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

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%.

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 association study (GWAS) 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. As we verify, even in a simplified setting in which there is no interaction at all (and so no heteroscedasticity), in a GWAS to detect GxG or GxE interaction with a fixed genetic variant or environmental factor, the distribution of the genome-wide p-values under the null hypothesis is not the i.i.d. uniform one that is commonly assumed. Using standard methods, even if all SNPs are independent, some GWASs 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 GWAS, and it may partly explain why such detection has so far proved challenging and difficult to replicate. 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.