Bayesian Equivalence Testing and Meta-Analysis in Two-Arm Trials with Binary Data.

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• Equivalence testing is crucial in clinical trials to demonstrate that a new treatment is not unacceptably worse than a standard one.
• Traditional methods for equivalence testing may have limitations, particularly with binary outcomes.

Purpose of the Study:

• To develop and evaluate a Bayesian approach for assessing hypotheses of equivalence in two-arm trials with binary data.
• To explore the utility of normal approximations for posterior distributions in this context.

Main Methods:

• Development of likelihood, prior, and posterior distributions for key parameters.
• Examination of normal approximation to posterior distributions using Taylor series expansion.
• Application of Markov Chain Monte Carlo (MCMC) methods for Bayesian inference.

Main Results:

• The study outlines the construction of Bayesian models for equivalence testing.
• It assesses the accuracy of normal approximations for posterior distributions.
• Demonstrates the practical application of the proposed methods.

Conclusions:

• The proposed Bayesian framework provides a viable alternative for equivalence hypothesis testing in binary data trials.
• MCMC methods offer a robust computational approach for Bayesian inference in this setting.
• The methods are illustrated with real-world clinical trial data, showing practical utility.