Mendelian randomization (MR) has emerged as a powerful approach to leverage genetic instruments to infer causality between pairs of traits in observational studies. However, the results of such studies are susceptible to biases owing to weak instruments, as well as the confounding effects of population stratification and horizontal pleiotropy. Here, we show that family data can be leveraged to design MR tests that are provably robust to confounding from population stratification, assortative mating, and dynastic effects. We show in simulations that our approach, MR-Twin, is robust to confounding from population stratification and is not affected by weak instrument bias, whereas standard MR methods yield inflated false positive rates. We then conduct an exploratory analysis of MR-Twin and other MR methods applied to 121 trait pairs in the UK Biobank data set. Our results suggest that confounding from population stratification can lead to false positives for existing MR methods, whereas MR-Twin is immune to this type of confounding, and that MR-Twin can help assess whether traditional approaches may be inflated owing to confounding from population stratification.

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 the power to detect epistasis by examining the aggregated effects of multiple variants. Nevertheless, these methods either do not scale to large Biobank data sets or lack interpretability. We propose QuadKAST, a scalable algorithm focused on testing pairwise interaction effects (quadratic effects) within small to medium-sized sets of genetic variants (window size ≤100) on a trait and provide quantified interpretation of these effects. Comprehensive simulations show that QuadKAST is well-calibrated. Additionally, QuadKAST is highly sensitive in detecting loci with epistatic signals and accurate in its estimation of quadratic effects. We applied QuadKAST to 52 quantitative phenotypes measured in ≈300,000 unrelated white British individuals in the UK Biobank to test for quadratic effects within each of 9515 protein-coding genes. We detect 32 trait-gene pairs across 17 traits and 29 genes that demonstrate statistically significant signals of quadratic effects (accounting for the number of genes and traits tested). Across these trait-gene pairs, the proportion of trait variance explained by quadratic effects is comparable to additive effects, with five pairs having a ratio >1. Our method enables the detailed investigation of epistasis on a large scale, offering new insights into its role and importance.

Our knowledge of non-linear genetic effects on complex traits remains limited, in part, due to the modest power to detect such effects. While kernel-based tests offer a versatile approach to test for non-linear relationships between sets of genetic variants and traits, current approaches cannot be applied to Biobank-scale datasets containing hundreds of thousands of individuals. We propose, FastKAST, a kernel-based approach that can test for non-linear effects of a set of variants on a quantitative trait. FastKAST provides calibrated hypothesis tests while enabling analysis of Biobank-scale datasets with hundreds of thousands of unrelated individuals from a homogeneous population. We apply FastKAST to 53 quantitative traits measured across ≈ 300 K unrelated white British individuals in the UK Biobank to detect sets of variants with non-linear effects at genome-wide significance.