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Detection of epistatic effects with logic regression and a classical linear regression model

Author

Listed:
  • Malina Magdalena

    (Section for Medical Statistics, Center of Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria)

  • Ickstadt Katja

    (Faculty of Statistics, Technische Universität Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany)

  • Schwender Holger

    (Heinrich Heine University Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany)

  • Posch Martin

    (Section for Medical Statistics, Center of Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria)

  • Bogdan Małgorzata

    (Department of Mathematics and Computer Science, Wrocław University of Technology, ul. Wybrzeze Wyspiańskiego 27, 50-370 Wrocław, Poland Department of Mathematics and Computer Science, Jan Dlugosz University in Czestochowa, Poland)

Abstract

To locate multiple interacting quantitative trait loci (QTL) influencing a trait of interest within experimental populations, usually methods as the Cockerham’s model are applied. Within this framework, interactions are understood as the part of the joined effect of several genes which cannot be explained as the sum of their additive effects. However, if a change in the phenotype (as disease) is caused by Boolean combinations of genotypes of several QTLs, this Cockerham’s approach is often not capable to identify them properly. To detect such interactions more efficiently, we propose a logic regression framework. Even though with the logic regression approach a larger number of models has to be considered (requiring more stringent multiple testing correction) the efficient representation of higher order logic interactions in logic regression models leads to a significant increase of power to detect such interactions as compared to a Cockerham’s approach. The increase in power is demonstrated analytically for a simple two-way interaction model and illustrated in more complex settings with simulation study and real data analysis.

Suggested Citation

  • Malina Magdalena & Ickstadt Katja & Schwender Holger & Posch Martin & Bogdan Małgorzata, 2014. "Detection of epistatic effects with logic regression and a classical linear regression model," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(1), pages 83-104, February.
    • Handle: RePEc:bpj:sagmbi:v:13:y:2014:i:1:p:83-104:n:6
    DOI: 10.1515/sagmb-2013-0028
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    References listed on IDEAS

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    1. Małgorzata Bogdan & Florian Frommlet & Przemysław Biecek & Riyan Cheng & Jayanta K. Ghosh & R.W. Doerge, 2008. "Extending the Modified Bayesian Information Criterion (mBIC) to Dense Markers and Multiple Interval Mapping," Biometrics, The International Biometric Society, vol. 64(4), pages 1162-1169, December.
    2. Ruczinski, Ingo & Kooperberg, Charles & L. LeBlanc, Michael, 2004. "Exploring interactions in high-dimensional genomic data: an overview of Logic Regression, with applications," Journal of Multivariate Analysis, Elsevier, vol. 90(1), pages 178-195, July.
    3. Boulesteix Anne-Laure & Strobl Carolin & Weidinger Stefan & Wichmann H.-Erich & Wagenpfeil Stefan, 2007. "Multiple Testing for SNP-SNP Interactions," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-24, December.
    4. Zehua Chen & Jianbin Liu, 2009. "Mixture Generalized Linear Models for Multiple Interval Mapping of Quantitative Trait Loci in Experimental Crosses," Biometrics, The International Biometric Society, vol. 65(2), pages 470-477, June.
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