Efficiently finding genome-wide three-way gene interactions from transcript- and genotype-data

Motivation: We address the issue of finding a three-way gene interaction, i.e. two interacting genes in expression under the genotypes of another gene, given a dataset in which expressions and genotypes are measured at once for each individual. This issue can be a general, switching mechanism in expression of two genes, being controlled by categories of another gene, and finding this type of interaction can be a key to elucidating complex biological systems. The most suitable method for this issue is likelihood ratio test using logistic regressions, which we call interaction test, but a serious problem of this test is computational intractability at a genome-wide level

A Kernel Test for Three-Variable Interactions

We introduce kernel nonparametric tests for Lancaster three-variable interaction and for total independence, using embeddings of signed measures into a reproducing kernel Hilbert space. The resulting test statistics are straightforward to compute, and are used in powerful interaction tests, which are consistent against all alternatives for a large family of reproducing kernels. We show the Lancaster test to be sensitive to cases where two independent causes individually have weak influence on a third dependent variable, but their combined effect has a strong influence. This makes the Lancaster test especially suited to finding structure in directed graphical models, where it outperforms competing nonparametric tests in detecting such V-structures

A General Model for Multilocus Epistatic Interactions in Case-Control Studies

Background: Epistasis, i.e., the interaction of alleles at different loci, is thought to play a central role in the formation and progression of complex diseases. The complexity of disease expression should arise from a complex network of epistatic interactions involving multiple genes. Methodology: We develop a general model for testing high-order epistatic interactions for a complex disease in a casecontrol study. We incorporate the quantitative genetic theory of high-order epistasis into the setting of cases and controls sampled from a natural population. The new model allows the identification and testing of epistasis and its various genetic components. Conclusions: Simulation studies were used to examine the power and false positive rates of the model under different sampling strategies. The model was used to detect epistasis in a case-control study of inflammatory bowel disease, in which five SNPs at a candidate gene were typed, leading to the identification of a significant three-locus epistasis