Set-based differential covariance testing for genomics.

Area of Science:

• Genomics
• Statistical Genetics
• Bioinformatics

Background:

• Existing methods for covariance matrix analysis are often limited to two-sample problems and specific feature-to-sample size ratios.
• General covariance regression approaches lack structured interpretability for hypothesis testing.
• Detecting changes in covariance for genomic features requires more robust and flexible statistical frameworks.

Purpose of the Study:

• To propose a unified framework for testing the association between covariance matrices and experimental variables (discrete or continuous).
• To develop novel summary statistics, including a connectivity statistic, to enhance power and flexibility.
• To provide a framework applicable to situations where the number of features (p) is greater than the sample size (n).

Main Methods:

• Development of a simple, uniform framework for covariance matrix association testing.
• Introduction of four distinct summary statistics, including a novel connectivity statistic.
• Establishment of asymptotic results under mild conditions, accommodating p > n scenarios.

Main Results:

• The proposed framework effectively tests covariance matrix associations with experimental variables.
• New statistics, including connectivity, demonstrate sensitivity to changes in covariance magnitude.
• Asymptotic results are established for both continuous and discrete responses, supporting p > n.
• Permutational equivalence shown with existing methods in the two-sample case.
• The R package CorDiff is available on CRAN, facilitating practical application.

Conclusions:

• The proposed framework provides a powerful and flexible approach to covariance matrix association testing.
• The methods are broadly applicable, including complex genomic data scenarios where p > n.
• The CorDiff package enables researchers to readily apply these advanced statistical techniques.