Network-based hierarchical heterogeneity analysis and applications to cancer omics data

In the study of complex diseases, heterogeneity analysis has been routinely conducted. A series of recent studies have suggested that network (graph)-based heterogeneity analysis can take a system perspective and be more informative than that based on simpler statistics such as mean and variance. In this article, we conduct Gaussian graphical model (GGM)-based heterogeneity analysis. Significantly advancing from the existing literature, we consider the scenario, where measurements can be decomposed into two parts, with the first and second parts for a rough grouping and a refined subgrouping, respectively. Additionally, the groups and subgroups have a nested structure, which enhances interpretability. A penalization approach is developed for simultaneous sparse estimation, grouping and subgrouping, and achieving the hierarchical structure. Its theoretical properties are rigorously established, and an effective computational algorithm is developed. Simulation demonstrates its competitive empirical performance. The analysis of data from the Pan-Cancer Analysis of Whole Genomes (PCAWG) further demonstrates its practical utility and leads to sensible findings.