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Mendelian randomization (MR) is a powerful approach to examine the causalrelationships between health risk factors and outcomes from observationalstudies. Due to the proliferation of genome-wide association studies (GWASs)and abundant fully accessible GWASs summary statistics, a variety of two-sampleMR methods for summary data have been developed to either detect or account forhorizontal pleiotropy, primarily based on the assumption that the effects ofvariants on exposure ({\gamma}) and horizontal pleiotropy ({\alpha}) areindependent. This assumption is too strict and can be easily violated becauseof the correlated horizontal pleiotropy (CHP). To account for this CHP, wepropose a Bayesian approach, MR-Corr2, that uses the orthogonal projection toreparameterize the bivariate normal distribution for {\gamma} and {\alpha}, anda spike-slab prior to mitigate the impact of CHP. We develop an efficientalgorithm with paralleled Gibbs sampling. To demonstrate the advantages ofMR-Corr2 over existing methods, we conducted comprehensive simulation studiesto compare for both type-I error control and point estimates in variousscenarios. By applying MR-Corr2 to study the relationships between pairs in twosets of complex traits, we did not identify the contradictory causalrelationship between HDL-c and CAD. Moreover, the results provide a newperspective of the causal network among complex traits. The developed R packageand code to reproduce all the results are available athttps://github.com/QingCheng0218/MR.Corr2.

Accounting for correlated horizontal pleiotropy in two-sample Mendelian randomization using correlated instrumental variants