A great many confirmatory phase 3 clinical trials have as their primary endpoint a comparison of the distribution of time to some event (e.g., time to death or progression free survival). The most common statistical analysis models include the logrank test (usually unweighted, but possibly weighted) and/or the proportional hazards regression model. Just as commonly, the true distributions do not satisfy a proportional hazards assumption. Providing users are aware of the nuances of those methods, such departures need not preclude the use of those analytic techniques any more than violations of the location shift hypothesis precludes the use of the t test. However, with the increasing interest in the use of adaptive sample size re-estimation, adaptive enrichment, response-adaptive randomization, and adaptive selection of doses and/or treatments, there are many issues (scientific, ethical, statistical, and logistical) that need to be considered. In fact, when considering references to “less well understood” methods in the draft FDA guidance on adaptive designs, it is likely the case that many of the difficulties in adaptive time to event analyses can relate as much to aspects of survival analysis that are “less well understood” as to aspects of the adaptive methodology that has not been fully vetted. In this course we discuss some aspects of the analysis of censored time to event data that must be carefully considered in sequential and adaptive sampling. In particular, we discuss how the changing censoring distribution during a sequential trial affects the analysis of distributions with crossing hazards and crossing survival curves, as well as issues that arise owing to the ancillary information about eventual event times that might be available on subjects who are censored at an adaptive analysis.