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Theses

Modélisation conjointe de données longitudinales et de durées de vie

Abstract : The Cox regression model is widely used for the statistical analysis of lifetime data. However, the statistical inference for this model, based on the partial likelihood, often faces problem of missing covariate values. This thesis propose an estimation method for the Cox model with missing values of a time-dependent covariate, and establishes asymptotic properties of the estimators obtained by this method. This method can be applied under less restrictive conditions than other existing methods. It consists in jointly modeling the survival and longitudinal data, and to derive from this joint model a likelihood allowing for estimation in the Cox model with missing covariate values. We first propose a joint model for survival and longitudinal data. This model is made of the Cox model and a model for the covariate which is a step function with jumps at the prespecified observation times. Then, we prove identifiability of the joint model. We then adapt the semiparametric maximum likelihood estimation method to this joint model. We first show existence of semiparametric maximum likelihood estimators. We then obtain a characterization of these estimators, by applying to the joint model the principle underlying the Expectation-Maximization (EM) algorithm. From this characterization, we show that the estimators are consistent and converge in law to a gaussian process. We obtain a convergent estimator of the asymptotic variance of these estimators. We describe the EM algorithm we implemented to estimate the parameters in the joint model. We apply the joint modeling approach to the analysis of informative dropouts in a longitudinal study. Finally, we compare estimations of the regression parameter in the Cox model with missing time-dependent covariate, we obtained from the joint modeling approach and two imputation methods.
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https://tel.archives-ouvertes.fr/tel-00002667
Contributor : Jean-Francois Dupuy <>
Submitted on : Tuesday, April 1, 2003 - 11:18:51 AM
Last modification on : Tuesday, April 1, 2003 - 11:18:51 AM
Long-term archiving on: : Tuesday, September 11, 2012 - 8:10:25 PM

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  • HAL Id : tel-00002667, version 1

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Jean-François Dupuy. Modélisation conjointe de données longitudinales et de durées de vie. Mathématiques [math]. Université René Descartes - Paris V, 2002. Français. ⟨tel-00002667⟩

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