Cost considerations and the need to report the results promptly make it desirable to examine data as it accumulates and to terminate an experimental study as soon as definite statistical conclusions can be drawn. These ideas are illustrated in a retrospective analysis of the Pennsylvania Reemployment Bonus experiment. Recently developed large-sample theory for a variety of sequentially computed score processes of time-to-event (duration) data with staggered entry enables one to construct stopping boundaries of a prescribed level of significance. The gains from the use of sequential methodology appear to be worth while.