Identifiability of Population Pharmacokinetic-Pharmacodynamic Models

Background: Mathematical models are routinely used in clinical pharmacology to study the time course of concentration and effect of a drug in the body. Identifiability of these models is an essential prerequisite for the success of these studies.1 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. Though various approaches are available for assessment of structural identifiability of fixed effects models, no specific approaches are proposed to formally assess population models.

Objective: In this study, we developed a unified numerical approach for simultaneous assessment of both structural and deterministic identifiability for fixed and mixed effects pharmacokinetic (PK) or pharmacokinetic-pharmacodynamic models. The approach was based on an information theoretic framework.  This approach was applied to both simple PK models to explore known identifiability properties and also to a parent-metabolite PK model as a motivating example to illustrate its utility.

Methods & Results: One-compartment first order input PK models (Bateman & Dost) were assessed for fixed effects and mixed effects models using the criterion developed in this study. Results from the assessment of mixed effects models revealed that the bioavailable fraction F and its between subject variability (BSV) parameter ωF were unidentifiable in the Dost model whereas only F was unidentifiable in the Bateman model. The parent-metabolite model described the PK (intravenous and oral) of ivabradine and its metabolite and assessed identifiability for fixed and mixed effects models. Assessment of the models revealed that V3 (volume of distribution of the metabolite in the central compartment) was unidentifiable in the intravenous PK model, whereas V3 and FI (bioavailable fraction of the parent) were unidentifiable in the oral PK model. All BSV parameters were identifiable in both mixed effects models of ivabradine.

Conclusions: Results from the analysis of simple and more complicated fixed and mixed effects PK models demonstrated the ability of this approach in assessing identifiability of population models.

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2. Mentré F et al. (1997). Biometrika 84:429-442.
3. Evans N D et al. (2001). J. Pharmacokinetics and Pharmacodynamics 28:93-105.