Evaluation of Hazard Ratio Estimators of Survival Data

• Activity Number: 123 - Topics for the Statistician Clinical Trialist
• Type: Contributed
• Date/Time: Monday, July 31, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Gang Li* and Yining Wang and Weichung Joe Shih
• Companies: Johnson & Johnson and Johnson & Johnson and Rutgers School of Public Health
• Keywords: Cox estimator ; Pike estimator ; Kaplan-Meier based estimator

Abstract

Several estimators for the hazard ratio of the proportional hazards model are proposed in literature (see Cox, 1972, Pike, 1972). Berry et al. (1991) reported the Pike estimator is biased and concluded that the Cox estimator is preferred to the Pike estimator based on simulations for the Pike estimator only, in absence of the simulation results for the Cox estimator. We evaluate the performance of Cox, Pike via systematic simulation study, together with an estimator based on Kaplan-Meier method. The Pike estimator is uniformly better than the Cox estimator under Berry's setting, and it is quite a contradiction to the suggestion of Berry, which is widely accepted. The magnitude of bias of the estimators depends on the hazard ratio and sample size. When sample size is relatively small and the hazard ratio is greater than 1, all estimators are over-estimates; the Cox estimator is more biased. When sample size is large, the biases of all estimators shrink to zero. In conclusion, for small sample sizes, Pike estimator should be recommended.