A Scalable Adaptive Quadratic Kernel Method for Interpretable Epistasis Analysis in Complex Traits

Our knowledge of the contribution of genetic interactions ( epistasis ) to variation in human complex traits remains limited, partly due to the lack of efficient, powerful, and interpretable algorithms to detect interactions. Recently proposed approaches for set-based association tests show promise in improving power to detect epistasis by examining the aggregated effects of multiple variants. Nevertheless, these methods either do not scale to large numbers of individuals available in Biobank datasets or do not provide interpretable results. We, therefore, propose QuadKAST, a scalable algorithm focused on testing pairwise interaction effects (also termed as quadratic effects ) of a set of genetic variants on a trait and quantifying the proportion of phenotypic variance explained by these effects.

We performed comprehensive simulations and demonstrated that QuadKAST is well-calibrated. Additionally, QuadKAST is highly sensitive in detecting loci with epistatic signal and accurate in its estimation of quadratic effects. We applied QuadKAST to 53 quantitative phenotypes measured in ≈ 300, 000 unrelated white British individuals in the UK Biobank to test for quadratic effects within each of 9, 515 protein-coding genes (after accounting for linear additive effects). We detected 32 trait-gene pairs across 17 traits that demonstrate statistically significant signals of quadratic effects ( accounting for the number of genes and traits tested). Our method enables the detailed investigation of epistasis on a large scale, offering new insights into its role and importance.