Cancer Heterogeneity Modeling With Omics Data via Network‐Based Block‐Wise Regulatory Analysis

Omics data have been extensively analyzed to quantify the heterogeneity of cancer and other diseases. Recent studies have suggested that interconnections among omics variables, as reflected in network structures, can be more informative than simpler measures. Multiple types of omics variables can be connected via regulatory relationships, and there are studies modeling heterogeneity based on such regulations. Here, we conduct heterogeneity analysis based on both network structures and regulatory relationships. Significantly different from the existing literature, we consider network structures of regulators, as opposed to regulatees-such networks describe more essential biological mechanisms and are less likely to be blurred by the mixture of direct and indirect interconnections. Another significant advancement is that we incorporate (unknown) blocking structures of regulators, which contain information complementary to network structures. A novel penalization approach is developed to simultaneously identify sample groups and estimate block structures, group-specific networks, and regulation relationships. An effective computational algorithm is developed. It is rigorously proved that the proposed approach enjoys consistency in estimation, selection, and block identification. Simulation studies demonstrate its competitiveness against multiple alternatives. In the analysis of TCGA breast cancer data, we consider the (gene expression, protein expression) dual and make sensible findings that differ from those of the alternatives.