In the post-genome-wide association era, two-sample Mendelian Randomization (MR) methods have been applied to detect genetically-regulated risk factors for complex diseases. Two-sample MR considers single nucleotide polymorphisms (SNPs) associated with a putative exposure as instrumental variables (IVs) to assess the effect of the exposure on an outcome by leveraging two sets of summary statistics: IV-to-exposure and IV-to-outcome statistics from existing GWASs. Traditional MR methods impose strong assumptions on the validity of IVs, and recent literature has relaxed the assumptions allowing some IVs to be invalid but generally requiring a large number of nearly independent IVs. When treating expression-quantitative-trait-loci (eQTLs) as IVs to detect gene expression levels affecting diseases, existing methods are limited in applicability since the numbers of independent eQTLs for most genes in the genome are limited. To address those challenges, we propose a robust two-sample MR framework that requires fewer IVs and allows moderate IV correlations and some IVs to be invalid. This is achieved by leveraging existing multi-tissue eQTL summary statistics (multiple sets of IV-to-exposure statistics) and GWAS statistics in a mixed model framework. We conducted simulation studies to evaluate the performance of the proposed method and apply it to detect putative causal genes for schizophrenia. ### Competing Interest Statement The authors have declared no competing interest.
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