A nonparametric test to detect quantitative trait loci where the phenotypic distribution differs by genotypes

Searching for genetic variants involved in gene-gene and gene-environment interactions in large-scale data raises multiple methodological issues. Many existing methods have focused on the problem of dimensionality, trying to explore the largest number of combinations between risk factors while considering simple interaction models. Despite evidence demonstrating the efficacy of these methods in simulated data, their application in real data has been unsuccessful so far. The classical test of a linear marginal genetic effect has been widely used for agnostic genome-wide association studies, with the underlying idea that most variants involved in interactions might display marginal effect on the phenotypic mean. Although this approach may allow for the identification of genetic variants involved in interactions in many scenarios, the linear marginal effects of some causal alleles on the phenotypic mean might not be always detectable at genome-wide significance level. We introduce in this study a general association test for quantitative trait loci that compare the distributions of phenotypic values by genotypic classes as opposed to most standard tests that compare phenotypic means by genotypic classes. Using simulations we show that in presence of interactions, this approach can be more powerful than the standard test of the linear marginal effect, with a gain of power increasing with increasing interaction effect and decreasing frequencies of the interacting exposures. We demonstrate the potential utility of our method on real data by analyzing mammographic density genome-wide data from the Nurses' Health Study.