Assessment of Penalized Regression for Genome-wide Association  Studies

The data from genome-wide association studies (GWAS) in humans are still predominantly analyzed using single marker association methods. As an alternative to Single Marker Analysis (SMA), all or subsets of markers can be tested simultaneously. This approach requires a form of Penalized Regression (PR) as the number of SNPs is much larger than the sample size. Here we review PR methods in the context of GWAS, extend them to perform penalty parameter and SNP selection by False Discovery Rate (FDR) control, and assess their performance (including penalties incorporating linkage disequilibrium) in comparison with SMA. PR methods were compared with SMA on realistically simulated GWAS data consisting of genotype data from single and multiple chromosomes and a continuous phenotype and on real data. Based on our comparisons our analytic FDR criterion may currently be the best approach to SNP selection using PR for GWAS. We found that PR with FDR control provides substantially more power than SMA with genome-wide type-I error control but somewhat less power than SMA with Benjamini-Hochberg FDR control. PR controlled the FDR conservatively while SMA-BH may not achieve FDR control in all situations. Differences among PR methods seem quite small when the focus is on variable selection with FDR control. Incorporating LD into PR by adapting penalties developed for covariates measured on graphs can improve power but also generate morel false positives or wider regions for follow-up. We recommend using the Elastic Net with a mixing weight for the Lasso penalty near 0.5 as the best method.