Cure Models: What is Meant by a Survival 'Plateau', and Do Experts Agree on What Constitutes One?

Cure models are becoming more popular for modelling survival data where long-term survival, or 'cure', is considered plausible. One criterion for considering fitting cure models is evidence for a plateau in the Kaplan-Meier survival curve. However, what constitutes a mathematical definition of a plateau in survival probability is unclear, and visual inspections of survival curves are subjective.

We investigate these issues and clarify what is meant by a plateau in this context.

We begin by describing an activity where five experts were presented with 10 survival curves from oncology trials. They were asked to rank these curves in order of their potential suitability for mixture cure modelling. We explore mathematically what features of data are required to produce a positive estimated cure fraction under an exponential mixture cure model. We show how these results can be generalised to a Weibull mixture cure model. A case study was performed using one of the survival curves.

We found weak correlations between the experts' rankings. Mathematical investigations revealed the features of data required for mixture cure models to be potentially useful, such as a decreasing event rate, but this is highly model dependent. The case study illustrated similar statistical issues.

We conclude that a precise definition of the extent to which a Kaplan-Meier survival curve demonstrates a plateau is likely to prove elusive. External evidence or subject matter expert knowledge about the plausibility of cure must therefore play a key role.