Bootstrapping the conditional survival function estimator in the partial Koziol–Green model

Abstract

In the partial Koziol–Green regression model, the lifetime variable may be censored by two types of censoring variables. One is called informative because it satisfies the Koziol–Green assumption on proportionality of hazards and the other one is general. Braekers and Veraverbeke proposed a non-parametric estimator for the conditional lifetime distribution and obtained a Gaussian approximation for the corresponding process. In the present paper, we propose an appropriate resampling scheme and show that this leads to a valid bootstrap approximation for the process.

Keywords:

• Bootstrap
• Fixed design
• Informative censoring
• Nonparametric regression
• Proportional hazards
• Right censoring
• Weak convergence

Acknowledgements

This work was supported by the Ministry of the Flemish Community (Project BIL00/28) and by the IAP research network nr P5/24 of the Belgian State. The authors are also grateful to the associate editor and two anonymous referees for their critical comments which led to an improvement of the paper.