Efficient genome-wide association studies via low-rank approximations

In genome-wide association studies (GWASs), gene-based large-scale score tests such as the adaptive sum of powered score (aSPU) test have some attractive features (such as nice data adaptivity and effective information aggregation) that lead to high statistical powers. However, these test methods are computationally expensive due to the need of a large number of matrix-vector multiplications. To address such a limitation, a series of effective and efficient strategies for association studies is proposed based on low-rank approximations. A low-rank approximation to a SNP matrix, constructed using fast randomized SVDs, yields an aSPU-LR test method that significantly reduces the cost of aSPU tests while ensuring the reliability. Furthermore, leveraging the low-rank approximation, a procedure is developed to quickly select certain effective parameters in the aSPU tests that give valuable insights into the association patterns. Additionally, a fast pivoting approach is designed using the low-rank approximation so as to quickly identify representative SNPs which help capture major genetic information of the data. The efficiency and the effectiveness of the proposed strategies are demonstrated through extensive simulations and real data studies. For a large-scale International Cancer Genome Consortium (ICGC) dataset, the proposed aSPU-LR test rapidly identifies associations between germline variations and somatic mutations across multiple cancer types, offering a significant speed advantage over the original aSPU test while maintaining similar accuracy. The low-rank approximations are further used to quickly extract useful SNP information about the germline variations and identify the patterns of their associations with the somatic mutations.