statistical Methods in Medical Research, 2015. DOI:  10.1177/0962280215574320.Google Scholar
  8. Fang, H.B. Huang, H. Clarke, R. and Tan, M. Predicting multi-drug inhibition interactions based on signaling networks and single drug dose–response information. Journal of Computational Systems Biology, 2, 2016. Google Scholar
  9. Fang, H.B. Ross, D.D. Sausville, E. and Tan, M. Experimental design and interaction analysis of combination studies of drugs with log-linear dose responses. Statistics in Medicine, 27(16):3071–3083, 2008.MathSciNetCrossRefGoogle Scholar
  10. Fang, K.T. Li, R. and Sudjianto, A. Design and Modeling for Computer Experiments. Chapman & Hall/CRC: New York, 2006.zbMATHGoogle Scholar
  11. Fang, K.T. and Wang, Y. Number-Theoretic Methods in Statistics. London: Chapman and Hall, 1994.CrossRefzbMATHGoogle Scholar
  12. Fitzgerald, J.B. Schoeberl, B. Nielsen, U.B. and Sorger, P.K. Systems biology and combination therapy in the quest for clinical efficacy. Nature Chemical Biology 2: 458–466, 2006.CrossRefGoogle Scholar
  13. Gojo, I. Tan, M. Fang, H.B. Sadowska, M. Lapidus, R. Baer, M.R. Carrier, F. Beumer, J.H. Anyang, B.N. Srivastava, R.K. Espinoza-Delgado, I. and Ross, D.D. Translational phase I trial of Vorinostat (suberoylanilid.e hydroxamic acid) combined with cytarabine and etoposide in patients with relapsed, refractory, or high-risk acute myeloid leukemia, Clinical Cancer Research 19:1838–1851, 2013.CrossRefGoogle Scholar
  14. Goldoni, M. and Johansson, C. A mathematical approach to study combined effects of toxicants in vitro: Evaluation of the Bliss independence criterion and the Loewe additivity model. Toxicology in Vitro 21: 759–769, 2007.CrossRefGoogle Scholar
  15. Greco, W.R. Bravo, G. and Parsons, J. C. The Search for Synergy: A Critical Review from a Response Surface Perspective. Pharmcological Reviews 47: 331–385, 1995.Google Scholar
  16. Hopkins, A.L. Network pharmacology: the next paradigm in drug discovery. Nature Chemical Biology 4(11): 682–690, 2008.MathSciNetCrossRefGoogle Scholar
  17. Krzywinski, M. and Altman, N. Two-factor designs. Nature Methods 11: 1187–1188, 2014.CrossRefGoogle Scholar
  18. Lee, L.W. et al. Generic enzymatic rate equation under living conditions. Journal of Biological Systems 15: 495–514, 2007.CrossRefzbMATHGoogle Scholar
  19. Loewe, S. Isobols of Dose-Effect Relations in the Combination of Pentylenetetrazole and Phenobarbital. Journal of Pharmacology and Experimental Therapeutics 114: 185–191, 1955.Google Scholar
  20. Meng, X.L. and Rubin, D.B. Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 80: 267–278, 1993.MathSciNetCrossRefzbMATHGoogle Scholar
  21. Pei, X.Y. Dai, Y. and Grant, S. The proteasome inhibitor bortezomib promotes mitochondrial injury and apoptosis induced by the small molecule Bcl-2 inhibitor HA14-1 in multiple myeloma cells. Leukemia 17: 2036–2045, 2003.CrossRefGoogle Scholar
  22. Pei, X.Y. Dai, Y. and Grant, S. The small-molecule Bcl-2 inhibitor HA14-1 interacts synergistically with flavopiridol to induce mitochondrial injury and apoptosis in human myeloma cells through a free radical-dependent and Jun NH2-terminal kinase-dependent mechanism. Molecular Cancer Therapeutics 3: 1513–1524, 2004.Google Scholar
  23. Peterson, J.J. and Novick, S. J. Nonlinear Blending: A Useful General Concept for the Assessment of Combination Drug Synergy, Journal of Receptors and Signal Transduction 27(2): 125 – 146, 2007.CrossRefGoogle Scholar
  24. Shiozawa, K., Nakanishi, T., Tan, M., Fang, H.B., Wang, W.C., Edelman, M.J., et al. Preclinical studies of Vorinostat (suberoylanilide hydroxamic acid) combined with cytosine arabinoside and etoposide for treatment of acute leukemias. Clinical Cancer Research 15:1698–1707, 2009.CrossRefGoogle Scholar
  25. Sobol, I.M. Sensitivity analysis for nonlinear mathematical models. Mathematical Modeling and Computational Experiment 1: 407–414, 1993.MathSciNetzbMATHGoogle Scholar
  26. Sobol, I.M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. & Comp. in Simulation 55: 271–280, 2001.MathSciNetCrossRefzbMATHGoogle Scholar
  27. Sobol, IM. Theorems and examples on high dimensional model representation. Reliability Engineering & System Safety 79: 187–193, 2003.CrossRefGoogle Scholar
  28. Sun, Z. and Braun, T.M. A two-dimensional biased coin design for dual-agent dose-finding trials. Clinical Trials, doi:  10.1177/1740774515592404, 2015.Google Scholar
  29. Tan, M. Fang, H.B. and Tian, G.L. Dose and sample size determination for multi-drug combination studies. Statistics in Biopharmaceutical Research 1: 301–316, 2009.CrossRefGoogle Scholar
  30. Tan, M. Fang, H.B. Tian, G.L. and Houghton, P.J. Experimental design and sample size determination for drug combination studies based on uniform measures. Statistics in Medicine 22: 2091–2100, 2003.CrossRefGoogle Scholar
  31. Tian, G.L. Fang, H.B. Tan, M. Qin, H. and Tang, M.L. Uniform distributions in a class of convex polyhedrons with applications to drug combination studies. Journal of Multivariate Analysis 100: 1854–1865, 2009.MathSciNetCrossRefzbMATHGoogle Scholar
  32. Wages, N.A., Conaway M.R., and O’Quigley J. Continual reassessment method for partial ordering. Biometrics 67(4): 1555–63, 2011.MathSciNetCrossRefzbMATHGoogle Scholar
  33. Weiss, J.N. The hill equation revised: uses and misuses. FASEB journal 11: 835--841, 1997.Google Scholar
  34. Xavier, J.B. and Sander, C. Principle of System Balance for Drug Interactions. The New England Journal of Medicine 362(14): 1339–1340, 2010.CrossRefGoogle Scholar
  35. Yang, Y., Fang, H.B., Roy, A. and Tan, M. An adaptive Bayesian dose finding approach for drug combinations with drug-drug interaction. Statistics and Its Interface (in review), 2016.Google Scholar
  36. Yin, G. and Yuan, Y. A latent contingency table approach to dose finding for combinations of two agents. Biometrics 65(3): 866–875, 2009a.MathSciNetCrossRefzbMATHGoogle Scholar
  37. Yin, G. and Yuan, Y. Bayesian dose finding in oncology for drug combinations by copula regression. Journal of the Royal Statistical Society: Series C (Applied Statistics) 58(2): 211–224, 2009b.Google Scholar
  38. Yuan, Y. and Yin, G. Sequential continual reassessment method for two-dimensional dose finding. Statistics in Medicine 27(27): 5664–5678, 2008.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Ming T. Tan
    • 1
    Email author
  • Hong-Bin Fang
    • 1
  • Hengzhen Huang
    • 1
  • Yang Yang
    • 2
  1. 1.Department of Biostatistics, Bioinformatics and BiomathematicsGeorgetown University Medical CenterWashington, DCUSA
  2. 2.Division of Biometrics 1, Office of BiostatisticsCenter for Drug Evaluation and Research, US Food and Drug AdministrationSilver SpringUSA

Personalised recommendations