An extension of the Koziol–Green model under dependent censoring

Abstract

In survival analysis, the classical Koziol–Green model under random censorship is commonly used for informative censoring. We propose in this paper an extension of this model in which we derive a nonparametric estimator for the distribution function of a survival time under two types of informative censoring. For the first type of informative censoring, we assume that the censoring time depends on the survival time through the expression of their joint distribution by an Archimedean copula. For the second type of informative censoring, we assume that the marginal distribution of the censoring time is a function of the marginal distribution of the survival time where this function is found through a section of a known copula function on the observed lifetime and the censoring indicator. We prove in this paper the uniform consistency of the new estimator and show the weak convergence of the associated process. Afterwards, we give some finite sample simulation results and illustrate this estimator on a real-life data set.

Keywords:

• almost sure representation
• copula function
• exponential bound
• informative censoring
• right censoring
• simulation
• strong consistency
• weak convergence

Mathematics Subject Classifications :

• 62N02
• 62G05
• 62G20

Acknowledgements

The authors gratefully acknowledge the financial support from the IAP research Network P6/03 of the Belgian Government (Belgian Science Policy). Furthermore, the authors would like to thank the associate editor and two anonymous referees for their comments which improved the first version of this paper.