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Optimal Design of Experiments for Hybrid Nonlinear Models, with Applications to Extended Michaelis–Menten Kinetics

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  • Yuanzhi Huang

    (Newcastle University)

  • Steven G. Gilmour

    (King’s College London, Strand)

  • Kalliopi Mylona

    (King’s College London, Strand)

  • Peter Goos

    (KU Leuven)

Abstract

Biochemical mechanism studies often assume statistical models derived from Michaelis–Menten kinetics, which are used to approximate initial reaction rate data given the concentration level of a single substrate. In experiments dealing with industrial applications, however, there are typically a wide range of kinetic profiles where more than one factor is controlled. We focus on optimal design of such experiments requiring the use of multifactor hybrid nonlinear models, which presents a considerable computational challenge. We examine three different candidate models and search for tailor-made D- or weighted-A-optimal designs that can ensure the efficiency of nonlinear least squares estimation. We also study a compound design criterion for discriminating between two candidate models, which we recommend for design of advanced kinetic studies. Supplementary materials accompanying this paper appear on-line

Suggested Citation

  • Yuanzhi Huang & Steven G. Gilmour & Kalliopi Mylona & Peter Goos, 2020. "Optimal Design of Experiments for Hybrid Nonlinear Models, with Applications to Extended Michaelis–Menten Kinetics," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 601-616, December.
    • Handle: RePEc:spr:jagbes:v:25:y:2020:i:4:d:10.1007_s13253-020-00405-3
    DOI: 10.1007/s13253-020-00405-3
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    References listed on IDEAS

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    1. Barbara Bogacka & Mahbub A. H. M. Latif & Steven G. Gilmour & Kuresh Youdim, 2017. "Optimum designs for non-linear mixed effects models in the presence of covariates," Biometrics, The International Biometric Society, vol. 73(3), pages 927-937, September.
    2. Yuanzhi Huang & Steven G. Gilmour & Kalliopi Mylona & Peter Goos, 2019. "Optimal design of experiments for non‐linear response surface models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(3), pages 623-640, April.
    3. Dette, Holger & Biedermann, Stefanie, 2003. "Robust and Efficient Designs for the Michaelis-Menten Model," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 679-686, January.
    4. Steven G. Gilmour & Luzia A. Trinca, 2012. "Bayesian L‐optimal exact design of experiments for biological kinetic models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(2), pages 237-251, March.
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    Cited by:

    1. Elham Yousefi & Werner G. Müller, 2023. "Impact of the Error Structure on the Design and Analysis of Enzyme Kinetic Models," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 31-56, April.
    2. Hans-Peter Piepho & Robert J. Tempelman & Emlyn R. Williams, 2020. "Guest Editors’ Introduction to the Special Issue on “Recent Advances in Design and Analysis of Experiments and Observational Studies in Agriculture”," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 453-456, December.
    3. Chen, Ping-Yang & Chen, Ray-Bing & Chen, Yu-Shi & Wong, Weng Kee, 2023. "Numerical Methods for Finding A-optimal Designs Analytically," Econometrics and Statistics, Elsevier, vol. 28(C), pages 155-162.

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