Molecular signatures are sets of genes, proteins, genetic variants or other variables that can be used as markers for a particular phenotype. Reliable signature discovery methods could yield valuable insight into cell biology and mechanisms of human disease. However, it is currently not clear how to control error rates such as the false discovery rate (FDR) in signature discovery. Moreover, signatures for cancer gene expression have been shown to be unstable, that is, difficult to replicate in independent studies, casting doubts on their reliability.

We demonstrate that with modern prediction methods, signatures that yield accurate predictions may still have a high FDR. Further, we show that even signatures with low FDR may fail to replicate in independent studies due to limited statistical power. Thus, neither stability nor predictive accuracy are relevant when FDR control is the primary goal. We therefore develop a general statistical hypothesis testing framework that for the first time provides FDR control for signature discovery. Our method is demonstrated to be correct in simulation studies. When applied to five cancer data sets, the method was able to discover molecular signatures with 5% FDR in three cases, while two data sets yielded no significant findings. Molecular signatures are sets of genes, mRNA transcripts, proteins, genetic variants or other variables that can be used as markers for a particular cell or tissue phenotype, such as a cancerous or diabetic state. Signatures have a two-fold purpose: they may be useful for disease diagnosis or risk assessment (prediction), but they may also implicate molecules not previously known to be involved in the underlying molecular pathology