Testing High Dimensional Covariance Matrices, with Application to Detecting Schizophrenia Risk Genes

TL;DR

This paper introduces a novel statistical test called sLED for comparing high-dimensional covariance matrices, specifically applied to gene expression data to identify genes associated with schizophrenia, outperforming existing methods.

Contribution

The paper develops the sLED test, a new approach for high-dimensional covariance comparison that leverages spectral analysis and is proven to be asymptotically powerful, with demonstrated superior performance.

Findings

sLED outperforms existing methods in simulations

Identifies new schizophrenia-associated genes

Reveals gene co-expression patterns in schizophrenia

Abstract

Scientists routinely compare gene expression levels in cases versus controls in part to determine genes associated with a disease. Similarly, detecting case-control differences in co-expression among genes can be critical to understanding complex human diseases; however statistical methods have been limited by the high dimensional nature of this problem. In this paper, we construct a sparse-Leading-Eigenvalue-Driven (sLED) test for comparing two high-dimensional covariance matrices. By focusing on the spectrum of the differential matrix, sLED provides a novel perspective that accommodates what we assume to be common, namely sparse and weak signals in gene expression data, and it is closely related with Sparse Principal Component Analysis. We prove that sLED achieves full power asymptotically under mild assumptions, and simulation studies verify that it outperforms other existing procedures under many biologically plausible scenarios. Applying sLED to the largest gene-expression dataset obtained from post-mortem brain tissue from Schizophrenia patients and controls, we provide a novel list of genes implicated in Schizophrenia and reveal intriguing patterns in gene co-expression change for Schizophrenia subjects. We also illustrate that sLED can be generalized to compare other gene-gene "relationship" matrices that are of practical interest, such as the weighted adjacency matrices.