James W.T. Yates (1), S.Y. Amy Cheung (2) and Neil D. Evans (3)
(1) DMPK, Oncology, Innovative Medicines and Early Development, AstraZeneca, Cambridge, UK, (2) Quantitative Clinical Pharmacology, Early Clinical Development, Innovative Medicines and Early Development, AstraZeneca, Cambridge, UK, (3) School of Engineering, University of Warwick, Coventry, UK
Objectives: Structural identifiability is an often overlooked, but essential, prerequisite to the experimental design stage. The property of identifiability arises in the validation process because experiments for data collection give rise to an input-output behaviour for the model, which defines how external inputs (perturbations) arise in the model and what functions of the model variables correspond to directly measured species. Structural identifiability considers the uniqueness of the unknown parameters with respect to this input-output behaviour, and is fundamental since estimates for unidentifiable parameters are effectively meaningless. Moreover, the presence of unidentifiable parameters can result in errors in predictions or inferences made from the model. The application of structural identifiability analysis to models of myelosuppression is used to demonstrate the importance of its consideration. Secondly, the consistency of system parameter estimates for the Friberg et al paper was investigated via a meta-analysis of the literature.
Methods: The model first published by Friberg et al [1] and 3 modifications, Bender et al [2], Mangas-sanjuan et al [3] and Quartino et al [4], were investigated. Structural identifiability analysis was carried out using the observable normal form approach [5] and the IdentifiabilityAnalysis [6] package in Mathematica. Symbolic computation was carried out in Mathematica and Maple. Consistency of parameter estimates for the Friberg et al model were visualised using Galbraith plots [7]. In this plot the reported parameter estimate divided by the reported standard error (SE) is plotted on the ordinate versus 1/SE. This plot serves two purposes: Firstly, if estimates are consistent given their precision, points will lie on a straight line. Secondly, the estimates with greater precision will aggregate away from the origin and so the slope of the regression will be the mean of the parameter estimates weighted by their precision.
Results: Assuming that the model is started at baseline from pre-treatment steady state, all four models are structurally globally identifiable under certain conditions. For Friberg et al this is under the assumption that the rates of proliferation and maturation are numerically equal (kprol = ktr). This is also the same for Bender et al. For Mangas-sanjuan et al the model is similarly structurally globally identifiable for the case kprol = Fprol ktr = Fprol kcirc, where Fprol is the fraction of proliferating cells entering maturation. Finally, if GCSF concentrations are not observed then Quartino et al is structurally globally identifiable only by reparametrizing the model so that the G-CSF state has a steady state of 1. The meta-analysis of reported parameter estimates for the Friberg et al model demonstrates striking consistency of estimates across reports in the literature (mean maturation time of 109 hours, baseline circulating neutrophils of 5.15×109/L and feedback power of 0.148) and demonstrates the application of a structurally identifiable model that can separate system and drug specific effects.
Conclusions: It is shown that, under certain assumptions, these models are structural identifiable and so drug and system specific parameters can truly be separated. Further it is shown via a meta-analysis of the literature that because of this the reported system parameter estimates for the “Friberg” or “Uppsala” model are consistent in the literature.
References:
[1] L. E. Friberg et al J. Clin. Oncol., 20: 4713–4721, 2002.
[2] B. C. Bender et al , Cancer Chemotherapy and Pharmacology, 70: pp. 591–601, 2012.
[3] V. Mangas-Sanjuan et al J. Pharmacol. Exp. Ther., 354:55–64, 2015.
[4] A. L. Quartino et al Pharm Res 31:3390-3403, 2014.
[5] Evans, N.D. et al Automatica, 49:48–57, 2013.
[6] Karlsson, J., Jirstrand, M. In: Proceedings of the 16th IFAC Symposium on System Identification. 2012.
[7] R. Galbraith Technometrics, 30: 271–281, 1988.
Reference: PAGE 27 (2018) Abstr 8593 [www.page-meeting.org/?abstract=8593]
Poster: Methodology - Model Evaluation