ADVAN-style analytical solutions for common pharmacokinetic models

Abuhelwa, Ahmad Y.; Foster, David J. R.; Upton, Richard N.

doi:10.1016/j.vascn.2015.03.004

Cited by 9 publications

(1 citation statement)

References 4 publications

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“…The authors thank Ahmad Y. Abuhelwa and Richard N. Upton (University of South Australia, Adelaide) for providing the NONMEM ADVAN‐style R implementation of typical PK models that is used in the software provided online.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Confidence and Prediction Intervals for Pharmacometric Models

Kümmel¹,

Bonate

Dingemanse

et al. 2018

CPT Pharmacom & Syst Pharma

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Supporting decision making in drug development is a key purpose of pharmacometric models. Pharmacokinetic models predict exposures under alternative posologies or in different populations. Pharmacodynamic models predict drug effects based on exposure to drug, disease, or other patient characteristics. Estimation uncertainty is commonly reported for model parameters; however, prediction uncertainty is the key quantity for clinical decision making. This tutorial reviews confidence and prediction intervals with associated calculation methods, encouraging pharmacometricians to report these routinely.

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Section: Acknowledgmentsmentioning

confidence: 99%

Confidence and Prediction Intervals for Pharmacometric Models

Kümmel¹,

Bonate

Dingemanse

et al. 2018

CPT Pharmacom & Syst Pharma

View full text Add to dashboard Cite

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Exploring inductive linearization for pharmacokinetic–pharmacodynamic systems of nonlinear ordinary differential equations

Hasegawa

Duffull

2017

J Pharmacokinet Pharmacodyn

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Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

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