Estimation dans le modèle de transformation linéaire avec données manquantes

Mezaouer, Amel; Boukhetala, Kamal; Dupuy, Jean-François

Journal de la société française de statistique, Tome 155 (2014) no. 3, pp. 120-134.

La classe des modèles de transformation linéaire est une classe de modèles de régression semi-paramétriques de durées. Elle comprend comme cas particuliers les modèles à risques proportionnels et à risques convergents, très utilisés en fiabilité. Cheng et al. (Biometrika, 1995) ont proposé des équations d’estimation simples pour en estimer le paramètre de régression. Dans cet article, nous considérons la situation où l’observation de la durée jusqu’à défaillance (éventuellement censurée) n’est possible que pour un sous-échantillon aléatoire de l’échantillon initial des items. Cette situation de données manquantes se rencontre en particulier en fiabilité lorsque des contraintes inattendues viennent interrompre un essai en cours. Tout d’abord, nous adaptons les équations d’estimation de Cheng et al. (Biometrika, 1995) à ce problème. Puis nous montrons la consistance de l’estimateur ainsi construit. Enfin, nous évaluons les propriétés de cet estimateur par simulations et nous illustrons la méthode sur un jeu de données réelles.

The class of linear transformation models is a class of semi-parametric regression models for lifetime data. This class includes the proportional hazards and proportional odds models as special cases. Cheng et al. (Biometrika, 1995) proposed simple estimating equations for the regression parameter in this class of models. In the present paper, we consider the situation where the lifetime data is only observed in a random subset of the initial sample. This may happen, for example, in reliability testing where unexpected issues arising during the experiment may prevent engineers from observing the duration for all the tested items. We adapt Cheng et al.’s estimating equations to this setting and we prove the consistency of the resulting estimator. We evaluate its finite-sample properties via simulations and we illustrate our methodology on a real-data set.

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