Gains in Power from Structured Two-Sample Tests of Means on Graphs

TL;DR

This paper introduces structured two-sample tests of means on graphs that leverage known graph structures to improve detection power of distribution shifts, with applications in gene expression analysis.

Contribution

It develops methods that incorporate graph structure into two-sample tests, enhancing power and enabling detection of non-homogeneous subgraphs in high-dimensional data.

Findings

Graph-structured tests outperform traditional methods in simulations.

Application to breast cancer data reveals biologically relevant subgraphs.

Structured tests increase detection sensitivity for gene expression shifts.

Abstract

We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially expressed genes between two patient populations, as shifts in expression levels are expected to be coherent with the structure of graphs reflecting gene properties such as biological process, molecular function, regulation, or metabolism. For a fixed graph of interest, we demonstrate that accounting for graph structure can yield more powerful tests under the assumption of smooth distribution shift on the graph. We also investigate the identification of non-homogeneous subgraphs of a given large graph, which poses both computational and multiple testing problems. The relevance and benefits of the proposed approach are illustrated on synthetic data and on breast cancer gene expression data analyzed in context of KEGG pathways.