Crossing Hazard Functions in Common Survival Models

• Activity Number: 237
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jiajia Zhang*+ and Yingwei Peng
• Companies: University of South Carolina and Queen's University
• Keywords: Accelerated hazard model ; Accelerated failure time model ; monotone hazard ; U-shape hazard ; Bell-shape hazard

Abstract

Crossing hazard functions have extensive applications in modeling survival data. However, existing studies in the literature mainly focus on comparing crossed hazard functions and estimating the time at which the hazard functions cross, and there is little theoretical work on conditions under which hazard functions from a model will have a crossing. In this paper, we investigate crossing status of hazard functions from the proportional hazards (PH) model, the accelerated hazard (AH) model, and the accelerated failure time (AFT) model. We provide and prove conditions under which the hazard functions from the AH and the AFT models have no crossings or a single crossing. A few examples are also provided to demonstrate how the conditions can be used to determine the crossing status of hazard functions from the three models.