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      Delay differential equations based models in NONMEM.

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          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.

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          Author and article information

          Journal
          J Pharmacokinet Pharmacodyn
          Journal of pharmacokinetics and pharmacodynamics
          Springer Science and Business Media LLC
          1573-8744
          1567-567X
          Dec 2021
          : 48
          : 6
          Affiliations
          [1 ] School of Pharmacy, Faculty of Medicine, The Chinese University of Hong Kong, Shatin, Hong Kong.
          [2 ] Pharmacometrics R&D, ICON Clinical Research LLC, Gaithersburg, MD, USA.
          [3 ] Pediatric Pharmacology and Pharmacometrics, University Children's Hospital Basel UKBB, University of Basel, Basel, Switzerland.
          [4 ] Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany.
          [5 ] Janssen R&D, a Division of Janssen Pharmaceutica NV, Beerse, Belgium.
          [6 ] Department of Pharmaceutical Sciences, The State University of New York at Buffalo, Buffalo, NY, USA. wk@buffalo.edu.
          Article
          10.1007/s10928-021-09770-z
          10.1007/s10928-021-09770-z
          34302262
          fbb03e10-cc14-4ef4-8074-c5a50e3e09e1
          History

          Stiff differential equations,DDE solver,Delay differential equations,NONMEM

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