Analysis flowchart of this study. The present study is aimed to systematically explore optimal conditions and related biological functions of ceRNA regulation in GBM, and confer cancer type specific and independent effects. (A) First we defined 47,451,423 putative ceRNA pairs as pairs of genes (i.e., pairs of ceRNAs) sharing any number of predicted targeting miRNAs in the TargetScan database. Pairwise correlation coefficients of putative ceRNA pairs were computed in 481-sample TCGA GBM datasets. (B) Correlation coefficients were partitioned into groups based on the states of each essential factor of putative ceRNA pairs, followed by inter-group goodness-of-fit tests (K-S tests) that pinpointed the essential factors and optimal conditions for ceRNA regulation. (C) 551,175 pairs of ceRNAs fulfilling all of the identified optimal conditions were defined as optimal ceRNA pairs. In order to address differential and constitutive functions, we then included TCGA OV, LUSC, and LAML datasets and performed pan-cancer analysis.