Improving the Effciency of the Log-Rank Test Using Auxiliary Covariates

• Activity Number: 545
• Type: Contributed
• Date/Time: Thursday, August 10, 2006 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Xiaomin Lu*+ and Anastasios A. Tsiatis
• Companies: North Carolina State University and North Carolina State University
• Keywords: log-rank test ; proportional hazard model ; nuisance tangent space ; influence function ; RAL estimators ; efficient estimators

Abstract

The log-rank test is widely used in many clinical trials for comparing censored survival times between two treatments. Under the assumption of proportional hazards, that is, the logarithm of hazard ratio between two survival times is a constant ß, it is optimal for testing the null hypothesis of H0 : ß = 0. In practice, additional auxiliary covariates are collected together with the survival times and treatment assignment. If the covariates correlate with survival times, making use of their information will increase the efficiency of log-rank test. In this paper, we apply the theory of semiparametrics to characterize a class of regular and asymptotic linear (RAL) estimators for ß when auxiliary covariates are incorporated into the model, and derive estimators that are more efficient. The Wald tests induced by these estimators are shown to be more powerful than the log-rank test.