Abstract Background In cancer prognosis studies with gene expression measurements, an important goal is to construct gene signatures with predictive power. In this study, we describe the coordination among genes using the weighted coexpression network, where nodes represent genes and nodes are connected if the corresponding genes have similar expression patterns across samples. There are subsets of nodes, called modules, that are tightly connected to each other. In several published studies, it has been suggested that the first principal components of individual modules, also referred to as "eigengenes", may sufficiently represent the corresponding modules. Results In this article, we refer to principal components and their functions as representative features". We investigate higher-order representative features, which include the principal components other than the first ones and second order terms (quadratics and interactions). Two gradient thresholding methods are adopted for regularized estimation and feature selection. Analysis of six prognosis studies on lymphoma and breast cancer shows that incorporating higher-order representative features improves prediction performance over using eigengenes only. Simulation study further shows that prediction performance can be less satisfactory if the representative feature set is not properly chosen. Conclusions This study introduces multiple ways of defining the representative features and effective thresholding regularized estimation approaches. It provides convincing evidence that the higher-order representative features may have important implications for the prediction of cancer prognosis.