LLR: A latent low-rank approach to colocalizing genetic risk variants in multiple GWAS

Motivation: Genome-wide association studies (GWAS), which genotype millions of single nucleotide polymorphisms (SNPs) in thousands of individuals, are widely used to identify the risk SNPs underlying complex human phenotypes (quantitative traits or diseases). Most conventional statistical methods in GWAS only investigate one phenotype at a time. However, an increasing number of reports suggest the ubiquity of pleiotropy, i.e. many complex phenotypes sharing common genetic bases. This motivated us to leverage pleiotropy to develop new statistical approaches to joint analysis of multiple GWAS. Results: In this study, we propose a latent low-rank (LLR) approach to colocalizing genetic risk variants using summary statistics. In the presence of pleiotropy, there exist risk loci that affect multiple phenotypes. To leverage pleiotropy, we introduce a low-rank structure to modulate the probabilities of the latent association statuses between loci and phenotypes. Regarding the computational efficiency of LLR, a novel expectation-maximization-path (EM-path) algorithm has been developed to greatly reduce the computational cost and facilitate model selection and inference. We demonstrate the advantages of LLR over competing approaches through simulation studies and joint analysis of 18 GWAS datasets.