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Optimal design for goodness-of-fit of the Michaelis-Menten enzyme kinetic function

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  • Wong, Weng Kee
  • Melas, Viatcheslav B.
  • Dette, Holger

Abstract

We construct efficient designs for the Michaelis-Menten enzyme kinetic model capable of checking model assumption. An extended model, called EMAX model is also considered for this purpose. This model is widely used in pharmacokinetics and reduces to the Michaelis- Menten model for a specific choice of the parameter setting. Our strategy is to find efficient designs for estimating the parameters in the EMAX model and at the same time test the validity of the Michaelis-Menten model against the EMAX model by maximizing a minimum of the D- or D1-efficiencies taken over a range of values for the nonlinear parameters. In addition, we show that the designs obtained from maximizing the D-efficiencies are (i) efficient for estimating parameters in the EMAX model or the Michaelis-Menten model, (ii) efficient for testing the Michaelis-Menten model against the EMAX model and (iii) robust with respect to misspecification of the unknown parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:sfb475:200424
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    References listed on IDEAS

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    1. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
    2. Dette, Holger & Wong, Weng Kee, 1999. "E-optimal designs for the Michaelis-Menten model," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 405-408, October.
    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. Holger Dette & Viatcheslav B. Melas & Andrey Pepelyshev & Nikolai Strigul, 2003. "Efficient design of experiments in the Monod model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 725-742, August.
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    1. Melas, Viatcheslav B., 2004. "On the functional approach to optimal designs for nonlinear models," Technical Reports 2004,13, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. 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.
    3. 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.

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