CorDiff

CorDiff tests equality of covariance matrices across genomic features to detect changes in covariance associated with discrete or continuous experimental variables and to study genetic interactions.

Key Features:

• Uniform Framework: Tests associations between covariance matrices and an experimental variable, extending beyond two-sample problems and restrictive p versus n assumptions.
• Summary Statistics: Implements four distinct summary statistics tailored to detect different types of changes in covariance.
• Connectivity Statistic: Includes a connectivity statistic sensitive to global changes in covariance magnitude.
• Risk Score Association: Associates a natural individual risk score with several statistics for continuous experimental variables.
• Asymptotic Results: Provides asymptotic inference valid for continuous and discrete responses under mild conditions, including settings where the number of features (p) may exceed the sample size (n).
• Permutational Equivalence: Demonstrates permutational equivalence of the proposed statistics to some existing methods in specific two-sample cases.

Scientific Applications:

• Differential Covariance Analysis: Detects changes in covariance structure among genomic features across experimental conditions.
• High-Dimensional Genomics: Applies to large-scale genetic datasets where the number of features (p) can exceed sample size (n).
• Genetic Interaction Studies: Explores associations between covariance patterns and discrete or continuous experimental variables to inform studies of genetic interactions.

Methodology:

Performs covariance regression and computes four summary statistics including a connectivity statistic, employs asymptotic inference applicable when p may exceed n, and reports permutational equivalence results in two-sample cases.