There is much confusion as to what defines epistasis and gene-gene interaction in the literature. The definition you use will ultimately be determined by the data you have.

Epistasis is when a gene at a particular locus has an effect on a gene at another locus (in contrast to dominance where the affects are at the same locus). Epistasis is a form of gene-gene interaction but gene-gene interactions can also be tentatively inferred by looking at pairwise correlations between gene expression profiles from microarrays. This form of gene-gene interaction essentially relates to coexpression.

Epistasis can be further subdivided into functional and statistical. Functional epistasis is the definition used in experimental studies (e.g., coat colour in mice) whereas statistical epistasis refers to the proportion of variance in a given trait explained by the 'interaction term', i.e., the interaction between two genes or variants across a population. This is the definition used in eQTL studies, i.e., transcriptome mapping, genetical genomics, etc.

The best way to highlight what this means is to look at a sample model.

Assume a quantitative expression profile for gene X for n individuals. Assume also two SNPs, snp1 and snp2 determined for n individuals.

There are many ways to model this but for convenience sake, take a simple dosage model based on linear regression.

1. We can model single main effects as:

   X ~ snp1

   X ~ snp2

2. We can model multiple main effects as:

   X ~ snp1 + snp2

3. We can model main effects and the effect of interaction as:

   X ~ snp1 + snp2 + snp1*snp2,

where snp1*snp2 is the interaction term. The interaction poses the following question: given the occurence of these two SNPs, does having both SNPs explain a significant proportion of the variance in trait X.

This area is something of a statistical minefieled and there are many subtleties to grapple with, e.g., cis effects, trans effects, cis-trans effects, appropriate genetic models, and worst of all, multiple testing.

Below are some papers/reviews that may prove useful.

Epistasis — the essential role of gene interactions in the structure and evolution of genetic systems

Using Biological Knowledge to Uncover the Mystery in the Search for Epistasis in Genome-Wide Association Studies

Mapping the Genetic Architecture of Gene Expression in Human Liver

Travelling the world of Gene-Gene Interactions

WGCNA: an R package for weighted correlation network analysis.

Genome-Wide Interaction-Based Association Analysis Identified Multiple New Susceptibility Loci for Common Diseases

And oh, check out this great blog on epistasis!!!

Hi,

the distinction that Cordell introduce about testing interaction or testing association allowing interaction refers to regression models. In the next I will refer to logistic regression since my experience is with case-control data.

Assuming the notation of Darren: X ~ snp1 + snp2 + snp1*snp2

"testing interaction" means testing the beta coefficient of the term snp1*snp2 against the null hypotheses. In this case we are testing the effect of a couple of snps

"testing association allowing interaction" suppose a model like X ~ snp1 + snp1*snpOrCovOrOther. Here we are interested in the effect of snp1 alone or with a partner that help us to discover its association with the dependent variable (e.g. disease)

Hope this help. If you work with plink look at the --interaction option of the single snp test section. It allows for interaction of a snp with a cov. But I think the best way to deal with this kind of models is to dig into R/bioconductor