On testing proportionality in the Cox regression model by Andersen's plot

ABSTRACT

Andersen's plot, a graphical method for testing the proportionality assumption in the Cox Regression Model (Cox, 1972), first proposed by Kay (1977) and popularized by Andersen (1982), has been used widely in biomedical research to check the validity of applying this popular regression model in survival analysis. Our theoretical derivation and examples show that the theoretical basis of this method is flawed. The graphical method should not be used in testing the proportionality. Instead, formal analytical methods based on residuals such as Cox–Snell residual and martingale residual should be used in practice.

KEYWORDS:

• Cox model
• partial likelihood
• semiparametric estimation
• stratification

Acknowledgments

We would like to thank Arthur Moss, MD (PI of MADIT II clinical trial), for allowing us to use the MADIT II data in our paper.

Funding

This study was supported by a pilot grant (PI: Feng) from the Clinical and Translational Sciences Institute at the University of Rochester Medical Center.