Evaluation of the lasso and the elastic net in genome-wide association studies

The number of publications performing genome-wide association studies (GWAS) has increased dramatically. Penalized regression approaches have been developed to overcome the challenges caused by the high dimensional data, but these methods are relatively new in the GWAS field. In this study we have compared the statistical performance of two methods (the least absolute shrinkage and selection operator-lasso and the elastic net) on two simulated data sets and one real data set from a 50 K genome-wide single nucleotide polymorphism (SNP) panel of 5570 Fleckvieh bulls. The first simulated data set displays moderate to high linkage disequilibrium between SNPs, whereas the second simulated data set from the QTLMAS 2010 workshop is biologically more complex. We used cross-validation to find the optimal value of regularization parameter λ with both minimum MSE and minimum MSE + 1SE of minimum MSE. The optimal λ values were used for variable selection. Based on the first simulated data, we found that the minMSE in general picked up too many SNPs. At minMSE + 1SE, the lasso didn't acquire any false positives, but selected too few correct SNPs. The elastic net provided the best compromise between few false positives and many correct selections when the penalty weight α was around 0.1. However, in our simulation setting, this α value didn't result in the lowest minMSE + 1SE. The number of selected SNPs from the QTLMAS 2010 data was after correction for population structure 82 and 161 for the lasso and the elastic net, respectively. In the Fleckvieh data set after population structure correction lasso and the elastic net identified from 1291 to 1966 important SNPs for milk fat content, with major peaks on chromosomes 5, 14, 15, and 20. Hence, we can conclude that it is important to analyze GWAS data with both the lasso and the elastic net and an alternative tuning criterion to minimum MSE is needed for variable selection.