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Open AccessArticle

Use of Information Measures and Their Approximations to Detect Predictive Gene-Gene Interaction

by Jan Mielniczuk 1,2,*,† and Marcin Rdzanowski 2,†
1
Institute of Computer Science, Polish Academy of Sciences, Jana Kazimierza 5, 01-248 Warsaw, Poland
2
Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Jinfeng Wang
Entropy 2017, 19(1), 23; https://doi.org/10.3390/e19010023
Received: 7 November 2016 / Revised: 23 December 2016 / Accepted: 31 December 2016 / Published: 7 January 2017
(This article belongs to the Special Issue Transfer Entropy II)
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. View Full-Text
Keywords: predictive interaction; interaction information; logistic interaction; Single Nucleotide Polymorphism (SNP); copula; Kirkwood approximation and parameter predictive interaction; interaction information; logistic interaction; Single Nucleotide Polymorphism (SNP); copula; Kirkwood approximation and parameter
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Mielniczuk, J.; Rdzanowski, M. Use of Information Measures and Their Approximations to Detect Predictive Gene-Gene Interaction. Entropy 2017, 19, 23.

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