Improved repeated confidence bounds in trials with a maximal goal

Repeated confidence intervals can be computed at every interim analysis of a flexible group sequential design without the need to stop the trial with a pre-planned stopping rule. Often, however, there is a maximal goal such that the trial is surely stopped if this goal is reached. This. induces a maximal stopping rule, and repeated confidence intervals are strictly conservative, when adhering to it. A modification is proposed which uniformly improves the one sided repeated confidence interval in such a situation. It preserves the monitoring character, and leads to uniformly smaller intervals, when reaching the maximal goal at an interim analysis. The modification is worked out for two stage designs and is indicated for multi-stage trials. The extent of the improvement is quantified for two simple scenarios.