Convex approaches to isolate the shared and distinct genetic components of complex traits.

motivationGroups of complex diseases, such as coronary heart disease, neuropsychiatric disorders, and cancers, often display overlapping clinical symptoms and pharmacological responses. Genetic variants with shared associations across diseases have the potential to help explain their underlying biological processes, but this sharing remains poorly understood.

resultsWe model the matrix of summary statistics of trait-associated genetic variants as the sum of a low-rank component-representing shared biological processes-and a sparse component representing disease-unique processes and arbitrarily corrupted or contaminated components. We introduce Clorinn, an open-source Python library that uses convex optimization algorithms to recover these components by minimizing a weighted combination of nuclear norm and L1 terms. Clorinn provides two significant benefits: (i) convex optimization guarantees reproducibility of the components and (ii) the low-rank "uncorrupted" matrix allows robust singular value decomposition and principal component analysis, which are otherwise highly sensitive to outliers and noise in the input matrix. In extensive simulations, we observe that Clorinn is uniquely able to recover the disease-group structure while remaining competitive on factor-level reconstruction error. We apply Clorinn to estimate 200 latent factors from GWAS summary statistics for 2110 phenotypes from the Pan-UK Biobank (N = 420 531 European-ancestry individuals) and 10 latent factors from 14 psychiatric disorders. AVAILABILITY AND IMPLEMENTATION: Clorinn is available at https://github.com/daklab/clorinn.