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Effect of Probability Distribution of the Response Variable in Optimal Experimental Design with Applications in Medicine

Author

Listed:
  • Sergio Pozuelo-Campos

    (Department of Mathematics, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
    These authors contributed equally to this work.)

  • Víctor Casero-Alonso

    (Department of Mathematics, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
    These authors contributed equally to this work.)

  • Mariano Amo-Salas

    (Department of Mathematics, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
    These authors contributed equally to this work.)

Abstract

In optimal experimental design theory it is usually assumed that the response variable follows a normal distribution with constant variance. However, some works assume other probability distributions based on additional information or practitioner’s prior experience. The main goal of this paper is to study the effect, in terms of efficiency, when misspecification in the probability distribution of the response variable occurs. The elemental information matrix, which includes information on the probability distribution of the response variable, provides a generalized Fisher information matrix. This study is performed from a practical perspective, comparing a normal distribution with the Poisson or gamma distribution. First, analytical results are obtained, including results for the linear quadratic model, and these are applied to some real illustrative examples. The nonlinear 4-parameter Hill model is next considered to study the influence of misspecification in a dose-response model. This analysis shows the behavior of the efficiency of the designs obtained in the presence of misspecification, by assuming heteroscedastic normal distributions with respect to the D-optimal designs for the gamma, or Poisson, distribution, as the true one.

Suggested Citation

  • Sergio Pozuelo-Campos & Víctor Casero-Alonso & Mariano Amo-Salas, 2021. "Effect of Probability Distribution of the Response Variable in Optimal Experimental Design with Applications in Medicine," Mathematics, MDPI, vol. 9(9), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1010-:d:546226
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    References listed on IDEAS

    as
    1. Idais, Osama, 2020. "Locally optimal designs for multivariate generalized linear models," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    2. Mariano Amo-Salas & Elvira Delgado-Márquez & Lenka Filová & Jesús López-Fidalgo, 2016. "Optimal designs for model discrimination and fitting for the flow of particles," Statistical Papers, Springer, vol. 57(4), pages 875-891, December.
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    Cited by:

    1. 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.

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