Subgroup Analysis of Differential Networks with Latent Variables

Differential network analysis serves as a crucial tool in capturing variations in network rewiring patterns across different biological conditions. Real-world observational data often contain subgroup structures with differing statistical properties, potentially leading to heterogeneity among differential networks. However, existing graphical model-based heterogeneity analysis methods are designed for subgroup networks rather than differential networks. Moreover, these methods require sparsity within each network, which is ineffective for dense networks, especially when observed variables are confounded by latent (unobserved) variables. In this article, we focus on estimating differential networks between an unlabeled heterogeneous group and a baseline group, and develop subgroup analysis from the perspective of differential networks. By imposing a sparse plus low-rank structure on the baseline network and sparsity on differential networks, which characterize and balance the influence of latent variables, the proposed method allows for effective estimation of sparse differential networks and non-sparse subgroup networks. We develop an efficient computational algorithm for this purpose. Simulation studies demonstrate the competitive performance of the proposed approach over closely related alternatives. An application to a set of data on Non-Small Cell Lung Cancer (NSCLC) further confirms the utility of the methodology.