Empirical Likelihood Methods for Comparison of Survival Functions

• Activity Number: 288
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section*
• Author(s): Yi-Chuan Zhao*+ and Ian McKeague
• Affiliation(s): Florida State University and Florida State University
• Keywords: Distribution-free ; Goodness-of-fit ; K-sample comparison ; Kaplan-Meier estimator ; Martingale ; Right censoring

Abstract

The use of empirical likelihood in survival analysis was initiated by Thomas and Grunkemeier (1975), who derived pointwise confidence intervals for the survival function. Since the breakthrough work of Owen (1988, 1990), the method has been applied to a variety of statistical problems. The goal is to develop the approach for the comparison of survival functions for k-sample problems in survival analysis. We derive an empirical likelihood simultaneous confidence band for the ratio of two survival functions based on independent right-censored data. Earlier authors have studied such bands for the difference of two survival functions, but the ratio provides a more appropriate comparison in some applications, e.g., in comparing two treatments in biomedical settings. A test for equality of corresponding hazard functions is also constructed. Cumulative hazard ratios appear to be more tractable than ratio of survival functions of cumulative hazard functions in the k-sample setting. A goodness of fit test is developed for checking proportional hazards in k-sample problems. We extend our approach to adjust covariate effects. The proposed methods are illustrated with a clinic trial data.