{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T09:41:25Z","timestamp":1762249285584},"reference-count":54,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Bioinform. Comput. Biol."],"published-print":{"date-parts":[[2010,8]]},"abstract":"<jats:p>Wiener and Granger have introduced an intuitive concept of causality (Granger causality) between two variables which is based on the idea that an effect never occurs before its cause. Later, Geweke generalized this concept to a multivariate Granger causality, i.e. n variables Granger-cause another variable. Although Granger causality is not \"effective causality\" in the Aristothelic sense, this concept is useful to infer directionality and information flow in observational data. Granger causality is usually identified by using VAR (Vector Autoregressive) 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 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 for the understanding of 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.<\/jats:p>","DOI":"10.1142\/s0219720010004860","type":"journal-article","created":{"date-parts":[[2010,3,31]],"date-time":"2010-03-31T11:50:22Z","timestamp":1270036222000},"page":"679-701","source":"Crossref","is-referenced-by-count":14,"title":["IDENTIFICATION OF GRANGER CAUSALITY BETWEEN GENE SETS"],"prefix":"10.1142","volume":"08","author":[{"given":"ANDR\u00c9","family":"FUJITA","sequence":"first","affiliation":[{"name":"Computational Science Research Program, RIKEN, 2-1, Hirosawa, Wako, Saitama, 351-0198, Japan"}]},{"given":"JO\u00c3O RICARDO","family":"SATO","sequence":"additional","affiliation":[{"name":"Center of Mathematics, Computation and Cognition, Universidade Federal do ABC, Rua Santa Ad\u00e9lia, 166 \u2013 Santo Andr\u00e9, Brazil"}]},{"given":"KANAME","family":"KOJIMA","sequence":"additional","affiliation":[{"name":"Human Genome Center, Institute of Medical Science, University of Tokyo, 4-6-1 Shirokanedai, Minato-ku, Tokyo, 108-8639, Japan"}]},{"given":"LUCIANA RODRIGUES","family":"GOMES","sequence":"additional","affiliation":[{"name":"Chemistry Institute, University of S\u00e3o Paulo, Av. 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