  We calculate finite sample and asymptotic distributions for the largest
censored and uncensored survival times, and some related statistics, from a
sample of survival data generated according to an iid censoring model. These
statistics are important for assessing whether there is sufficient followup in
the sample to be confident of the presence of immune or cured individuals in
the population. A key structural result obtained is that, conditional on the
value of the largest uncensored survival time, and knowing the number of
censored observations exceeding this time, the sample partitions into two
independent subsamples, each subsample having the distribution of an iid sample
of censored survival times, of reduced size, from truncated random variables.
This result provides valuable insight into the construction of censored
survival data, and facilitates the calculation of explicit finite sample
formulae. We illustrate for distributions of statistics useful for testing for
sufficient followup in a sample, and apply extreme value methods to derive
asymptotic distributions for some of those.
