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Optimal designs for the emax, log-linear and exponential models

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  • H. Dette
  • C. Kiss
  • M. Bevanda
  • F. Bretz

Abstract

We derive locally D- and ED p -optimal designs for the exponential, log-linear and three-parameter emax models. For each model the locally D- and ED p -optimal designs are supported at the same set of points, while the corresponding weights are different. This indicates that for a given model, D-optimal designs are efficient for estimating the smallest dose that achieves 100p% of the maximum effect in the observed dose range. Conversely, ED p -optimal designs also yield good D-efficiencies. We illustrate the results using several examples and demonstrate that locally D- and ED p -optimal designs for the emax, log-linear and exponential models are relatively robust with respect to misspecification of the model parameters. Copyright 2010, Oxford University Press.

Suggested Citation

  • H. Dette & C. Kiss & M. Bevanda & F. Bretz, 2010. "Optimal designs for the emax, log-linear and exponential models," Biometrika, Biometrika Trust, vol. 97(2), pages 513-518.
    • Handle: RePEc:oup:biomet:v:97:y:2010:i:2:p:513-518
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    File URL: http://hdl.handle.net/10.1093/biomet/asq020
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    Cited by:

    1. Yu, Jun & Meng, Xiran & Wang, Yaping, 2023. "Optimal designs for semi-parametric dose-response models under random contamination," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    2. Younan Chen & Michael Fries & Sergei Leonov, 2023. "Longitudinal model for a dose-finding study for a rare disease treatment," Statistical Papers, Springer, vol. 64(4), pages 1343-1360, August.
    3. Yu, Jun & Kong, Xiangshun & Ai, Mingyao & Tsui, Kwok Leung, 2018. "Optimal designs for dose–response models with linear effects of covariates," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 217-228.
    4. 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.
    5. Kira Alhorn & Holger Dette & Kirsten Schorning, 2021. "Optimal Designs for Model Averaging in non-nested Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 745-778, August.

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