Mapping molecular QTLs has emerged as an important tool for understanding the genetic basis of cell functions. With the increasing availability of functional genomic data, it is natural to incorporate genomic annotations into QTL discovery. In this paper, we describe a novel method, named TORUS, for integrative QTL discovery. Using hierarchical modeling, our approach embeds a rigorous enrichment analysis to quantify the enrichment level of each annotation in target QTLs. This enrichment information is then used to identify QTLs by up-weighting the genetic variants with relevant annotations using a Bayesian false discovery rate control procedure. Our proposed method only requires summary-level statistics and is highly efficient computationally: it runs a few hundreds times faster than the current gold-standard QTL discovery approach that relies on permutations. Through simulation studies, we demonstrate that the proposed method performs accurate enrichment analysis and controls the desired type I error rate while greatly improving the power of QTL discovery when incorporating informative annotations. Finally, we analyze the recently released expression-genotype data from 44 human tissues generated by the GTEx project. By integrating the simple annotation of SNP distance to transcription start sites, we discover more genes that harbor expression-associated SNPs in all 44 tissues, with an average increase of 1,485 genes.
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