SNPs that effect expression levels of genes (eQTLs, expression quantitative trait loci), have been found for many genes. Often genes have more than one. These eQTLs are usually found using linear models where the effects are modeled as independent. But are the really? Are there interactions? Are the haplotypes formed by eQTL tagging as of yet unknown eQTLs?

If there are non-additive effects, or unknown eQTLs, one could test this in a straight forward manner. Assuming there are 3 known eQTLs, that results in at most 8 haplotypes that they form. Once could fit the effects of the 8 haplotypes in a single model, and then see if the effect estimates for each haplotype is equal to the sum of the effects of the eQTLs that lie on it.

Observed deviations from additivity would then be interesting for multiple reasons. They would give insight into the underlying biology by demonstrating the presence of either and interaction effect or of additional eQTLs. They may also boost predictive power for performing TWAS analysis.