Jiansong Yang & Peiming Ma
Clinical Pharmacology Modelling & Simulation, GlaxoSmithKline R&D China
Objectives: To develop diagnostic plots to aid model selection among the general model for target-mediated drug disposition [1] and its approximations, such as the quasi-equilibrium (QE, or rapid binding), quasi-steady-state (QSS) and Michaelis-Menten (MM) models[2,3].
Methods & Results:
Diagnostic plots for QSS/QE approximation
The QSS approximation assumes: kon∙R∙C-(koff+kmet)∙M=0 (1)
thus kon∙R∙C-(koff+kmet)∙M should be close to 0, and it should not lead to trends in the distribution in a plot of kon∙R∙C-(koff+kmet)∙M vs. time.
Eq. 1 is equivalent to Eq. 2 and Eq. 3.
M=Rtot ∙C/(Km+C) (2)
R=Rtot ∙Km/(Km+C) (3)
where Km=(koff+kmet)/kon is the Michaelis-Menten constant. Plotting observed M (or R) against predicted M (or R) should be around the line of identity, otherwise it suggests the assumption for QSS (i.e. Eq 1) is not valid.
Similarly, the QE approximation assumes: kon∙R∙C-koff∙M=0 (4)
thus kon∙R∙C-kmet∙M should be close to 0 and it should not lead to trends in the distribution in a plot of kon∙R∙C-koff∙M vs. time.
Diagnostic plot for the assumption that Rtot is constant
If Rtot is constant, QSS and QE models can be further simplified. The validity of the assumption needs to be checked by the Rtot vs. time plot. However, if Rtot is not measured, or it is measured but the data are quite noisy, a plot of observed Rfree% vs. predicted values from Eq. 5 (derived from Eq. 3) can help judging if the assumption of Rtot being constant is valid.
Rfree%=Km/(Km+C) (5)
Conclusions: The proposed diagnostic plots, together with conventional model diagnostic tools, should aid the model selection for drugs exhibiting TMDD.
References:
[1] Mager DE, Jusko WJ. General pharmacokinetic model for drugs exhibiting target-mediated drug disposition. J Pharmacokin Pharmacodyn (2001) 28(6):507-32.
[2] Gibiansky L, Gibiansky E, Kakkar T, Ma P. Approximations of the target-mediated drug disposition model and identifiability of model parameters. J Pharmacokin Pharmacodyn (2008) 35(5):573-91.
[3] Ma P. Theoretical considerations of target-mediated drug disposition models: simplifications and approximations. Pharm Res (2012) 29(3):866-82.
Reference: PAGE 22 () Abstr 2734 [www.page-meeting.org/?abstract=2734]
Poster: Model evaluation