Sample size optimization and initial allocation of the significance levels in group sequential trials with multiple...

Area of Science:

• Statistics
• Biostatistics
• Clinical Trial Design

Background:

• Multistage hypothesis testing is crucial for adaptive clinical trials.
• Flexible settings for calendar time and information fraction are needed.
• Optimizing sample size and significance level allocation is key for efficiency.

Purpose of the Study:

• To develop a numerical method for finding the optimal sample size in multistage tests.
• To derive explicit statistical power expressions for two-hypothesis testing.
• To determine the best allocation of the initial significance level for group sequential designs.

Main Methods:

• Derivation of explicit statistical power functions.
• Proof of existence and uniqueness for the optimization solution.
• Development of a numerical search algorithm for optimal sample size.

Main Results:

• Explicit statistical power expressions were derived.
• A numerical method was developed to find the optimal sample size.
• The method successfully determines significance level allocation and minimum sample size.

Conclusions:

• The proposed numerical method efficiently identifies optimal sample sizes for group sequential designs.
• This approach is applicable to designs with or without hierarchical endpoint structures.
• The method enhances the statistical power and efficiency of multistage testing.