  Revealing relationships between genes and disease phenotypes is a critical
problem in biomedical studies. This problem has been challenged by the
heterogeneity of diseases. Patients of a perceived same disease may form
multiple subgroups, and different subgroups have distinct sets of important
genes. It is hence imperative to discover the latent subgroups and reveal the
subgroup-specific important genes. Some heterogeneity analysis methods have
been proposed in recent literature. Despite considerable successes, most of the
existing studies are still limited as they cannot accommodate data
contamination and ignore the interconnections among genes. Aiming at these
shortages, we develop a robust structured heterogeneity analysis approach to
identify subgroups, select important genes as well as estimate their effects on
the phenotype of interest. Possible data contamination is accommodated by
employing the Huber loss function. A sparse overlapping group lasso penalty is
imposed to conduct regularization estimation and gene identification, while
taking into account the possibly overlapping cluster structure of genes. This
approach takes an iterative strategy in the similar spirit of K-means
clustering. Simulations demonstrate that the proposed approach outperforms
alternatives in revealing the heterogeneity and selecting important genes for
each subgroup. The analysis of Cancer Cell Line Encyclopedia data leads to
biologically meaningful findings with improved prediction and grouping
stability.
