## Abstract

**Background:** Structural identifiability concerns whether the parameters in a postulated model structure can be uniquely determined given the input and output functions to and from that model. What this means in practice is that if a model is structurally unidentifiable, the model structure itself allows a subset (or all) of the model parameters to vary while the model output remains unchanged. Conclusions drawn from such a model are potentially unreliable. For instance, if the estimated value of Emax is of interest, but if Emax is a member of the subset of unidentifiable parameters as a result of the model structure, the estimated value of Emax is effectively meaningless.
For deterministic models, there exist several different structural identifiability analysis techniques for both linear and nonlinear systems. However, little has been done on the identifiability analysis of models having a mixed-effects framework. Here the main challenge comes from the fact that, apart from having a deterministic part describing the typical individual, there is also an additional statistical sub-model describing the random effects for the parameters and the covariance between them. In population modelling, these parameters represent the variability in the population. Since estimation of the variability is often one of the main goals in population modelling, it is important to determine whether these parameters can be uniquely determined or otherwise. This motivates the need to extend the concept of structural identifiability for deterministic models to non-deterministic models such as mixed-effects models.

**Aim:** To develop ways of analysing structural identifiability in mixed-effects models.
Methods: In statistics, and in particular statistical inference, there exist problems which are similar to those encountered in parameter estimation for mixed-effect models. In this work, we make use of these similarities and use these relevant relations to study structural identifiability in mixed-effects models.

**Results:** Some initial results from a structural identifiability analysis on a particular mixed-effects model structure are presented.

## Acknowledgement

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).

## Authors and Affiliations

- Robert Andersson, School of Engineering
- Mats Jirstrand, Fraunhofer-Chalmers Centre
- Johan Gabrielsson, Swedish University of Agricultural Sciences