Using information from allele-specific gene expression (ASE) can sub-stantially improve the power to map gene expression quantitative trait loci (eQTLs). However, such practice has been limited, partly due to high computational cost and the requirement to access raw data that can take a large amount of storage space. To address these computational challenges, we have developed a computational framework that uses a statistical method named TReCASE as its computational engine, and it is computationally feasible for large scale analysis. We applied it to map eQTLs in 28 human tissues using the data from the Genotype-Tissue Expression (GTEx) project. Compared with a popular linear regression method that does not use ASE data, TReCASE can double the number of eGenes (i.e., genes with at least one significant eQTL) when sample size is relatively small, e.g., n 200.

We consider the problem of estimating a sparse multi-response regression function, with an application to expression quantitative trait locus (eQTL) mapping, where the goal is to discover genetic variations that influence gene-expression levels. In particular, we investigate a shrinkage technique capable of capturing a given hierarchical structure over the responses, such as a hierarchical clustering tree with leaf nodes for responses and internal nodes for clusters of related responses at multiple granularity, and we seek to leverage this structure to recover covariates relevant to each hierarchically-defined cluster of responses. We propose a tree-guided group lasso, or tree lasso, for estimating such structured sparsity under multi-response regression by employing a novel penalty function constructed from the tree. We describe a systematic weighting scheme for the overlapping groups in the tree-penalty such that each regression coefficient is penalized in a balanced manner despite the inhomogeneous multiplicity of group memberships of the regression coefficients due to overlaps among groups. For efficient optimization, we employ a smoothing proximal gradient method that was originally developed for a general class of structured-sparsity-inducing penalties. Using simulated and yeast data sets, we demonstrate that our method shows a superior performance in terms of both prediction errors and recovery of true sparsity patterns, compared to other methods for learning a multivariate-response regression.