Estimating the personal cure rate of cancer patients using population-based grouped cancer survival data

Cancer patients are subject to multiple competing risks of death and may die from causes other than the cancer diagnosed. The probability of not dying from the cancer diagnosed, which is one of the patients' main concerns, is sometimes called the 'personal cure' rate. Two approaches of modelling competing-risk survival data, namely the cause-specific hazards approach and the mixture model approach, have been used to model competing-risk survival data. In this article, we first show the connection and differences between crude cause-specific survival in the presence of other causes and net survival in the absence of other causes. The mixture survival model is extended to population-based grouped survival data to estimate the personal cure rate. Using the colorectal cancer survival data from the Surveillance, Epidemiology and End Results Programme, we estimate the probabilities of dying from colorectal cancer, heart disease, and other causes by age at diagnosis, race and American Joint Committee on Cancer stage.