Lavezzi Silvia Maria (1), Zamuner Stefano (2), De Nicolao Giuseppe (1), Ma Peiming (3), Simeoni Monica (2)
(1) Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Pavia, Italy, (2) Clinical Pharmacology Modelling and Simulation, GlaxoSmithKline, UK, (3) Clinical Pharmacology Modelling and Simulation, GlaxoSmithKline, China
Objectives: In model building the study of structural (a priori) and practical (a posteriori) identifiability is a crucial step. A priori identifiability is a necessary but not sufficient condition for a posteriori identifiability [1]. In [2], four mPBPK-TMDD models (Full, A, A+B and A+B+C, including up to 3 quasi-steady-state approximations) have been presented and compared, detecting practical identifiability issues on the basis of preliminary fitting tests. The aims of the present work are to verify whether such identifiability issues originated from the lack of structural identifiability and investigate via a Monte Carlo (MC) approach the influence of noise on parameter estimates.
Methods: A local a priori identifiability analysis of the models was carried out via the Identifiability Analysis package [3,4]. Since this tool requires the model to be rational [3], the models were rationalized by adding a dummy state whenever needed. Availability of the following output measures was assumed: i) plasma drug concentration, ii) drug concentration both in plasma and in binding tissue, iii) plasma drug concentration together with target concentration in binding tissue. The input is an i.v. bolus of 1 or 5 mg/kg.
The steps of MC a posteriori identifiability analysis were: simulation of different datasets in R 3.1.2, identification of the models in NONMEM 7.3, study of the distribution of estimates and concentration profiles.
Results: A priori identifiability could be assessed in three models. Full Model and Model A were found to be a priori identifiable for every output choice (i,ii,iii). Model A+B is a priori identifiable only with the output choice iii); in cases i) and ii) kdeg and kss are the non-identifiable parameters. As for MC analysis, conditional weighted residuals and goodness of fit plots did not show any significant trend; a ranking of the parameters based on RMSE quantified the sensitivity of parameter estimates to noise in the data, with some CV% exceeding 150.
Conclusions: A priori and a posteriori identifiability of four mPBPK-TMDD models [2] were investigated. For the Full Model and Model A, it was found that practical identifiability issues previously detected are not due to a lack of structural identifiability. The MC analysis confirms that all the four models have practical identifiability issues. Further development may concern the potential benefits ensuing from adopting optimal design methods.
References:
[1] Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods. O.-T. Chis, J.R. Banga, E. Balsa-Canto. PLoS ONE, 6 (11), 1-16, 2011.
[2] Integrating Target Mediated Drug Disposition (TMDD) into a minimal physiologically based modelling framework: evaluation of different quasi-steady-state approximations. E. Mezzalana, S.M. Lavezzi, S. Zamuner, G. De Nicolao, P. Ma, M. Simeoni. PAGE 24 (2015) Abstr 3598
[3] An Efficient Method for Structural Identifiability Analysis of Large Dynamic Systems. J. Karlsson, M. Anguelova, M. Jirstrand. 16th IFAC Symposium on System Identification, 16 (1), 941-946, 2012.
[4] Minimal output sets for identifiability. M. Anguelova, J. Karlsson, M. Jirstrand. Math Biosci, 239, 139-153, 2012
Reference: PAGE 25 () Abstr 5876 [www.page-meeting.org/?abstract=5876]
Poster: Methodology - Model Evaluation