Optimal Design for Multiresponse Pharmacokinetic–Pharmacodynamic Models – Dealing with Unbalanced Designs

This paper addresses the problem of determining D-optimal designs for multiresponse pharmacokinetic–pharmacodynamic (PKPD) experiments where data on each response variable can be collected at different times. Most previous multiresponse model optimal design applications have considered the case where all response variables are measured at the same time points. However in practice it may not be possible to have all responses measured at the same sampling times. We propose an optimal design method to take into account the unbalanced nature of the problem. The method developed was applied to a PKPD problem that involved describing the time course of drug plasma concentrations, heart rate and mean arterial blood pressure for both a fixed effects and mixed effects regression model. Additionally a simulation study was carried out in NONMEM for one such population optimal design problem.

[1]  L Aarons,et al.  Population pharmacokinetics. , 1992, International journal of clinical pharmacology, therapy, and toxicology.

[2]  France Mentré,et al.  Further Developments of the Fisher Information Matrix in Nonlinear Mixed Effects Models with Evaluation in Population Pharmacokinetics , 2003, Journal of biopharmaceutical statistics.

[3]  Malcolm Rowland,et al.  Optimal Design for Multivariate Response Pharmacokinetic Models , 2006, Journal of Pharmacokinetics and Pharmacodynamics.

[4]  L Aarons,et al.  Population pharmacokinetics: theory and practice. , 1991, British journal of clinical pharmacology.

[5]  M Davidian,et al.  Population pharmacokinetic/pharmacodynamic methodology and applications: a bibliography. , 1994, Biometrics.

[7]  M. J. Box,et al.  Estimation and Design Criteria for Multiresponse Non‐Linear Models with Non‐Homogeneous Variance , 1972 .

[8]  L Aarons,et al.  Software for Population Pharmacokinetics and Pharmacodynamics , 1999, Clinical pharmacokinetics.

[9]  Aaron Tucker,et al.  A Bibliography. , 1902, British medical journal.

[10]  Tamar Frankel.  [The theory and the practice...]. , 2001, Tijdschrift voor diergeneeskunde.

[11]  Stephen B. Duffull,et al.  The use of simulated annealing for finding optimal population designs , 2002, Comput. Methods Programs Biomed..

[12]  Stephen B. Duffull,et al.  Optimal Design for Model Discrimination and Parameter Estimation for Itraconazole Population Pharmacokinetics in Cystic Fibrosis Patients , 2005, Journal of Pharmacokinetics and Pharmacodynamics.

[13]  Gordon Graham,et al.  The use of a modified Fedorov exchange algorithm to optimise sampling times for population pharmacokinetic experiments , 2005, Comput. Methods Programs Biomed..

[14]  David Z. D'Argenio,et al.  Optimal sampling times for pharmacokinetic experiments , 1981, Journal of Pharmacokinetics and Biopharmaceutics.

[15]  J. Wagner.  Pharmacokinetics for the Pharmaceutical Scientist , 1993 .

[16]  Paolo Vicini,et al.  Simultaneous population optimal design for pharmacokinetic-pharmacodynamic experiments , 2005, The AAPS Journal.

[17]  M. Foracchia,et al.  POPED, a software for optimal experiment design in population kinetics , 2004, Comput. Methods Programs Biomed..

[18]  Anthony C. Atkinson,et al.  Optimum Experimental Designs , 1992 .

[19]  France Mentré,et al.  Fisher information matrix for non‐linear mixed‐effects models: evaluation and application for optimal design of enoxaparin population pharmacokinetics , 2002, Statistics in medicine.

[20]  W. G. Hunter,et al.  Design of experiments for parameter estimation in multiresponse situations , 1966 .

[21]  L B Sheiner,et al.  Kinetics of pharmacologic response. , 1982, Pharmacology & therapeutics.

[22]  Leon Aarons,et al.  Optimum blood sampling time windows for parameter estimation in population pharmacokinetic experiments , 2006, Statistics in medicine.

[23]  P. Laycock,et al.  Optimum Experimental Designs , 1995 .

[24]  France Mentré,et al.  Optimization of Individual and Population Designs Using Splus , 2003, Journal of Pharmacokinetics and Pharmacodynamics.

[25]  France Mentré,et al.  Development and implementation of the population Fisher information matrix for the evaluation of population pharmacokinetic designs , 2001, Comput. Methods Programs Biomed..

[26]  Sergei Leonov,et al.  OPTIMAL POPULATION DESIGNS FOR PK MODELS WITH SERIAL SAMPLING , 2004, Journal of biopharmaceutical statistics.

[27]  Linda M. Haines,et al.  14 Designs for nonlinear and generalized linear models , 1996, Design and analysis of experiments.