Genetic association studies have been less successful than expected in detecting causal genetic variants, with frequent non-replication when such variants are claimed. Numerous possible reasons have been postulated, including inadequate sample size and possible unobserved stratification. Another possibility, and the focus of this paper, is that of epistasis, or gene-gene interaction. Although unlikely that we may glean information about disease mechanism, based purely upon the data, it may be possible to increase our power to detect an effect by allowing for epistasis within our test statistic. This paper derives an appropriate "omnibus" test for detecting causal loci whist allowing for numerous possible interactions and compares the power of such a test with that of the usual main effects test. This approach differs from that commonly used, for example by Marchini et al. [2005], in that it tests simultaneously for main effects and interactions, rather than interactions alone. The alternative hypothesis being tested by the "omnibus" test is whether a particular locus of interest has an effect on disease status, either marginally or epistatically and is therefore directly comparable to the main effects test at that locus. The paper begins by considering the direct case, in which the putative causal variants are observed and then extends these ideas to the indirect case in which the causal variants are unobserved and we have a set of tag single nucleotide polymorphisms (tag SNPs) representing the regions of interest. In passing, the derivation of the indirect omnibus test statistic leads to a novel "indirect case-only test for interaction".
