Estimation of the cumulative baseline hazard function for dependently right-censored failure time data

Abstract

In this paper, we study the properties of a special class of frailty models when the frailty is common to several failure times. The models are closely linked to Archimedean copula models. We establish a useful formula for cumulative baseline hazard functions and develop a new estimator for cumulative baseline hazard functions in bivariate frailty regression models. Based on our proposed estimator, we present a graphical model checking procedure. We fit a leukemia data set using our model and end our paper with some discussions.

Keywords:

• Archimedean copula models
• bivariate frailty models
• cumulative hazard functions

2010 Mathematics Subject Classification:

• survival analysis

Acknowledgments

The authors thank an associate editor and a reviewer for thorough reviews and for their comments that led to great improvement of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).