Like the PAM50 RNA tumor signatures, the mRNA expression of luminal genes (e.g., ESR1 and GATA3) was positively correlated with luminal ctDNA-based signatures, while proliferation and cell cycle-related genes by mRNA (e.g., MKI67, AURKA, TTK, E2F1 and CCNE1) were positively correlated with proliferation-related ctDNA-based signatures (Supplementary Fig. 5). This evidence concerns the gene GATA3 and neoplasm.