Inference for a Linear Functional of Cumulative Hazard Function Via Empirical Likelihood

Abstract

Owen (1988), (1990) constructed a confidence interval for a general functional without censoring. Linear functional of cumulative hazard function provides a flexible choice for medical researchers to assess effectiveness of treatments, which include (a) partial mean lifetime, (b) distribution function, and (c) cumulative hazard function. In this article, we consider two linear functionals of cumulative hazard function (a) and (b), and derive simultaneous confidence bands for them based on independent right-censored data. Our approach extends essentially without change to (c) as well. Our approach is formulated in terms of empirical likelihood and the simultaneous confidence band is very useful to describe the overall shape of the linear functional. The proposed method is illustrated with simulation and real data examples.

Keywords:

• Confidence band
• Counting process
• Kaplan–Meier estimator
• Martingale
• Nelson–Aalen estimator
• Right censoring

Mathematics Subject Classification:

• Primary 62G10
• Secondrary 62G05

Acknowledgments

Yichuan Zhao acknowledges partial support under National Security Agency Grant and Faculty Mentored Grant of Georgia State University. The authors are grateful to the referees for the detailed comments and helpful suggestions which improved the presentation of an old version of the manuscript.