## Delay differential equations based models in NONMEM

2021
##### Authors
Yan, Xiaoyu
Bauer, Robert
Pérez-Ruixo, Juan Jose
Krzyzanski, Wojciech
Journal article
Published
##### Published in
Journal of Pharmacokinetics and Pharmacodynamics ; 48 (2021), 6. - pp. 763-802. - Springer. - ISSN 1567-567X. - eISSN 1573-8744
##### Abstract
Delay differential equations (DDEs) are commonly used in pharmacometric models to describe delays present in pharmacokinetic and pharmacodynamic data analysis. Several DDE solvers have been implemented in NONMEM 7.5 for the first time. Two of them are based on algorithms already applied elsewhere, while others are extensions of existing ordinary differential equations (ODEs) solvers. The purpose of this tutorial is to introduce basic concepts underlying DDE based models and to show how they can be developed using NONMEM. The examples include previously published DDE models such as logistic growth, tumor growth inhibition, indirect response with precursor pool, rheumatoid arthritis, and erythropoiesis-stimulating agents. We evaluated the accuracy of NONMEM DDE solvers, their ability to handle stiff problems, and their performance in parameter estimation using both first-order conditional estimation (FOCE) and the expectation–maximization (EM) method. NONMEM control streams and excerpts from datasets are provided for all discussed examples. All DDE solvers provide accurate and precise solutions with the number of significant digits controlled by the error tolerance parameters. For estimation of population parameters, the EM method is more stable than FOCE regardless of the DDE solver.
510 Mathematics
##### Cite This
ISO 690YAN, Xiaoyu, Robert BAUER, Gilbert KOCH, Johannes SCHROPP, Juan Jose PÉREZ-RUIXO, Wojciech KRZYZANSKI, 2021. Delay differential equations based models in NONMEM. In: Journal of Pharmacokinetics and Pharmacodynamics. Springer. 48(6), pp. 763-802. ISSN 1567-567X. eISSN 1573-8744. Available under: doi: 10.1007/s10928-021-09770-z
BibTex
@article{Yan2021-12Delay-54527,
year={2021},
doi={10.1007/s10928-021-09770-z},
title={Delay differential equations based models in NONMEM},
number={6},
volume={48},
issn={1567-567X},
journal={Journal of Pharmacokinetics and Pharmacodynamics},
pages={763--802},
author={Yan, Xiaoyu and Bauer, Robert and Koch, Gilbert and Schropp, Johannes and Pérez-Ruixo, Juan Jose and Krzyzanski, Wojciech}
}

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<dcterms:abstract xml:lang="eng">Delay differential equations (DDEs) are commonly used in pharmacometric models to describe delays present in pharmacokinetic and pharmacodynamic data analysis. Several DDE solvers have been implemented in NONMEM 7.5 for the first time. Two of them are based on algorithms already applied elsewhere, while others are extensions of existing ordinary differential equations (ODEs) solvers. The purpose of this tutorial is to introduce basic concepts underlying DDE based models and to show how they can be developed using NONMEM. The examples include previously published DDE models such as logistic growth, tumor growth inhibition, indirect response with precursor pool, rheumatoid arthritis, and erythropoiesis-stimulating agents. We evaluated the accuracy of NONMEM DDE solvers, their ability to handle stiff problems, and their performance in parameter estimation using both first-order conditional estimation (FOCE) and the expectation–maximization (EM) method. NONMEM control streams and excerpts from datasets are provided for all discussed examples. All DDE solvers provide accurate and precise solutions with the number of significant digits controlled by the error tolerance parameters. For estimation of population parameters, the EM method is more stable than FOCE regardless of the DDE solver.</dcterms:abstract>
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Yes
Yes