{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T15:44:22Z","timestamp":1785426262437,"version":"3.56.0"},"reference-count":47,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2024,11,21]],"date-time":"2024-11-21T00:00:00Z","timestamp":1732147200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12201630"],"award-info":[{"award-number":["12201630"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000057","name":"National Institute Of General Medical Sciences","doi-asserted-by":"publisher","award":["R35GM155070"],"award-info":[{"award-number":["R35GM155070"]}],"id":[{"id":"10.13039\/100000057","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,4,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Mendelian randomization (MR) is a powerful method that uses genetic variants as instrumental variables to infer the causal effect of a modifiable exposure on an outcome. We study inference for bi-directional causal relationships and causal directions with possibly pleiotropic genetic variants. We show that assumptions for common MR methods are often impossible or too stringent given the potential bi-directional relationships. We propose a new focusing framework for testing bi-directional causal effects and it can be coupled with many state-of-the-art MR methods. We provide theoretical guarantees for our proposal and demonstrate its performance using several simulated and real datasets.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkae101","type":"journal-article","created":{"date-parts":[[2024,11,21]],"date-time":"2024-11-21T12:19:21Z","timestamp":1732191561000},"page":"529-548","source":"Crossref","is-referenced-by-count":6,"title":["A focusing framework for testing bi-directional causal effects in Mendelian randomization"],"prefix":"10.1093","volume":"87","author":[{"given":"Sai","family":"Li","sequence":"first","affiliation":[{"name":"Institute of Statistics and Big Data, Renmin University of China , Beijing 100872 ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6009-641X","authenticated-orcid":false,"given":"Ting","family":"Ye","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Washington , Seattle 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