Design evaluation and optimisation in crossover pharmacokinetic studies analyzed by nonlinear mixed effects models
Thu Thuy Nguyen, Caroline Bazzoli, France Mentré
UMR738 INSERM and University Paris Diderot, Paris, France
Objectives: Nonlinear mixed effects models (NLMEM) can be used to analyze crossover pharmacokinetic (PK) bioequivalence trials. Before modelling, it is important to define an appropriate design. The main approach for design evaluation and optimisation has been for a long time based on simulations but it is a cumbersome method. An alternative approach is based on the population Fisher information matrix (MF) which expression for NLMEM [1,2] was implemented in the R function PFIM [3,4,5]. We aim to propose an extension of the evaluation of MF for NLMEM in crossover trials and to apply this extension to design a future crossover PK study of amoxicillin in piglets.
Methods: We extended MF for NLMEM with inclusion of within subject variability, in addition to between subject variability, and with discrete covariates changing between periods. We used a linearization of the model around the random effects expectation. The power of the Wald test of comparison or equivalence was computed using the predicted standard error (SE). We evaluated these developments by simulations mimicking a crossover study with two periods, where piglets received amoxicillin and placebo at period 1 then amoxicillin and a product X at period 2. The objective of the trial is to show the absence of interaction of X on the PK of amoxicillin. Simulations were performed for a rich design as well as for an optimal sparse design derived from the rich one and with different values of treatment effect on amoxicillin clearance. We then used the extension of MF to plan a future study, with similar crossover design as the simulation study, based on results of a previous study of amoxicillin in piglets.
Results: For various simulated scenario, predictions of SE and powers by MF were close to the empirical ones obtained after fitting the simulated trials with the SAEM algorithm [6,7] in MONOLIX 2.4 [8]. The optimal sparse design had similar power as the rich design. These extensions were implemented in the new version 3.2 of PFIM, available since January 2010 [5]. For the application, from the expected SE computed by PFIM 3.2 for the future study, we predicted much more needed subjects than the previous study to show the absence of interaction of X on the PK of amoxicillin with good power.
Conclusions: This extension of MF for NLMEM is relevant. PK bioequivalence trials analyzed through NLMEM allow sparse designs and can be performed in patients. PFIM can be used to efficiently design these trials.
References:
[1] Mentré, F., Mallet, A., Baccar, D. (1997) Optimal design in random effect regression models, Biometrika, 84(2):429-442.
[2] Bazzoli, C., Retout, S., Mentré, F. (2009) Fisher information matrix for nonlinear mixed effects multiple response models: Evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model, Statistics in Medicine, 28:1940-1956.
[3] Retout, S., Duffull, S., Mentré, F. (2001) Development and implementation of the population Fisher information matrix for evaluation of population pharmacokinetic designs, Computer Methods and Programs in Biomedicine, 65:141-151.
[4] Bazzoli, C., Retout, S., Mentré, F. (2010) Design evaluation and optimisation in multiple response nonlinear mixed effect models: PFIM 3.0, Computer Methods and Programs in Biomedicine, 98:55-65.
[5] http://www.pfim.biostat.fr/.
[6] Kuhn, E., Lavielle, M. (2005) Maximum likelihood estimation in nonlinear mixed effects model, Computational Statistics and Data Analysis, 49:1020-1038.
[7] Panhard, X. and Samson, A. (2009) Extension of the SAEM algorithm for non linear mixed effects models with two levels of random effects, Biostatistics, 10:121-135.
[8] http://www.monolix.org/
