Efficient population structure-adjusted logistic regression for genome-wide interaction studies via clustered covariates

Genome-wide association interaction studies (GWAIS) are a powerful approach for detecting epistasis, but they pose a computational challenge due to the large search space. Logistic regression is the gold-standard for statistical interaction testing; however, covariates capturing population structure, typically derived from principal component analysis (PCA), are often omitted for performance reasons. This can lead to distorted test statistics and effect estimates. We present a novel approximation that combines clustered proxy-covariates with contingency tables to substantially reduce the computational complexity of covariate-adjusted logistic regression for epistasis detection. Instead of including per-sample PCA covariates, population structure is summarized using a small number of proxy-covariates. This reduces the runtime complexity from O ( N I ) to O ( N + I K ) , where N is the number of samples, I the number of regression iterations, and K the number of proxy-covariates, while maintaining close agreement with the full covariate-adjusted model, measured by mean relative error (MRE). We evaluated the proposed method on two real-world case-control genome-wide association studies (GWAS) datasets. In both settings, clustered proxy-covariates reduced the MRE by 40% to 60% compared to logistic regression without covariates, while achieving speedups of up to 92-fold relative to logistic regression with per-sample PCA covariates. These results demonstrate that covariate clustering enables fast and practically useful GWAIS screening while retaining substantially better agreement with the covariate-adjusted reference model than covariate-free analysis, making population-structure-adjusted interaction testing feasible at the genome-wide scale. This article is an extended version of our International Conference on Computational Science proceedings paper Neff et al. “Logistic Regression with Covariate Clustering in Genome-wide Association Interaction Studies”, 2025 (Neff et al., 2025 [1] ).