Robust inference with censored survival data

Pierre-Yves Deléamont & Elvezio Ronchetti

Résumé Randomly censored survival data appear in a wide variety of applications in which the time until the occurrence of a certain event is not completely observable. In this paper, we assume that the statistician observes a possibly censored survival time along with a censoring indicator. In this setting, we study a class of M-estimators with a bounded influence function, in the spirit of the infinitesimal approach to robustness. We outline the main asymptotic properties of the robust M-estimators and characterize the optimal B-robust estimator according to two possible measures of sensitivity. Building on these results, we define robust testing procedures which are natural counterparts to the classical Wald, score, and likelihood ratio tests. The empirical performance of our robust estimators and tests is assessed in two extensive simulation studies. An application to data from a well-known medical study on head and neck cancer is also presented.
Mots-clés censoring, influence function, multiplicative intensity model, robustness, survival analysis
Citation Deléamont, P. Y., & Ronchetti, E. (2022). Robust inference with censored survival data. Scandinavian Journal of Statistics, 49(4), 1496-1533.
Type Article de périodique (Anglais)
Date de publication 9-1-2022
Nom du périodique Scandinavian Journal of Statistics
Volume 49
Numéro 4
Pages 1496-1533
URL https://onlinelibrary.wiley.com/doi/10.1111/sjos.12570