  An important research topic in survival analysis is related to the modeling
and estimation of the cure rate, i.e. the proportion of subjects that will
never experience the event of interest. However, most estimation methods
proposed so far in the literature do not handle the case of insufficient
follow-up, that is when the right end point of the support of the censoring
time is strictly less than that of the survival time of the susceptible
subjects, and consequently these estimators overestimate the cure rate in that
case. We fill this gap by proposing a new estimator of the cure rate that makes
use of extrapolation techniques from the area of extreme value theory. We
establish the asymptotic normality of the proposed estimator, and show how the
estimator works for small samples by means of a simulation study. We also
illustrate its practical applicability through the analysis of data on the
survival of breast cancer patients.
