TESTING HIGH-DIMENSIONAL COVARIANCE MATRICES, WITH APPLICATION TO DETECTING SCHIZOPHRENIA RISK GENES

Area of Science:

• Genomics
• Biostatistics
• Computational Biology

Background:

• Comparing gene expression and co-expression between cases and controls is crucial for understanding disease mechanisms.
• High-dimensional statistical methods for detecting these differences, especially in gene co-expression, are limited.

Purpose of the Study:

• To introduce a novel statistical test, sparse-Leading-Eigenvalue-Driven (sLED), for comparing high-dimensional covariance matrices.
• To provide a powerful and flexible method for analyzing gene expression and co-expression data in case-control studies.

Main Methods:

• Developed the sparse-Leading-Eigenvalue-Driven (sLED) test, focusing on the spectrum of the differential matrix.
• Utilized sparse and weak signal assumptions common in gene expression data.
• Related sLED to Sparse Principal Component Analysis.

Main Results:

• Proved that sLED achieves full asymptotic power under mild assumptions.
• Simulation studies demonstrated sLED's superior performance compared to existing methods in biologically plausible scenarios.
• Applied sLED to a large gene-expression dataset from Schizophrenia patients and controls, identifying novel implicated genes and co-expression patterns.

Conclusions:

• sLED offers a powerful new approach for comparing high-dimensional covariance matrices, particularly in genomics.
• The method successfully identified novel genes and co-expression changes associated with Schizophrenia.
• sLED is generalizable to other gene-gene relationship matrices, highlighting its broad applicability.