Vittal Shivva (1), Stephen Duffull (1)
(1) School of Pharmacy, University of Otago, Dunedin, New Zealand
Objectives: PK and PKPD models are often complicated due to the inclusion of mechanistic elements to improve their predictive performance. In some circumstances they may be developed from systems models using formal methods of model order reduction. In all circumstances it is important to assess the identifiability of the model to ensure that it can be used for estimation purposes. Identifiability has been extensively studied and formal methods are available for fixed effects models. Recently, local identifiability analysis has been generalized to the mixed effects model framework [1]. The aim of this work is to explore the influence of parameterization of a simple nonlinear mixed effects model on the identifiability of the fixed and random effects parameters.
Methods: Local identifiability was established by generalising the principle that |J’J|=0 (where J is the Jacobian matrix and |.| signifies the determinant) for models that are not locally identifiable due to rank deficiency [2]. However, because of numerical issues with computation of the Fisher information matrix (FIM) for nonlinear mixed effects models the criteria for (practical) local identifiability was defined as the |FIM| monotonically approaches an asymptote as the residual variance approaches zero, for identifiable models [1].
In this work we consider two parameterisations of the simple one compartment first-order input-output model:
(i) {CL, V, ka, F, var(CL), var(V), var(ka), var(F), sigma2} and
(ii) {k, V, ka, F, var(k), var(V), var(ka), var(F), sigma2}
Results: For this simple model we see that: (1) F is not identifiable in either parameterisation, (2) var(F) is identifiable in parameterisation (i) but not in parameterisation (ii), (3) parameterisation (i) is identifiable if any one of F or CL or V are fixed, (4) parameterisation (ii) is only identifiable if both F or V and var(F) or var (V) are fixed.
Discussion: Even though identifiability of the fixed effects parameters for simple models is well known we see that identifiability of the associated variance of the random effects is not always obvious. Importantly we see that local identifiability is dependent on parameterisation.
References:
[1] Shivva et al CPT:PSP 2013,2(6):1-9; e49, doi:10.1038/psp.2013.25
[2] Jacquez et al Math Biosci 1985;77:201-227
Reference: PAGE 25 () Abstr 3697 [www.page-meeting.org/?abstract=3697]
Poster: Methodology - Other topics