Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials

Area of Science:

• Biostatistics
• Clinical Trial Design
• Bayesian Inference

Background:

• Credible intervals are crucial for Bayesian inference in clinical trials, estimating parameters like treatment effects.
• Highest Posterior Density (HPD) intervals offer the shortest length but often lack closed-form solutions.
• Normal approximations provide intervals but may lack calibration for small sample sizes.

Purpose of the Study:

• To propose a predictive analysis method for selecting optimal sample sizes in clinical trials.
• To ensure approximate Bayesian credible intervals achieve pre-specified calibration levels.
• To improve the reliability of interval estimation for parameters like proportions and log-odds.

Main Methods:

• Utilizing predictive analysis to evaluate sample size requirements.
• Assessing the calibration of approximate intervals based on normal approximations of posterior distributions.
• Applying the methodology to interval estimation of proportions and log-odds.

Main Results:

• Demonstrated that approximate intervals improve calibration and approach exact sets with increasing sample sizes.
• Provided a method to select sample sizes ensuring approximate intervals meet desired posterior probability levels.
• Illustrated the application with examples for proportions and log-odds estimation.

Conclusions:

• The proposed predictive analysis is effective for determining sample sizes needed for calibrated approximate Bayesian intervals.
• This approach enhances the reliability of inference in clinical trials, particularly when exact HPD intervals are intractable.
• The findings support better-informed clinical trial design for accurate parameter estimation.