标题： 基因集之间格兰杰因果关系的识别和量化 显示英文标题

标题： Identification and quantification of Granger causality between gene sets

摘要： 维纳和格兰杰引入了两个变量之间因果关系的一个直观概念，这一概念基于“效应永远不会发生在其原因之前”的思想。后来，格韦克进一步将其推广为多变量格兰杰因果性，即n个变量格兰杰导致另一个变量。尽管格兰杰因果性并非“有效因果性”，但这一概念对于推断观察数据中的方向性和信息流是有用的。通常由于向量自回归（VAR）模型的简单性，格兰杰因果性一般通过这些模型来识别。在过去几年里，提出了几种基于VAR的模型以建模基因调控网络。 在这里，我们推广了多变量格兰杰因果性概念，以识别一组基因表达之间的格兰杰因果性，即是否一组n个基因格兰杰导致另一组m个基因，旨在识别和量化基因网络（或通路）之间信息流的方向和强度。变量集的格兰杰因果性概念被提出。此外，还提出了一种使用自助法检验进行识别的方法。该方法应用于模拟数据以及实际的生物基因表达数据中，以构建调控网络模型。这一概念可能有助于理解从一个网络或通路到另一个网络或通路的整体信息流，尤其是在调控网络中。 将这一概念与图论相结合，可以将汇点和源点推广到节点集。此外，可以根据总信息流定义基因集的枢纽和中心性。另一种应用是在注释中，当一组基因的功能未知时，但如果这组基因被另一组已研究得很好的基因所格兰杰导致，则此信息可能有助于推断或构建关于这组未知基因的一些假设。 显示英文摘要

摘要： Wiener and Granger have introduced an intuitive concept of causality between two variables which is based on the idea that an effect never occurs before its cause. Later, Geweke has generalized this concept to a multivariate Granger causality, i.e., n variables Granger-cause another variable. Although Granger causality is not "effective causality", this concept is useful to infer directionality and information flow in observational data. Granger causality is usually identified by using VAR models due to their simplicity. In the last few years, several VAR-based models were presented in order to model gene regulatory networks. Here, we generalize the multivariate Granger causality concept in order to identify Granger causalities between sets of gene expressions, i.e., whether a set of n genes Granger-causes another set of m genes, aiming at identifying and quantifying the flow of information between gene networks (or pathways). The concept of Granger causality for sets of variables is presented. Moreover, a method for its identification with a bootstrap test is proposed. This method is applied in simulated and also in actual biological gene expression data in order to model regulatory networks. This concept may be useful to understand the complete information flow from one network or pathway to the other, mainly in regulatory networks. Linking this concept to graph theory, sink and source can be generalized to node sets. Moreover, hub and centrality for sets of genes can be defined based on total information flow. Another application is in annotation, when the functionality of a set of genes is unknown, but this set is Granger caused by another set of genes which is well studied. Therefore, this information may be useful to infer or construct some hypothesis about the unknown set of genes.