Abstract
Epistasis is the interactions among multiple genetic variants. It has emerged to explain the 'missing heritability' that a marginal genetic effect does not account for by genome-wide association studies, and also to understand the hierarchical relationships between genes in the genetic pathways. The Fisher's geometric model is common in detecting the epistatic effects. However, despite the substantial successes of many studies with the model, it often fails to discover the functional dependence between genes in an epistasis study, which is an important role in inferring hierarchical relationships of genes in the biological pathway. We justify the imperfectness of Fisher's model in the simulation study and its application to the biological data. Then, we propose a novel generic epistasis model that provides a flexible solution for various biological putative epistatic models in practice. The proposed method enables one to efficiently characterize the functional dependence between genes. Moreover, we suggest a statistical strategy for determining a recessive or dominant link among epistatic expression quantitative trait locus to enable the ability to infer the hierarchical relationships. The proposed method is assessed by simulation experiments of various settings and is applied to human brain data regarding schizophrenia. The MATLAB source codes are publicly available at: http://biomecis.uta.edu/epistasis.
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