Practical approaches to Bayesian sample size determination in non-inferiority trials with binary outcomes

Area of Science:

• Biostatistics
• Clinical Trials
• Epidemiology

Background:

• Traditional non-inferiority trials rely on arbitrary margins, limiting direct probability interpretation.
• Bayesian analysis allows direct probability statements about treatment differences, enhancing interpretability.
• Consistency between Bayesian analysis and sample size determination is crucial for robust trial design.

Purpose of the Study:

• To demonstrate and evaluate three Bayesian approaches for sample size determination in non-inferiority trials with binary outcomes.
• To compare the advantages and disadvantages of predictive power, expected posterior probability, and precision-based methods.
• To apply these Bayesian methods to a real-world non-inferiority trial in pediatric HIV treatment.

Main Methods:

• Predictive power approach: Calculates sample size based on the probability of a convincing trial result.
• Expected posterior probability approach: Determines sample size by considering the anticipated probability of non-inferiority.
• Precision-based approach: Focuses on achieving a desired level of precision in treatment effect estimation.

Main Results:

• Bayesian sample sizes are generally larger than frequentist calculations due to accounting for parameter uncertainty, unless informative priors are used.
• The predictive power approach is practical and analogous to frequentist methods.
• The expected posterior probability approach yields smaller sample sizes, suitable for estimation-focused trials.
• The precision-based approach is useful under resource constraints but may be challenging for sole decision-making.

Conclusions:

• Bayesian sample size determination provides a consistent and interpretable framework for non-inferiority trials.
• The choice of Bayesian approach depends on trial objectives, balancing predictive power, estimation precision, and practical constraints.
• These methods offer a more nuanced approach to sample size calculation compared to traditional frequentist methods.