A minimum version of log-rank test for testing the existence of cancer cure using relative survival data

Cancer survival is one of the most important measures to evaluate the effectiveness of treatment and early diagnosis. The ultimate goal of cancer research and patient care is the cure of cancer. As cancer treatments progress, cure becomes a reality for many cancers if patients are diagnosed early and get effective treatment. If a cure does exist for a certain type of cancer, it is useful to estimate the time of cure. For cancers that impose excess risk of mortality, it is informative to understand the difference in survival between cancer patients and the general cancer-free population. In population-based cancer survival studies, relative survival is the standard measure of excess mortality due to cancer. Cure is achieved when the survival of cancer patients is equivalent to that of the general population. This definition of cure is usually called the statistical cure, which is an important measure of burden due to cancer. In this paper, a minimum version of the log-rank test is proposed to test the equivalence of cancer patients' survival using the relative survival data. Performance of the proposed test is evaluated by simulation. Relative survival data from population-based cancer registries in SEER Program are used to examine patients' survival after diagnosis for various major cancer sites.