Penalized Multimarkervs.Single-Marker Regression Methods for Genome-Wide Association Studies of Quantitative Traits

Abstract

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 in comparison with SMA. PR methods were compared with SMA, using realistically simulated GWAS data with a continuous phenotype and real data. Based on these 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 genomewide type-I error control but somewhat less power than SMA with Benjamini-Hochberg FDR control (SMA-BH). PR with FDR-based penalty parameter selection controlled the FDR somewhat conservatively while SMA-BH may not achieve FDR control in all situations. Differences among PR methods seem quite small when the focus is on SNP selection with FDR control. Incorporating linkage disequilibrium into the penalization by adapting penalties developed for covariates measured on graphs can improve power but also generate more false positives or wider regions for follow-up. We recommend the elastic net with a mixing weight for the Lasso penalty near 0.5 as the best method.T HE goal of genome-wide association studies (GWAS) in humans and model organisms is to select a small subset of DNA markers, typically single-nucleotide polymorphisms (SNPs), which are in strong linkage disequilibrium (LD) with functional polymorphisms affecting a biomedical/clinical trait of interest. The selected markers are then replicated in other GWAS, fine-mapped, and further validated. GWAS may be viewed as a large-scale variable selection problem, with several millions of common SNPs, measured directly or imputed, available in current studies in humans.GWAS practitioners still strongly rely on single-marker analysis (SMA), including linear regression for continuous phenotypes, with control of the genome-wise error rate (GWER) [a special case of the family-wise error rate (FWER)], which accounts for the multiplicity of the entire genome. Assuming that a biomedical trait of interest is affected by multiple polymorphisms with "detectable" effects, SMA fits an incorrect model, and it is sensible to consider alternative methods that test all or subsets of markers simultaneously. This approach requires a form of penalized regression (PR) as the number of SNPs is much larger than the sample size.A major practical issue with the use of penalized regression is the determination of "optimal" values for the tuning parameter(s) and the lack of an error rate associated with the selection of SNPs. Common approaches for tuning parameter value determination include cross-validati...

Dynamic Quantitative Trait Locus Analysis of Plant Phenomic Data

“…In reality, many quantitative traits in plants are controlled by multiple genes, indicating that single-locus models are inadequate for these complex traits [41,42], and may not provide accurate estimates of SNP effects and residual covariance. In addition, the residual covariance has to be repeatedly estimated for every single SNP, making the single-locus functional method computationally expensive for datasets with thousands of SNPs.…”

A simulated SNP experiment indicates a high risk of over-fitting and false positive results when a predictive multiple SNP model is established and tested within the same dataset

“…These methods are referred to as 'penalized multi marker regression models' [23]. Examples of such models are 'the lasso' and 'the elastic net'.…”

“…Nor was a test setvalidation set approach used to verify the model. Compared to the usual single marker analysis, penalized multi-marker analysis may have certain advantages [23]. Nevertheless, it should be emphasized that such approaches do not eliminate the fundamental challenges that relate to the analysis of complex genomic data.…”

“…Nevertheless, it should be emphasized that such approaches do not eliminate the fundamental challenges that relate to the analysis of complex genomic data. Large sample sizes will still be required to achieve sufficient statistical power while keeping the false discovery rate low [23]. The last decade has provided a reasonable insight into complex trait genetics [1,2].…”

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“…We note that such standardization can be justified by the fact that the LASSO is often performed on standardized variables (Li et al, 2012;Hastie et al, 2009;Yi et al, 2014). However, when it comes to the construction of PGS, we ought to use unstandardized coefficients as weights.…”