  Mid-study design modifications are becoming increasingly accepted in
confirmatory clinical trials, so long as appropriate methods are applied such
that error rates are controlled. It is therefore unfortunate that the important
case of time-to-event endpoints is not easily handled by the standard theory.
We analyze current methods that allow design modifications to be based on the
full interim data, i.e., not only the observed event times but also secondary
endpoint and safety data from patients who are yet to have an event. We show
that the final test statistic may ignore a substantial subset of the observed
event times. Since it is the data corresponding to the earliest recruited
patients that is ignored, this neglect becomes egregious when there is specific
interest in learning about long-term survival. An alternative test
incorporating all event times is proposed, where a conservative assumption is
made in order to guarantee type I error control. We examine the properties of
our proposed approach using the example of a clinical trial comparing two
cancer therapies.
