Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations

Handle URI:
http://hdl.handle.net/10754/599154
Title:
Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations
Authors:
Cao, Jiguo; Huang, Jianhua Z.; Wu, Hulin
Abstract:
Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.
Citation:
Cao J, Huang JZ, Wu H (2012) Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations. Journal of Computational and Graphical Statistics 21: 42–56. Available: http://dx.doi.org/10.1198/jcgs.2011.10021.
Publisher:
Informa UK Limited
Journal:
Journal of Computational and Graphical Statistics
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
Jan-2012
DOI:
10.1198/jcgs.2011.10021
PubMed ID:
23155351
PubMed Central ID:
PMC3496750
Type:
Article
ISSN:
1061-8600; 1537-2715
Sponsors:
Cao's work was supported by a discovery grant from the Natural Science and Engineering Research Council of Canada (NSERC). Huang's research was partly supported by NCI (CA57030), NSF (DMS-0907170), and by Award No. KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST). Wu's work was partially supported by grants from NIH/NIAID.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorCao, Jiguoen
dc.contributor.authorHuang, Jianhua Z.en
dc.contributor.authorWu, Hulinen
dc.date.accessioned2016-02-25T13:53:53Zen
dc.date.available2016-02-25T13:53:53Zen
dc.date.issued2012-01en
dc.identifier.citationCao J, Huang JZ, Wu H (2012) Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations. Journal of Computational and Graphical Statistics 21: 42–56. Available: http://dx.doi.org/10.1198/jcgs.2011.10021.en
dc.identifier.issn1061-8600en
dc.identifier.issn1537-2715en
dc.identifier.pmid23155351en
dc.identifier.doi10.1198/jcgs.2011.10021en
dc.identifier.urihttp://hdl.handle.net/10754/599154en
dc.description.abstractOrdinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.en
dc.description.sponsorshipCao's work was supported by a discovery grant from the Natural Science and Engineering Research Council of Canada (NSERC). Huang's research was partly supported by NCI (CA57030), NSF (DMS-0907170), and by Award No. KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST). Wu's work was partially supported by grants from NIH/NIAID.en
dc.publisherInforma UK Limiteden
dc.subjectDynamic modelsen
dc.subjectFunction estimationen
dc.subjectPenalized splinesen
dc.titlePenalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equationsen
dc.typeArticleen
dc.identifier.journalJournal of Computational and Graphical Statisticsen
dc.identifier.pmcidPMC3496750en
dc.contributor.institutionDepartment of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, Canada V5A 1S6 ( jca76@sfu.ca ).en
kaust.grant.numberKUS-CI-016-04en
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