Pharmaceutical Research

, Volume 32, Issue 10, pp 3159–3169 | Cite as

Influence of the Size of Cohorts in Adaptive Design for Nonlinear Mixed Effects Models: An Evaluation by Simulation for a Pharmacokinetic and Pharmacodynamic Model for a Biomarker in Oncology

Research Paper

Abstract

Purpose

In this study we aimed to evaluate adaptive designs (ADs) by clinical trial simulation for a pharmacokinetic-pharmacodynamic model in oncology and to compare them with one-stage designs, i.e., when no adaptation is performed, using wrong prior parameters.

Methods

We evaluated two one-stage designs, ξ0 and ξ*, optimised for prior and true population parameters, Ψ0 and Ψ*, and several ADs (two-, three- and five-stage). All designs had 50 patients. For ADs, the first cohort design was ξ0. The next cohort design was optimised using prior information updated from the previous cohort. Optimal design was based on the determinant of the Fisher information matrix using PFIM. Design evaluation was performed by clinical trial simulations using data simulated from Ψ*.

Results

Estimation results of two-stage ADs and ξ* were close and much better than those obtained with ξ0. The balanced two-stage AD performed better than two-stage ADs with different cohort sizes. Three- and five-stage ADs were better than two-stage with small first cohort, but not better than the balanced two-stage design.

Conclusions

Two-stage ADs are useful when prior parameters are unreliable. In case of small first cohort, more adaptations are needed but these designs are complex to implement.

KEY WORDS

adaptive design Fisher information matrix nonlinear mixed effects model optimal design pharmacokinetic-pharmacodynamic 

ABBREVIATIONS

AD

Adaptive design

FIM

Fisher information matrix

NLMEM

Nonlinear mixed effects model

PD

Pharmacodynamic

PK

Pharmacokinetic

REE

Relative estimation error

RRMSE

Relative root mean squared error

TGF-β

Transforming growth factor β

References

  1. 1.
    Lavielle M. Mixed effects models for the population approach: models, tasks, methods and tools. Chapman and Hall/CRC; 2014. 383 p.Google Scholar
  2. 2.
    Mould D, Upton R. Basic concepts in population modeling, simulation, and model-based drug development. CPT Pharmacometrics Syst Pharmacol. 2012;1(9):e6.PubMedCentralCrossRefPubMedGoogle Scholar
  3. 3.
    Van der Graaf PH. CPT: pharmacometrics and systems pharmacology. CPT Pharmacometrics Syst Pharmacol. 2012;1:e8.PubMedCentralCrossRefPubMedGoogle Scholar
  4. 4.
    Al-Banna MK, Kelman AW, Whiting B. Experimental design and efficient parameter estimation in population pharmacokinetics. J Pharmacokinet Biopharm. 1990;18(4):347–60.CrossRefPubMedGoogle Scholar
  5. 5.
    Holford N, Ma SC, Ploeger BA. Clinical trial simulation: a review. Clin Pharmacol Ther. 2010;88(2):166–82.CrossRefPubMedGoogle Scholar
  6. 6.
    Mentré F, Mallet A, Baccar D. Optimal design in random-effects regression models. Biometrika. 1997;84(2):429–42.CrossRefGoogle Scholar
  7. 7.
    Mentré F, Chenel M, Comets E, Grevel J, Hooker A, Karlsson M, et al. Current use and developments needed for optimal design in pharmacometrics: a study performed among DDMoRe’s european federation of pharmaceutical industries and associations members. CPT Pharmacometrics Syst Pharmacol. 2013;2(6):e46.PubMedCentralCrossRefPubMedGoogle Scholar
  8. 8.
    Nyberg J, Bazzoli C, Ogungbenro K, Aliev A, Leonov S, Duffull S, et al. Methods and software tools for design evaluation for population pharmacokinetics-pharmacodynamics studies. Br J Clin Pharmacol. 2014.Google Scholar
  9. 9.
    Bazzoli C, Retout S, Mentré F. Design evaluation and optimisation in multiple response nonlinear mixed effect models: PFIM 3.0. Comput Methods Prog Biomed. 2010;98(1):55–65.CrossRefGoogle Scholar
  10. 10.
    Mentré F, Thu Thuy N, Lestini G, Dumont C, PFIM group. PFIM 4.0: new features for optimal design in nonlinear mixed effects models using R. PAGE 2014 Abstr 3032 [Internet]. Available from: [http://www.page-meeting.org/default.asp?abstract=3032]
  11. 11.
    Nyberg J, Ueckert S, Strömberg EA, Hennig S, Karlsson MO, Hooker AC. PopED: an extended, parallelized, nonlinear mixed effects models optimal design tool. Comput Methods Prog Biomed. 2012;108(2):789–805.CrossRefGoogle Scholar
  12. 12.
    Gueorguieva I, Ogungbenro K, Graham G, Glatt S, Aarons L. A program for individual and population optimal design for univariate and multivariate response pharmacokinetic-pharmacodynamic models. Comput Methods Prog Biomed. 2007;86(1):51–61.CrossRefGoogle Scholar
  13. 13.
  14. 14.
    Foo L-K, Duffull S. Methods of robust design of nonlinear models with an application to pharmacokinetics. J Biopharm Stat. 2010;20(4):886–902.CrossRefPubMedGoogle Scholar
  15. 15.
    Foo LK, McGree J, Eccleston J, Duffull S. Comparison of robust criteria for D-optimal designs. J Biopharm Stat. 2012;22(6):1193–205.CrossRefPubMedGoogle Scholar
  16. 16.
    Pronzato L, Walter E. Robust experiment design via maximin optimization. Math Biosci. 1988;89(2):161–76.CrossRefGoogle Scholar
  17. 17.
    Dodds MG, Hooker AC, Vicini P. Robust population pharmacokinetic experiment design. J Pharmacokinet Pharmacodyn. 2005;32(1):33–64.CrossRefPubMedGoogle Scholar
  18. 18.
    Chang M. Adaptive design theory and implementation using SAS and R. 1st ed. Boca Raton: Chapman and Hall/CRC; 2007. 440.Google Scholar
  19. 19.
    Foo L, Duffull S. Adaptive optimal design for bridging studies with an application to population pharmacokinetic studies. Pharm Res. 2012;29(6):1530–43.CrossRefPubMedGoogle Scholar
  20. 20.
    Zamuner S, Di Iorio VL, Nyberg J, Gunn RN, Cunningham VJ, Gomeni R, et al. Adaptive-optimal design in PET occupancy studies. Clin Pharmacol Ther. 2010;87(5):563–71.CrossRefPubMedGoogle Scholar
  21. 21.
    Fedorov V, Wu Y, Zhang R. Optimal dose-finding designs with correlated continuous and discrete responses. Stat Med. 2012;31(3):217–34.CrossRefPubMedGoogle Scholar
  22. 22.
    Chen TT. Optimal three-stage designs for phase II cancer clinical trials. Stat Med. 1997;16(23):2701–11.CrossRefPubMedGoogle Scholar
  23. 23.
    Dumont C, Chenel M, Mentré F. Two-stage adaptive design in nonlinear mixed effects models: application to pharmacokinetics in children. Commun Stat. ACCEPTED.Google Scholar
  24. 24.
    Bueno L, de Alwis D, Pitou C, Yingling J, Lahn M, Glatt S, et al. Semi-mechanistic modelling of the tumour growth inhibitory effects of LY2157299, a new type I receptor TGF-beta kinase antagonist, in mice. Eur J Cancer Oxf Engl 1990. 2008;44(1):142–50.Google Scholar
  25. 25.
    Gueorguieva I, Cleverly A, Stauber A, Sada Pillay N, Rodon J, Miles C, et al. Defining a therapeutic window for the novel TGF-β inhibitor LY2157299 monohydrate based on a pharmacokinetic/pharmacodynamic model. Br J Clin Pharmacol. 2014;77(5):796–807.PubMedCentralCrossRefPubMedGoogle Scholar
  26. 26.
    Mielke T, Schwabe R. Some considerations on the fisher information in nonlinear mixed effects models. In: Giovagnoli A, Atkinson AC, Torsney B, May C, editors. mODa 9 – Advances in Model-oriented design and analysis [Internet]. Physica-Verlag HD; 2010 [cited 2014 Sep 2]. p. 129–36. Available from: http://link.springer.com.gate2.inist.fr/chapter/10.1007/978-3-7908-2410-0_17.
  27. 27.
    Hoeting J, Madigan D, Raftery A, Volinsky C. Bayesian model averaging: a tutorial. Stat Sci. 1999;14(4):382–417.CrossRefGoogle Scholar
  28. 28.
    Tod M, Rocchisani JM. Comparison of ED, EID, and API criteria for the robust optimization of sampling times in pharmacokinetics. J Pharmacokinet Biopharm. 1997;25(4):515–37.CrossRefPubMedGoogle Scholar
  29. 29.
    Vajjah P, Duffull SB. A generalisation of T-optimality for discriminating between competing models with an application to pharmacokinetic studies. Pharm Stat. 2012;11(6):503–10.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Giulia Lestini
    • 1
  • Cyrielle Dumont
    • 1
  • France Mentré
    • 1
  1. 1.IAME, UMR 1137, INSERMUniversité Paris DiderotParisFrance

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