A model and test for coordinated polygenic epistasis in complex traits

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.

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

Epistasis is central in many domains of biology, but it has not yet been proven useful for understanding the etiology of complex traits. This is partly because complex-trait epistasis involves polygenic interactions that are poorly captured in current models. To address this gap, we developed a model called Epistasis Factor Analysis (EFA). EFA assumes that polygenic epistasis can be factorized into interactions between a few epistasis factors (EFs), which represent latent polygenic components of the observed complex trait. The statistical goals of EFA are to improve polygenic prediction and to increase power to detect epistasis, while the biological goal is to unravel genetic effects into more-homogeneous units. We mathematically characterize EFA and use simulations to show that EFA outperforms current epistasis models when its assumptions approximately hold. Applied to predicting yeast growth rates, EFA outperforms the additive model for several traits with large epistasis heritability and uniformly outperforms the standard epistasis model. We replicate these prediction improvements in a second dataset. We then apply EFA to four previously characterized traits in the UK Biobank and find statistically significant epistasis in all four, including two that are robust to scale transformation. Moreover, we find that the inferred EFs partly recover pre-defined biological pathways for two of the traits. Our results demonstrate that more realistic models can identify biologically and statistically meaningful epistasis in complex traits, indicating that epistasis has potential for precision medicine and characterizing the biology underlying GWAS results.

A biobank-scale test of marginal epistasis reveals genome-wide signals of polygenic epistasis

The contribution of epistasis (interactions among genes or genetic variants) to human complex trait variation remains poorly understood. Methods that aim to explicitly identify pairs of genetic variants, usually single nucleotide polymorphisms (SNPs), associated with a trait suffer from low power due to the large number of hypotheses tested while also having to deal with the computational problem of searching over a potentially large number of candidate pairs. An alternate approach involves testing whether a single SNP modulates variation in a trait against a polygenic background. While overcoming the limitation of low power, such tests of polygenic or marginal epistasis (ME) are infeasible on Biobank-scale data where hundreds of thousands of individuals are genotyped over millions of SNPs. We present a method to test for ME of a SNP on a trait that is applicable to biobank-scale data. We performed extensive simulations to show that our method provides calibrated tests of ME. We applied our method to test for ME at SNPs that are associated with 53 quantitative traits across ≈ 300 K unrelated white British individuals in the UK Biobank (UKBB). Testing 15, 601 trait-loci associations that were significant in GWAS, we identified 16 trait-loci pairs across 12 traits that demonstrate strong evidence of ME signals (p-value p < 5 × 10 - 8 53 ). We further partitioned the significant ME signals across the genome to identify 6 trait-loci pairs with evidence of local (within-chromosome) ME while 15 show evidence of distal (cross-chromosome) ME. Across the 16 trait-loci pairs, we document that the proportion of trait variance explained by ME is about 12x as large as that explained by the GWAS effects on average (range: 0.59 to 43.89). Our results show, for the first time, evidence of interaction effects between individual genetic variants and overall polygenic background modulating complex trait variation.

Applying an evolutionary mismatch framework to understand disease susceptibility

Noncommunicable diseases (NCDs) are on the rise worldwide. Obesity, cardiovascular disease, and type 2 diabetes are among a long list of "lifestyle" diseases that were rare throughout human history but are now common. The evolutionary mismatch hypothesis posits that humans evolved in environments that radically differ from those we currently experience; consequently, traits that were once advantageous may now be "mismatched" and disease causing. At the genetic level, this hypothesis predicts that loci with a history of selection will exhibit "genotype by environment" (GxE) interactions, with different health effects in "ancestral" versus "modern" environments. To identify such loci, we advocate for combining genomic tools in partnership with subsistence-level groups experiencing rapid lifestyle change. In these populations, comparisons of individuals falling on opposite extremes of the "matched" to "mismatched" spectrum are uniquely possible. More broadly, the work we propose will inform our understanding of environmental and genetic risk factors for NCDs across diverse ancestries and cultures.

Gene Interactions in Human Disease Studies-Evidence Is Mounting

Despite monumental advances in molecular technology to generate genome sequence data at scale, there is still a considerable proportion of heritability in most complex diseases that remains unexplained. Because many of the discoveries have been single-nucleotide variants with small to moderate effects on disease, the functional implication of many of the variants is still unknown and, thus, we have limited new drug targets and therapeutics. We, and many others, posit that one primary factor that has limited our ability to identify novel drug targets from genome-wide association studies may be due to gene interactions (epistasis), gene-environment interactions, network/pathway effects, or multiomic relationships. We propose that many of these complex models explain much of the underlying genetic architecture of complex disease. In this review, we discuss the evidence from multiple research avenues, ranging from pairs of alleles to multiomic integration studies and pharmacogenomics, that supports the need for further investigation of gene interactions (or epistasis) in genetic and genomic studies of human disease. Our goal is to catalog the mounting evidence for epistasis in genetic studies and the connections between genetic interactions and human health and disease that could enable precision medicine of the future.

Leveraging the genetic correlation between traits improves the detection of epistasis in genome-wide association studies

Epistasis, commonly defined as the interaction between genetic loci, is known to play an important role in the phenotypic variation of complex traits. As a result, many statistical methods have been developed to identify genetic variants that are involved in epistasis, and nearly all of these approaches carry out this task by focusing on analyzing one trait at a time. Previous studies have shown that jointly modeling multiple phenotypes can often dramatically increase statistical power for association mapping. In this study, we present the "multivariate MArginal ePIstasis Test" (mvMAPIT)-a multioutcome generalization of a recently proposed epistatic detection method which seeks to detect marginal epistasis or the combined pairwise interaction effects between a given variant and all other variants. By searching for marginal epistatic effects, one can identify genetic variants that are involved in epistasis without the need to identify the exact partners with which the variants interact-thus, potentially alleviating much of the statistical and computational burden associated with conventional explicit search-based methods. Our proposed mvMAPIT builds upon this strategy by taking advantage of correlation structure between traits to improve the identification of variants involved in epistasis. We formulate mvMAPIT as a multivariate linear mixed model and develop a multitrait variance component estimation algorithm for efficient parameter inference and P-value computation. Together with reasonable model approximations, our proposed approach is scalable to moderately sized genome-wide association studies. With simulations, we illustrate the benefits of mvMAPIT over univariate (or single-trait) epistatic mapping strategies. We also apply mvMAPIT framework to protein sequence data from two broadly neutralizing anti-influenza antibodies and approximately 2,000 heterogeneous stock of mice from the Wellcome Trust Centre for Human Genetics. The mvMAPIT R package can be downloaded at https://github.com/lcrawlab/mvMAPIT.

Improving Genetic Association Studies with a Novel Methodology that Unveils the Hidden Complexity of All-Cause Heart Failure

Motivation

Genome-Wide Association Studies (GWAS) commonly assume phenotypic and genetic homogeneity that is not present in complex conditions. We designed Transformative Regression Analysis of Combined Effects (TRACE), a GWAS methodology that better accounts for clinical phenotype heterogeneity and identifies gene-by-environment (GxE) interactions. We demonstrated with UK Biobank (UKB) data that TRACE increased the variance explained in All-Cause Heart Failure (AHF) via the discovery of novel single nucleotide polymorphism (SNP) and SNP-by-environment (i.e. GxE) interaction associations. First, we transformed 312 AHF-related ICD10 codes (including AHF) into continuous low-dimensional features (i.e., latent phenotypes) for a more nuanced disease representation. Then, we ran a standard GWAS on our latent phenotypes to discover main effects and identified GxE interactions with target encoding. Genes near associated SNPs subsequently underwent enrichment analysis to explore potential functional mechanisms underlying associations. Latent phenotypes were regressed against their SNP hits and the estimated latent phenotype values were used to measure the amount of AHF variance explained.

Results

Our method identified over 100 main GWAS effects that were consistent with prior studies and hundreds of novel gene-by-smoking interactions, which collectively accounted for approximately 10% of AHF variance. This represents an improvement over traditional GWAS whose results account for a negligible proportion of AHF variance. Enrichment analyses suggested that hundreds of miRNAs mediated the SNP effect on various AHF-related biological pathways. The TRACE framework can be applied to decode the genetics of other complex diseases.

Availability

All code is available at https://github.com/EpistasisLab/latent_phenotype_project.

Evolutionary mismatch and the role of GxE interactions in human disease

Globally, we are witnessing the rise of complex, non-communicable diseases (NCDs) related to changes in our daily environments. Obesity, asthma, cardiovascular disease, and type 2 diabetes are part of a long list of "lifestyle" diseases that were rare throughout human history but are now common. A key idea from anthropology and evolutionary biology-the evolutionary mismatch hypothesis-seeks to explain this phenomenon. It posits that humans evolved in environments that radically differ from the ones experienced by most people today, and thus traits that were advantageous in past environments may now be "mismatched" and disease-causing. This hypothesis is, at its core, a genetic one: it predicts that loci with a history of selection will exhibit "genotype by environment" (GxE) interactions and have differential health effects in ancestral versus modern environments. Here, we discuss how this concept could be leveraged to uncover the genetic architecture of NCDs in a principled way. Specifically, we advocate for partnering with small-scale, subsistence-level groups that are currently transitioning from environments that are arguably more "matched" with their recent evolutionary history to those that are more "mismatched". These populations provide diverse genetic backgrounds as well as the needed levels and types of environmental variation necessary for mapping GxE interactions in an explicit mismatch framework. Such work would make important contributions to our understanding of environmental and genetic risk factors for NCDs across diverse ancestries and sociocultural contexts.

MOAI: a multi-outcome interaction identification approach reveals an interaction between vaspin and carcinoembryonic antigen on colorectal cancer prognosis

Identifying and characterizing the interaction between risk factors for multiple outcomes (multi-outcome interaction) has been one of the greatest challenges faced by complex multifactorial diseases. However, the existing approaches have several limitations in identifying the multi-outcome interaction. To address this issue, we proposed a multi-outcome interaction identification approach called MOAI. MOAI was motivated by the limitations of estimating the interaction simultaneously occurring in multi-outcomes and by the success of Pareto set filter operator for identifying multi-outcome interaction. MOAI permits the identification for the interaction of multiple outcomes and is applicable in population-based study designs. Our experimental results exhibited that the existing approaches are not effectively used to identify the multi-outcome interaction, whereas MOAI obviously exhibited superior performance in identifying multi-outcome interaction. We applied MOAI to identify the interaction between risk factors for colorectal cancer (CRC) in both metastases and mortality prognostic outcomes. An interaction between vaspin and carcinoembryonic antigen (CEA) was found, and the interaction indicated that patients with CRC characterized by higher vaspin (≥30%) and CEA (≥5) levels could simultaneously increase both metastases and mortality risk. The immunostaining evidence revealed that determined multi-outcome interaction could effectively identify the difference between non-metastases/survived and metastases/deceased patients, which offers multi-prognostic outcome risk estimation for CRC. To our knowledge, this is the first report of a multi-outcome interaction associated with a complex multifactorial disease. MOAI is freely available at https://sites.google.com/view/moaitool/home.

A polygenic-score-based approach for identification of gene-drug interactions stratifying breast cancer risk

An individual's genetics can dramatically influence breast cancer (BC) risk. Although clinical measures for prevention do exist, non-invasive personalized measures for reducing BC risk are limited. Commonly used medications are a promising set of modifiable factors, but no previous study has explored whether a range of widely taken approved drugs modulate BC genetics. In this study, we describe a quantitative framework for exploring the interaction between the genetic susceptibility of BC and medication usage among UK Biobank women. We computed BC polygenic scores (PGSs) that summarize BC genetic risk and find that the PGS explains nearly three-times greater variation in disease risk within corticosteroid users compared to non-users. We map 35 genes significantly interacting with corticosteroid use (FDR < 0.1), highlighting the transcription factor NRF2 as a common regulator of gene-corticosteroid interactions in BC. Finally, we discover a regulatory variant strongly stratifying BC risk according to corticosteroid use. Within risk allele carriers, 18.2% of women taking corticosteroids developed BC, compared to 5.1% of the non-users (with an HR = 3.41 per-allele within corticosteroid users). In comparison, there are no differences in BC risk within the reference allele homozygotes. Overall, this work highlights the clinical relevance of gene-drug interactions in disease risk and provides a roadmap for repurposing biobanks in drug repositioning and precision medicine.