New features for population design evaluation and optimisation using PFIM3.2: illustration on warfarin pharmacokinetics - pharmacodynamics
Caroline Bazzoli, Anne Dubois, Thu-Thuy Nguyen, France Mentré
UMR 738 INSERM and University Paris Diderot, Paris, France
Objectives: We developed the free R function PFIM  for population design evaluation and optimisation. Here, we illustrate the use of PFIM 3.2 that we recently launched.
Methods: Compared to PFIM 3.0 , PFIM 3.2 includes several new features in terms of model specification and expression of the Fisher information matrix (MF). The library of pharmacokinetic (PK) models has been completed. Furthermore, a library of pharmacodynamic (PD) models is now available. PFIM 3.2 can handle a block diagonal MF or a complete one. It is now also possible to use models including fixed effects for the influence of discrete covariates on the parameters , and/or inter-occasion variability (IOV) . The predicted power of the Wald test for comparison or equivalence tests, as well as the number of subjects needed to achieve a given power can be computed.
Results: We use the standard example of warfarin PKPD. Warfarin is administered as a single oral dose to 32 subjects. Plasma concentration and effect on prothrombin complex activity (PCA) are measured. A one compartment PK model with first order absorption and elimination is used and the effect on PCA is described by a turnover model with inhibition of the input. First, we evaluated the empirical rich design and compared it to a design optimised using the Fedorov-Wynn algorithm. With 2.1 less samples than the empirical design, the optimal design provides similar predicted standard errors for the fixed effects. Then, as CYP2C9 is involved in warfarin metabolism, we wanted to evaluate designs with this genetic covariate effect on clearance. With the optimal design and a clearance assumed to decrease by 50% for patients with a mutant genotype, only 8 subjects are needed to obtain a power of 90% for the comparison test detecting the genetic effect. Finally, we planned a crossover PK study to assess the absence of interaction of drug X on warfarin absorption rate-constant (ka). We assume some IOV on ka. With the empirical PK design, the expected power is 46% to assess the absence of interaction on ka. To achieve a power of 90% for this equivalence test, 116 subjects would be needed.
Conclusions: We illustrated the use of PFIM 3.2 showing the consequence of the design and of the number of patients on the power of the Wald test for discrete covariate. PFIM 3.2 is a great tool to evaluate and/or optimise designs and to control expected power of the Wald test for comparison or equivalence tests.
 Bazzoli C, Retout S and Mentré F. Design evaluation and optimisation in multiple response nonlinear mixed effect models: PFIM 3.0. Computer Methods and Programs in Biomedicine. 98:55-65, 2010.
 Retout S, Comets E, Samson A and Mentré F. Design in nonlinear mixed effects models: Optimization using the Federov-Wynn algorithm and power of the Wald test for binary covariates. Statistics in Medicine. 26:5162-5179, 2007.
 Nguyen TT, Bazzoli C and Mentré F. Design evaluation and optimization in crossover pharmacokinetic studies analysed by nonlinear mixed effects models: application to bioequivalence or interaction trials. American Conference in Pharmacometrics, Mashantucket, United-States, October 4-7, 2009 (poster).