Gaussian graphical model-based heterogeneity analysis via penalized fusion

Heterogeneity is a hallmark of cancer, diabetes, cardiovascular diseases, and many other complex diseases. This study has been partly motivated by the unsupervised heterogeneity analysis for complex diseases based on molecular and imaging data, for which, network-based analysis, by accommodating the interconnections among variables, can be more informative than that limited to mean, variance, and other simple distributional properties. In the literature, there has been very limited research on network-based heterogeneity analysis, and a common limitation shared by the existing techniques is that the number of subgroups needs to be specified a priori or in an ad hoc manner. In this article, we develop a penalized fusion approach for heterogeneity analysis based on the Gaussian graphical model. It applies penalization to the mean and precision matrix parameters to generate regularized and interpretable estimates. More importantly, a fusion penalty is imposed to "automatedly" determine the number of subgroups and generate more concise, reliable, and interpretable estimation. Consistency properties are rigorously established, and an effective computational algorithm is developed. The heterogeneity analysis of non-small-cell lung cancer based on single-cell gene expression data of the Wnt pathway and that of lung adenocarcinoma based on histopathological imaging data not only demonstrate the practical applicability of the proposed approach but also lead to interesting new findings.