NETWORK DIFFERENTIAL CONNECTIVITY ANALYSIS

Abstract

Identifying differences in networks has become a canonical problem in many biological applications. Existing methods try to accomplish this goal by either directly comparing the estimated structures of two networks, or testing the null hypothesis that the covariance or inverse covariance matrices in two populations are identical. However, estimation approaches do not provide measures of uncertainty, e.g., p-values, whereas existing testing approaches could lead to misleading results, as we illustrate in this paper. To address these shortcomings, we propose a qualitative hypothesis testing framework, which tests whether the connectivity structures in the two networks are the same. our framework is especially appropriate if the goal is to identify nodes or edges that are differentially connected. No existing approach could test such hypotheses and provide corresponding measures of uncertainty. Theoretically, we show that under appropriate conditions, our proposal correctly controls the type-I error rate in testing the qualitative hypothesis. Empirically, we demonstrate the performance of our proposal using simulation studies and applications in cancer genomics.

Keywords: biological networks; differential connectivity; high-dimensional data; lasso; significance test.

FIG 1.

Differentially connected edges between ER− and ER+ breast cancer patients found by group graphical lasso. Yellow edges are genetic interactions that are found in ER− but not ER+ breast cancer patients; gray edges are genetic interactions that are found in ER+ but not ER− breast cancer patients. Identically connected edges are omitted.

FIG 2.

Conditional dependency structures of variables in populations I and II.

FIG 3.

Differentially connected edges between ER− and ER+ breast cancer patients. Yellow edges are genetic interactions that are found in ER− but not ER+ breast cancer patients by the GraceI test; gray edges are genetic interactions that are found in ER+ but not ER− breast cancer patients by the GraceI test. Identically connected edges are omitted.

FIG 4.

The average false positive rate and power of rejecting $H_{0,j}^{\ast }$. The axis for false positive rate is on the left of each panel, whereas the axis for power is on the right.