A.M. (Marinda) van der Kuijl (1), E.H.J. Krekels (1), C.A.J. Knibbe (1,2), J.G.C. van Hasselt (1)
(1) Division of Systems Pharmacology and Pharmacy, Leiden Academic Centre for Drug Research, Leiden University, Leiden, the Netherlands (2) Department of Clinical Pharmacy, St. Antonius Hospital, Nieuwegein, The Netherlands
Introduction
Quantitative system pharmacology (QSP) models are applied with increasing frequency to describe and study complex biological systems including drug effects characterisation1,2. Identifiability of drug- and system-related parameters is important when creating a QSP model3,4. We hypothesize that including non-linear motives, such as a precursor or feedback loops, may result in challenges with identifying a drug effect and/or leads to more bias in the parameter estimates. This project is investigating practical identifiability of drug effects and the influence on estimated parameter values, with the objective to determine (1) drug effect identifiability on the correct system-parameter of turn-over models and (2) potential bias in the parameter estimates.
Methods
Model definition
Two turn-over model structures were defined, one without a precursor, the other with a precursor. For each structure, variants were created by including the drug effect on different rate constants. For both model structures two variants were created in which the drug effect was placed on the production rate (kin) or degradation rate (kout) of the response measure, respectively. For the model structure with the precursor, a third variant was defined in which the drug effect is placed on the production rate of the precursor (kin,pre). In all variants, the same 1-compartment pharmacokinetic model was used.
Simulation study design
Stochastic simulation and estimation was performed for each model variant, with the drug effect on one parameter (the true model). The true model was used to generate a simulated dataset with one baseline observation and eight observations up to 48 hours after dose. The observation times were selected to yield optimal visual coverage of the PD profile with measurements obtained during feasible hours. The simulated dataset was fitted to each model variant, so both to the true model and the alternate model(s) with drug effect placed on different parameters.
Evaluation
The model variant with the lowest objective function value (OFV) and more than 3.84 difference in OFV compared to all other model variants, was referred to as the selected model. In case there was less than 3.84 points difference the sample was deemed inconclusive. 50 datasets were simulated and re-estimated, after which the percentage of samples in which the true model was selected, was calculated. Of the correctly selected models, Prediction Error (PE) and relative Bias (rBias) was determined for each structural parameter.
Results
Correct identification
In 24% of the samples, the true model was selected for the turn-over model with the drug effect on kin, while 74% of the samples resulted in inconclusive model selection. In one sample (2%), the alternative model variant was selected as the true model. The true model being the model with the drug effect on kout, was correctly selected in 100% of the samples. The true model being the model with the precursor was also correctly selected in 100% of the samples, for all variants. Considering the chosen sampling design and parameter values, for the true model being a turn-over model with a drug effect placed on kin, drug effect identification is not always possible. However, for the same model structure with a drug effect placed on kout, this was always possible. The addition of the precursor had no influence on drug effect identification.
PE and rBias
For all variants of both models, the variance of PE was larger for the rate constants (mean interquartile range (mIQR) of 19%) than for the drug effect parameters (mIQR of 10%). This indicates that the estimation of structural parameters is less precise than the estimation of the drug effect. Some extreme outliers of PE were seen on the drug effect parameters of the turn-over model with precursor with its drug effect on kin. For most variants of both models, the bias was not substantial (< 6%), however for the variant of the turn-over model with precursor with its drug effect on kin,pre, a substantial bias (~13%) in kin,pre and kout was seen.
Conclusions
Based on the current results with dense data and relatively simple model structures, the drug effect on the turn-over model was not always identifiable, while the drug effect on the turn-over model with precursor was always identifiable. Next steps in this project is to study other turn-over model structures with more complexity (e.g. with feedback loops) to further investigate this relationship.
References:
[1] Sayama H, Nagasaka Y, Tabata K. [An introduction to QSP modeling for pharmacologists]. Nihon Yakurigaku Zasshi. 2019;154(3):143-150.
[2] Yates JWT, Jones RDO, Walker M, Cheung SYA. Structural identifiability and indistinguishability of compartmental models. Expert Opinion on Drug Metabolism & Toxicology. 2009;5(3):295-302.
[3] Iliadis A. Structural identifiability and sensitivity. J Pharmacokinet Pharmacodyn. 2019;46(2):127-135.
[4] Siripuram VK, Wright DFB, Barclay ML, Duffull SB. Deterministic identifiability of population pharmacokinetic and pharmacokinetic-pharmacodynamic models. J Pharmacokinet Pharmacodyn. 2017;44(5):415-423.
Reference: PAGE 30 (2022) Abstr 10045 [www.page-meeting.org/?abstract=10045]
Poster: Methodology - Other topics