{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T03:06:42Z","timestamp":1792033602971,"version":"4.4.0"},"reference-count":33,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T00:00:00Z","timestamp":1569283200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100008982","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100008982","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100005246","name":"Institute of Education Sciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100005246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,12,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>It is important to draw causal inference from observational studies, but this becomes challenging if the confounders have missing values. Generally, causal effects are not identifiable if the confounders are missing not at random. In this article we propose a novel framework for nonparametric identification of causal effects with confounders subject to an outcome-independent missingness, which means that the missing data mechanism is independent of the outcome, given the treatment and possibly missing confounders. We then propose a nonparametric two-stage least squares estimator and a parametric estimator for causal effects.<\/jats:p>","DOI":"10.1093\/biomet\/asz048","type":"journal-article","created":{"date-parts":[[2019,8,19]],"date-time":"2019-08-19T19:23:59Z","timestamp":1566242639000},"page":"875-888","source":"Crossref","is-referenced-by-count":49,"title":["Causal inference with confounders missing not at random"],"prefix":"10.1093","volume":"106","author":[{"given":"S","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, North Carolina, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Statistical Sciences, University of Toronto, 100 St. George Street, Toronto, Ontario, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P","family":"Ding","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California, 367 Evans Hall, Berkeley, California, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,9,24]]},"reference":[{"key":"2020092320044128500_B1","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.jeconom.2012.01.036","article-title":"Well-posedness of measurement error models for self-reported data","volume":"168","author":"An,","year":"2012","journal-title":"J. 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