Bayesian hypothesis testing in two-arm trials with dichotomous outcomes

Area of Science:

• Statistics
• Biostatistics
• Hypothesis Testing

Background:

• Comparing Bayesian and frequentist statistical inference is crucial for robust data analysis.
• One-sided superiority and noninferiority tests are common in clinical trials and research.

Purpose of the Study:

• To investigate Bayesian one-sided superiority and noninferiority tests.
• To compare Bayesian inferences with frequentist approaches using the binomial distribution.
• To explore the relationship between posterior probabilities and frequentist p-values.

Main Methods:

• Utilized Bayesian tests for one-sided superiority and noninferiority.
• Employed conjugate beta priors with integer parameters for the binomial distribution.
• Transformed posterior probabilities into frequentist probabilities of Bernoulli trials with adjusted parameters.

Main Results:

• Bayesian posterior probabilities were expressed using credible limits.
• The transformation allowed a direct comparison with frequentist Bernoulli trial probabilities.
• Posterior probabilities could be made smaller or larger than frequentist p-values by selecting appropriate prior parameters.

Conclusions:

• Bayesian methods, specifically with conjugate priors, can be adapted to resemble frequentist test formulations.
• The choice of prior parameters in Bayesian testing offers flexibility in influencing the outcome relative to frequentist p-values.
• This approach provides a bridge between Bayesian and frequentist statistical inference for specific hypothesis testing scenarios.