Inference of causal and pleiotropic effects with multiple weak genetic instruments: application to effect of adiponectin on type 2 diabetes

Current methods for Mendelian randomization (MR) analyses are restricted to single SNP instruments, and cannot reliably infer causality with instruments that are mostly weak and pleiotropic. We describe methods to overcome these limitations: key innovations are construction of scalar instruments from multiple SNPs, use of a regularized horseshoe prior, and hypothesis tests based on the marginal likelihood of the causal effect parameter. To demonstrate the approach, we constructed genotypic instruments from unlinked trans-pQTLs detected in two large GWAS studies of plasma proteins, and tested the top 20 genes for which the aggregated effects of the instruments was associated with type 2 diabetes in the UK Biobank cohort. The only protein with clear evidence of a causal effect on type 2 diabetes was adiponectin, encoded by ADIPOQ: standardized log odds ratio -0.34 (95% CI -0.44 to -0.24) using UK Biobank instruments. These results have implications for the design and analysis of Mendelian randomization studies. Where the exposure under study is expression of a gene, restricting the instruments to cis-acting variants is likely to miss causal effects. Tests based on the marginal likelihood should supersede other methods of testing for causality in the presence of pleiotropy.