Fig. 2
Genomic regression analysis of co-expression (GRACE) corrects for correlation bias due to copy number variation. a Relative copy number levels vs. RNA levels of EIF2D for all 1075 tumor samples. The residuals from the linear regression model fitted with all 1075 tumor samples were marked by purple lines. b Average autocorrelation of neighboring genes in TCGA BRCA samples. Correlations between neighboring genes separated by 0–40 genes in between were calculated as autocorrelation for each sample. The average of autocorrelations was taken for 1075 tumor samples and 112 normal samples. The autocorrelation of neighboring genes based on copy number-adjusted expression levels variation (tumor residuals) was markedly reduced compared to autocorrelation based on tumor RNA. Average autocorrelation from normal samples represent the gene–gene autocorrelation baseline in diploid cells. c, d Top 10 EIF2D correlated genes by standard method (c) or GRACE (d) based on Spearman correlation. Top 10 EIF2D correlated genes by standard method are all located in cytoband 1q whereas top 10 EIF2D correlated genes by GRACE are all outside cytoband 1q and are all ribosomal protein genes. e, f Enrichment of KEGG_RIBOSOME genes from the top 100 EIF2D correlated genes by standard method with a p value of 0.10 (e) or by GRACE with a p value of 9.0e−143 (f). g, h Enrichment of genes from chromosome 1q in the top 100 EIF2D correlated genes by standard method with a p value of 8.7e−119 (g) or by GRACE with a p value of 0.99 (h). i Relative frequency distribution of chromosomal neighbors in top 10 co-expressing genes for all genes. GRACE markedly reduced the number of chromosomal neighbors in the top 10 co-expressing genes. j, k Kernel density estimation plots that visualize the distribution of pooled Spearman rank correlation coefficients for top 10 co-expressing genes from the same chromosome (j) or not from the same chromosome (k). Compared to the standard method, GRACE decreased intra-chromosomal gene–gene correlation and increased inter-chromosomal gene–gene correlation. All analyses are based on TCGA BRCA data
