Statistics and Its Interface

Volume 3 (2010)

Number 4

Empirical likelihood confidence intervals for ratio of hazard rates under right censorship

Pages: 455 – 464



Shan Jiang (Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada)

Dongsheng Tu (Cancer Clinical Trials Division, Cancer Research Institute, Queen’s University, Kingston, Ontario, Canada)


Hazard ratio is an important measure for relative difference between treatment groups in clinical trials or other types of studies with time-to-event as an endpoint. Nonparametric confidence intervals for hazard ratio were derived in [26] based on asymptotic normality of the kernel estimate for hazard ratio. Simulation studies found that, however, the actual coverage probabilities of these confidence intervals were still below the nominal level. In this paper, empirical likelihood ratio method is used to construct confidence intervals for hazard ratio functions under right censorship. The asymptotic distribution of the empirical likelihood ratio is established and simulation studies show that empirical likelihood method improves the coverage probabilities of confidence intervals based on asymptotic normality.


empirical likelihood, hazard ratio, kernel estimate, undersmoothing

2010 Mathematics Subject Classification


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