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.
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.
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Ion Grama 1; Jean-Marie Tricot 1; Jean-François Petiot 1
@article{CRMATH_2011__349_13-14_807_0, author = {Ion Grama and Jean-Marie Tricot and Jean-Fran\c{c}ois Petiot}, title = {Estimation of the survival probabilities by adjusting a {Cox} model to the tail}, journal = {Comptes Rendus. Math\'ematique}, pages = {807--811}, publisher = {Elsevier}, volume = {349}, number = {13-14}, year = {2011}, doi = {10.1016/j.crma.2011.06.011}, language = {en}, }
TY - JOUR AU - Ion Grama AU - Jean-Marie Tricot AU - Jean-François Petiot TI - Estimation of the survival probabilities by adjusting a Cox model to the tail JO - Comptes Rendus. Mathématique PY - 2011 SP - 807 EP - 811 VL - 349 IS - 13-14 PB - Elsevier DO - 10.1016/j.crma.2011.06.011 LA - en ID - CRMATH_2011__349_13-14_807_0 ER -
%0 Journal Article %A Ion Grama %A Jean-Marie Tricot %A Jean-François Petiot %T Estimation of the survival probabilities by adjusting a Cox model to the tail %J Comptes Rendus. Mathématique %D 2011 %P 807-811 %V 349 %N 13-14 %I Elsevier %R 10.1016/j.crma.2011.06.011 %G en %F CRMATH_2011__349_13-14_807_0
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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