Comparison of Sample Size by Bootstrap and by Formulas Based on Normal Distribution Assumption

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Methods

Background:

• Clinical trial sample size estimation is crucial for study validity.
• Traditional methods often assume normal distribution, which may not hold true.
• Bootstrapping offers a distribution-independent alternative for sample size estimation.

Purpose of the Study:

• To present sample size estimation for two parallel-design arms using bootstrap procedures for various test types.
• To compare bootstrap methods with traditional mathematical formulas based on normal distribution assumptions.
• To evaluate the performance of both methods when data violates the normal distribution assumption.

Main Methods:

• Sample size estimation using bootstrap procedures for inequality, non-inferiority, superiority, and equivalence tests.
• Sample size calculation using mathematical formulas assuming normal distribution.
• Power comparison between bootstrap and formula-based methods under normal and non-normal data conditions.
• Application of the Wilcoxon test within the bootstrap procedure for non-normally distributed data.

Main Results:

• Bootstrap and formula-based sample size estimations showed acceptably small power differences for all test types under normal distribution assumptions.
• When data violated normal distribution, the normal distribution-based formula overestimated power compared to the bootstrap method.
• The Wilcoxon test, used with bootstrapping for non-normal data, provided more accurate power estimations.

Conclusions:

• The bootstrap procedure is a credible and robust technique for clinical trial sample size estimation.
• For data violating normal distribution assumptions, the bootstrap method is preferable for sample size calculation.
• It is recommended to use the bootstrap method with the same statistical test as planned for the main analysis, using representative historical data.