New Bayesian approaches to equivalence testing

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.

Keywords:

• Bayes factor
• clinical trials
• hypotheses testing
• optimal decision
• sample size

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).

Additional information

Funding

We would like to thank the Editor and the anonymous referee for their constructive comments and suggestions. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. The work of the third author is partially funded by CNPq, Brazil.