Using the theory of set-indexed martingales, we develop a general model for survival analysis with censored data which is parameterized by sets instead of time points. We define a set-indexed Nelson--Aalen estimator for the integrated hazard function with the presence of a censoring by a random set which is a stopping set. We prove that this estimator is asymptotically unbiased and consistent. A central limit theorem is given. This model can be applied to cases when censoring occurs in geometrical objects or patterns, and is a generalization of models with multidimensional failure times.
@article{1031863176,
author = {Ivanoff, B. Gail and Merzbach, Ely},
title = {Random censoring in set-indexed survival analysis},
journal = {Ann. Appl. Probab.},
volume = {12},
number = {1},
year = {2002},
pages = { 944-971},
language = {en},
url = {http://dml.mathdoc.fr/item/1031863176}
}
Ivanoff, B. Gail; Merzbach, Ely. Random censoring in set-indexed survival analysis. Ann. Appl. Probab., Tome 12 (2002) no. 1, pp. 944-971. http://gdmltest.u-ga.fr/item/1031863176/