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Compound Optimum Designs for Clinical Trials in Personalized Medicine

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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

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

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