Processus empiriques pour l'inférence dans le modèle de survie à risques non proportionnels

Abstract : In this thesis, we focus on particular empirical processes on which we can base inference in the non-proportional hazards model. This time-varying coefficient model generalizes the widely used proportional hazards model in the field of survival analysis. Our focus is on the standardized score process that is a sequential sum of standardized model-based residuals. We consider first the process with one covariate in the model, before looking at its extension for multiple and possibly correlated covariates. The outline of the manuscript is composed of three parts. In the first part, we establish the limit properties of the process under the model as well as under a misspecified model. In the second part, we use these convergence results to derive tests for the value of the model parameter. We show that one proposed test is asymptotically equivalent to the log-rank test, which is a benchmark for comparing survival experience of two or more groups. We construct more powerful tests under some alternatives. Finally, in the last part, we propose a methodology linking prediction and goodness of fit in order to construct models. The resulting models will have a good fit and will optimize predictive ability. We also introduce a goodness-of-fit test of the proportional hazards model. The performances of our methods, either tests for the parameter value or goodness-of-fit tests, are compared to standard methods via simulations. The methods are illustrated on real life datasets.
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Cecile Chauvel. Processus empiriques pour l'inférence dans le modèle de survie à risques non proportionnels. Mathématiques générales [math.GM]. Université Pierre et Marie Curie - Paris VI, 2014. Français. ⟨NNT : 2014PA066399⟩. ⟨tel-01127777v2⟩

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