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Along with the proliferation of genome-wide association studies, a variety of two-sample MR methods for summary data have been developed to account for horizontal pleiotropy (HP), primarily based on the assumption that the effects of variants on exposure (\u03b3) and HP (\u03b1) are independent. In practice, this assumption is too strict and can be easily violated because of the correlated HP.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>To account for this correlated HP, we propose a Bayesian approach, MR-Corr2, that uses the orthogonal projection to reparameterize the bivariate normal distribution for \u03b3 and \u03b1, and a spike-slab prior to mitigate the impact of correlated HP. We have also developed an efficient algorithm with paralleled Gibbs sampling. To demonstrate the advantages of MR-Corr2 over existing methods, we conducted comprehensive simulation studies to compare for both type-I error control and point estimates in various scenarios. By applying MR-Corr2 to study the relationships between exposure\u2013outcome pairs in complex traits, we did not identify the contradictory causal relationship between HDL-c and CAD. Moreover, the results provide a new perspective of the causal network among complex traits.<\/jats:p><\/jats:sec><jats:sec><jats:title>Availability and implementation<\/jats:title><jats:p>The developed R package and code to reproduce all the results are available at https:\/\/github.com\/QingCheng0218\/MR.Corr2.<\/jats:p><\/jats:sec><jats:sec><jats:title>Supplementary information<\/jats:title><jats:p>Supplementary data are available at Bioinformatics online.<\/jats:p><\/jats:sec>","DOI":"10.1093\/bioinformatics\/btab646","type":"journal-article","created":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T11:46:10Z","timestamp":1631101570000},"page":"303-310","source":"Crossref","is-referenced-by-count":23,"title":["MR-Corr2: a two-sample Mendelian randomization method that accounts for correlated horizontal pleiotropy using correlated instrumental variants"],"prefix":"10.1093","volume":"38","author":[{"given":"Qing","family":"Cheng","sequence":"first","affiliation":[{"name":"School of Statistics, Southwestern University of Finance and Economics , Chengdu 611130, China"},{"name":"Centre for Quantitative Medicine, Program in Health Services and Systems Research, Duke-NUS Medical School , 169857 Singapore"}]},{"given":"Tingting","family":"Qiu","sequence":"additional","affiliation":[{"name":"School of Statistics, Southwestern University of Finance and Economics , Chengdu 611130, China"}]},{"given":"Xiaoran","family":"Chai","sequence":"additional","affiliation":[{"name":"Biomedical Pioneering Innovation Center (BIOPIC), Peking University , Beijing 100871, China"}]},{"given":"Baoluo","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Statistics and Applied Probability, NUS , 117546 Singapore"}]},{"given":"Yingcun","family":"Xia","sequence":"additional","affiliation":[{"name":"Department of Statistics and Applied Probability, NUS , 117546 Singapore"}]},{"given":"Xingjie","family":"Shi","sequence":"additional","affiliation":[{"name":"Academy of Statistics and Interdisciplinary Sciences, Faculty of Economics and Management, East China Normal University , Shanghai 200062, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5707-2078","authenticated-orcid":false,"given":"Jin","family":"Liu","sequence":"additional","affiliation":[{"name":"Centre for Quantitative Medicine, Program in Health Services and Systems Research, Duke-NUS Medical School , 169857 Singapore"}]}],"member":"286","published-online":{"date-parts":[[2021,9,9]]},"reference":[{"key":"2023020108420220800_btab646-B2","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1093\/bioinformatics\/btv546","article-title":"Approximately independent linkage disequilibrium blocks in human populations","volume":"32","author":"Berisa","year":"2016","journal-title":"Bioinformatics"},{"key":"2023020108420220800_btab646-B3","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1093\/ije\/dyv080","article-title":"Mendelian randomization with invalid instruments: effect estimation and bias detection through egger regression","volume":"44","author":"Bowden","year":"2015","journal-title":"Int. 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