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The motivation for this problem is that large datasets may contain numerous associations that are statistically significant and yet misleading, as they are induced by confounders or sampling imperfections. However, associations replicated under different conditions may be more interesting. In fact, sometimes consistency provably leads to valid causal inferences even if conditional associations do not. Although the proposed method is widely applicable, in this paper we highlight its relevance to genome-wide association studies, in which robustness across populations with diverse ancestries mitigates confounding due to unmeasured variants. The effectiveness of this approach is demonstrated by simulations and applications to UK Biobank data.<\/jats:p>","DOI":"10.1093\/biomet\/asab055","type":"journal-article","created":{"date-parts":[[2021,10,27]],"date-time":"2021-10-27T19:12:03Z","timestamp":1635361923000},"page":"611-629","source":"Crossref","is-referenced-by-count":26,"title":["Searching for robust associations with a multi-environment knockoff filter"],"prefix":"10.1093","volume":"109","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6272-4798","authenticated-orcid":false,"given":"S","family":"Li","sequence":"first","affiliation":[{"name":"Department of Statistics, Stanford University , 390 Serra Mall, Stanford, California 94305, U.S.A. lsn@stanford.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9046-907X","authenticated-orcid":false,"given":"M","family":"Sesia","sequence":"additional","affiliation":[{"name":"Department of Data Sciences and Operations, University of Southern California , 3670 Trousdale Parkway, Los Angeles, California 90089, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Y","family":"Romano","sequence":"additional","affiliation":[{"name":"Departments of Electrical Engineering and of Computer Science , Technion, Technion City, Haifa 32000, Israel yromano@technion.ac.il"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E","family":"Cand\u00e8s","sequence":"additional","affiliation":[{"name":"Department of Statistics, Stanford University , 390 Serra Mall, Stanford, California 94305, U.S.A. candes@stanford.edu \u2003 sabatti@stanford.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5829-9058","authenticated-orcid":false,"given":"C","family":"Sabatti","sequence":"additional","affiliation":[{"name":"Department of Statistics, Stanford University , 390 Serra Mall, Stanford, California 94305, U.S.A. candes@stanford.edu \u2003 sabatti@stanford.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,11,2]]},"reference":[{"key":"2022082420280440100_B1","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1038\/nature15393","article-title":"A global reference for human genetic variation","volume":"526","year":"2015","journal-title":"Nature"},{"key":"2022082420280440100_B2","doi-asserted-by":"crossref","first-page":"2055","DOI":"10.1214\/15-AOS1337","article-title":"Controlling the false discovery rate via knockoffs","volume":"43","author":"Barber,","year":"2015","journal-title":"Ann. 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