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An important research topic in survival analysis is related to the modelingand estimation of the cure rate, i.e. the proportion of subjects that willnever experience the event of interest. However, most estimation methodsproposed so far in the literature do not handle the case of insufficientfollow-up, that is when the right end point of the support of the censoringtime is strictly less than that of the survival time of the susceptiblesubjects, and consequently these estimators overestimate the cure rate in thatcase. We fill this gap by proposing a new estimator of the cure rate that makesuse of extrapolation techniques from the area of extreme value theory. Weestablish the asymptotic normality of the proposed estimator, and show how theestimator works for small samples by means of a simulation study. We alsoillustrate its practical applicability through the analysis of data on thesurvival of breast cancer patients.

Non-parametric cure rate estimation under insufficient follow-up using extremes