Analysis of time-dependent covariates in a regressive relative survival model

Relative survival is a method for assessing prognostic factors for disease-specific mortality. However, most relative survival models assume that the effect of covariate on disease-specific mortality is fixed-in-time, which may not hold in some studies and requires adapted modelling. We propose an extension of the Esteve et al. regressive relative survival model that uses the counting process approach to accommodate time-dependent effect of a predictor's on disease-specific mortality. This approach had shown its robustness, and the properties of the counting process give a simple and attractive computational solution to model time-dependent covariates. Our approach is illustrated with the data from the Stanford Heart Transplant Study and with data from a hospital-based study on invasive breast cancer. Advantages of modelling time-dependent covariates in relative survival analysis are discussed.