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Three novel approaches to structural identifiability analysis in mixed-effects models

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Janzén, David, Jirstrand, Mats, Chappell, M. J. (Michael J.) and Evans, Neil D. (2016) Three novel approaches to structural identifiability analysis in mixed-effects models. Computer Methods and Programs in Biomedicine . doi:10.1016/j.cmpb.2016.04.024 ISSN 0169-2607.

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Official URL: http://dx.doi.org/10.1016/j.cmpb.2016.04.024

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Abstract

Background and 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.

Item Type: Journal Article
Divisions: Faculty of Science, Engineering and Medicine > Engineering > Engineering
Journal or Publication Title: Computer Methods and Programs in Biomedicine
Publisher: Elsevier Ireland Ltd.
ISSN: 0169-2607
Official Date: 5 May 2016
Dates:
DateEvent
5 May 2016Available
21 April 2016Accepted
14 December 2016Submitted
DOI: 10.1016/j.cmpb.2016.04.024
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 11 May 2016
Is Part Of: This work is funded through the Marie Curie FP7 People ITN European Industrial Doctorate (EID) project, IMPACT (Innovative Modelling for Pharmacological Advances through Collaborative Training). Grant Agreement No 316736.

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