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

ABSTRACT

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.

KEYWORDS:

• Closure method
• Consonant procedure
• Family-wise error rate
• Group-sequential
• Multiple testing procedure

Supplementary Material

Supplementary material available includes simulation R codes and outputs.

Acknowledgments

The author thanks Dr. Frank Bretz and Professor Ajit Tamhane for their valuable comments. The author acknowledges the constructive comments of editor Dr. José Pinheiro, the associate editor, and four referees, who tremendously helped to enhance the ideas and improve the accuracy and the clarity of this manuscript.