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Preconditioning of Nonlinear Mixed Effects Models for Stabilisation of Variance-Covariance Matrix Computations
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics. Department of Mathematics, Uppsala University. (Pharmacometrics Group)
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. (Pharmacometrics Group)
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. (Pharmacometrics Group)
2016 (English)In: AAPS Journal, ISSN 1550-7416, E-ISSN 1550-7416, Vol. 18, no 2, 505-518 p.Article in journal (Refereed) Published
Abstract [en]

As the importance of pharmacometric analysis increases, more and more complex mathematical models are introduced and computational error resulting from computational instability starts to become a bottleneck in the analysis. We propose a preconditioning method for non-linear mixed effects models used in pharmacometric analyses to stabilise the computation of the variance-covariance matrix. Roughly speaking, the method reparameterises the model with a linear combination of the original model parameters so that the Hessian matrix of the likelihood of the reparameterised model becomes close to an identity matrix. This approach will reduce the influence of computational error, for example rounding error, to the final computational result. We present numerical experiments demonstrating that the stabilisation of the computation using the proposed method can recover failed variance-covariance matrix computations, and reveal non-identifiability of the model parameters.

Place, publisher, year, edition, pages
2016. Vol. 18, no 2, 505-518 p.
Keyword [en]
computational stability; identifiability; non-linear mixed effects model; parameter estimation uncertainty; preconditioning
National Category
Pharmaceutical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-276488DOI: 10.1208/s12248-016-9866-5ISI: 000375460900003PubMedID: 26857397OAI: oai:DiVA.org:uu-276488DiVA: diva2:903182
Available from: 2016-02-15 Created: 2016-02-15 Last updated: 2018-01-10Bibliographically approved

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Aoki, YasunoriNordgren, RikardHooker, Andrew C.

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