Identifiability of Population Pharmacokinetic-Pharmacodynamic Models
Vittal Shivva(1)*, Julia Korell(1,2), Ian G Tucker(1), Stephen B Duffull(1)
(1)School of Pharmacy, University of Otago, Dunedin, New Zealand (2)Department of Pharmaceutical Biosciences, Uppsala University, Sweden
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 . 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.
Aim & Objectives: 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 . The approach was applied to both simple PK models to explore known identifiability properties and also to a parent-metabolite PK model  to illustrate its utility.
Methods & Results: One compartment first order input PK models (Bateman & Dost) were assessed as fixed effects and mixed effects models using the criteria 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. A parent-metabolite model that described the oral PK of ivabradine and its metabolite was assessed for identifiability of both fixed and mixed effects. Assessment of the model revealed that Vm2 (volume of distribution of the metabolite in the central compartment) and FI (bioavailable fraction of the parent) were unidentifiable in the model. All BSV parameters were identifiable in the mixed effects model of ivabradine.
Discussion & Conclusions: Results from the analysis of simple and more complicated (multiple response) PK models have demonstrated the ability of this approach to assess structural identifiability of population models. This method also enables the assessment of deterministic identifiability by examining the diagonal elements of the inverse of the Fisher Information Matrix for a candidate design. The current approach can serve as a unified method for assessing both structural and deterministic identifiability of population models.
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