{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T16:09:02Z","timestamp":1784650142066,"version":"3.55.0"},"reference-count":39,"publisher":"Wiley","issue":"15-17","license":[{"start":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T00:00:00Z","timestamp":1783728000000},"content-version":"vor","delay-in-days":10,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2026,7]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Mendelian randomization (MR) uses genetic variants as instruments to study causal relationships between traits. Standard unidirectional MR approaches are vulnerable to pleiotropy and typically assume that pleiotropic effects are independent of instrument strength, assumptions that may fail when causation operates in both directions. We propose BayBiMR, a Bayesian bidirectional MR framework that jointly estimates causal effects in both directions while modeling both correlated and uncorrelated pleiotropy through a hierarchical spike\u2010and\u2010slab prior on pleiotropic effects and an Inverse\u2010Wishart prior on the joint covariance of direct and pleiotropic SNP effects. The likelihood is based on a small\u2010feedback reduced\u2010form approximation to the underlying simultaneous\u2010equation model, which preserves conjugacy and enables efficient closed\u2010form posterior computation. Posterior inference is carried out via a blocked Gibbs sampler, and a data\u2010perturbation extension, BayBiMR(DP), is provided to improve empirical frequentist calibration in finite samples. Simulation studies show that BayBiMR and BayBiMR(DP) provide better type I error control than existing methods in the settings considered, particularly under correlated and mixed pleiotropy. Applications to large\u2010scale GWAS summary statistics on white\u2010matter (WM) microstructures, BMI, sleep duration, and neuroticism illustrate the method's practical utility as an exploratory and sensitivity tool.<\/jats:p>","DOI":"10.1002\/sim.70667","type":"journal-article","created":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T08:54:07Z","timestamp":1783760047000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bayesian Bidirectional Mendelian Randomization Under Correlated and Uncorrelated Pleiotropy Using GWAS Summary Statistics"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8019-8149","authenticated-orcid":false,"given":"Siyi","family":"Chen","sequence":"first","affiliation":[{"name":"School of Public Health LSU Health Sciences Center New Orleans  New Orleans Louisiana 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