Large sample tests for simultaneous comparison to multiple controls in terms of binomial proportions

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• Comparing a single treatment to multiple control groups is common in clinical trials.
• Ensuring simultaneous superiority over all controls requires robust statistical methods.
• Existing methods may lack power or have inflated Type I error rates.

Purpose of the Study:

• To evaluate the performance of nine large-sample intersection-union tests for demonstrating simultaneous treatment superiority.
• To compare these tests regarding Type I error rates and statistical power.
• To assess methods for estimating minimum sample size requirements.

Main Methods:

• Application of nine intersection-union tests, including Min tests (Wald, pooled, Falk and Koch) and adjustments (Berger and Boos, Röhmel and Mansmann).
• A large-scale simulation study to assess Type I error rates and power.
• Investigation of approximate power calculations and alternative sample size estimation approaches.

Main Results:

• The simulation study compared the Type I error rate and power of the nine proposed tests.
• The study analyzed the accuracy of approximate power calculations.
• The proximity of alternative sample size estimation methods was investigated.

Conclusions:

• The study provides a comparative analysis of statistical tests for simultaneous superiority in multi-control trials.
• Findings inform the selection of appropriate tests and sample size calculations for clinical research.
• The research contributes to optimizing the design and analysis of studies comparing treatments to multiple controls.