Testing for gene–environment (GE) interactions in a gene-set defined by a biological pathway can help us understand the interplay between genes and environments and provide insight into disease etiology. A self-contained gene-set analysis can be performed by combining gene-level p-values using approaches such as the Gamma Method. In a gene-set analysis of genetic main effects, permutation approaches are commonly used to avoid inflated probability of a type 1 error caused by correlation of genes within the same pathway. However, when testing interaction effects, it is typically not possible to construct an exact permutation test. We therefore propose using a parametric bootstrap. For testing an interaction term, this approach requires fitting the null model, which only contains main effects; however, for a gene-set GE interaction model, the number of main effects can be large and therefore they may not be estimable. To estimate the main effects of SNPs in a gene-set, we propose modeling them as random effects. We then repetitively simulate null data from this model and analyze it to generate the null distribution of gene-set GE p-values, allowing for an empirical assessment of significance of the global GE effect in the gene-set of interest. Through simulation, we demonstrate that this approach maintains correct type I error, and is well powered to detect GE interactions. We apply our method to test whether the association of obesity with bipolar disorder (BD) is modified by genetic variation in the Wnt signaling pathway.
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