Step-Down Parametric Procedures for Testing Correlated Endpoints in a Group-Sequential Trial

Maurer and Bretz developed a class of group-sequential weighted Bonferroni procedures with multiple endpoints. Performed as a step-down consonant shortcut to the group-sequential closed testing procedure, the class of procedures of Maurer and Bretz is simple to use for testing multiple endpoints in classical group-sequential settings. This class uses the correlations of sequential statistics, but does not leverage the correlations between endpoints. Thus, there is room for power improvement by suitably using the between-endpoint correlations in a group-sequential trial while maintaining strong control of the family-wise error rate. To this end, we propose a Holm-type step-down exact parametric procedure for situations in which between-endpoint correlations are known a priori or estimable. An adaptive strategy is suggested for situations in which such correlations are unknown. In addition, we briefly discuss a natural group-sequential extension of the partially parametric Seneta-Chen procedure.