Some thoughts on sample size: a Bayesian-frequentist hybrid approach

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Power Analysis

Background:

• Standard sample size calculations do not account for effect size uncertainty.
• Using a normal prior for uncertainty can result in inadequate power as sample size increases.

Purpose of the Study:

• Develop methods for sample size and power calculations that include effect size uncertainty.
• Ensure power approaches 1 with increasing sample size and maintain ease of calculation.

Main Methods:

• Examined normal, truncated normal, and gamma priors for effect size computationally.
• Analytically demonstrated power approximation for truncated normal priors.
• Proposed a compromise method balancing fixed effect and normal prior approaches.

Main Results:

• Incorporating realistic prior distributions likely increases Phase 3 sample sizes.
• The fixed effect method overlooks Phase 2 estimate variability.
• Truncated normal priors suggest large sample sizes; gamma priors yield high power.

Conclusions:

• Standard fixed approaches may yield insufficient power.
• Other parametric priors lead to extreme sample sizes or unrealistic power.
• A compromise between fixed effect and normal prior is recommended.