Inspired by a newly discovered gene regulation mechanism known as competing endogenous RNA (ceRNA) interactions, several computational methods have been proposed to generate ceRNA networks. However, most of these methods have focused on deriving restricted types of ceRNA interactions such as lncRNA-miRNA-mRNA interactions. Competition for miRNA-binding occurs not only between lncRNAs and mRNAs but also between lncRNAs or between mRNAs. Furthermore, a large number of pseudogenes also act as ceRNAs, thereby regulate other genes. In this study, we developed a general method for constructing integrative networks of all possible interactions of ceRNAs in renal cell carcinoma (RCC). From the ceRNA networks we derived potential prognostic biomarkers, each of which is a triplet of two ceRNAs and miRNA (i.e., ceRNA-miRNA-ceRNA). Interestingly, some prognostic ceRNA triplets do not include mRNA at all, and consist of two non-coding RNAs and miRNA, which have been rarely known so far. Comparison of the prognostic ceRNA triplets to known prognostic genes in RCC showed that the triplets have a better predictive power of survival rates than the known prognostic genes. Our approach will help us construct integrative networks of ceRNAs of all types and find new potential prognostic biomarkers in cancer.