An adjusted variance estimator for improvement of test power in the Cox proportional hazards model

The Cox proportional hazards (PH) model is widely used in survival data analysis for the dependence of survival times on covariates. We focus on improvement of power on the significant test for the treatment effect in the Cox PH model. To improve the targeted test power, an adjusted variance estimator for the estimated log-hazard ratio is proposed and is compared theoretically and in the simulations with the variance estimators that have been developed under the null hypothesis, alternative hypothesis, and using the log-rank test. In the comparison, we utilize the relative bias and the test power in the Wald test to measure the performance of the proposed variance estimator. The simulation results demonstrate that the proposed variance estimator is more effective at estimating the variance of the estimated log-hazard ratio for the treatment effect. One application with a real-life example is illustrated to evaluate the effectiveness of the proposed variance estimator.