Identifying Nonproportional Covariates in the Cox Model

Abstract

This paper addresses problem of testing whether an individual covariate in the Cox model has a proportional (i.e., time-constant) effect on the hazard. Two existing methods are considered: one is based on the component of the score process, and the other is a Neyman type smooth test. Simulations show that, when the model contains both proportional and nonproportional covariates, these methods are not reliable tools for discrimination. A simple yet effective solution is proposed based on smooth modeling of the effects of the covariates not in focus.

Keywords:

• Cox model
• Goodness of fit
• Proportional hazards assumption
• Time-varying coefficients

Mathematics Subject Classification:

• Primary 62N03
• Secondary 62G10

Acknowledgments

The author gratefully acknowledges that the work has been supported by the GAČR grant 201/05/H007, GAAV grant IAA101120604 and MŠMT project 1M06047. Computations have been carried out in METACentrum (Czech academic supercomputer network).