Genomic selection using regularized linear regression models: ridge regression, lasso, elastic net and their extensions

Abstract

BackgroundGenomic selection (GS) is emerging as an efficient and cost-effective method for estimating breeding values using molecular markers distributed over the entire genome. In essence, it involves estimating the simultaneous effects of all genes or chromosomal segments and combining the estimates to predict the total genomic breeding value (GEBV). Accurate prediction of GEBVs is a central and recurring challenge in plant and animal breeding. The existence of a bewildering array of approaches for predicting breeding values using markers underscores the importance of identifying approaches able to efficiently and accurately predict breeding values. Here, we comparatively evaluate the predictive performance of six regularized linear regression methods-- ridge regression, ridge regression BLUP, lasso, adaptive lasso, elastic net and adaptive elastic net-- for predicting GEBV using dense SNP markers.MethodsWe predicted GEBVs for a quantitative trait using a dataset on 3000 progenies of 20 sires and 200 dams and an accompanying genome consisting of five chromosomes with 9990 biallelic SNP-marker loci simulated for the QTL-MAS 2011 workshop. We applied all the six methods that use penalty-based (regularization) shrinkage to handle datasets with far more predictors than observations. The lasso, elastic net and their adaptive extensions further possess the desirable property that they simultaneously select relevant predictive markers and optimally estimate their effects. The regression models were trained with a subset of 2000 phenotyped and genotyped individuals and used to predict GEBVs for the remaining 1000 progenies without phenotypes. Predictive accuracy was assessed using the root mean squared error, the Pearson correlation between predicted GEBVs and (1) the true genomic value (TGV), (2) the true breeding value (TBV) and (3) the simulated phenotypic values based on fivefold cross-validation (CV).ResultsThe elastic net, lasso, adaptive lasso and the adaptive elastic net all had similar accuracies but outperformed ridge regression and ridge regression BLUP in terms of the Pearson correlation between predicted GEBVs and the true genomic value as well as the root mean squared error. The performance of RR-BLUP was also somewhat better than that of ridge regression. This pattern was replicated by the Pearson correlation between predicted GEBVs and the true breeding values (TBV) and the root mean squared error calculated with respect to TBV, except that accuracy was lower for all models, most especially for the adaptive elastic net. The correlation between the predicted GEBV and simulated phenotypic values based on the fivefold CV also revealed a similar pattern except that the adaptive elastic net had lower accuracy than both the ridge regression methods.ConclusionsAll the six models had relatively high prediction accuracies for the simulated data set. Accuracy was higher for the lasso type methods than for ridge regression and ridge regression BLUP.

Exploring the areas of applicability of whole-genome prediction methods for Asian rice (Oryza sativa L.)

“…Methods include genomic BLUP (GBLUP) and its extension (VanRaden 2008;Aguilar et al 2010;Christensen and Lund 2010); penalized regression methods such as ridge regression, Lasso, and elastic net (ENet) (Usai et al 2009;Li and Sillanpaa 2012a;Ogutu et al 2012); Bayesian regression methods such as BayesA and BayesB (Meuwissen et al 2001;de los Campos et al 2009;Hayashi and Iwata 2010;Habier et al 2011); non-parametric regression methods to capture non-additive genetic effects (Gianola et al 2006;Gianola and van Kaam 2008;Long et al 2010;Ober et al 2011); methods developed in the field of machine learning such as support vector machine and random forest (RForest) (Long et al 2011a;Ogutu et al 2011); and regression methods based on dimension reduction (Solberg et al 2009;Long et al 2011b). Ridge regression and its equivalent GBLUP, BayesA and BayesB, and Bayesian lasso (Blasso; Park and Casella 2008) are popular methods, and have been evaluated in many studies (reviewed in de los .…”

Intracranial Pressure Forecasting in Children Using Dynamic Averaging of Time Series Data

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Polygenic scores via penalized regression on summary statistics

“…In principle, various machine learning methods or Bayesian methods can be applied in the construction of PGS, as they have been applied in the estimation of breeding values in animal studies (Meuwissen et al, 2001;Abraham et al, 2013;Szymczak et al, 2009;Habier et al, 2011;Pirinen et al, 2013;Erbe et al, 2012;Ogutu et al, 2012;Zhou et al, 2013). These methods do not require the assumption of SNP independence or near independence, and have been shown to perform better than simple PGS in simulation settings.…”