Jae Hoon Sul^{1, 2}, Towfique Raj^{2, 3, 4}, Simone de Jong⁵, Paul I.W. de Bakker⁶, Soumya Raychaudhuri^{1, 2, 7, 8}, Roel A. Ophoff^{5, 9, 10}, Barbara E. Stranger^{11, 12}, Eleazar Eskin^{10, 13,*}, Buhm Han^{14, 15,*}

¹ Division of Genetics, Brigham and Women’s Hospital, Harvard Medical School, Harvard University, Boston, MA 02115, USA

² Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA

³ Harvard Medical School, Harvard University, Boston, MA 02115, USA

⁴ Program in Translational NeuroPsychiatric Genomics, Institute for the Neurosciences, Department of Neurology, Brigham and Women’s Hospital, Boston, MA 02115, USA

⁵ Center for Neurobehavioral Genetics, Semel Institute for Neuroscience and Behavior, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, CA 90095, USA

⁶ Departments of Epidemiology and Medical Genetics, University Medical Center Utrecht, Utrecht 3584 CG, the Netherlands

⁷ Arthritis Research UK Epidemiology Unit, Musculoskeletal Research Group, University of Manchester, Manchester Academic Health Sciences Centre, Manchester M13 9PT, UK

⁸ Division of Rheumatology, Brigham and Women’s Hospital, Harvard Medical School, Harvard University, Boston, MA 02115, USA

⁹ Brain Center Rudolf Magnus, Department of Psychiatry, University Medical Center Utrecht, Utrecht 3584 CG, the Netherlands

¹⁰ Department of Human Genetics, University of California, Los Angeles, Los Angeles, CA 90095, USA

¹¹ Section of Genetic Medicine, Department of Medicine, University of Chicago, Chicago, IL 60637, USA

¹² Institute for Genomics and Systems Biology, University of Chicago, Chicago, IL 60637, USA

¹³ Computer Science Department, University of California, Los Angeles, Los Angeles, CA 90095, USA

¹⁴ Asan Institute for Life Sciences, Asan Medical Center, Seoul 138-736, Republic of Korea

¹⁵ Department of Medicine, University of Ulsan College of Medicine, Seoul 138-736, Republic of Korea

^*Corresponding author : Eleazar Eskin, Buhm Han

In studies of expression quantitative trait loci (eQTLs), it is of increasing interest to identify eGenes, the genes whose expression levels are associated with variation at a particular genetic variant. Detecting eGenes is important for follow-up analyses and prioritization because genes are the main entities in biological processes. To detect eGenes, one typically focuses on the genetic variant with the minimum p value among all variants in cis with a gene and corrects for multiple testing to obtain a gene-level p value. For performing multiple-testing correction, a permutation test is widely used. Because of growing sample sizes of eQTL studies, however, the permutation test has become a computational bottleneck in eQTL studies. In this paper, we propose an efficient approach for correcting for multiple testing and assess eGene p values by utilizing a multivariate normal distribution. Our approach properly takes into account the linkage-disequilibrium structure among variants, and its time complexity is independent of sample size. By applying our small-sample correction techniques, our method achieves high accuracy in both small and large studies. We have shown that our method consistently produces extremely accurate p values (accuracy > 98%) for three human eQTL datasets with different sample sizes and SNP densities: the Genotype-Tissue Expression pilot dataset, the multi-region brain dataset, and the HapMap 3 dataset.