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Saddle-Reset for Robust Parameter Estimation and Identifiability Analysis of Nonlinear Mixed Effects Models
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.ORCID iD: 0000-0002-2676-5912
Pharmacometrics R&D, ICON CLINICAL RESEARCH LLC, Gaithersburg, Maryland, USA.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.ORCID iD: 0000-0002-5881-2023
2020 (English)In: AAPS Journal, E-ISSN 1550-7416, Vol. 22, no 4, article id 90Article in journal (Refereed) Published
Abstract [en]

Parameter estimation of a nonlinear model based on maximizing the likelihood using gradient-based numerical optimization methods can often fail due to premature termination of the optimization algorithm. One reason for such failure is that these numerical optimization methods cannot distinguish between the minimum, maximum, and a saddle point; hence, the parameters found by these optimization algorithms can possibly be in any of these three stationary points on the likelihood surface. We have found that for maximization of the likelihood for nonlinear mixed effects models used in pharmaceutical development, the optimization algorithm Broyden-Fletcher-Goldfarb-Shanno (BFGS) often terminates in saddle points, and we propose an algorithm, saddle-reset, to avoid the termination at saddle points, based on the second partial derivative test. In this algorithm, we use the approximated Hessian matrix at the point where BFGS terminates, perturb the point in the direction of the eigenvector associated with the lowest eigenvalue, and restart the BFGS algorithm. We have implemented this algorithm in industry standard software for nonlinear mixed effects modeling (NONMEM, version 7.4 and up) and showed that it can be used to avoid termination of parameter estimation at saddle points, as well as unveil practical parameter non-identifiability. We demonstrate this using four published pharmacometric models and two models specifically designed to be practically non-identifiable.

Place, publisher, year, edition, pages
2020. Vol. 22, no 4, article id 90
Keywords [en]
NLME, estimation methods, parameter estimation, pharmacometrics, practical identifiability
National Category
Pharmaceutical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-419009DOI: 10.1208/s12248-020-00471-yISI: 000545830800001PubMedID: 32617704OAI: oai:DiVA.org:uu-419009DiVA, id: diva2:1464927
Available from: 2020-09-08 Created: 2020-09-08 Last updated: 2023-12-17Bibliographically approved
In thesis
1. Garnishing the smorgasbord of pharmacometric methods
Open this publication in new window or tab >>Garnishing the smorgasbord of pharmacometric methods
2024 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The smorgasbord of methods that we use within the field of pharmacometrics has developed steadily over several decades and is now a well-laid-out buffet. This thesis adds some garnish to the table in the form of small improvements to the handling of certain problems.

The first problem tackled by the thesis was the challenge of saddle points and local non-identifiability when estimating pharmacometric model parameters. Substituting the common method of randomly perturbing the initial parameter estimates with one saddle-reset step enhances the accuracy of maximum likelihood estimates by overcoming saddle points parameter values, a common issue in nonlinear mixed-effects models. This algorithm, as implemented in the NONMEM software, was applied to various identifiable and nonidentifiable pharmacometric models, showing improved performance over traditional methods.

Part of the thesis was dedicated to the development of a paediatric pharmacokinetic model for ethionamide, a drug used in treating multidrug-resistant tuberculosis. The resulting model was then used to simulate drug exposure under different dosing regimens, a new dosing regimen for children was proposed. The developed model, and therefore the proposed paediatric dosing regimen, considers factors like maturation of pharmacokinetic pathways and, administration by nasogastric tube, and concurrent rifampicin treatment. The regimen, with some modifications, was adopted in the 2022 update to the World Health Organization operational handbook on tuberculosis.

Finally, the thesis explored novel model-integrated evidence (MIE) approaches for bioequivalence (BE) determination. Such methods could offer more robust alternatives to standard BE approached using non-compartmental analysis (NCA). Model-based methods have been shown to be advantageous in sparse data situations, such as is found in studies of ophthalmic formulations, but have suffered from inflated type I error rates. MIE BE approaches using a single model or using model averaging were presented and shown to control type I error at the nominal level while demonstrating increased power in bioequivalence determination.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2024. p. 55
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 345
Keywords
pharmacometrics, pharmacokinetics, saddle points, nonidentifiability, modelling and simulation, tuberculosis, ethionamide, bioequivalence, model-integrated evidence
National Category
Pharmaceutical Sciences
Research subject
Pharmaceutical Science
Identifiers
urn:nbn:se:uu:diva-518178 (URN)978-91-513-1999-5 (ISBN)
Public defence
2024-02-16, BMC A1:107, Husargatan 3, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2024-01-25 Created: 2023-12-17 Last updated: 2024-01-25

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Bjugård Nyberg, HenrikHooker, Andrew C.Aoki, Yasunori

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