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

Pharm Res. 2015 Oct;32(10):3159-69. doi: 10.1007/s11095-015-1693-3. Epub 2015 Jun 30.


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 ξ 0. 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.

Keywords: Fisher information matrix; adaptive design; nonlinear mixed effects model; optimal design; pharmacokinetic-pharmacodynamic.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Biomarkers / metabolism*
  • Clinical Trials as Topic
  • Computer Simulation*
  • Humans
  • Medical Oncology / methods
  • Models, Biological
  • Models, Statistical
  • Nonlinear Dynamics*
  • Pharmaceutical Preparations / administration & dosage*
  • Research Design*
  • Sample Size*
  • Software


  • Biomarkers
  • Pharmaceutical Preparations