Approaches in modelling long-term survival: an application to breast cancer

Several modelling techniques have been proposed for non-proportional hazards. In this work we consider different models which can be classified into three wide categories: models with time-varying effects of the covariates; frailty models and cure rate models. We present those different extensions of the proportional hazards model on an application of 2433 breast cancer patients with a long follow-up. We comment on the differences and similarities among the models and evaluate their performance using survival and hazard plots, Brier scores and pseudo-observations.