The Relative Power of a Support Vector Regression Approach to Survival Analysis and the Cox Proportional Hazards Model

• Activity Number: 341
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Douglas A. Powell*+ and Faisal M. Khan
• Companies: Aureon Biosciences, Inc.
• Keywords: Statistical Power ; Survival Analysis ; Support Vector Machines ; Cox Proportiona Hazards Model

Abstract

The ability to distinguish between high and low risk is critical for survival models. The statistical power of the standard Cox model is known to be sensitive to the sample size, model size, and measurement error (noise) in the features and the event rate. We compared the Cox Model against a new Support Vector Regression for Censored Data (SVRc) approach to survival analysis. Data were simulated varying sample size (4 levels), model size (4 levels), feature noise (3 levels) and event rate (3 levels). Power was assessed by the model's hazard ratio (HR) and the proportion of statistically significant HRs. Results indicate that SVRc was superior to the Cox Model for both criteria in most of the 144 combinations. The HR improved by a median rate of 9.6% with over 25% of the 144 conditions manifesting more than a 40% increase. The SVRc empirical power matched or exceeded the Cox model's in 84% of conditions, with an increase of 24% or more for 30% of the conditions. The absolute worst performance of SVRc was a 12% decline in one experiment. The results suggest that SVRc improves predictive power compared to the Cox model and can attain a given power with smaller sample sizes.