Factorizing polygenic epistasis improves prediction and uncovers biological pathways in complex traits

Overcoming the "feast or famine" effect: improved interaction testing in genome-wide association studies

In genetic association analysis of complex traits, detection of interaction (either GxG or GxE) can help to elucidate the genetic architecture and biological mechanisms underlying the trait. Detection of interaction in a genome-wide interaction study (GWIS) can be methodologically challenging for various reasons, including a high burden of multiple comparisons when testing for epistasis between all possible pairs of a set of genomewide variants, as well as heteroscedasticity effects occurring in the presence of GxG or GxE interaction. In this paper, we address the problem of an even more striking phenomenon that we call the "feast or famine" effect that occurs when testing interaction in a genomewide context. We show that in any given GxE GWIS, the type 1 error of standard interaction tests performed genomewide can vary widely from the nominal level, where the actual type 1 error in any given GWIS varies as a predictable function of the observed trait and environmental values. Using standard methods, some GWISs will have systematically underinflated p-values ("feast"), and others will have systematically overinflated p-values ("famine"), which can lead to false detection of interaction, reduced power, inconsistent results across studies, and failure to replicate true signal. This startling phenomenon is specific to detection of interaction in a GWIS, and it may partly explain why such detection has often proved challenging and difficult to replicate. We show that the feast or famine effect occurs across a wide range of GxE analysis methods, including but not limited to (1) testing interaction in a linear or linear mixed model (LMM) using standard approaches such as t-tests/Wald tests, likelihood ratio tests, or score tests; (2) doing a combined interaction-association test in a linear model or LMM using standard approaches such as F-tests or likelihood ratio tests; (3) testing interaction with multiple environments or multiple SNPs, where these are modeled as random effects in a LMM using standard approaches; (4) performing tests of interaction in a GWIS where significance is assessed using permutation of the trait residuals. We show theoretically that the key cause of this phenomenon is which variables are conditioned on in the analysis, and this suggests an approach to correct the problem by changing the way the conditioning is done. Using this insight, we have developed the TINGA method to adjust the interaction test statistics to make their p-values closer to uniform under the null hypothesis. In simulations we show that TINGA both controls type 1 error and improves power. TINGA allows for covariates and population structure through use of a linear mixed model and accounts for heteroscedasticity. We apply TINGA to detection of epistasis in a study of flowering time in Arabidopsis thaliana.

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 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.

Cluster effect for SNP-SNP interaction pairs for predicting complex traits

Single nucleotide polymorphism (SNP) interactions are the key to improving polygenic risk scores. Previous studies reported several significant SNP-SNP interaction pairs that shared a common SNP to form a cluster, but some identified pairs might be false positives. This study aims to identify factors associated with the cluster effect of false positivity and develop strategies to enhance the accuracy of SNP-SNP interactions. The results showed the cluster effect is a major cause of false-positive findings of SNP-SNP interactions. This cluster effect is due to high correlations between a causal pair and null pairs in a cluster. The clusters with a hub SNP with a significant main effect and a large minor allele frequency (MAF) tended to have a higher false-positive rate. In addition, peripheral null SNPs in a cluster with a small MAF tended to enhance false positivity. We also demonstrated that using the modified significance criterion based on the 3 p-value rules and the bootstrap approach (3pRule + bootstrap) can reduce false positivity and maintain high true positivity. In addition, our results also showed that a pair without a significant main effect tends to have weak or no interaction. This study identified the cluster effect and suggested using the 3pRule + bootstrap approach to enhance SNP-SNP interaction detection accuracy.

Quantifying higher-order epistasis: beware the chimera

Epistasis, or interactions in which alleles at one locus modify the fitness effects of alleles at other loci, plays a fundamental role in genetics, protein evolution, and many other areas of biology. Epistasis is typically quantified by computing the deviation from the expected fitness under an additive or multiplicative model using one of several formulae. However, these formulae are not all equivalent. Importantly, one widely used formula - which we call the chimeric formula - measures deviations from a multiplicative fitness model on an additive scale, thus mixing two measurement scales. We show that for pairwise interactions, the chimeric formula yields a different magnitude, but the same sign (synergistic vs. antagonistic) of epistasis compared to the multiplicative formula that measures both fitness and deviations on a multiplicative scale. However, for higher-order interactions, we show that the chimeric formula can have both different magnitude and sign compared to the multiplicative formula - thus confusing negative epistatic interactions with positive interactions, and vice versa. We resolve these inconsistencies by deriving fundamental connections between the different epistasis formulae and the parameters of the multivariate Bernoulli distribution . Our results demonstrate that the additive and multiplicative epistasis formulae are more mathematically sound than the chimeric formula. Moreover, we demonstrate that the mathematical issues with the chimeric epistasis formula lead to markedly different biological interpretations of real data. Analyzing multi-gene knockout data in yeast, multi-way drug interactions in E. coli , and deep mutational scanning (DMS) of several proteins, we find that 10 - 60% of higher-order interactions have a change in sign with the multiplicative or additive epistasis formula. These sign changes result in qualitatively different findings on functional divergence in the yeast genome, synergistic vs. antagonistic drug interactions, and and epistasis between protein mutations. In particular, in the yeast data, the more appropriate multiplicative formula identifies nearly 500 additional negative three-way interactions, thus extending the trigenic interaction network by 25%.