Fig. 4

Two illustrative examples using 23 normal samples and 32 clear cell renal cell carcinoma samples from the GSE15641 dataset. a The MST of the pooled normal and tumor samples considering 67 genes from the KEGG renal cell carcinoma gene set. The samples of each phenotype are grouped together in the tree and the KS test rejects the null (\( {H}_1:\ {\overline{\mu}}_X\ne {\overline{\mu}}_Y \) is true) but not RKS test; b The MST of the pooled normal and tumor samples considering 19 genes from the KEGG glycosylphosphatidylinositol (GPI) anchor biosynthesis gene set. Normal samples constitute the backbone of the MST while tumor samples form the branches and RKS test rejects the null (\( {H}_1:\ {\overline{\sigma}}_X\ne {\overline{\sigma}}_Y \) is true) but not KS test. The roots of the HDP and radial ranking schemes in the MSTs are highlighted with rectangle and square shapes, respectively