Investigating Time Dependence in Cox's Proportional Hazards Model

Abstract

SUMMARY We consider the investigation of time dependence in Cox's proportional hazards model using the residuals of Schoenfeld. For data analysis and model development we consider smoothing these residuals to consider time-dependent effects. A model which considers time-dependent modulation of the linear predictor is introduced and suggested for use. The techniques are illustrated using simulated data and data concerning the failure response, measured as distance travelled, of turbochargers on railway carriages. For the latter case, a 'time'-dependent proportional hazards model of this type is suggested by smoothing the residuals and it is shown to give an improved fit to the data.