Learning High-Order Interactions for Polygenic Risk Prediction

Within the framework of precision medicine, the stratification of individual genetic susceptibility based on inherited DNA variation has paramount relevance. However, one of the most relevant pitfalls of traditional Polygenic Risk Scores (PRS) approaches is their inability to model complex high-order non-linear SNP-SNP interactions and their effect on the phenotype (e.g. epistasis). Indeed, they incur in a computational challenge as the number of possible interactions grows exponentially with the number of SNPs considered, affecting the statistical reliability of the model parameters as well. In this work, we address this issue by proposing a novel PRS approach, called High-order Interactions-aware Polygenic Risk Score (hiPRS), that incorporates high-order interactions in modeling polygenic risk. The latter combines an interaction search routine based on frequent itemsets mining and a novel interaction selection algorithm based on Mutual Information, to construct a simple and interpretable weighted model of user-specified dimensionality that can predict a given binary phenotype. Compared to traditional PRSs methods, hiPRS does not rely on GWAS summary statistics nor any external information. Moreover, hiPRS differs from Machine Learning-based approaches that can include complex interactions in that it provides a readable and interpretable model and it is able to control overfitting, even on small samples. In the present work we demonstrate through a comprehensive simulation study the superior performance of hiPRS w.r.t. state of the art methods, both in terms of scoring performance and interpretability of the resulting model. We also test hiPRS against small sample size, class imbalance and the presence of noise, showcasing its robustness to extreme experimental settings. Finally, we apply hiPRS to a case study on real data from DACHS cohort, defining an interaction-aware scoring model to predict mortality of stage II-III Colon-Rectal Cancer patients treated with oxaliplatin. Author summary In the precision medicine era, understanding how genetic variants affect the susceptibility to complex diseases is key, and great attention has been posed to Single Nucleotide Polymorphisms (SNPs) and their role in disease risk or clinical treatments outomes. Several approaches to quantify and model this impact have been proposed, called Polygenic Risk Scores (PRSs), but they traditionally do not account for possible interactions among SNPs. This is a significant drawback, as complex high-order SNP-SNP interactions can play an important role in determining the phenotype (a phenomenon called epistasis ). Nevertheless, the number of possible combinations grows exponentially with the number of SNPs considered and including them in a predictive model becomes computationally challenging and affects the statistical reliability of the model. Some Machine Learning algorithms can answer this problem, but they are hardly interpretable. Here, we tackle these and other drawbacks of existing approaches proposing our novel PRS approach, hi PRS, that provides an interpretable weighted model with a user-defined number of predictive interactions. We designed it to handle typical real-life research scenarios, like small sample sizes and class imbalance, and we demonstrate here its superiority with respect to state-of-the-art methods. ### Competing Interest Statement The authors have declared no competing interest.