Testing One Primary and Two Secondary Endpoints in a Two-Stage Group Sequential Trial With Extensions.

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• Group sequential procedures are crucial for adaptive clinical trial designs, allowing early stopping for efficacy or futility.
• Testing multiple secondary endpoints conditional on primary endpoint significance requires careful statistical control to maintain Type I error rates.
• Existing p-value based methods (Holm, Hochberg) are straightforward but may lack power due to ignoring endpoint correlations and gatekeeping effects.

Purpose of the Study:

• To develop normal theory analogs for testing multiple secondary endpoints in two-stage group sequential trials.
• To incorporate the gatekeeping effect of the primary endpoint and correlations between endpoints into the statistical testing procedures.
• To compare the power and Type I error rates of the proposed normal theory procedures against existing p-value based methods.

Main Methods:

• Development of normal theory based closed procedures for testing multiple secondary hypotheses.
• Determination of normal theory boundaries using the least favorable configuration of correlations, eliminating the need for prior knowledge of correlations.
• Comparison of secondary powers between normal theory and p-value based procedures, including sensitivity analyses for unequal information times.

Main Results:

• Normal theory analogs demonstrate higher statistical power compared to p-value based Holm and Hochberg procedures.
• The proposed normal theory methods effectively account for the gatekeeping effect and endpoint correlations, leading to improved power.
• Normal theory procedures are computationally intensive beyond two secondary endpoints or stages, while p-value based methods remain applicable.

Conclusions:

• Normal theory based procedures provide a more powerful approach for testing multiple secondary endpoints in specific clinical trial settings.
• These methods offer a valuable alternative when accurate correlation information is unavailable, relying on least favorable configurations.
• The study highlights the trade-offs between power and computational complexity in designing group sequential trials with multiple secondary endpoints.