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J Pharmacokinet Pharmacodyn. 2016 Feb;43(1):111-22. doi: 10.1007/s10928-015-9459-4. Epub 2015 Dec 10.

What do we mean by identifiability in mixed effects models?

Author information

1
Inria Saclay, Palaiseau, France. Marc.Lavielle@inria.fr.
2
University of Manchester, Manchester, UK.

Abstract

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.

KEYWORDS:

Mixed effects model; Model identifiability; Parameter estimation; Pharmacokinetics; Practical identifiability; Structural identifiability

PMID:
26660913
DOI:
10.1007/s10928-015-9459-4
[Indexed for MEDLINE]

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