SNP Selection in genome‐wide and candidate gene studies via penalized logistic regression

Abstract

Penalized regression methods offer an attractive alternative to single marker testing in genetic association analysis. Penalized regression methods shrink down to zero the coefficient of markers that have little apparent effect on the trait of interest, resulting in a parsimonious subset of what we hope are true pertinent predictors. Here we explore the performance of penalization in selecting SNPs as predictors in genetic association studies. The strength of the penalty can be chosen either to select a good predictive model (via methods such as computationally expensive cross validation), through maximum likelihood-based model selection criterion (such as the BIC), or to select a model that controls for type I error, as done here. We have investigated the performance of several penalized logistic regression approaches, simulating data under a variety of disease locus effect size and linkage disequilibrium patterns. We compared several penalties, including the elastic net, ridge, Lasso, MCP and the normal-exponential-γ shrinkage prior implemented in the hyperlasso software, to standard single locus analysis and simple forward stepwise regression. We examined how markers enter the model as penalties and P-value thresholds are varied, and report the sensitivity and specificity of each of the methods. Results show that penalized methods outperform single marker analysis, with the main difference being that penalized methods allow the simultaneous inclusion of a number of markers, and generally do not allow correlated variables to enter the model, producing a sparse model in which most of the identified explanatory markers are accounted for. Genet. Epidemiol. 34:879–891, 2010. © 2010 Wiley-Liss, Inc.

Genetic Diversity in Tomato (Solanum lycopersicum) and Its Wild Relatives

“…Yu and colleagues (2005) proposed a unified mixed model taking into account the genetic structure of the sample, based on single locus analysis. This model is being updated by integrating a multi-locus analysis (Ayers et al 2010).In autogamous crops, it is expected that large extent of LD will reduce the resolution and risks to lead to false positive associations. Nevertheless, successful results have been obtained in selfing crops (Atwell, Huang et al 2010;Ramsay, Comadran et al 2011).…”

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

“…The second value (T = 0.3) is just below the threshold of "useful LD" (r = 0.316 or r 2 = 0.1) as defined by Kruglyak (1999) and Pritchard and Przeworski (2001) as the value at which the sample size is increased at most 10-fold. The last value (T = 0.25) is close to the threshold used in a previous comparison study (Ayers and Cordell 2010). For completeness, we also provide tFDR values at the remaining thresholds used for TPR2 (0.9, 0.7).…”

“…The "usual" approaches include CV and the use of model selection criteria such as AIC, BIC, and EBIC. While CV and AIC are generally useful for prediction rather than model/variable selection, BIC tends to select a true sparse model but does not achieve sufficient sparsity in high-dimensional very sparse settings such as linkage (QTL) mapping and GWAS for which modified BIC criteria have been proposed (e.g., Bogdan et al 2004 Ayers and Cordell (2010) used data permutation to determine the value of the tuning parameter. Multistage strategies have also been suggested as an approach to performing error control with PR (Meinshausen et al 2009;Wasserman and Roeder 2009).…”

“…The absence in PR of the control of an appropriate error rate such as the FWER or the false discovery rate (FDR) (Benjamini and Hochberg 1995;Sabatti and Freimer 2003) has been recognized by several authors who have employed different strategies, including data permutation (Ayers and Cordell 2010), stability selection (Meinshausen and Bühlmann 2010) with FDR control (Ahmed et al 2011), and multistage (data splitting) approaches (Meinshausen et al 2009;Wasserman and Roeder 2009) to control FWER or FDR. However, these approaches require much more computation and may not be feasible on a genome-wide scale, and/or the provision of an error rate estimate comes at the expense of reduced power.…”

European Mathematical Genetics Meeting, Göttingen, Germany, 12–13 April 2012

“…We show that: (a) WGR behaves as a local smoother, (b) because of that, the problem of missing heritability and that of predictive performance are very distinct subjects: the former is largely dependent on the extent to which a WGR model can describe patterns of co-variability among true genetic values; on the other hand, prediction accuracy is largely dependent on local sample size, (c) that although imperfect LD between markers and QTL may explain part of the missing heritability, other factors such as miss-specified genetic architecture or familiar relationships play an important role on determining the extent of missing heritability and the predictive performance. Advocates of such models have postulated that they benefit from higher power and lower type-I error rates because they take into account all the available genetic information simultaneously (Hoggart et al, 2008;Ayers et al, 2010). Given the typical high dimensionality context of the studies, clear candidates for the joint modeling of genetic markers have been penalized regression methods as well as Bayesian methods (de los Campos et al, 2010).…”