  In survival analysis, it often happens that some individuals, referred to as
cured individuals, never experience the event of interest. When analyzing
time-to-event data with a cure fraction, it is crucial to check the assumption
of `sufficient follow-up', which means that the right extreme of the censoring
time distribution is larger than that of the survival time distribution for the
non-cured individuals. However, the available methods to test this assumption
are limited in the literature. In this article, we study the problem of testing
whether follow-up is sufficient for light-tailed distributions and develop a
simple novel test. The proposed test statistic compares an estimator of the
non-cure proportion under sufficient follow-up to one without the assumption of
sufficient follow-up. A bootstrap procedure is employed to approximate the
critical values of the test. We also carry out extensive simulations to
evaluate the finite sample performance of the test and illustrate the practical
use with applications to leukemia and breast cancer datasets.
