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.