Understanding Identifiability of random effects in mixed effects models

Aims: We discuss the question of model identifiability within the context of nonlinear mixed effects models and application to pharmacokinetic models.

Methods: 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.


Results: Essentially if the probabilistic models are different, even though the structural models are non-identifiable,  then they will lead to different likelihoods. This requires strong assumptions about the probabilistic models which may be difficult to validate in practice. The findings are supported through simulations.  


Conclusion: From a pharmacokinetic point of view it means that the differences between individuals can break the non-identifiability seen at the population level and this may allow better mechanistic understanding of the interindividual differences in pharmacokinetics. However, even if the models are identifiable at the individual level it may prove difficult to estimate the parameters of the model unless supported by good experimental design. A complete account of this research can be found in [1].



1. Lavielle M, Aarons L. What do we mean by identifiability in mixed effects models? J Pharmacokinet Pharmacodyn DOI 10.1007/s10928-015-9459-4 (2016).