Advertisement

Drug Combination Studies, Uniform Experimental Design and Extensions

  • Ming T. TanEmail author
  • Hong-Bin Fang
Chapter
  • 80 Downloads

Abstract

Drug combination has been an important therapeutic development approach for cancer, viral or microbial infections, and other diseases involving complex biological networks. Synergistic drug combinations, which are more effective than predicted from summing effects of individual drugs, often achieve improved therapeutic index. Because drug-effect is dose-dependent, multiple doses of an individual drug need to be evaluated, giving rapidly escalating 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. It is known that, in the presence of model uncertainties, uniform measures that scatter the design points (the dose levels) uniformly in the experiment domain is the best strategy to yield maximum information on the dose response relation. This chapter will review some efficient experimental designs for drug combination studies especially those related to uniform measures and extensions using maximum entropy design.

Notes

Acknowledgements

This research is partially supported by the National Cancer Institute (NCI) grant R01CA164717.

References

  1. 1.
    Abdelbasit, K.M., Plackett, R.L.: Experimental design for joint action. Biometrics 38, 171–179 (1982)zbMATHCrossRefGoogle Scholar
  2. 2.
    Berenbaum, M.C.: What is synergy? Pharmacol. Rev. 41, 93–141 (1989)Google Scholar
  3. 3.
    Berenbaum, M.C., Yu, V.L., Felegie, T.P.: Synergy with double and triple antibiotic combinations compared. J. Antimicrob. Chemother. 12, 555–563 (1983)CrossRefGoogle Scholar
  4. 4.
    Calzolari, D., et al.: Search algorithms as a framework for the optimization of drug combinations. PLoS Comput. Biol. 4(12), e1000249 (2008)CrossRefGoogle Scholar
  5. 5.
    Casey, M., Gennings, C., Carter Jr., W.H., et al.: \(D_s\)-Optimal designs for studying combinations of chemicals using multiple fixed-ratio ray experiments. Environmetrics 16, 129–147 (2005)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Chen, H.X., Dancey, J.E.: Combinations of moleculartargeted therapies: opportunities and challenges. In: Kaufman, H.L., Wadler, S., Antman, K. (eds.) Molecular targeting in oncology, pp. 693–705. Humana Press, New Jersey (2008)CrossRefGoogle Scholar
  7. 7.
    Carter Jr., W.H., Gennings, C., Staniswalis, J.G., et al.: A statistical approach to the construction and analysis of isobolograms. J. Am. Coll. Toxicol. 7, 963–973 (1988)CrossRefGoogle Scholar
  8. 8.
    Cox, D.R., Reid, N.: The Theory of the Design of Experiments. Chapman and Hall/CRC, London (2000)zbMATHCrossRefGoogle Scholar
  9. 9.
    Cressie, N.A.C.: Statistics for Spatial Data. Wiley, New York (1993)zbMATHCrossRefGoogle Scholar
  10. 10.
    Fang, H.B., Chen, X., Pei, X. Y. et al.: Experimental design and statistical analysis for three-drug combination studies. Stat. Methods Med. Res. 26, 1261–1280 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Fang, H.B., Huang, H., Clarke, R., Tan, M.: Predicting multi-drug inhibition interactions based on signaling networks and single drug dose-response information. J. Comput. Syst. Biol. 2, 1–9 (2016)Google Scholar
  12. 12.
    Fang, H.B., Ross, D.D., Sausville, E., Tan, M.: Experimental design and interaction analysis of combination studies of drugs with log-linear dose responses. Stat. Med. 27, 3071–3083 (2008)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Fang, H.B., Tian, G.L., Li, W., et al.: Design and sample size for evaluating combinations of drugs of linear and loglinear dose response curves. J. Biopharm. Stat. 19, 625–640 (2009)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Fang, K.T.: Uniform Design and Uniform Design Tables. Science Press, Beijing (1994)Google Scholar
  15. 15.
    Fang, K.T., Li, R., Sudjianto, A.: Design and Modeling for Computer Experiments. Chapman and Hall/CRC, New York (2006)zbMATHGoogle Scholar
  16. 16.
    Fang, K.T., Lin, D.K.J., Winker, P., Zhang, Y.: Uniform design: theory and application. Technometrics 42, 237–248 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Finney, D.J.: Probit Analysis, 3rd edn. Cambridge University Press, London (1971)zbMATHGoogle Scholar
  18. 18.
    Fitzgerald, J.B., Schoeberl, B., Nielsen, U.B., et al.: Systems biology and combination therapy in the quest for clinical efficacy. Nat. Chem. Biol. 2, 458–466 (2006)CrossRefGoogle Scholar
  19. 19.
    Gennings, C., Carter Jr., W.H., Carney, E.W., et al.: A novel flexible approach for evaluating fixed ratio mixtures of full and partial agonists. Toxicol. Sci. 80, 134–150 (2004)CrossRefGoogle Scholar
  20. 20.
    Greco, W.R., Bravo, G., Parsons, J.C.: The search for synergy: a critical review from a response surface perspective. Pharmacol. Rev. 47, 331–385 (1995)Google Scholar
  21. 21.
    Hait, W.N.: Targeted cancer therapeutics. Cancer Res. 69, 1263–1267 (2009)CrossRefGoogle Scholar
  22. 22.
    Hickernell, F.J.: A generalized discrepancy and quadrature error bound. Math. Comput. 67, 299–322 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Hopkins, A.L.: Network pharmacology: the next paradigm in drug discovery. Nat. Chem. Biol. 4, 682–690 (2008)CrossRefGoogle Scholar
  24. 24.
    Huang, H., Fang, H.B., Tan, M.T.: Experimental design for multi-drug combination studies using signaling networks. Biometrics 74, 538–547 (2018)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Laska, E.M., Meisner, M., Siegel, C.: Simple designs and model-free tests for synergy. Biometrics 50, 834–841 (1994)zbMATHCrossRefGoogle Scholar
  26. 26.
    Lindley, D.V.: On a measure of information provided by an experiment. Ann. Math. Stat. 27, 986–1005 (1956)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Loewe, S.: Isobols of dose-effect relations in the combination of pentylenetetrazole and phenobarbital. J. Pharmacol. Exp. Ther. 114, 185–191 (1955)Google Scholar
  28. 28.
    Meadows, S.L., Gennings, C., Carter Jr., W.H., Bae, D.S.: Experimental design for mixtures of chemicals along fixed ratio rays. Environ. Health Perspect. 110, 979–983 (2002)CrossRefGoogle Scholar
  29. 29.
    Santner, T.J., Williams, B.J., Notz, W.I.: The Design and Analysis of Computer Experiments. Springer, New York (2003)zbMATHCrossRefGoogle Scholar
  30. 30.
    Shiozawa, K., Nakanishi, T., Tan, M., et al.: Preclinical studies of vorinostat (suberoylanilide hydroxamic acid, saha) combined with cytosine arabinoside (ara-c) and etoposide for treatment of acute leukemias. Clin. Cancer Res. 15, 1698–1707 (2009)CrossRefGoogle Scholar
  31. 31.
    Sobol’, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 55, 271–280 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Sobol’, I.M.: Theorems and examples on high dimensional model representation. Reliab. Eng. Syst. Safety 79, 187–193 (2003)CrossRefGoogle Scholar
  33. 33.
    Straetemans, R., O’Brien, T., Wouters, L. et al.: Design and analysis of drug combination experiments. Biom. J. 47, 299–308 (2005)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Syracuse, K.C., Greco, W.R.: Comparison between the method of Chou and Talalay and a new method for the assessment of the combined effects of drugs: a Monte-Carlo simulation study. In: American Statistical Association Proceedings of the Biopharmaceutical Section, pp. 127–132 (1986)Google Scholar
  35. 35.
    Tallarida, R.J.: Drug Synergism and Dose-effect Data Analysis. Chapman and Hall/CRC, New York (2000)CrossRefGoogle Scholar
  36. 36.
    Tallarida, R.J., Stone, D.J., Raffa, R.B.: Efficient designs for studying synergistic drug combinations. Life Sci. 61, 417–425 (1997)CrossRefGoogle Scholar
  37. 37.
    Tan, M., Fang, H.B., Tian, G.L., Houghton, P.J.: Experimental design and sample size determination for drug combination studies based on uniform measures. Stat. Med. 22, 2091–2100 (2003)CrossRefGoogle Scholar
  38. 38.
    Tan, M., Fang, H.B., Tian, G.L.: Dose and sample size determination for multi-drug combination studies. Stat. Biopharm. Res. 1, 301–316 (2009)CrossRefGoogle Scholar
  39. 39.
    Tian, G.L., Fang, H.B., Tan, M., et al.: Uniform distributions in a class of convex polyhedrons with applications to drug combination studies. J. Multi. Anal. 100, 1854–1865 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Wan, W., Pei, X.Y., Grant, S.: Nonlinear response surface in the study of interaction analysis of three combination drugs. Biom. J. 59, 9–24 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Wiens, D.P.: Designs for approximately linear regression: two optimality properties of uniform designs. Stat. Probab. Lett. 12, 217–221 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    Xavier, J.B., Sander, C.: Principle of system balance for drug interactions. New Engl. J. Med. 362, 1339–1340 (2010)CrossRefGoogle Scholar
  43. 43.
    Yang, Y., Fang, H.B., Roy, A., Tan, M.: Adaptive oncology phase I trial design of drug combinations with drug-drug interaction modeling. Stat. Interface 11, 109–127 (2018)MathSciNetzbMATHCrossRefGoogle Scholar
  44. 44.
    Yin, G., Yuan, Y.: A latent contingency table approach to dose finding for combinations of two agents. Biometrics 65, 866–875 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  45. 45.
    Yin, G., Yuan, Y.: Bayesian dose finding in oncology for drug combinations by copula regression. J. R. Stat. Soc. Ser. C (Appl. Stat.) 58, 211–224 (2009)MathSciNetCrossRefGoogle Scholar
  46. 46.
    Yuan, Y., Yin, G.: Sequential continual reassessment method for two-dimensional dose finding. Stat. Med. 27, 5664–5678 (2008)MathSciNetCrossRefGoogle Scholar
  47. 47.
    Zhang, A.: Schur-convex discrimination of designs using power and exponential kernels. In: Fan, J., Li, G. (eds.) Contemporary Multivariate Analysis and Experimental Design, pp. 293–311. World Scientific Publisher, Singapore (2005)CrossRefGoogle Scholar
  48. 48.
    Zhang, A., Fang, K.T., Li, R., Sudjianto, A.: Majorization framework for balanced lattice designs. Ann. Stat. 33, 2837–2853 (2005)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Biostatistics, Bioinformatics and BiomathematicsGeorgetown University Medical CenterWashington, DCUSA

Personalised recommendations