Improved Efficiency in Relative Risk Estimation and Hypothesis Testing with Small Samples

• Activity Number: 700
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Rengyi Xu* and Pamela Shaw and Devan Mehrotra
• Companies: University of Pennsylvania and University of Pennsylvania and Merck
• Keywords: proportional hazards regression ; survival analysis ; small sample ; generalized log-rank statistic

Abstract

When comparing the hazard rates between two groups with proportional hazards, the Cox model is the preferred method for estimation and inference for relative risk, along with the log-rank test for comparisons of survival curves. However, in small samples, the traditional methods can lose efficiency. In this paper, we propose a novel statistic based on a new formulation of the generalized log-rank (GLR) that leads to better efficiency in hazard ratio estimation and hypothesis testing with small samples (Mehrotra and Roth 2001). We show through simulation study that when sample size is small (less than 40 subjects per group), our new GLR statistic provides a higher relative efficiency, ranging from 5% to 90%, than both the parametric and Cox model. With respect to hypothesis testing, the improved GLR statistic preserves the Type I error under 5%, while methods based on parametric and Cox model tend to provide an inflated Type I error. Illustration of our proposed method is also carried out in a real dataset example.