Inférence pour les modèles statistiques mal spécifiés, application à une étude sur les facteurs pronostiques dans le cancer du sein

Abstract : The thesis focuses on inference of statistical misspecified models. Every result finds its application in a prognostic factors study for breast cancer, thanks to the data collection of Institut Curie. We consider first non-proportional hazards models, and make use of the marginal survival of the failure time. This model allows a time-varying regression coefficient, and therefore generalizes the proportional hazards model. On a second time, we study step regression models. We propose an inference method for the changepoint of a two-step regression model, and an estimation method for a multiple-step regression model. Then, we study the influence of the subsampling rate on the performance of median forests and try to extend the results to random survival forests through an application. Finally, we present a new dose-finding method for phase I clinical trials, in case of partial ordering.
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Roxane Duroux. Inférence pour les modèles statistiques mal spécifiés, application à une étude sur les facteurs pronostiques dans le cancer du sein. Statistiques [math.ST]. Université Pierre et Marie Curie - Paris VI, 2016. Français. ⟨NNT : 2016PA066224⟩. ⟨tel-01507600⟩

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