Sample size determination for a binary response in a superiority clinical trial using a hybrid classical and Bayesian...

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Power Analysis

Background:

• Sample size and power calculations for binary outcomes rely on hypothesized proportions (π1, π2).
• Current methods often use point estimates from historical data, neglecting uncertainty.
• This uncertainty in parameter estimates is rarely addressed in study design.

Purpose of the Study:

• To present a hybrid classical and Bayesian procedure for integrating prior information on π1 and π2 distributions into power calculations.
• To introduce Conditional Expected Power (CEP) for robust sample size determination.
• To equate pre-specified frequentist power with CEP for trial design.

Main Methods:

• A hybrid classical and Bayesian procedure is proposed.
• Conditional Expected Power (CEP) is calculated by averaging the power curve using prior distributions of π1 and π2.
• Sample size is determined by equating frequentist power (1-β) with CEP.

Main Results:

• CEP-based designs demonstrate more consistent and robust performance compared to traditional designs when study parameters have uncertainty.
• Traditional sample size calculations based on point estimates tend to underestimate the required sample size.
• The greatest benefit of the CEP method is observed when parameter uncertainty is not excessively large.

Conclusions:

• The procedure formally integrates prior information on parameter uncertainty into study design within a frequentist framework.
• Determining sample size for high CEP protects against misspecification of treatment effects.
• This method provides a substantiated estimate for discussing study feasibility during the design phase.