A powerful nonparametric method for detecting differentially co-expressed genes: distance correlation screening and edge-count test

Limitation of permutation-based differential correlation analysis

The comparison of biological systems, through the analysis of molecular changes under different conditions, has played a crucial role in the progress of modern biological science. Specifically, differential correlation analysis (DCA) has been employed to determine whether relationships between genomic features differ across conditions or outcomes. Because ascertaining the null distribution of test statistics to capture variations in correlation is challenging, several DCA methods utilize permutation which can loosen parametric (e.g., normality) assumptions. However, permutation is often problematic for DCA due to violating the assumption that samples are exchangeable under the null. Here, we examine the limitations of permutation-based DCA and investigate instances where the permutation-based DCA exhibits poor performance. Experimental results show that the permutation-based DCA often fails to control the type I error under the null hypothesis of equal correlation structures.

Differential Co-Expression Analyses Allow the Identification of Critical Signalling Pathways Altered during Tumour Transformation and Progression

Biological systems respond to perturbations through the rewiring of molecular interactions, organised in gene regulatory networks (GRNs). Among these, the increasingly high availability of transcriptomic data makes gene co-expression networks the most exploited ones. Differential co-expression networks are useful tools to identify changes in response to an external perturbation, such as mutations predisposing to cancer development, and leading to changes in the activity of gene expression regulators or signalling. They can help explain the robustness of cancer cells to perturbations and identify promising candidates for targeted therapy, moreover providing higher specificity with respect to standard co-expression methods. Here, we comprehensively review the literature about the methods developed to assess differential co-expression and their applications to cancer biology. Via the comparison of normal and diseased conditions and of different tumour stages, studies based on these methods led to the definition of pathways involved in gene network reorganisation upon oncogenes' mutations and tumour progression, often converging on immune system signalling. A relevant implementation still lagging behind is the integration of different data types, which would greatly improve network interpretability. Most importantly, performance and predictivity evaluation of the large variety of mathematical models proposed would urgently require experimental validations and systematic comparisons. We believe that future work on differential gene co-expression networks, complemented with additional omics data and experimentally tested, will considerably improve our insights into the biology of tumours.

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

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.

Model-free feature screening for categorical outcomes: Nonlinear effect detection and false discovery rate control

Feature screening has become a real prerequisite for the analysis of high-dimensional genomic data, as it is effective in reducing dimensionality and removing redundant features. However, existing methods for feature screening have been mostly relying on the assumptions of linear effects and independence (or weak dependence) between features, which might be inappropriate in real practice. In this paper, we consider the problem of selecting continuous features for a categorical outcome from high-dimensional data. We propose a powerful statistical procedure that consists of two steps, a nonparametric significance test based on edge count and a multiple testing procedure with dependence adjustment for false discovery rate control. The new method presents two novelties. First, the edge-count test directly targets distributional difference between groups, therefore it is sensitive to nonlinear effects. Second, we relax the independence assumption and adapt Efron's procedure to adjust for the dependence between features. The performance of the proposed procedure, in terms of statistical power and false discovery rate, is illustrated by simulated data. We apply the new method to three genomic datasets to identify genes associated with colon, cervical and prostate cancers.

Gene-Based Nonparametric Testing of Interactions Using Distance Correlation Coefficient in Case-Control Association Studies

Among the various statistical methods for identifying gene⁻gene interactions in qualitative genome-wide association studies (GWAS), gene-based methods have recently grown in popularity because they confer advantages in both statistical power and biological interpretability. However, most of these methods make strong assumptions about the form of the relationship between traits and single-nucleotide polymorphisms, which result in limited statistical power. In this paper, we propose a gene-based method based on the distance correlation coefficient called gene-based gene-gene interaction via distance correlation coefficient (GBDcor). The distance correlation (dCor) is a measurement of the dependency between two random vectors with arbitrary, and not necessarily equal, dimensions. We used the difference in dCor in case and control datasets as an indicator of gene⁻gene interaction, which was based on the assumption that the joint distribution of two genes in case subjects and in control subjects should not be significantly different if the two genes do not interact. We designed a permutation-based statistical test to evaluate the difference between dCor in cases and controls for a pair of genes, and we provided the p-value for the statistic to represent the significance of the interaction between the two genes. In experiments with both simulated and real-world data, our method outperformed previous approaches in detecting interactions accurately.