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. 2023 May 5;13:7352. doi: 10.1038/s41598-023-34069-z

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© The Author(s) 2023

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Interaction entropy model. This graphical model, describes the percent entropy that is explained by each selected attributes or pair-wise combination in our study population. Positive percent entropy indicates information gain (IG) or synergy and negative percent indicates lack of information gain (IG) or redundancy. Schematic coloration used in the visualization tools represents a continuum from synergy (i.e. non-additive) to redundancy. Red represents a high degree of synergy interaction, orange a lesser degree (both colors are not apparent in the current analysis), brown represents medium-level interaction or independence; and green and blue represent redundancy between the markers. This image was created by MDR software (3.0.3. dev. Jar) (https://sourceforge.net/projects/mdr/)³⁶.