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

Magdalena Malina1 / Katja Ickstadt2 / Holger Schwender3 / Martin Posch1 / Małgorzata Bogdan4, 5

1Section for Medical Statistics, Center of Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria

2Faculty of Statistics, Technische Universität Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany

3Heinrich Heine University Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany

4Department of Mathematics and Computer Science, Wrocław University of Technology, ul. Wybrzeze Wyspiańskiego 27, 50-370 Wrocław, Poland

5Department of Mathematics and Computer Science, Jan Dlugosz University in Czestochowa, Poland

Corresponding author: Magdalena Malina, Section for Medical Statistics, Center of Medical Statistics, Informatics and Intelligent Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria, e-mail: (email)

Citation Information: Statistical Applications in Genetics and Molecular Biology. Volume 13, Issue 1, Pages 83–104, ISSN (Online) 1544-6115, ISSN (Print) 2194-6302, DOI: 10.1515/sagmb-2013-0028, January 2014

Publication History:

Published Online:: 2014-01-07

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.

Keywords: Cockerham’s model; epistatic effects; experimental study; high order interactions; generalized linear models;logic regression