Assessing interactions of binary time-dependent covariates with time in Cox proportional hazards regression models using cubic spline functions

Abstract

The Cox proportional hazards model is the most popular model for the analysis of survival data. Time-dependent covariates can be included in a straightforward manner. In most cases such covariates will be binary, indicating some form of changing group membership, with individuals starting in group 0, and changing into group 1 after the occurrence of a specific event. If there is evidence that the hazard ratio between these two groups depends on the sojourn time in group 1, then the use of cubic spline functions will allow investigation of the shape of the supposed effect and provide two main advantages - no particular functional form has to be specified and standard computer software packages like SAS or BMDP can be used.