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 with good statistical power. We applied QuadKAST to 53 quantitative phenotypes measured in \(\approx 300,000\) 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 ( \(p \le \frac{0.05}{9,515\times 53}\) 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.