What do we mean by identifiability in mixed effects models?
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We discuss the question of model identifiability within the context of nonlinear mixed effects models. Although there has been extensive research in the area of fixed effects models, much less attention has been paid to random effects models. In this context we distinguish between theoretical identifiability, in which different parameter values lead to non-identical probability distributions, structural identifiability which concerns the algebraic properties of the structural model, and practical identifiability, whereby the model may be theoretically identifiable but the design of the experiment may make parameter estimation difficult and imprecise. We explore a number of pharmacokinetic models which are known to be non-identifiable at an individual level but can become identifiable at the population level if a number of specific assumptions on the probabilistic model hold. Essentially if the probabilistic models are different, even though the structural models are non-identifiable, then they will lead to different likelihoods. The findings are supported through simulations.
KeywordsModel identifiability Practical identifiability Structural identifiability Parameter estimation Mixed effects model Pharmacokinetics
The research leading to these results received support from the Innovative Medicines Initiative Joint Undertaking under Grant agreement 115156, resources of which are composed of financial contributions from the European Union’s Seventh Framework Programme (FP7/2007-2013) and EFPIA companies’ in kind contribution. The DDMoRe project is also supported by financial contribution from Academic and SME partners.
- 2.Bonate PL (2011) Pharmacokinetic–pharmacodynamic modeling and simulation. Springer, New YorkGoogle Scholar
- 5.Cobelli C, Distefano JJ 3rd (1980) Parameter and structural identifiability concepts and ambiguities: a critical review and analysis. Am J Physiol-Regul Integr Comp Physiol 239(1):R7–R24Google Scholar
- 7.Fröhlich, F., Theis, F.J., Hasenauer, J.: Uncertainty analysis for non-identifiable dynamical systems: Profile likelihoods, bootstrapping and more. In: Computational Methods in Systems Biology, pp. 61–72. Springer (2014)Google Scholar
- 12.Lavielle M (2014) Mixed Effects Models for the Population Approach: Models, Tasks, Methods and Tools. Chapman and Hall/CRCGoogle Scholar
- 15.Shivva V, Korell J, Tucker I, Duffull S (2013) An approach for identifiability of population pharmacokinetic-pharmacodynamic models. CPT: Pharmacometrics Syst Pharmacol 2(6):e49Google Scholar
- 17.Tikhonov AN, Goncharsky A, Stepanov VV, Yagola AG (1995) Numerical methods for the solution of ill-posed problems. Springer Science & Business Media, DordrechtGoogle Scholar
- 20.Wu L (2010) Mixed effects models for complex data. CRC Press, Boca RatonGoogle Scholar