Confidence Interval of the Survival Probability Under the Cox Model

• Activity Number: 596
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Shihong Zhu*+ and Mai Zhou
• Companies: University of Kentucky and Univ of Kentucky
• Keywords: Empirical Likelihood ; Residual Lifetime ; Wilks Theorem

Abstract

Under the framework of the Cox model, it is often of interest to derive an interval estimate of the survival probability for a subject with given covari- ates. The standard approach to the construction of such an interval estimate is through the asymptotic normality of the point estimate. This is also the method used by the current R package survival. In this paper, we propose an empirical likelihood ratio test based confidence interval. The test statistics is shown to have an asymptotic chi-square distribution with one degree of freedom under the null hypothesis. Our simulation studies show that the new method consistently provides confidence intervals that have shorter average width and better coverage probabilities. Extensions to interval esti- mation of the residual lifetime and the case of stratified Cox model are also considered.