Optimal multiple testing under a Gaussian prior on the effect sizes.

Area of Science:

• Statistics
• Genetics
• Bioinformatics

Background:

• Multiple testing is crucial in large-scale studies like genome-wide association studies (GWAS).
• Integrating prior information can improve statistical power but is challenging with frequentist methods.
• Existing methods struggle with computational complexity when incorporating uncertain prior information.

Purpose of the Study:

• To develop a novel method for large-scale frequentist multiple testing that effectively incorporates Bayesian prior information.
• To optimize weighted Bonferroni methods by finding optimal weights that maximize average power.
• To provide an efficient algorithm for discovering new loci in GWAS.

Main Methods:

• Developed a new method for frequentist multiple testing using Bayesian prior information.
• Formulated an optimization problem to find optimal [Formula: see text]-value weights for the weighted Bonferroni method.
• Designed an efficient algorithm for Gaussian priors on effect sizes, guaranteeing near-exact optimal weights.
• Utilized an open-source implementation for practical application.

Main Results:

• The proposed method achieves optimal [Formula: see text]-value weights, maximizing average power.
• The efficient algorithm overcomes the computational challenges of previous methods for uncertain priors.
• Demonstrated the method's ability to discover new loci in genome-wide association studies.
• Showcased favorable comparisons against existing competitor methods.

Conclusions:

• The new method offers a powerful and efficient approach for large-scale frequentist multiple testing with Bayesian priors.
• This technique enhances the discovery of genetic loci in GWAS.
• The availability of an open-source implementation facilitates its adoption in the research community.