  Heterogeneity is a hallmark of many complex diseases. There are multiple ways
of defining heterogeneity, among which the heterogeneity in genetic
regulations, for example GEs (gene expressions) by CNVs (copy number
variations) and methylation, has been suggested but little investigated.
Heterogeneity in genetic regulations can be linked with disease severity,
progression, and other traits and is biologically important. However, the
analysis can be very challenging with the high dimensionality of both sides of
regulation as well as sparse and weak signals. In this article, we consider the
scenario where subjects form unknown subgroups, and each subgroup has unique
genetic regulation relationships. Further, such heterogeneity is "guided" by a
known biomarker. We develop an MSF (Multivariate Sparse Fusion) approach, which
innovatively applies the penalized fusion technique to simultaneously determine
the number and structure of subgroups and regulation relationships within each
subgroup. An effective computational algorithm is developed, and extensive
simulations are conducted. The analysis of heterogeneity in the GE-CNV
regulations in melanoma and GE-methylation regulations in stomach cancer using
the TCGA data leads to interesting findings.
