The Transitivity Misconception of Pearson’s Correlation Coefficient

Sotos, Ana Elisa Castro; Vanhoof, Stijn; Noortgate, Wim Van Den; Onghena, Patrick

doi:10.52041/serj.v8i2.394

Cited by 23 publications

(5 citation statements)

References 16 publications

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“…Here the complex relations refers to the non-bivariate normal data and non-linear and non-monotonic relations. Generally, the correlation value greater than 0.8 is described as strong correlation while the value less than 0.5 is described as weak correlation [ 34 ]. To measure the proportion of complex relationships in the microarray and RNA-seq datasets, we selected pairs of genes with distance correlation coefficients greater than 0.5 from the four datasets.…”

Section: Resultsmentioning

confidence: 99%

Distance correlation application to gene co-expression network analysis

Hou

Feng

et al. 2022

BMC Bioinformatics

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Background To construct gene co-expression networks, it is necessary to evaluate the correlation between different gene expression profiles. However, commonly used correlation metrics, including both linear (such as Pearson’s correlation) and monotonic (such as Spearman’s correlation) dependence metrics, are not enough to observe the nature of real biological systems. Hence, introducing a more informative correlation metric when constructing gene co-expression networks is still an interesting topic. Results In this paper, we test distance correlation, a correlation metric integrating both linear and non-linear dependence, with other three typical metrics (Pearson’s correlation, Spearman’s correlation, and maximal information coefficient) on four different arrays (macrophage and liver) and RNA-seq (cervical cancer and pancreatic cancer) datasets. Among all the metrics, distance correlation is distribution free and can provide better performance on complex relationships and anti-outlier. Furthermore, distance correlation is applied to Weighted Gene Co-expression Network Analysis (WGCNA) for constructing a gene co-expression network analysis method which we named Distance Correlation-based Weighted Gene Co-expression Network Analysis (DC-WGCNA). Compared with traditional WGCNA, DC-WGCNA can enhance the result of enrichment analysis and improve the module stability. Conclusions Distance correlation is better at revealing complex biological relationships between gene profiles compared with other correlation metrics, which contribute to more meaningful modules when analyzing gene co-expression networks. However, due to the high time complexity of distance correlation, the implementation requires more computer memory.

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Section: Resultsmentioning

confidence: 99%

Distance correlation application to gene co-expression network analysis

Hou

Feng

et al. 2022

BMC Bioinformatics

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“…Therefore, if the distance correlation coefficient between two random variables is greater than the Pearson correlation coefficient then a complex relationship exists between them - non-binary normal data and non-linear nonmonotonic relationship. In general, correlation values greater than 0.8 are described as strong correlation, while values less than 0.5 are described as weak correlation ( Castro Sotos et al, 2009 ). To measure the proportion of complex relationships in the dataset, we selected gene pairs with distance correlation coefficients greater than 0.5 from eight datasets.…”

Section: Resultsmentioning

confidence: 99%

KISL: knowledge-injected semi-supervised learning for biological co-expression network modules

et al. 2023

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The exploration of important biomarkers associated with cancer development is crucial for diagnosing cancer, designing therapeutic interventions, and predicting prognoses. The analysis of gene co-expression provides a systemic perspective on gene networks and can be a valuable tool for mining biomarkers. The main objective of co-expression network analysis is to discover highly synergistic sets of genes, and the most widely used method is weighted gene co-expression network analysis (WGCNA). With the Pearson correlation coefficient, WGCNA measures gene correlation, and uses hierarchical clustering to identify gene modules. The Pearson correlation coefficient reflects only the linear dependence between variables, and the main drawback of hierarchical clustering is that once two objects are clustered together, the process cannot be reversed. Hence, readjusting inappropriate cluster divisions is not possible. Existing co-expression network analysis methods rely on unsupervised methods that do not utilize prior biological knowledge for module delineation. Here we present a method for identification of outstanding modules in a co-expression network using a knowledge-injected semi-supervised learning approach (KISL), which utilizes apriori biological knowledge and a semi-supervised clustering method to address the issue existing in the current GCN-based clustering methods. To measure the linear and non-linear dependence between genes, we introduce a distance correlation due to the complexity of the gene-gene relationship. Eight RNA-seq datasets of cancer samples are used to validate its effectiveness. In all eight datasets, the KISL algorithm outperformed WGCNA when comparing the silhouette coefficient, Calinski-Harabasz index and Davies-Bouldin index evaluation metrics. According to the results, KISL clusters had better cluster evaluation values and better gene module aggregation. Enrichment analysis of the recognition modules demonstrated their effectiveness in discovering modular structures in biological co-expression networks. In addition, as a general method, KISL can be applied to various co-expression network analyses based on similarity metrics. Source codes for the KISL and the related scripts are available online at https://github.com/Mowonhoo/KISL.git.

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“…Eleven CAD candidate genes in the quiescent condition and 12 CAD candidate genes in the proliferative condition were moderate to highly correlated with AMT (Pearson r values between |0.5 and 0.75|). 45,46 AMT gene expression has previously been shown to be associated with CAD risk. 47 AMT was also differentially expressed between quiescent and proliferative conditions, suggesting that gene expression levels of CAD genome-wide association studies genes functioning in nitrogen metabolic enriched modules were reprogrammed due to changes in AMT expression levels, or vice versa.…”

Section: Metabolic Pathway Enrichment In Unpreserved Modulesmentioning

confidence: 98%

Network Preservation Analysis Reveals Dysregulated Metabolic Pathways in Human Vascular Smooth Muscle Cell Phenotypic Switching

Perry

Albarracin

Aherrahrou

et al. 2023

Circ: Genomic and Precision Medicine

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Background: Vascular smooth muscle cells are key players involved in atherosclerosis, the underlying cause of coronary artery disease. They can play either beneficial or detrimental roles in lesion pathogenesis, depending on the nature of their phenotypic changes. An in-depth characterization of their gene regulatory networks can help better understand how their dysfunction may impact disease progression. Methods: We conducted a gene expression network preservation analysis in aortic smooth muscle cells isolated from 151 multiethnic heart transplant donors cultured under quiescent or proliferative conditions. Results: We identified 86 groups of coexpressed genes (modules) across the 2 conditions and focused on the 18 modules that are least preserved between the phenotypic conditions. Three of these modules were significantly enriched for genes belonging to proliferation, migration, cell adhesion, and cell differentiation pathways, characteristic of phenotypically modulated proliferative vascular smooth muscle cells. The majority of the modules, however, were enriched for metabolic pathways consisting of both nitrogen-related and glycolysis-related processes. Therefore, we explored correlations between nitrogen metabolism-related genes and coronary artery disease–associated genes and found significant correlations, suggesting the involvement of the nitrogen metabolism pathway in coronary artery disease pathogenesis. We also created gene regulatory networks enriched for genes in glycolysis and predicted key regulatory genes driving glycolysis dysregulation. Conclusions: Our work suggests that dysregulation of vascular smooth muscle cell metabolism participates in phenotypic transitioning, which may contribute to disease progression, and suggests that AMT and mannose phosphate isomerase may play an important role in regulating nitrogen and glycolysis-related metabolism in smooth muscle cells.

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The Transitivity Misconception of Pearson’s Correlation Coefficient

Cited by 23 publications

References 16 publications

Distance correlation application to gene co-expression network analysis

Distance correlation application to gene co-expression network analysis

KISL: knowledge-injected semi-supervised learning for biological co-expression network modules

Network Preservation Analysis Reveals Dysregulated Metabolic Pathways in Human Vascular Smooth Muscle Cell Phenotypic Switching

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