{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T00:39:42Z","timestamp":1791851982348,"version":"4.3.4"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2016,10,2]],"date-time":"2016-10-02T00:00:00Z","timestamp":1475366400000},"content-version":"vor","delay-in-days":2613,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000002","name":"U.S. National Institutes of Health","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000002","name":"NIH","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Considerable recent interest has focused on doubly robust estimators for a population mean response in the presence of incomplete data, which involve models for both the propensity score and the regression of outcome on covariates. The usual doubly robust estimator may yield severely biased inferences if neither of these models is correctly specified and can exhibit nonnegligible bias if the estimated propensity score is close to zero for some observations. We propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods, even with some estimated propensity scores close to zero.<\/jats:p>","DOI":"10.1093\/biomet\/asp033","type":"journal-article","created":{"date-parts":[[2009,8,7]],"date-time":"2009-08-07T21:30:55Z","timestamp":1249680655000},"page":"723-734","source":"Crossref","is-referenced-by-count":215,"title":["Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data"],"prefix":"10.1093","volume":"96","author":[{"given":"Weihua","family":"Cao","sequence":"first","affiliation":[{"name":"Department of Statistics,North Carolina State University,Raleigh, North Carolina 27695-8203,U.S.A.wcao5@ncsu.edutsiatis@stat.ncsu.edudavidian@stat.ncsu.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anastasios A.","family":"Tsiatis","sequence":"additional","affiliation":[{"name":"Department of Statistics,North Carolina State University,Raleigh, North Carolina 27695-8203,U.S.A.wcao5@ncsu.edutsiatis@stat.ncsu.edudavidian@stat.ncsu.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marie","family":"Davidian","sequence":"additional","affiliation":[{"name":"Department of Statistics,North Carolina State University,Raleigh, North Carolina 27695-8203,U.S.A.wcao5@ncsu.edutsiatis@stat.ncsu.edudavidian@stat.ncsu.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2009,8,7]]},"reference":[{"key":"2021061508293309000_R1","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1111\/j.1541-0420.2005.00377.x","article-title":"Doubly robust estimation in missing data and causal inference models","volume":"61","author":"Bang","year":"2005","journal-title":"Biometrics"},{"key":"2021061508293309000_R2","first-page":"523","article-title":"Demystifying double robustness: a comparison of alternative strategies for estimating a population mean from incomplete data (with discussion and rejoinder)","volume":"22","author":"Kang","year":"2007","journal-title":"Statist. 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