Graph-regularized dual Lasso for robust eQTL mapping

Abstract

Motivation: As a promising tool for dissecting the genetic basis of complex traits, expression quantitative trait loci (eQTL) mapping has attracted increasing research interest. An important issue in eQTL mapping is how to effectively integrate networks representing interactions among genetic markers and genes. Recently, several Lasso-based methods have been proposed to leverage such network information. Despite their success, existing methods have three common limitations: (i) a preprocessing step is usually needed to cluster the networks; (ii) the incompleteness of the networks and the noise in them are not considered; (iii) other available information, such as location of genetic markers and pathway information are not integrated.

Results: To address the limitations of the existing methods, we propose Graph-regularized Dual Lasso (GDL), a robust approach for eQTL mapping. GDL integrates the correlation structures among genetic markers and traits simultaneously. It also takes into account the incompleteness of the networks and is robust to the noise. GDL utilizes graph-based regularizers to model the prior networks and does not require an explicit clustering step. Moreover, it enables further refinement of the partial and noisy networks. We further generalize GDL to incorporate the location of genetic makers and gene-pathway information. We perform extensive experimental evaluations using both simulated and real datasets. Experimental results demonstrate that the proposed methods can effectively integrate various available priori knowledge and significantly outperform the state-of-the-art eQTL mapping methods.

Availability: Software for both C++ version and Matlab version is available at http://www.cs.unc.edu/∼weicheng/.

Fig. 1.

Examples of prior knowledge on genetic-interaction network S and gene–gene interactions represented by PPI network or gene co-expression network G. W is the regression coefficients to be learned

Fig. 2.

Ground truth of matrix W and that estimated by different methods. The x-axis represents traits and y-axis represents SNPs. Normalized absolute values of regression coefficients are used. Darker color implies stronger association

Fig. 3.

The ground truth networks, prior partial networks and the refined networks

Fig. 4.

Power curves for synthetic data. The left plots show the ROC curve, where our model GDL achieved maximum power. The black solid line denotes what random guessing would have achieved. The right plots illustrate the areas under the precision-recall curve (AUCs) of different methods

Fig. 5.

The areas under the TPR-FPR curve (AUCs) of Lasso, LORS, G-Lasso and GDL. In each panel, we vary the percentage of noises in the prior networks $S_0$ and $G_0$

Fig. 6.

The top-1000 significant associations identified by different methods. In each plot, the x-axis represents SNPs and y-axis represents genes. Both SNPs and genes are arranged by their locations in the genome

Fig. 7.

Ratio of correct interactions refined when varying κ. The initial input networks only contain 25% correct interactions