[Regression models for crude and relative survival: a comparative review]

Statistical analysis of lifetime data is frequently used in the biomedical area. Our objective was to present a comparative review of the different regression models according to the survival concept (crude survival or relative survival) in order to express guidelines.

From a methodological point of view, we compared a regressive crude survival model (Cox model) and regressive relative survival models for grouped data (Hakulinen and Tenkanen) and for individuals data (Esteve et al.). We illustrated our work with an analysis of survival data of 3,355 incident cases of breast cancer identified by a hospital registry. Comportment of the models was studied in situation where censors rates ranged from 31.7 to 96.5%.

Because relative survival analysis takes into account natural mortality, the risk of death was smaller for women older than 50 years than for women aged from 35 to 49; this was not demonstrated in the crude survival analysis (Cox). Estimations obtained from Cox model were more accurate than those obtained from both studied regressive relative survival models. Estimations obtained from Esteve et al. model were not very different from those obtained from Hakulinen and Tenkanen model and they were more accurate.

By definition, analysis of relative survival is more appropriate to estimate survival to a specific cause of death. It is preferable to use models based on individual estimation when data set is small or when the number of individual per strata is small.