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Article

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

Department of Mathematics, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
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This paper is an extended version of a published conference paper as a part of the proceedings of the 35th International Workshop on Statistical Modeling (IWSM), Bilbao, Spain, 19–24 July 2020.
These authors contributed equally to this work.
Academic Editor: Lev Klebanov
Mathematics 2021, 9(9), 1010; https://doi.org/10.3390/math9091010
Received: 18 March 2021 / Revised: 22 April 2021 / Accepted: 27 April 2021 / Published: 29 April 2021
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. View Full-Text
Keywords: elemental information matrix; gamma distribution; poisson distribution; D-optimization; misspecification elemental information matrix; gamma distribution; poisson distribution; D-optimization; misspecification
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MDPI and ACS Style

Pozuelo-Campos, S.; Casero-Alonso, V.; Amo-Salas, M. Effect of Probability Distribution of the Response Variable in Optimal Experimental Design with Applications in Medicine. Mathematics 2021, 9, 1010. https://doi.org/10.3390/math9091010

AMA Style

Pozuelo-Campos S, Casero-Alonso V, Amo-Salas M. Effect of Probability Distribution of the Response Variable in Optimal Experimental Design with Applications in Medicine. Mathematics. 2021; 9(9):1010. https://doi.org/10.3390/math9091010

Chicago/Turabian Style

Pozuelo-Campos, Sergio, Víctor Casero-Alonso, and Mariano Amo-Salas. 2021. "Effect of Probability Distribution of the Response Variable in Optimal Experimental Design with Applications in Medicine" Mathematics 9, no. 9: 1010. https://doi.org/10.3390/math9091010

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