Abstract: A simple class of stopping rules is introduced for time-sequential rank tests to compare time to failure between two treatment groups, such as in the case of a clinical trial in which patients enter serially and in which interim analyses of the data are performed periodically so that the trial may be stopped early when one treatment is found to be significantly better than the other. These time-sequential rank tests are shown to achieve both savings in study duration and increase in power over their nonsequential counterparts, and provide a simple but statistically efficient method to circumvent the difficulty of ``calendar time'' versus ``information time'' in the design of group sequential trials with failure-time endpoints.
Key words and phrases: Censored survival data, clinical trials, group sequential tests, rank statistics, stopping rules, use function.