  When analyzing time-to-event data, it often happens that some subjects do not
experience the event of interest. Survival models that take this feature into
account (called `cure models') have been developed in the presence of
covariates. However, the current literature on nonparametric cure models with
covariates cannot be applied when the follow-up is insufficient, i.e., when the
right endpoint of the support of the censoring time is strictly smaller than
that of the survival time of the susceptible subjects. In this paper we attempt
to fill this gap in the literature by proposing new estimators of the
conditional cure rate and the conditional survival function using extrapolation
techniques coming from extreme value theory. We establish the asymptotic
normality of the proposed estimators, and show how the estimators work for
small samples by means of a simulation study. We also illustrate their
practical applicability through the analysis of data on the survival of colon
cancer patients.
