Network Differential Connectivity Analysis

TL;DR

This paper introduces a new hypothesis testing framework for comparing two Gaussian graphical models, focusing on identifying differences in connectivity patterns with valid measures of uncertainty, applicable in biological research.

Contribution

It proposes a novel qualitative hypothesis testing approach that effectively tests for differences in network connectivity patterns and provides p-values, addressing limitations of existing methods.

Findings

The framework correctly controls the type-I error rate under certain conditions.

Simulation studies show accurate detection of network differences.

Applications in cancer genetics and brain imaging demonstrate practical utility.

Abstract

Identifying differences in networks has become a canonical problem in many biological applications. Here, we focus on testing whether two Gaussian graphical models are the same. Existing methods try to accomplish this goal by either directly comparing their estimated structures, or testing the null hypothesis that the partial correlation matrices are equal. However, estimation approaches do not provide measures of uncertainty, e.g., $p$-values, which are crucial in drawing scientific conclusions. On the other hand, existing testing approaches could lead to misleading results in some cases. To address these shortcomings, we propose a qualitative hypothesis testing framework, which tests whether the connectivity patterns 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, e.g., $p$-values. We investigate theoretical and numerical properties of our proposal and illustrate its utility in biological applications. 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 datasets and applications in cancer genetics and brain imaging studies.