Analysis of Survival Curves: Statistical Methods Accounting for the Presence of Long-Term Survivors

Some anti-cancer treatments (e. g., immunotherapies) determine, on the long term, a durable survival in a small percentage of treated patients; in graphical terms, long-term survivors typically give rise to a plateau in the right tail of the survival curve. In analysing these datasets, medians are unable to recognize the presence of this plateau. To account for long-term survivors, both value-frameworks of ASCO and ESMO have incorporated post-hoc corrections that upgrade the framework scores when a survival plateau is present. However, the empiric nature of these post-hoc corrections is self-evident. To capture the presence of a survival plateau by quantitative methods, two approaches have thus far been proposed: the milestone method and the area-under-the-curve (AUC) method. The first approach identifies a long-term time-point in the follow-up (milestone) at which survival percentages are extracted. The second approach, which is based on the measurement of AUC of survival curves, essentially is the rearrangement of previous methods determining mean lifetime survival; similarly to the milestone method, the application of AUC can be restricted to a pre-specified time-point of the follow-up. This Mini-Review examines the literature published on this topic. The main characteristics of these two methods are highlighted along with their advantages and disadvantages. The conclusion is that both the milestone method and the AUC method are able to capture the presence of a survival plateau.