S.Y. Amy Cheung (1), James W. T. Yates (2), Leon Aarons (3)
(1) Clinical Pharmacometrics, Clinical Pharmacology Science, AstraZeneca R&D Alderley Park, UK, (2) Oncology innovative medicines DMPK, AstraZeneca R&D Alderley Park, UK, (3) School of Pharmacy and Pharmaceutical Sciences, The University of Manchester, Oxford Road, Manchester, M13 9PT, United Kingdom
Background and Objectives: Structural identifiability is the property of whether an experiment can uniquely identify the unknown model parameters. The usefulness of incorporation of parallel pharmacokinetics experiments as a formal model structure for validation using structural identifiability has previously been discussed [1-3]. Also, the parallel methodology and the implication to the structural identifiability have been illustrated through a number of examples ranging from a basic one compartmental model to a mechanistic parent-metabolite model [4]. The previous focus of the development of the parallel methodology was to understand the impact and relationship of the perturbation of individual unknown parameters, due to changes in experimental conditions and the preservation of mutual parameters in between experiments to the identifiability status of the model. The objective of the present work was to develop new strategies whereby models are rendered globally identifiable by considering other types of perturbation to the model parameters via the parallel experiments.
Methods: The ‘same' experiment may sometimes be carried out several times on a system, in which it can be assumed a priori that some, but not all, of its rate constants change between experiments. Such a situation might arise in population PK experiments where there are covariate effects. The models representing each experimental observation thus share some common rate constant values depending on the dosing method and physiological nature of the model. This forms a much more constrained structure, encapsulates more information of the system and still can be readily analysed. The extended methodology is applied to a number of examples, including classic compartmental models and a series of mechanistic compartmental models to understand the impact of on identifiability status
Results: It is shown that by considering parallel experimental strategies, including the covariates effect perturbation, individually unidentifiable or locally identifiable models, in many cases are rendered uniquely identifiable.
Conclusions: A formulation has been presented that places the concept of parallel experiment in the context of a single constrained model structure. Incorporation of prior knowledge into parallel experiment model structures with constrained parameterization allows sufficient information to be present in the input-output behaviour to give unique parameter estimates. The results show that the parallel experiment strategy can be very powerful in providing globally uniquely identifiable models.
References:
[1] Bellman R. and Astrom, K. J. (1970) On Structural identifiability, Mathematical Biosciences. 7 329-339
[2] Cheung, S. Y. A., Yates, J. W. T., Aarons, L., (2006) Strucutural identifiability of parallel pharmacokinetic experiments as constrained systems: Proceedings of the 6th IFAC Symposium on Modeling and Control in Biomedical Systems held at Reims Congress Center, France
[3] Cheung, S.Y.A., Yates, J. W. T., Aarons, L., Rostami-Hodjegan, A., Structural identifiability of parallel pharmacokinetic experiments as constrained systems. PAGE 20 (2011) Abstr 2074 [www.page-meeting.org/?abstract=2074]
[4] Moghadamnia, A. A., Rostami-Hodjegan, A., Abudl-Manap, R., Wright, C. E., Morice, A. H. and Tucker, G. T., (2003) Physiologically based modelling of inhibition of metabolism and assessment of the relative potency of drug and metabolite: dextromethorphan vs dextrophan using quinidine inhibition. Bristish Journal of Clinical Pharmacology. 56: 57-67
Reference: PAGE 21 () Abstr 2496 [www.page-meeting.org/?abstract=2496]
Poster: Model evaluation