Predicting survival using disease history: a model combining relative survival and frailty

Information on disease history and comorbidity of patients can often be of great value to predict survival, for example in cancer research. In this paper a model is presented that accommodates such information by combining relative survival and frailty. Relative survival is used to model the excess risk of dying from recent concurrent diseases. Individual frailty allows estimation of a ‘selection effect’, which occurs if patients who have survived much hazard in the past are tougher and therefore tend to live longer than those who have survived less. Results are shown to be independent of the chosen family of frailty distributions if heterogeneity is small and to lead to a simple proportional excess hazards model. The model is applied to data from the Leiden University Medical Center on patients with head/neck tumors using information on previous tumors.