PUMA: A Unified Framework for Penalized Multiple Regression Analysis of GWAS Data

Penalized Multiple Regression (PMR) can be used to discover novel disease associations in GWAS datasets. In practice, proposed PMR methods have not been able to identify well-supported associations in GWAS that are undetectable by standard association tests and thus these methods are not widely applied. Here, we present a combined algorithmic and heuristic framework for PUMA (Penalized Unified Multiple-locus Association) analysis that solves the problems of previously proposed methods including computational speed, poor performance on genome-scale simulated data, and identification of too many associations for real data to be biologically plausible. The framework includes a new minorize-maximization (MM) algorithm for generalized linear models (GLM) combined with heuristic model selection and testing methods for identification of robust associations. The PUMA framework implements the penalized maximum likelihood penalties previously proposed for GWAS analysis (i.e. Lasso, Adaptive Lasso, NEG, MCP), as well as a penalty that has not been previously applied to GWAS (i.e. LOG). Using simulations that closely mirror real GWAS data, we show that our framework has high performance and reliably increases power to detect weak associations, while existing PMR methods can perform worse than single marker testing in overall performance. To demonstrate the empirical value of PUMA, we analyzed GWAS data for type 1 diabetes, Crohns's disease, and rheumatoid arthritis, three autoimmune diseases from the original Wellcome Trust Case Control Consortium. Our analysis replicates known associations for these diseases and we discover novel etiologically relevant susceptibility loci that are invisible to standard single marker tests, including six novel associations implicating genes involved in pancreatic function, insulin pathways and immune-cell function in type 1 diabetes; three novel associations implicating genes in pro- and anti-inflammatory pathways in Crohn's disease; and one novel association implicating a gene involved in apoptosis pathways in rheumatoid arthritis. We provide software for applying our PUMA analysis framework.Author Summary: Genome-wide association studies (GWAS) have identified hundreds of regions of the human genome that are associated with susceptibility to common diseases. Yet many lines of evidence indicate that many susceptibility loci, which cannot be detected by standard statistical methods, remain to be discovered. We have developed PUMA, a framework for applying a family of penalized regression methods that simultaneously consider multiple susceptibility loci in the same statistical model. We demonstrate through simulations that our framework has increased power to detect weak associations compared to both standard GWAS analysis methods and previous applications of penalized methods. We applied PUMA to identify novel susceptibility loci for type 1 diabetes, Crohn's disease and rheumatoid arthritis, where the novel disease loci we identified have been previously associated with similar diseases or are known to function in relevant biological pathways.