An approach for identifiability of population pharmacokinetic-pharmacodynamic models

Abstract

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.CPT: Pharmacometrics & Systems Pharmacology (2013) 2, e49; doi:10.1038/psp.2013.25; advance online publication 19 June 2013.

Figure 1

Graphical representation of log |M_F| vs. log random noise (σ²) for simple fixed-effects pharmacokinetic models. In this graph, log |M_F| above the abscissa are as represented. Data below the abscissa represent the negative determinants that do not have log values and are shown for the purpose of displaying discontinuity of the line. (a,c) Bateman model, (b,d) Dost model; upper row: all parameters estimated, lower row: F fixed.

Figure 2

Graphical representation of log |M_F| vs. log random noise (σ²) for simple mixed-effects pharmacokinetic models. In this graph, log |M_F| above the abscissa are as represented. Data below the abscissa represent the negative determinants that do not have log values and are shown for the purpose of displaying discontinuity of the line. (a,c,e) Bateman model, (b,d,f) Dost model; left column: all parameters estimated, middle column: F fixed, right row: F and ω_F fixed.

Figure 3

Graphical representation of log |M_F| vs. log random noise (σ²) for parent-metabolite PK model of ivabradine. In this graph, log |M_F| above the abscissa are as represented. Data below the abscissa represent the negative determinants that do not have log values and are shown for the purpose of displaying discontinuity of the line. (a,c,e,g) Intravenous model, (b,d,f,h) oral model; (a,b): all parameters estimated (fixed-effects model), (c,d): V₃ ± F_I fixed (fixed-effects model), (e,f): all parameters estimated (mixed-effects model), (g,h): V₃ ± F_I fixed (mixed-effects model).

Figure 4

Schematic representation of the combined parent-metabolite pharmacokinetic model of ivabradine. y₁ represents the observations corresponding to the parent (ivabradine) and y₂ represents the observations corresponding to the metabolite (S-18982).