Center of Information Technology, University of Groningen, Groningen 9747 AJ, The Netherlands.
Department of Mathematics, Bernoulli Institute, University of Groningen, Groningen 9747 AG, The Netherlands.
Bioinformatics. 2022 Nov 15;38(22):5049-5054. doi: 10.1093/bioinformatics/btac657.
Gaussian graphical models (GGMs) are network representations of random variables (as nodes) and their partial correlations (as edges). GGMs overcome the challenges of high-dimensional data analysis by using shrinkage methodologies. Therefore, they have become useful to reconstruct gene regulatory networks from gene-expression profiles. However, it is often ignored that the partial correlations are 'shrunk' and that they cannot be compared/assessed directly. Therefore, accurate (differential) network analyses need to account for the number of variables, the sample size, and also the shrinkage value, otherwise, the analysis and its biological interpretation would turn biased. To date, there are no appropriate methods to account for these factors and address these issues.
We derive the statistical properties of the partial correlation obtained with the Ledoit-Wolf shrinkage. Our result provides a toolbox for (differential) network analyses as (i) confidence intervals, (ii) a test for zero partial correlation (null-effects) and (iii) a test to compare partial correlations. Our novel (parametric) methods account for the number of variables, the sample size and the shrinkage values. Additionally, they are computationally fast, simple to implement and require only basic statistical knowledge. Our simulations show that the novel tests perform better than DiffNetFDR-a recently published alternative-in terms of the trade-off between true and false positives. The methods are demonstrated on synthetic data and two gene-expression datasets from Escherichia coli and Mus musculus.
The R package with the methods and the R script with the analysis are available in https://github.com/V-Bernal/GeneNetTools.
Supplementary data are available at Bioinformatics online.
高斯图形模型（GGM）是随机变量（作为节点）及其部分相关系数（作为边）的网络表示。GGM 通过收缩方法克服了高维数据分析的挑战。因此，它们已成为从基因表达谱重建基因调控网络的有用工具。然而，人们常常忽略部分相关系数是“收缩”的，不能直接比较/评估。因此，准确的（差异）网络分析需要考虑变量的数量、样本大小，以及收缩值，否则，分析及其生物学解释将产生偏差。迄今为止，还没有适当的方法来考虑这些因素并解决这些问题。
我们推导出了 Ledoit-Wolf 收缩得到的部分相关系数的统计性质。我们的结果为（差异）网络分析提供了一个工具箱，包括（i）置信区间，（ii）零部分相关系数（零效应）的检验，以及（iii）部分相关系数的比较检验。我们的新（参数）方法考虑了变量的数量、样本大小和收缩值。此外，它们计算速度快，实现简单，只需要基本的统计知识。我们的模拟表明，与最近发布的替代方法 DiffNetFDR 相比，新的检验在真阳性和假阳性之间的权衡中表现更好。该方法在合成数据和大肠杆菌和小家鼠的两个基因表达数据集上进行了演示。
带有方法的 R 包和带有分析的 R 脚本可在 https://github.com/V-Bernal/GeneNetTools 上获得。
补充数据可在 Bioinformatics 在线获得。
