The relative survival framework: theory, history, and discussion

Cancer survival analysis in population-based settings relies on the relative survival framework, which enables the estimation of survival specific to the disease of interest in the absence of information on the individual cause of death. Within this framework, the overall hazard is decomposed into the excess hazard due to cancer and hazard due to the other competing causes of death, the latter derived from routine sources such as national or regional life tables. The survival function associated only with the excess hazard corresponds to the estimand of interest, known as net survival. Non-parametric estimators of this quantity, including Ederer I, Ederer II, Hakulinen, and Pohar-Perme, have been widely used in cancer epidemiology, yet their application has been the subject of long-standing methodological debates regarding bias, variability, and consistency. In this review, we introduce the relative survival framework and outline the mathematical foundations of the non-parametric estimators used in this field, highlighting their key statistical properties, historical development, and continued relevance in population-based cancer research.