Can we Find Molecular Signatures from Gene Expression Data?

“Molecular signatures” or “gene-expression signatures” are a key feature in many studies that use microarray data in cancer research (e.g., Alizadeh et al., 2000; Golub et al., 1999; Pomeroy et al., 2002; Rosenwald et al., 2002; Shipp et al., 2002). Shaffer et al. (2001, p. 375) refer to signatures as“(...) genes that are coordinately expressed in samples related by some identifiable criterion such as cell type, differentiation state, or signaling response” (emphasis is ours). Molecular signatures are often used to model patients’ clinically relevant information (e.g., prognosis, survival time, etc) as a function of the gene expression data, but instead of using individual genes as predictors, the predictors are the signature components or “metagenes”. In spite of the widespread use of the term “molecular signature”, no explicit definition is available. Following the conventions of the literature, we will consider a signature to be composed of one or more signature components or metagenes, where each signature component is a weighted combination of one or more coexpressed genes, and such that statistical models that use signatures both have good predictive performance and are easy to interpret biologically. Based on the litearture, we can try to formalize these goals by requiring that signatures and signature components satisfy the following conditions: