Unveiling Commonalities and Differences in Genetic Regulations via Two-Way Fusion.

Understanding the genetic regulation, for example, gene expressions (GEs) by copy number variations and methylations, is crucial to uncover the development and progression of complex diseases. Advancing from early studies that are mostly focused on homogeneous groups of patients, some recent studies have shifted their focus toward different patient groups, explored their commonalities and differences, and led to insightful findings. However, the analysis can be very challenging with one GE possibly regulated by multiple regulators and one regulator potentially regulating the expressions of multiple genes, leading to two distinct types of commonalities/differences in the patterns of genetic regulation. In addition, the high dimensionality of both sides of regulation poses challenges to computation. In this study, we develop a two-way fusion integrative analysis approach, which innovatively applies two fusion penalties to simultaneously identify commonalities/differences in the regulated pattern of GEs and regulating pattern of regulators, and adopt a Huber loss function to accommodate the possible data contamination. Moreover, a simple yet efficient iterative optimization algorithm is developed, which does not need to introduce any auxiliary variables and extra tuning parameters and is guaranteed to converge to a globally optimal solution. The advantages of the proposed approach are demonstrated in extensive simulations. The analysis of The Cancer Genome Atlas data on melanoma and lung cancer leads to interesting findings and satisfactory prediction performance.