Comptes Rendus
Probability Theory/Statistics
Estimation of the survival probabilities by adjusting a Cox model to the tail
[Estimation des probabilités de survie par lʼajustement sur la queue dʼun modèle de Cox]
Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 807-811.

Dans le contexte dʼun modèle dʼanalyse de survie avec données censurées et en présence dʼune covariable explicative, on veut prédire la probabilité de survie au-delà de la plus grande observation. Un modèle de Cox dont la fonction de risque de base est constante, est ajusté sur la queue de la distribution de la durée de vie. Sous certaines conditions de régularité, on démontre la convergence des estimateurs des paramètres du modèle.

Within the framework of a survival analysis model with censored life time data and an explanatory covariate, our goal is to predict the survival probability beyond the largest observed time. A Cox model with a constant underlying hazard function is proposed to adjust the tail of the life time distribution. Under some regularity conditions, we prove that the parameter estimators are convergent.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.06.011

Ion Grama 1 ; Jean-Marie Tricot 1 ; Jean-François Petiot 1

1 Université de Bretagne Sud, centre de recherche Yves-Coppens, BP 573, 56017 Vannes, France
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     title = {Estimation of the survival probabilities by adjusting a {Cox} model to the tail},
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Ion Grama; Jean-Marie Tricot; Jean-François Petiot. Estimation of the survival probabilities by adjusting a Cox model to the tail. Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 807-811. doi : 10.1016/j.crma.2011.06.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.06.011/

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[2] I. Grama; V. Spokoiny Pareto approximation of the tail by local exponential modeling, Bull. Acad. Sci. Moldova, Volume 1 (2007) no. 53, pp. 1-22

[3] I. Grama; V. Spokoiny Statistics of extremes by oracle estimation, Ann. Statist., Volume 36 (2008), pp. 1619-1648

[4] P. Hall; A.H. Welsh Best attainable rates of convergence for estimates of parameters of regular variation, Ann. Statist., Volume 12 (1984), pp. 1079-1084

[5] P. Hall; A.H. Welsh Adaptive estimates of regular variation, Ann. Statist., Volume 13 (1985), pp. 331-341

[6] J.D. Kalbfleisch; R.L. Prentice The Statistical Analysis of Failure Time Data, Wiley, 2002

[7] J.P. Klein; M.L. Moeschberger Survival Analysis: Techniques for Censored and Truncated Data, Springer, 2003

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