Empirical Likelihood Confidence Bands of the Survival and Hazard Ratios with Covariate Adjustment

• Activity Number: 29
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Shihong Zhu*+ and Yifan Yang and Mai Zhou
• Companies: University of Kentucky and and University of Kentucky
• Keywords: Two-sample Comparison ; Survival Analysis ; Stratified Cox Model ; Scaled Chi-square

Abstract

In medical studies comparing two treatments in the presence of censored data, the stratified Cox model is an important tool that could 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 about how the treatment effect evolves over time. Recently, Dong and Matthews (Biometircs, 68(2):408-418, 2012) proposed to construct a pointwise confidence interval of the ratio using a plug-in type empirical likelihood approach. However, their result is generally incorrect and the resulting confidence interval is asymptotically undercovering. In this manuscript, we use the same plug-in empirical likelihood framework to study the ratio of the baseline cumulative hazards and the ratio of individualized survival functions. Both pointwise and simultaneous confidence bands are provided using the weak convergence of the empirical likelihood ratio statistics. Simulation studies are presented to d