No cure for cure models: killed by competing risks

Cure models have become increasingly popular over the last couple of decades. An appealing element of cure models is the idea that part of the population is immune to the event of interest. We argue that, in medical applications, the use of cure models is limited. Thus, true cure cannot exist if the event of interest includes death, as death is inevitable, and if death is excluded then competing risks must be accounted for. In this case, we find it more natural to model the cumulative incidence of both the event of interest and competing events over time, avoiding unreliable estimates at infinity and using observed data. Further, we point out two more technical difficulties with cure models arising, first, from the fact that cure models rely on identifying plateaus in survival curves at the tail, where data may be sparse and unreliable and, second, the mixture cure model faces issues with practical identifiability of covariate effects in the incidence model (probability of cure), especially alongside proportional hazards assumptions in the latency model (survival model, conditionally on not being cured). We also comment on hybrid extensions of the classical single event cure model that allow for both competing risks and a cured fraction. We support our arguments with real and simulated data. Full data and code are available online.