A note on the power of Fisher's least significant difference procedure

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• Fisher's least significant difference (LSD) is a two-step procedure for multiple comparisons.
• It involves a global test followed by pairwise comparisons if the global null hypothesis is rejected.
• Fisher's LSD preserves experimentwise type I error rate only when exactly three treatment groups are compared.

Purpose of the Study:

• To examine the power properties of Fisher's LSD procedure in phase III clinical trials.
• To assess the impact of the global test on the overall power of the procedure.
• To compare sample size requirements for Fisher's LSD versus Bonferroni adjustment for achieving desired power.

Main Methods:

• Analysis of the power of the first-step global test in Fisher's LSD procedure.
• Evaluation of the overall procedure's power in the context of pairwise comparisons.
• Comparison of sample size calculations for Fisher's LSD and Bonferroni alpha adjustment.

Main Results:

• The power of the initial global test in Fisher's LSD can be substantially lower than pairwise comparison power.
• Achieving desired power for a specific comparison may necessitate larger sample sizes with Fisher's LSD compared to Bonferroni adjustment.
• The power loss is dependent on the effect size in less favorable dose groups.

Conclusions:

• Fisher's LSD procedure's global test can lead to reduced statistical power in phase III clinical trials.
• Potential power deficits should be carefully considered during study planning when using Fisher's LSD to avoid alpha adjustments.
• Alternative methods or careful sample size calculation are recommended to mitigate power loss.