title: Three novel approaches to structural identifiability analysis in mixed-effects models.
abstract: OBJECTIVE
  Structural identifiability is a concept that considers whether the structure of a model together with a set of input-output relations uniquely determines the model parameters. In the mathematical modelling of biological systems, structural identifiability is an important concept since biological interpretations are typically made from the parameter estimates. For a system defined by ordinary differential equations, several methods have been developed to analyse whether the model is structurally identifiable or otherwise. Another well-used modelling framework, which is particularly useful when the experimental data are sparsely sampled and the population variance is of interest, is mixed-effects modelling. However, established identifiability analysis techniques for ordinary differential equations are not directly applicable to such models.
  
  
  METHODS
  In this paper, we present and apply three different methods that can be used to study structural identifiability in mixed-effects models. The first method, called the repeated measurement approach, is based on applying a set of previously established statistical theorems. The second method, called the augmented system approach, is based on augmenting the mixed-effects model to an extended state-space form. The third method, called the Laplace transform mixed-effects extension, is based on considering the moment invariants of the systems transfer function as functions of random variables.
  
  
  RESULTS
  To illustrate, compare and contrast the application of the three methods, they are applied to a set of mixed-effects models.
  
  
  CONCLUSIONS
  Three structural identifiability analysis methods applicable to mixed-effects models have been presented in this paper. As method development of structural identifiability techniques for mixed-effects models has been given very little attention, despite mixed-effects models being widely used, the methods presented in this paper provides a way of handling structural identifiability in mixed-effects models previously not possible.
authors.affiliation: Department of Systems and Data Analysis, Fraunhofer-Chalmers Centre, Chalmers Science Park, SE-412 88 Gothenburg, Sweden; AstraZeneca RD, SE-431 83 Mölndal, Sweden; School of Engineering, University of Warwick, Coventry CV4 7AL, UK. Electronic address: d.l.i.janzen@warwick.ac.uk.
authors.forename: David L I
authors.initials: DLI
authors.lastname: Janzén
authors.affiliation: Department of Systems and Data Analysis, Fraunhofer-Chalmers Centre, Chalmers Science Park, SE-412 88 Gothenburg, Sweden.
authors.forename: Mats
authors.initials: M
authors.lastname: Jirstrand
authors.affiliation: School of Engineering, University of Warwick, Coventry CV4 7AL, UK.
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Chappell
authors.affiliation: School of Engineering, University of Warwick, Coventry CV4 7AL, UK.
authors.forename: Neil D
authors.initials: ND
authors.lastname: Evans
mesh_terms: D000465:Algorithms; D056808:Biostatistics / Q000379:methods*; D003198:Computer Simulation; D015233:Models, Statistical
keywords: Laplace transform; Mixed-effects modelling; Random differential equation; Structural identifiability