Rank-adaptive covariance testing with applications to genomics and neuroimaging

Area of Science:

• Biostatistics
• Genomics
• Neuroimaging

Background:

• Covariance testing is crucial in biomedical studies for understanding complex joint behaviors.
• Existing methods lack power when differences are subtle and low-rank, common in genomics and neuroimaging.
• The Ky-Fan(k) norm captures low-rank structure differences but lacks statistical testing properties.

Purpose of the Study:

• To investigate the statistical properties of the Ky-Fan(k) norm in two-sample covariance testing.
• To propose a novel, powerful covariance testing methodology leveraging low-rank structures.
• To develop a method with exact Type I error control for hypothesis testing.

Main Methods:

• Investigated the Ky-Fan(k) norm for detecting low-rank covariance differences.
• Developed rank-adaptive covariance testing (RACT) methodology.
• Employed permutation for statistical inference to ensure Type I error control.

Main Results:

• Proposed RACT, a novel method enhancing power in covariance testing.
• RACT effectively leverages low-rank structures for signal detection.
• Validated RACT through simulations and real-world data.

Conclusions:

• RACT offers a powerful approach for two-sample covariance testing, especially in high-dimensional data.
• The method demonstrates utility in analyzing gene expression networks and diffusion tensor imaging data.
• RACT provides a statistically sound method for detecting subtle covariance differences.