Multiplicity-calibrated Bayesian hypothesis tests.

Area of Science:

• Statistics
• Biostatistics
• Bayesian Inference

Background:

• Simultaneous hypothesis testing requires adjusting individual test levels to control the family-wise error rate (FWER).
• Traditional frequentist methods for FWER control can be conservative and do not utilize prior information.
• There is a need for more powerful statistical methods that leverage prior knowledge in multiple testing scenarios.

Purpose of the Study:

• To propose and evaluate a novel Bayesian hypothesis testing approach for multiplicity.
• To demonstrate how incorporating prior information can increase statistical power in multiple testing.
• To ensure robust control of the family-wise error rate (FWER) using Bayesian methods.

Main Methods:

• Developed a multiplicity-calibrated Bayesian hypothesis testing framework.
• Utilized prior information to set individual critical values for hypothesis tests.
• Controlled the family-wise error rate (FWER) using the Bonferroni inequality.
• Validated the method through simulations and real-world data from a pharmacogenetic trial and a cancer study.

Main Results:

• The proposed Bayesian method demonstrated effective control of the family-wise error rate (FWER).
• When prior information was accurate, the Bayesian approach showed substantially greater statistical power compared to standard frequentist methods.
• Simulations confirmed the error rate control and power advantages of the Bayesian method.

Conclusions:

• Multiplicity-calibrated Bayesian hypothesis testing offers a powerful alternative to frequentist approaches for simultaneous hypothesis testing.
• Incorporating accurate prior information significantly enhances the power of statistical tests while maintaining error rate control.
• This Bayesian framework provides a valuable tool for researchers dealing with multiple comparisons in complex studies.