An Approach for Identifiability of Population Pharmacokinetic–Pharmacodynamic Models

Mathematical models are routinely used in clinical pharmacology to study the pharmacokinetic and pharmacodynamic properties of a drug in the body. Identifiability of these models is an important requirement for the success of these clinical studies. Identifiability is classified into two types, structural identifiability related to the structure of the mathematical model and deterministic identifiability which is related to the study design. There are existing approaches for assessment of structural identifiability of fixed‐effects models, although their use appears uncommon in the literature. In this study, we develop an informal unified approach for simultaneous assessment of structural and deterministic identifiability for fixed and mixed‐effects pharmacokinetic or pharmacokinetic–pharmacodynamic models. This approach uses an information theoretic framework. The method is applied both to simple examples to explore known identifiability properties and to a more complex example to illustrate its utility.

[1]  C. Cobelli,et al.  Parameter and structural identifiability concepts and ambiguities: a critical review and analysis. , 1980, The American journal of physiology.

[2]  Maria Pia Saccomani,et al.  DAISY: A new software tool to test global identifiability of biological and physiological systems , 2007, Comput. Methods Programs Biomed..

[3]  J. Adam.  A simplified mathematical model of tumor growth , 1986 .

[4]  C. R. Rao,et al.  Information and the Accuracy Attainable in the Estimation of Statistical Parameters , 1992 .

[5]  Eva Balsa-Canto,et al.  Bioinformatics Applications Note Systems Biology Genssi: a Software Toolbox for Structural Identifiability Analysis of Biological Models , 2022 .

[6]  H. Stoeckel,et al.  Grundlagen der Pharmakokinetik , 1981 .

[7]  Andrew C. Hooker,et al.  PopED: An extended, parallelized, nonlinear mixed effects models optimal design tool , 2012, Comput. Methods Programs Biomed..

[8]  J. Yates,et al.  Structural identifiability and indistinguishability of compartmental models. , 2009, Expert opinion on drug metabolism & toxicology.

[9]  J A Jacquez,et al.  Parameter estimation: local identifiability of parameters. , 1990, The American journal of physiology.

[10]  France Mentré,et al.  Design evaluation and optimisation in multiple response nonlinear mixed effect models: PFIM 3.0 , 2010, Comput. Methods Programs Biomed..

[11]  Claudio Cobelli,et al.  An integrated mathematical model of the dynamics of blood glucose and its hormonal control , 1982 .

[12]  Gordon Graham,et al.  A program for individual and population optimal design for univariate and multivariate response pharmacokinetic-pharmacodynamic models , 2007, Comput. Methods Programs Biomed..

[13]  Alain Mallet,et al.  Optimal design in random-effects regression models , 1997 .

[14]  Keith R. Godfrey,et al.  Identifiability and indistinguishability of nonlinear pharmacokinetic models , 1994, Journal of Pharmacokinetics and Biopharmaceutics.

[15]  J A Jacquez.  Identifiability: the first step in parameter estimation. , 1987, Federation proceedings.

[16]  E. R. Garrett.  The Bateman function revisited: A critical reevaluation of the quantitative expressions to characterize concentrations in the one compartment body model as a function of time with first-order invasion and first-order elimination , 1994, Journal of Pharmacokinetics and Biopharmaceutics.

[17]  A. Karim.  The pharmacokinetics of Norpace. , 1975, Angiology.

[18]  V. Fedorov,et al.  Optimal Design of Dose Response Experiments: A Model-Oriented Approach , 2001 .

[19]  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.

[20]  L Aarons,et al.  A pharmacokinetic simulation model for ivabradine in healthy volunteers. , 2000, European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences.

[21]  Jacquez Ja.  Identifiability: the first step in parameter estimation. , 1987 .

[22]  T. Wajima,et al.  A Comprehensive Model for the Humoral Coagulation Network in Humans , 2009, Clinical pharmacology and therapeutics.

[23]  K R Godfrey,et al.  Global identifiability of the parameters of nonlinear systems with specified inputs: a comparison of methods. , 1990, Mathematical biosciences.

[24]  Keith R. Godfrey,et al.  Identifiable pharmacokinetic models: The role of extra inputs and measurements , 1980, Journal of Pharmacokinetics and Biopharmaceutics.

[25]  S. Duffull,et al.  Interpreting population pharmacokinetic-pharmacodynamic analyses - a clinical viewpoint. , 2011, British journal of clinical pharmacology.

[26]  Arild Thowsen,et al.  Structural identifiability , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[27]  James W. Haefner,et al.  Modeling Biological Systems , 1996, Springer US.

[28]  D M Bortz,et al.  Model Selection and Mixed-Effects Modeling of HIV Infection Dynamics , 2006, Bulletin of mathematical biology.

[29]  M. J. Hatcher,et al.  Modeling Biological Systems: Principles and Applications , 1997 .

[30]  D Commenges,et al.  Practical Identifiability of HIV Dynamics Models , 2007, Bulletin of mathematical biology.

[31]  Keith R. Godfrey,et al.  An Identifiability Analysis of a Parent–Metabolite Pharmacokinetic Model for Ivabradine , 2001, Journal of Pharmacokinetics and Pharmacodynamics.