Perform PCA on a standardized version of X. Compute gene-level statistics, z j, j=1,…, p, for all p genomic variables that quantify the association between the genomic variable and the PC.
This schematic is based on the general gene set testing workflow of Ackermann and Strimmer [ 37 ] Compute gene-level statistics, z j, j =1,…, p, for all p genomic variables that quantify the association between the genomic variable and the PC.
The PCGSE method supports the following gene-level statistics, represented using the notation z j, j=1,…, p, for quantifying the association between genomic variable j and the target PC.
Cell cycle studies, particularly in epigenetics, may involve hundreds or thousands of short series, one for each epigenetic or genomic variable and each cell cycle.
Things changed with the advent of functional genomics and systems biology in the beginning of the 21st century when it became possible to measure the correlations between many "genomic" variables [ 3- 7].
The rows of the annotation matrix A represent f distinct biological functions, e.g., GO categories, and the elements a i, j hold indicator variables whose value depends on whether an annotation exists between the function i and genomic variable j.
Most of the observed correlations between genomic variables are relatively weak.
Because the Pearson correlation coefficients between genomic variables and PCs of the sample correlation matrix are proportional to the PC loadings (see (1) below), all of these gene-level statistics provide a measure of the correlation between genomic variables and PCs.
This can be phrased in statistical terminology as developing a significance test for associations between genomic variables and a given set, subset, or linear combination of PCs estimated from genomic data.
