PURPOSE: Epistasis, the interaction between two or more genes, is integral to the study of genetics and is present throughout nature. Yet, it is seldom fully explored as most approaches primarily focus on single-locus effects, partly because analyzing all pairwise and higher-order interactions requires significant computational resources. Furthermore, existing methods for epistasis detection only consider a Cartesian (multiplicative) model for interaction terms. This is likely limiting as epistatic interactions can evolve to produce varied relationships between genetic loci, some complex and not linearly separable. METHODS: We present new algorithms for the interaction coefficients for standard regression models for epistasis that permit many varied models for the interaction terms for loci and efficient memory usage. The algorithms are given for two-way and three-way epistasis and may be generalized to higher order epistasis. Statistical tests for the interaction coefficients are also provided. We also present an efficient matrix based algorithm for permutation testing for two-way epistasis. We offer a proof and experimental evidence that methods that look for epistasis only at loci that have main effects may not be justified. Given the computational efficiency of the algorithm, we applied the method to a rat data set and mouse data set, with at least 10,000 loci and 1,000 samples each, using the standard Cartesian model and the XOR model to explore body mass index. RESULTS: This study reveals that although many of the loci found to exhibit significant statistical epistasis overlap between models in rats, the pairs are mostly distinct. Further, the XOR model found greater evidence for statistical epistasis in many more pairs of loci in both data sets with almost all significant epistasis in mice identified using XOR. In the rat data set, loci involved in epistasis under the XOR model are enriched for biologically relevant pathways. CONCLUSION: Our results in both species show that many biologically relevant epistatic relationships would have been undetected if only one interaction model was applied, providing evidence that varied interaction models should be implemented to explore epistatic interactions that occur in living systems.

Background

The additive model of inheritance assumes that heterozygotes (Aa) are exactly intermediate in respect to homozygotes (AA and aa). While this model is commonly used in single-locus genetic association studies, significant deviations from additivity are well-documented and contribute to phenotypic variance across many traits and systems. This assumption can introduce type I and type II errors by overestimating or underestimating the effects of variants that deviate from additivity. Alternative genotype encoding strategies have been explored to account for different inheritance patterns, but they often incur significant computational or methodological costs. To address these challenges, we introduce PAGER (Phenotype Adjusted Genotype Encoding and Ranking), an efficient pre-processing method that encodes each genetic variant based on normalized mean phenotypic differences between diallelic genotype classes (AA, Aa, and aa). This approach more accurately reflects each variant's true inheritance model, improving model precision while minimizing the costs associated with alternative encoding strategies.

Results

Through extensive benchmarking on SNPs simulated with both binary and continuous phenotypes, we demonstrate that PAGER accurately represents various inheritance patterns (including additive, dominant, recessive, and heterosis), achieves levels of statistical power that meet or exceed other encoding strategies, and attains computation speeds up to 55 times faster than a similar method, EDGE. We also apply PAGER to publicly available real-world data and identify a novel, relevant putative QTL associated with body mass index in rats (Rattus norvegicus) that is not detected with the additive model.

Conclusions

Overall, we show that PAGER is an efficient genotype encoding approach that can uncover sources of missing heritability and reveal novel insights in the study of complex traits while incurring minimal costs.

Background

Quantitative Trait Locus (QTL) analysis and Genome-Wide Association Studies (GWAS) have the power to identify variants that capture significant levels of phenotypic variance in complex traits. However, effort and time are required to select the best methods and optimize parameters and pre-processing steps. Although machine learning approaches have been shown to greatly assist in optimization and data processing, applying them to QTL analysis and GWAS is challenging due to the complexity of large, heterogenous datasets. Here, we describe proof-of-concept for an automated machine learning approach, AutoQTL, with the ability to automate many complicated decisions related to analysis of complex traits and generate solutions to describe relationships that exist in genetic data.

Results

Using a publicly available dataset of 18 putative QTL from a large-scale GWAS of body mass index in the laboratory rat, Rattus norvegicus, AutoQTL captures the phenotypic variance explained under a standard additive model. AutoQTL also detects evidence of non-additive effects including deviations from additivity and 2-way epistatic interactions in simulated data via multiple optimal solutions. Additionally, feature importance metrics provide different insights into the inheritance models and predictive power of multiple GWAS-derived putative QTL.

Conclusions

This proof-of-concept illustrates that automated machine learning techniques can complement standard approaches and have the potential to detect both additive and non-additive effects via various optimal solutions and feature importance metrics. In the future, we aim to expand AutoQTL to accommodate omics-level datasets with intelligent feature selection and feature engineering strategies.