Signal identification for rare and weak features: higher criticism or false discovery rates?

Area of Science:

• Biostatistics
• Statistical inference
• High-dimensional data analysis

Background:

• Signal identification in large-dimensional datasets presents significant challenges.
• The method of higher criticism (HC) has emerged as a valuable tool for setting decision thresholds.
• Understanding HC's performance within a false discovery rate (FDR) framework is crucial.

Purpose of the Study:

• To investigate the higher criticism (HC) method from a false discovery rate (FDR) perspective.
• To establish the relationship between HC thresholds and class boundary (CB) thresholds in discriminant analysis.
• To evaluate the practical equivalence of HC and FDR-based thresholds in specific data regimes.

Main Methods:

• Theoretical analysis of the higher criticism (HC) threshold in relation to class boundary (CB) thresholds.
• Investigation of the equivalence between HC thresholding and local FDR cutoffs.
• Empirical validation through simulations and application to real-world cancer gene expression data.

Main Results:

• The HC threshold serves as an approximation to the natural class boundary (CB) threshold.
• In rare-weak signal settings, HC thresholding is practically indistinguishable from using a local FDR cutoff.
• Analytical and simulation studies confirm the relationship and properties of HC and CB thresholds.

Conclusions:

• The higher criticism (HC) method provides an effective and interpretable approach to signal identification in high-dimensional data.
• HC thresholding aligns with FDR-based methods, offering a robust statistical framework.
• The findings are validated across diverse datasets, including cancer gene expression data, highlighting practical applicability.