title: A note on the empirical likelihood confidence band for hazards ratio with covariate adjustment.
abstract: 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.
authors.affiliation: Department of Statistics, University of Kentucky, Lexington, Kentucky 40506, U.S.A.
authors.forename: Shihong
authors.initials: S
authors.lastname: Zhu
authors.affiliation: Department of Statistics, University of Kentucky, Lexington, Kentucky 40506, U.S.A.
authors.forename: Yifan
authors.initials: Y
authors.lastname: Yang
authors.affiliation: Department of Statistics, University of Kentucky, Lexington, Kentucky 40506, U.S.A.
authors.forename: Mai
authors.initials: M
authors.lastname: Zhou
mesh_terms: D001699:Biometry / Q000379:methods*; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D016016:Proportional Hazards Models
keywords: Gaussian process; Scaled Chi-square; Stratified Cox model; Survival analysis