Empirical likelihood for the contrast of two hazard functions with right censoring

Novel empirical likelihood inference for the mean difference with right-censored data

This paper focuses on comparing two means and finding a confidence interval for the difference of two means with right-censored data using the empirical likelihood method combined with the independent and identically distributed random functions representation. In the literature, some early researchers proposed empirical link-based confidence intervals for the mean difference based on right-censored data using the synthetic data approach. However, their empirical log-likelihood ratio statistic has a scaled chi-squared distribution. To avoid the estimation of the scale parameter in constructing confidence intervals, we propose an empirical likelihood method based on the independent and identically distributed representation of Kaplan-Meier weights involved in the empirical likelihood ratio. We obtain the standard chi-squared distribution. We also apply the adjusted empirical likelihood to improve coverage accuracy for small samples. In addition, we investigate a new empirical likelihood method, the mean empirical likelihood, within the framework of our study. The performances of all the empirical likelihood methods are compared via extensive simulations. The proposed empirical likelihood-based confidence interval has better coverage accuracy than those from existing methods. Finally, our findings are illustrated with a real data set.

A note on the empirical likelihood confidence band for hazards ratio with covariate adjustment

In medical studies comparing two treatments in the presence of censored data, the stratified Cox model is an important tool that has the ability to flexibly handle non-proportional hazards while allowing parsimonious covariate adjustment. In order to capture the cumulative treatment effect, the ratio of the treatment specific cumulative baseline hazards is often used as a measure of the treatment effect. Pointwise and simultaneous confidence bands associated with the estimated ratio provide a global picture of how the treatment effect evolves over time. Recently, Dong and Matthews (2012, Biometrics 68, 408-418) proposed to construct a pointwise confidence interval for the ratio using a plug-in type empirical likelihood approach. However, their result on the limiting distribution of the empirical likelihood ratio is generally incorrect and the resulting confidence interval is asymptotically undercovering. In this article, we derive the correct limiting distribution for the likelihood ratio statistic. We also present simulation studies to demonstrate the effectiveness of our approach.