IDEAS home Printed from https://ideas.repec.org/a/spr/jagbes/v25y2020i4d10.1007_s13253-020-00405-3.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13253-020-00405-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13253-020-00405-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lenka Filová & Mária Trnovská & Radoslav Harman, 2012. "Computing maximin efficient experimental designs using the methods of semidefinite programming," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 709-719, July.
    2. Pepelyshev, Andrey & Melas, Viatcheslav B. & Strigul, Nikolay & Dette, Holger, 2004. "Design of experiments for the Monod model : robust and efficient designs," Technical Reports 2004,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Dette, Holger & Kiss, Christine, 2007. "Optimal experimental designs for inverse quadratic regression models," Technical Reports 2007,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Chiara Tommasi & Juan M. Rodríguez-Díaz & Jesús F. López-Fidalgo, 2023. "An equivalence theorem for design optimality with respect to a multi-objective criterion," Statistical Papers, Springer, vol. 64(4), pages 1041-1056, August.
    5. Braess, Dietrich & Dette, Holger, 2004. "On the number of support points of maximin and Bayesian D-optimal designs in nonlinear regression models," Technical Reports 2004,78, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Wong, Weng Kee & Melas, Viatcheslav B. & Dette, Holger, 2004. "Optimal design for goodness-of-fit of the Michaelis-Menten enzyme kinetic function," Technical Reports 2004,24, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    7. Lo Huang, Mong-Na & Lin, Chun-Sui, 2006. "Minimax and maximin efficient designs for estimating the location-shift parameter of parallel models with dual responses," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 198-210, January.
    8. Dette, Holger & Biedermann, Stefanie & Pepelyshev, Andrey, 2004. "Some robust design strategies for percentile estimation in binary response models," Technical Reports 2004,19, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    9. Sheng Wu & Weng Kee Wong & Catherine M. Crespi, 2017. "Maximin optimal designs for cluster randomized trials," Biometrics, The International Biometric Society, vol. 73(3), pages 916-926, September.
    10. Dette, Holger & Kiss , Christine & Wong, Weng Kee, 2008. "Robustness of optimal designs for the Michaelis-Menten model under a variation of criteria," Technical Reports 2008,23, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    11. Biedermann, Stefanie & Dette, Holger & Pepelyshev, Andrey, 2005. "Optimal Discrimination Designs for Exponential Regression Models," Technical Reports 2005,22, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    12. García-Ródenas, Ricardo & García-García, José Carlos & López-Fidalgo, Jesús & Martín-Baos, José Ángel & Wong, Weng Kee, 2020. "A comparison of general-purpose optimization algorithms for finding optimal approximate experimental designs," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    13. Ul Hassan, Mahmood & Miller, Frank, 2021. "An exchange algorithm for optimal calibration of items in computerized achievement tests," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    14. Lei He & Rong-Xian Yue, 2022. "$$I_L$$ I L -optimal designs for regression models under the second-order least squares estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 53-66, January.
    15. Dette, Holger & Pepelyshev, Andrey, 2005. "Efficient experimental designs for sigmoidal growth models," Technical Reports 2005,13, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    16. Masoudi, Ehsan & Holling, Heinz & Wong, Weng Kee, 2017. "Application of imperialist competitive algorithm to find minimax and standardized maximin optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 330-345.
    17. Nadja Malevich & Christine H. Müller, 2019. "Optimal design of inspection times for interval censoring," Statistical Papers, Springer, vol. 60(2), pages 449-464, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jagbes:v:25:y:2020:i:4:d:10.1007_s13253-020-00405-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.