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

Abstract

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.

Keywords: Kaplan-Meier estimator; adult; area under the curve; median survival; survival; survival plateau.

Figure 1

(A) Progression-free survival curves reported by Fukuoka et al. (21) in patients treated with gefinitib (upper curve) or chemotherapy (lower curve); the series of red circles shows how the automated digitalizer identified the points that define the upper boundary of the area under the curve comprised between 0 and 23 months (area = 11.31 months). (B) Overall survival curves reported by Maio et al. (22) in patients treated with ipilimumab (upper curve) or chemotherapy (lower curve); also these two curves were analyzed by the automated analyser to determine the two values of area under the curve. Survival expressed in percentage and time in months.