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Compound Optimum Designs for Clinical Trials in Personalized Medicine

Author

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  • Belmiro P. M. Duarte

    (Instituto Politécnico de Coimbra, Instituto Superior de Engenharia de Coimbra, Rua Pedro Nunes, 3030-199 Coimbra, Portugal
    INESC Coimbra—Instituto de Engenharia de Sistemas e Computadores de Coimbra, Universidade de Coimbra, Rua Sílvio Lima—Pólo II, 3030-790 Coimbra, Portugal
    Research Center for Chemical Engineering and Renewable Resources for Sustainability, Universidade de Coimbra, Rua Sílvio Lima—Pólo II, 3030-790 Coimbra, Portugal)

  • Anthony C. Atkinson

    (Department of Statistics, London School of Economics, London WC2A 2AE, UK)

  • David Pedrosa

    (Department of Neurology, University Hospital Marburg, 35043 Marburg, Germany
    Centre of Brain, Mind and Behavior, Philipps-University Marburg, 35043 Marburg, Germany)

  • Marlena van Munster

    (Department of Neurology, University Hospital Marburg, 35043 Marburg, Germany)

Abstract

We consider optimal designs for clinical trials when response variance depends on treatment and covariates are included in the response model. These designs are generalizations of Neyman allocation, and commonly employed in personalized medicine where external covariates linearly affect the response. Very often, these designs aim at maximizing the amount of information gathered but fail to assure ethical requirements. We analyze compound optimal designs that maximize a criterion weighting the amount of information and the reward of allocating the patients to the most effective/least risky treatment. We develop a general representation for static (a priori) allocation and propose a semidefinite programming (SDP) formulation to support their numerical computation. This setup is extended assuming the variance and the parameters of the response of all treatments are unknown and an adaptive sequential optimal design scheme is implemented and used for demonstration. Purely information theoretic designs for the same allocation have been addressed elsewhere, and we use them to support the techniques applied to compound designs.

Suggested Citation

  • Belmiro P. M. Duarte & Anthony C. Atkinson & David Pedrosa & Marlena van Munster, 2024. "Compound Optimum Designs for Clinical Trials in Personalized Medicine," Mathematics, MDPI, vol. 12(19), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3007-:d:1486729
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    References listed on IDEAS

    as
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    3. 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.
    4. Dimitris Bertsimas & Mac Johnson & Nathan Kallus, 2015. "The Power of Optimization Over Randomization in Designing Experiments Involving Small Samples," Operations Research, INFORMS, vol. 63(4), pages 868-876, August.
    5. Alessandro Baldi Antognini & Alessandra Giovagnoli, 2010. "Compound optimal allocation for individual and collective ethics in binary clinical trials," Biometrika, Biometrika Trust, vol. 97(4), pages 935-946.
    6. 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.
    7. Jianhua Hu & Hongjian Zhu & Feifang Hu, 2015. "A Unified Family of Covariate-Adjusted Response-Adaptive Designs Based on Efficiency and Ethics," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 357-367, March.
    Full references (including those not matched with items on IDEAS)

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