  Gene expression-based heterogeneity analysis has been extensively conducted.
In recent studies, it has been shown that network-based analysis, which takes a
system perspective and accommodates the interconnections among genes, can be
more informative than that based on simpler statistics. Gene expressions are
highly regulated. Incorporating regulations in analysis can better delineate
the "sources" of gene expression effects. Although conditional network analysis
can somewhat serve this purpose, it does render enough attention to the
regulation relationships. In this article, significantly advancing from the
existing heterogeneity analyses based only on gene expression networks,
conditional gene expression network analyses, and regression-based
heterogeneity analyses, we propose heterogeneity analysis based on gene
expression networks (after accounting for or "removing" regulation effects) as
well as regulations of gene expressions. A high-dimensional penalized fusion
approach is proposed, which can determine the number of sample groups and
parameter values in a single step. An effective computational algorithm is
proposed. It is rigorously proved that the proposed approach enjoys the
estimation, selection, and grouping consistency properties. Extensive
simulations demonstrate its practical superiority over closely related
alternatives. In the analysis of two breast cancer datasets, the proposed
approach identifies heterogeneity and gene network structures different from
the alternatives and with sound biological implications.
