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Theses

MODÉLISATION ET ANALYSE STATISTIQUE DES PLANS D'EXPÉRIENCE SÉQUENTIELS

Abstract : Two distinct sections constitute this thesis. The first part concerns the study of sequential experimental designs applied to clinical trials. We study the modelling of these designs. We develop a generalization of the \ play-the-winner” rule. Theoretical and numerical results show that these designs perform better than the designs recently developed, in the framework of the Freedman's urn models, which are a generalization of the \randomized play-the-winner ” rule or of a modified version of this rule. In the second part, we develop inference methods for analyszing the data from the considered sequential designs. In the case of two treatments, and for \play-the-winner” rule, we made explicit the sampling distributions and their factorial moments. We derive frequentist inference procedures (tests and conditional confidence intervals) and Bayesian methods for these designs. In the Bayesian framework, for a family of appropriate priors we found the posterior distributions and the credible intervals about the relevant parameters, and the predictive distributions. The link between conditional tests and Bayesian procedures is made explicit. The Bayesian methods are generalized to cover more complex plans (several treatments and delayed responses). Non informative Bayesian procedures are remarkable frequentist properties.
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https://tel.archives-ouvertes.fr/tel-00377114
Contributor : Khadija Yousfi Elqasyr <>
Submitted on : Monday, April 20, 2009 - 10:55:19 PM
Last modification on : Tuesday, February 5, 2019 - 11:44:10 AM
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  • HAL Id : tel-00377114, version 1

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Khadija Yousfi Elqasyr. MODÉLISATION ET ANALYSE STATISTIQUE DES PLANS D'EXPÉRIENCE SÉQUENTIELS. Mathématiques [math]. Université de Rouen, 2008. Français. ⟨tel-00377114⟩

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