A Comparison of Test Statistics for Cox's Proportional Hazards Assumption

• Activity Number: 388
• Type: Contributed
• Date/Time: Thursday, August 15, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section*
• Author(s): Rana Ezzeddine*+ and Lisa Weissfeld
• Affiliation(s): University of Pittsburgh and University of Pittsburgh
• Keywords: Cox proportional hazards ; survival analysis ; proportional hazards assumption ; Gray's model ; Grambsch and Therneau ; Hess's test

Abstract

The Cox proportional hazards model is widely used for the analysis of censored survival data. One of the limitations of this method is its reliance on the assumption of proportionality. Numerous tests have been proposed to check the validity of this assumption. These tests include: Harrell's (1986) test, based on the correlation between the residuals and the rank order of the failure time; Lin's (1991) goodness-of-fit test comparing the maximum partial likelihood estimator with a weighted parameter estimator; Hess's (1994) test based on cubic splines; and Grambsch and Therneau's (1994) test, based on a weighted least-squares line fitted to the residual plot. Extensions of the Cox model that relax the assumption of proportionality have also been proposed. Gray's (1992) time-varying coefficients model is such an example. Included in the construction of this model is a test for the proportionality of the hazard function. We compare the test for proportionality based on Gray's model with Harrell's, Lin's, Hess's, Grambsch and Therneau's tests, and Cox's test--based on the inclusion of a time-varying covariate. We simulate data and examine the performance of these tests under various settings.