{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:19Z","timestamp":1760208199856,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,1,7]],"date-time":"2017-01-07T00:00:00Z","timestamp":1483747200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We reconsider the properties and relationships of the interaction information and its modified versions in the context of detecting the interaction of two SNPs for the prediction of a binary outcome when interaction information is positive. This property is called predictive interaction, and we state some new sufficient conditions for it to hold true. We also study chi square approximations to these measures. It is argued that interaction information is a different and sometimes more natural measure of interaction than the logistic interaction parameter especially when SNPs are dependent. We introduce a novel measure of predictive interaction based on interaction information and its modified version. In numerical experiments, which use copulas to model dependence, we study examples when the logistic interaction parameter is zero or close to zero for which predictive interaction is detected by the new measure, while it remains undetected by the likelihood ratio test.<\/jats:p>","DOI":"10.3390\/e19010023","type":"journal-article","created":{"date-parts":[[2017,1,9]],"date-time":"2017-01-09T11:03:23Z","timestamp":1483959803000},"page":"23","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Use of Information Measures and Their Approximations to Detect Predictive Gene-Gene Interaction"],"prefix":"10.3390","volume":"19","author":[{"given":"Jan","family":"Mielniczuk","sequence":"first","affiliation":[{"name":"Institute of Computer Science, Polish Academy of Sciences, Jana Kazimierza 5, 01-248 Warsaw, Poland"},{"name":"Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcin","family":"Rdzanowski","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2463","DOI":"10.1093\/hmg\/11.20.2463","article-title":"Epistasis: What it means, what it doesn\u2019t mean, and statistical methods to detect it in humans","volume":"11","author":"Cordell","year":"2002","journal-title":"Hum. 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