An omnibus permutation test on ensembles of two-locus analyses for the detection of purely epistatic multi-locus interactions

Purely epistatic multi-locus interactions cannot generally be detected via single-locus analysis in case-control studies of complex diseases. Recently, many two-locus and multi-locus analysis techniques have been shown to be promising for the epistasis detection. However, exhaustive multi-locus analysis requires prohibitively large computational efforts when problems involve large-scale or genome-wide data. Furthermore, there is no explicit proof that a combination of multiple two-locus analyses can lead to the correct identification of multi-locus interactions. 2LOmb which performs an omnibus permutation test on ensembles of two-locus analyses is proposed. The algorithm consists of four main steps: two-locus analysis, a permutation test, global p-value determination and a progressive search for the best ensemble. 2LOmb is benchmarked against a set association approach, a correlation-based feature selection technique and a tuned ReliefF technique. The simulation results from multi-locus interaction problems indicate that 2LOmb has a low false-positive error. Moreover, 2LOmb has the best performance in terms of an ability to identify all causative single nucleotide polymorphisms (SNPs), which signifies a high detection power. 2LOmb is subsequently applied to type 1 and type 2 diabetes mellitus (T1D and T2D) data sets, which are obtained as a part of the UK genome-wide genetic epidemiology study by the Wellcome Trust Case Control Consortium. After primarily screening for SNPs that locate within or near candidate genes and exhibit no marginal single-locus effects, the T1D and T2D data sets are reduced to 2,359 SNPs from 350 genes and 7,065 SNPs from 370 genes, respectively. The 2LOmb search reveals that 28 SNPs in 21 genes are associated with T1D while 11 SNPs in four genes are associated with T2D. The findings provide an alternative explanation for the aetiology of T1D and T2D in a UK population.