Fig. 2
Illustration of bivariate GSEA. Panel A depicts the assessment of yF1F2(x) at x = 20. The two bars on top represent the distributions of functional genes along F1 and F2 ranks, where each vertical line with a unique color denotes a distinct functional gene. Here yF1F2(20) =9. Panel B illustrates estimation of yF2 ∣ F1(x). F1 is fixed; F21, F22, …, F2n represent distinct random permutations of F2 ranks. The dashed black line denotes the mean of the random walks over permutations. Panel C elucidates the relations of genes selected from the sorted F1 and F2 lists at a given rank n. Black and red circles denote the top-n genes according to F1 and randomized F2 ranks. The blue ellipse denotes the gene set members among the union of genes in the F1 (black) and F2 (red) circles. Both F1 and F2 circles have the size of n. The intersection of the functional genes and F1 genes (the purple area) has the size of k. By taking the union of F1 and F2 genes nextra genes are appended (the brown and yellow areas combined), among them there are kextra gene set members (the yellow area)