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Optimal designs for dose–response models with linear effects of covariates

Author

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  • Yu, Jun
  • Kong, Xiangshun
  • Ai, Mingyao
  • Tsui, Kwok Leung

Abstract

Personalized medicine is becoming more and more important nowadays since the efficacy of a certain medicine vary among different patients. This requires to combine the effects of the prognostic factors or covariates along with different dosages when planning a dose–response experiment. Statistically, this corresponds to the construction of optimal designs for estimating dose–response curves in the presence of covariates. Some characteristics of the optimal designs are derived in order to search such optimal designs efficiently, and an equivalence theorem of the locally ϕs-optimal designs is established accordingly. Computational issues are also studied and presented with theoretical backups. As applications of the above theories, the locally optimal designs are searched out in several situations. Some simulations reveal that the searched locally optimal designs are robust to the moderate misspecification of the prespecified parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:127:y:2018:i:c:p:217-228
    DOI: 10.1016/j.csda.2018.05.017
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    References listed on IDEAS

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    1. A. C. Atkinson, 2015. "Optimum designs for two treatments with unequal variances in the presence of covariates," Biometrika, Biometrika Trust, vol. 102(2), pages 494-499.
    2. 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.
    3. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    4. F. Bretz & J. C. Pinheiro & M. Branson, 2005. "Combining Multiple Comparisons and Modeling Techniques in Dose-Response Studies," Biometrics, The International Biometric Society, vol. 61(3), pages 738-748, September.
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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. Huang, Hengzhen & Chen, Xueping, 2021. "Compromise design for combination experiment of two drugs," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

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