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

Maurer &amp; Bretz (2013) 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 (Tang &amp; Geller, 1999), the class of procedures of Maurer &amp; Bretz (2013) is simple to use for testing multiple endpoints in classical group-sequential settings. This class utilizes 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 familywise error rate. To this end, we propose a Holm-type step-down exact parametric procedure for situations in which between-endpoint correlations are known <i>a priori</i> 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 (2005).