Daniel F.B. Wright (presenting author) Co-authors: Qing Xi Ooi, Chihiro Hasegawa, Stephen B. Duffull)
(1) School of Pharmacy, University of Otago, Dunedin, New Zealand
Objectives:
In the absence of pharmacokinetic (PK) data, the time course of drug effects can be modelled using kinetic-pharmacodynamic (KPD) models. A typical KPD model will include an ‘effect compartment’-like kinetic model to describe the time course of the drug in the body combined with a full pharmacodynamic (PD) model for drug effects.
It is generally stated that KPD models can only be used in the setting of linear PK when the drug exhibits first-order elimination [1,2]. The prevailing assumption is therefore that the ‘kinetic’ model requires a rigid structure comprising a standard one-compartment model with intravenous bolus input and linear elimination. Generally, other structural forms for the ‘kinetic’ model are not considered.
Two parameterisations for KPD models have been proposed. Most commonly, the estimated elimination rate of the drug from the ‘kinetic’ compartment is used to drive the PD effect [3]. This involves substituting the C50 value in a standard Emaxmodel with EDK50, a composite of drug clearance and C50 (EDK50=CL*C50). An alternative parameterisation is to use the amount of drug in the body to drive the PD effect [4]. In this case, the C50 parameter is substituted with A50 representing the amount of drug in the body that gives half the maximal effect.
We propose that a KPD model using the EDK50 parameterisation will result in a poor model fit when the drug exhibits non-linear elimination, while the A50 method will allow a KPD model to be applied in this scenario. Therefore, the aim of this study is to compare the performance of a KPD model with EDK50 and A50 parameterisations in the setting of non-linear elimination.
Methods:
A stochastic simulation and estimation (SSE) study was conducted.
Reference datasets were simulated using a pharmacokinetic-pharmacodynamic model for a hypothetical drug using NONMEM (v.7,3). The PK model was a one-compartment model with an intravenous bolus input and a non-linear elimination. The time course of the biomarker for drug response was described using a turnover model with a zero-order input (Rin) and a first-order output (kout). The drug effects were assumed to result from the inhibition of Rin. Individual model parameters were assumed to be lognormally distributed. The residual error was described using a proportional error model.
The parameter values for generating the reference datasets were; Vmax=0.08mg/h, Km=1mg, V=10L, R_in=7units/h, kout=0.1h-1, Imax=1, C50=0.4mg/L. Between subject variance was set to 0.1 for all parameters and proportional error to 0.01.
500 datasets, each with 90 patients, were simulated with equal number of patients (n=30) receiving a single dose of 4mg, 8mg, or 16mg. For each patient, nine PD biomarker observations were made at 0, 6, 12, 24, 48, 72, 96, 120, and 144 hours.
Four KPD models were fitted to simulated PD biomarker data using NONMEM (v.7.3). All KPD models tested consisted of a one-compartment ‘kinetic’ model linked to a turnover model via an inhibitory Emax function. The following variations were considered; (1)A50 parameterisation with a linear ‘kinetic’ model (‘Lin-A50’), (2) EDK50 parameterisation with a linear ‘kinetic’ model (‘Lin-EDK50’), (3) A50 parameterisation with a non-linear ‘kinetic’ model (‘NonLin-A50’), (4) EDK50 parameterisation with a non-linear ‘kinetic’ model (‘NonLin-EDK50’).
The four KPD models were compared using the Akaike’s Information Criterion (AIC), visual predictive checks, goodness of fit plots, the relative bias in parameter estimates, and, the precision of parameter estimates (relative standard error [RSE]).
Results:
The KPD model parameterised using A50 with a non-linear ‘kinetic’ model (NonLin-A50) provided with best fit to the data as assessed by AIC, VPC and goodness of fit plots. Of the four competing KPD models, only NonLin-A50 was associated with unbiased parameter estimates. The model parameters for Lin-A50 and NonLin-A50 were estimated precisely with %RSE of less than 30% for fixed-effects and %RSE of less than 50% for random-effects parameters.
Conclusions:
In this work, a KPD model with a non-linear ‘kinetic’ structure and A50 parameterisation, provided unbiased and precise parameter estimates when fitted to data generated under a non-linear drug elimination model. In contrast to the prevailing assumption, our results suggest that KPD models can be used in the setting of non-linear elimination provided the A50 parameterisation is used.
References:
[1] Smolen VF. J Pharm Sci (1971) 60,354-65
[2] Gonzalez-Sales M et al. Br J Clin Pharmacol (2017) 83, 1240-51
[3] Jacqmin P et al. J Pharmacokinet Pharmacodyn (2007) 34, 57-85
[4] Gabrielsson J et al. Biopharm Drug Dispos (2000) 21, 41-52
Reference: PAGE 28 (2019) Abstr 8879 [www.page-meeting.org/?abstract=8879]
Poster: Methodology - Other topics