Interaction models matter: an efficient, flexible computational framework for model-specific investigation of epistasis

Sandra Batista; Vered Senderovich Madar; Philip J Freda; Priyanka Bhandary; Attri Ghosh; Nicholas Matsumoto; Apurva S Chitre; Abraham A Palmer; Jason H Moore

doi:10.1186/s13040-024-00358-0

Interaction models matter: an efficient, flexible computational framework for model-specific investigation of epistasis

BioData Min. 2024 Feb 28;17(1):7. doi: 10.1186/s13040-024-00358-0.

Authors

Affiliations

¹ Department of Computational Biomedicine, Cedars-Sinai Medical Center, 700 N San Vicente Blvd., Pacific Design Center, Guite G540, West Hollywood, CA, 90069, USA. sandraleeresearch@gmail.com.
² , Chapel Hill, NC, USA.
³ Department of Computational Biomedicine, Cedars-Sinai Medical Center, 700 N San Vicente Blvd., Pacific Design Center, Guite G540, West Hollywood, CA, 90069, USA.
⁴ Department of Psychiatry, University of California, San Diego, 9500 Gilman Dr., Mailcode: 0667, La Jolla, CA, 92093-0667, USA.
⁵ Institute for Genomic Medicine, University of California, San Diego, 9500 Gilman Dr., Mailcode: 0667, La Jolla, CA, 92093-0667, USA.
⁶ Department of Computational Biomedicine, Cedars-Sinai Medical Center, 700 N San Vicente Blvd., Pacific Design Center, Guite G540, West Hollywood, CA, 90069, USA. jason.moore@csmc.edu.

^# Contributed equally.

Abstract

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.

Keywords: Epistasis; GWAS; Interaction model; Linear regression; Partial correlation; XOR.

Abstract

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