  Expression quantitative trait loci (eQTL) analysis identifies genetic markers
associated with the expression of a gene. Most existing eQTL analyses and
methods investigate association in a single, readily available tissue, such as
blood. Joint analysis of eQTL in multiple tissues has the potential to improve,
and expand the scope of, single-tissue analyses. Large-scale collaborative
efforts such as the Genotype-Tissue Expression (GTEx) program are currently
generating high quality data in a large number of tissues. However,
computational constraints limit genome-wide multi-tissue eQTL analysis. We
develop an integrative method under a hierarchical Bayesian framework for eQTL
analysis in a large number of tissues. The model fitting procedure is highly
scalable, and the computing time is a polynomial function of the number of
tissues. Multi-tissue eQTLs are identified through a local false discovery rate
approach, which rigorously controls the false discovery rate. Using simulation
and GTEx real data studies, we show that the proposed method has superior
performance to existing methods in terms of computing time and the power of
eQTL discovery. We provide a scalable method for eQTL analysis in a large
number of tissues. The method enables the identification of eQTL with different
configurations and facilitates the characterization of tissue specificity.
