eQTL epistasis: Detecting complex interaction effects between multiple loci from eQTL data

The identification of expression quantitative trait loci (eQTL) epistasis, which is a non-linear interaction effect between two or more genetic loci that control quantitative traits, play an essential role in understanding the mechanisms of gene interactions in the complex diseases. However, many studies have ignored the possibility of the epistasis in spite of the countless empirical evidence of epistasis in Genetics. Thus, the epistasis research is still in its infancy. Furthermore, most eQTL epistasis studies have involved only the interaction model with additive effects, which lacks the power to represent either 1) other biologically putative interaction models or 2) the genetic dominance that is a superior relationship of an allele against another one at the same locus. To tackle the problems, we propose a general eQTL epistasis model that provides the capability to incorporate diverse interaction models so that it can be widely utilized as a generic equation of epistasis in the multiple testing of eQTL studies. The extensibility of the eQTL epistasis model into multivariate methods is also proposed to reduce the computational burden of the multiple testing and to consider group effects. As the example of the extensibility, we provide the methodology that embeds the eQTL epistasis model into the sparse canonical correlation analysis (SCCA) method. A globally optimal solution is provided and the performance was assessed by realistic simulation experiments. A study of psychiatric disorder diseases with the method was conducted as a target application.