Structural identifiability in mixed-effects models: Two different approaches

Structural identifiability analysis is a theoretical concept that ascertains whether unknown model parameters can be uniquely determined for a given experimental setup. If this condition is not fulfilled numerical parameter estimates will be meaningless and the model prediction may not necessarily be reliable. Therefore, structural identifiability should be considered a prerequisite in any project where model predictions are a part of the decision making process. For models defined by ordinary differential equations, there are several methods developed both for the linear and nonlinear cases. In systems pharmacology pharmaceutical drug development projects there is, apart from an interest in understanding the biological mechanisms, also an interest in subject variability. For this, mixed-effects models are typically used. However, despite the wide use of mixed-effects models and being a part of the decision making process in pharmaceutical drugs projects, very little has been done on developing methods for structural identifiability analysis of mixed-effects models. In this paper, we propose and compare two methods for performing such an analysis. The first method is based on applying a set of established statistical theorems while in the second method the system is augmented to yield a random differential equation system format followed by subsequent analysis.