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A geometric characterization of optimal designs for regression models with correlated observations

Holland-Letz, Tim, Dette, Holger and Pepelyshev, Andrey ORCID: 2011. A geometric characterization of optimal designs for regression models with correlated observations. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73 (2) , pp. 239-252. 10.1111/j.1467-9868.2010.00757.x

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We consider the problem of optimal design of experiments for random-effects models, especially population models, where a small number of correlated observations can be taken on each individual, whereas the observations corresponding to different individuals are assumed to be uncorrelated. We focus on c-optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of Elfving from the case of uncorrelated data can be adapted to the problem of selecting optimal sets of observations for the n individual patients. The theory is demonstrated by finding optimal designs for a linear model with correlated observations and a non-linear random-effects population model, which is commonly used in pharmaco-kinetics.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: c-optimal design; Correlated observations; Elfving's theorem; Geometric characterization; Locally optimal design; Pharmaco-kinetic models; Random effects
Publisher: Wiley-Blackwell
ISSN: 1369-7412
Last Modified: 24 Oct 2022 11:42

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