Optimal Control of Directional False Discovery Rates in Large-Scale Testing

Area of Science:

• Biomedical data analysis
• Genomics
• Statistical genetics

Background:

• High-throughput technologies measure thousands of gene expression levels simultaneously.
• Identifying over-expressed and under-expressed genes is crucial for analyzing gene expression data.
• Existing two-group models fail to control specific false discovery rates for over- and under-expressed genes.

Purpose of the Study:

• To propose a general three-group model for gene expression data analysis.
• To develop a decision rule that controls both over- and under-expressed false discovery rates.
• To optimize the expected number of true discoveries while maintaining desired false discovery proportions.

Main Methods:

• Development of a general three-group model accommodating dependence between test statistics.
• Design of a decision rule with a monotonic structure for controlling false discovery rates.
• Linearization of two-directional false discovery rate constraints using the monotonic structure.

Main Results:

• The proposed decision rule optimizes true discoveries while controlling false discovery rates for both over- and under-expression.
• Data-driven versions of the procedures are suggested and their consistency is established.
• The new procedures demonstrate strong performance in comparisons with existing methods and in genomic applications.

Conclusions:

• The proposed three-group model and decision rule offer improved control over false discoveries in gene expression analysis.
• This approach enhances the reliability of identifying differentially expressed genes.
• The findings have significant implications for genomic studies and biomedical research.