Testing Differential Gene Networks under Nonparanormal Graphical Models with False Discovery Rate Control.

Qingyang Zhang

doi:10.3390/genes11020167

Abstract

The nonparanormal graphical model has emerged as an important tool for modeling dependency structure between variables because it is flexible to non-Gaussian data while maintaining the good interpretability and computational convenience of Gaussian graphical models. In this paper, we consider the problem of detecting differential substructure between two nonparanormal graphical models with false discovery rate control. We construct a new statistic based on a truncated estimator of the unknown transformation functions, together with a bias-corrected sample covariance. Furthermore, we show that the new test statistic converges to the same distribution as its oracle counterpart does. Both synthetic data and real cancer genomic data are used to illustrate the promise of the new method. Our proposed testing framework is simple and scalable, facilitating its applications to large-scale data. The computational pipeline has been implemented in the R package DNetFinder, which is freely available through the Comprehensive R Archive Network.

Highlights

Inferring the structural change of a network under different conditions is essential in many problems arising in biology, medicine, and other scientific fields
The computational pipeline has been implemented in the R package DNetFinder, which is freely available through the Comprehensive R Archive Network
Most of these applications have relied on the prevailing Gaussian graphical models (GGMs) because of its good interpretability and computational convenience, and there is a rich and growing literature on learning differential networks under GGMs

Summary

Introduction

Inferring the structural change of a network under different conditions is essential in many problems arising in biology, medicine, and other scientific fields. In the field of brain mapping, it is critical to identify the difference in brain connectivity between groups (for example, the brain connectivity network of normal subjects and patients often possess different structures). Most of these applications have relied on the prevailing Gaussian graphical models (GGMs) because of its good interpretability and computational convenience, and there is a rich and growing literature on learning differential networks under GGMs. To name a few, Guo et al. (2015) [1] introduced a joint estimation for multiple GGMs by a group lasso approach, under the assumption that the GGMs being studied are sparse and only differ in a small portion of edges. Danaher et al (2014) [2] proposed a fused graphical lasso method which is free from the sparsity assumption on condition-specific networks and only requires the sparsity of the differential network

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