High-dimensional covariance matrices tests for analyzing multi-tumor gene expression data

Abstract

By collecting multiple sets per subject in microarray data, gene sets analysis requires characterize intra-subject variation using gene expression profiling. For each subject, the data can be written as a matrix with the different subsets of gene expressions (e.g. multiple tumor types) indexing the rows and the genes indexing the columns. To test the assumption of intra-subject (tumor) variation, we present and perform tests of multi-set sphericity and multi-set identity of covariance structures across subjects (tumor types). We demonstrate by both theoretical and empirical studies that the tests have good properties. We applied the proposed tests on The Cancer Genome Atlas (TCGA) and tested covariance structures for the gene expressions across several tumor types.

Kimma: flexible linear mixed effects modeling with kinship covariance for RNA-seq data

“…These matrices consist of more than one measure per observation, such as pairwise comparisons, and thus, cannot be modeled as fixed or simple random effects in current software. In addition, covariance random effects are distinct from the challenges of covariance within transcriptomic data which have been explored in several recent studies using coexpressed genes ( Kochan et al 2021 ) or gene sets ( Chang et al 2017 ; Qayed and Han 2021 ).…”