Assessing time-by-covariate interactions in proportional hazards regression models using cubic spline functions.

Proportional hazards (or Cox) regression is a popular method for modelling the effects of prognostic factors on survival. Use of cubic spline functions to model time-by-covariate interactions in Cox regression allows investigation of the shape of a possible covariate-time dependence without having to specify a specific functional form. Cubic spline functions allow one to graph such time-by-covariate interactions, to test formally for the proportional hazards assumption, and also to test for non-linearity of the time-by-covariate interaction. The functions can be fitted with existing software using relatively few parameters; the regression coefficients are estimated using standard maximum likelihood methods.