Abstract
The main goal of this work is to propose two new Bayesian approaches to equivalence tests for two binomial proportions. As a result, we prove that these Bayesian hypothesis tests are equivalent. In this way, aiming to improve the safety of clinical trials, we use optimal decision rules to minimize the linear combination of the type I and type II error probabilities. Moreover, a significance level that is a function of the sample size is used. These Bayesian methodologies overcome some limitations of the frequentist approach predominantly used for these equivalence tests. A simulation study was carried out to assess the rate of the type I error probability and the power of the tests under different scenarios. We present a table for determining the optimal sample size in a practical way. The methodologies are illustrated with a data set on acute maxillary sinusitis.
Acknowledgments
We would like to thank the Editor and the anonymous referee for their constructive comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).