Comparison of results of the different software for design evaluation in population pharmacokinetics and pharmacodynamics
France Mentré (1), Joakim Nyberg (2), Kay Ogungbenro (3), Sergei Leonov (4), Alexander Aliev (5), Stephen Duffull (6), Caroline Bazzoli (7), Andrew C. Hooker (2).
(1) INSERM U738 and University Paris Diderot, Paris, France; (2) Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden; (3) Centre for Applied Pharmacokinetic Research, School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Manchester, United Kingdom; (4) GlaxoSmithKline Pharmaceuticals, Collegeville, PA 19426, USA; (5) Institute for Systems Analysis, Russian Academy of Sciences, Moscow, Russia; (6) School of Pharmacy, University of Otago, Dunedin, New Zealand; (7) Laboratoire Jean Kuntzmann, Département Statistique, Grenoble, France.
Objectives: To compare the standard errors (SE) and criterion provided by the different software for population designs on two examples: a simple pharmacokinetic (PK) model and a complex pharmacokinetic-pharmacodynamic (PKPD) example.
Methods: Following the first theoretical work on optimal design for nonlinear mixed effect models, this research theme has rapidly grown in methodological and application developments. There are now several different software tools that implement an evaluation of the Fisher information matrix for population PKPD models. Five software tools were evaluated (in alphabetical order): PFIM (C. Bazzoli & F. Mentré), PkStaMP (S. Leonov, A. Aliev), PopDes (K. Ogungbenro), PopED (J. Nyberg & A. Hooker), and WinPOPT (S. Duffull). Each of the software uses approximations in the evaluation of the Fisher Information Matrix. The comparison was performed using two models: i) a simple one compartment PK model used for warfarin; ii) a more complex PKPD model for Peg-interferon with both concentration and response of viral load of hepatitis C virus (HCV). The HCV model was written as a system of differential equations. A fixed design was used for both examples (i.e. no optimization was considered). The results of the software were compared in terms of SE and were also compared to the empirical SE obtained in a clinical trial simulation with 1000 replications analyzed both by the SAEM algorithm in MONOLIX and the FOCEI algorithm in NONMEM.
Results: For the warfarin PK model, when the block diagonal Fisher Information Matrix was obtained using the first order approximation, all software gave identical SE very close to those obtained through simulation. Simulation-estimation performed in both MONOLIX and NONMEM gave similar results. Different approximations to the information matrix provided different SE even for the simple PK example. For the more complex PKPD model, similar trends are observed with good prediction of the SE of all PKPD parameters even using a first order approximation.
Conclusions: When similar approximation of the Fisher Information Matrix is used, all software provided identical results and were close to those obtained by clinical trial simulation. Statistical work is ongoing to improve the calculation of the Fisher Information Matrix for highly nonlinear models. For most PKPD model, using one of these various available software tools will provide meaningful results avoiding cumbersome simulation and allowing design optimization.