{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T11:07:42Z","timestamp":1791889662912,"version":"4.3.4"},"reference-count":17,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2004,2,11]],"date-time":"2004-02-11T00:00:00Z","timestamp":1076457600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2004,3,15]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Robins introduced marginal structural models (MSMs) and inverse probability of treatment weighted (IPTW) estimators for the causal effect of a time\u2010varying treatment on the mean of repeated measures. We investigate the sensitivity of IPTW estimators to unmeasured confounding. We examine a new framework for sensitivity analyses based on a nonidentifiable model that quantifies unmeasured confounding in terms of a sensitivity parameter and a user\u2010specified function. We present augmented IPTW estimators of MSM parameters and prove their consistency for the causal effect of an MSM, assuming a correct confounding bias function for unmeasured confounding. We apply the methods to assess sensitivity of the analysis of Hern\u00e1n<jats:italic>et al.<\/jats:italic>, who used an MSM to estimate the causal effect of zidovudine therapy on repeated CD4 counts among HIV\u2010infected men in the Multicenter AIDS Cohort Study. Under the assumption of no unmeasured confounders, a 95 per cent confidence interval for the treatment effect includes zero. We show that under the assumption of a moderate amount of unmeasured confounding, a 95 per cent confidence interval for the treatment effect no longer includes zero. Thus, the analysis of Hern\u00e1n<jats:italic>et al.<\/jats:italic>is somewhat sensitive to unmeasured confounding. We hope that our research will encourage and facilitate analyses of sensitivity to unmeasured confounding in other applications. Copyright \u00a9 2004 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.1657","type":"journal-article","created":{"date-parts":[[2004,2,19]],"date-time":"2004-02-19T08:03:31Z","timestamp":1077177811000},"page":"749-767","source":"Crossref","is-referenced-by-count":169,"title":["Sensitivity analyses for unmeasured confounding assuming a marginal structural model for repeated measures"],"prefix":"10.1002","volume":"23","author":[{"given":"Babette A.","family":"Brumback","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miguel A.","family":"Hern\u00e1n","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sebastien J. P. A.","family":"Haneuse","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James M.","family":"Robins","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2004,2,11]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"95","volume-title":"Statistical Models in Epidemiology: The Environment and Clinical Trials","author":"Robins JM","year":"1999"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1144"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1093\/aje\/126.2.310"},{"key":"e_1_2_1_5_2","first-page":"173","article-title":"Smoking and lung cancer: recent evidence and a discussion of some questions","volume":"22","author":"Cornfield J","year":"1959","journal-title":"Journal of the National Cancer Institute"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1198\/01621450338861905"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2533848"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2443-1"},{"key":"e_1_2_1_9_2","first-page":"3","article-title":"Assessing effects of confounding variables","volume":"108","author":"Schlesselman JJ","year":"1978","journal-title":"American Journal of Epidemiology"},{"key":"e_1_2_1_10_2","first-page":"1","volume-title":"Statistical Models in Epidemiology: The Environment and Clinical Trials","author":"Robins JM","year":"1999"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1005285815569"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1056\/NEJM199204163261601"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.7326\/0003-4819-90-2-257"},{"key":"e_1_2_1_14_2","first-page":"422","volume-title":"Mathematical Statistics: Basic Ideas and Selected Topics","author":"Bickel PJ","year":"2001"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.2307\/2669983"},{"key":"e_1_2_1_16_2","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1111\/j.2517-6161.1983.tb01242.x","article-title":"Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome","volume":"45","author":"Rosenbaum PR","year":"1983","journal-title":"Journal of Royal Statistical Society B"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1111\/1541-0420.00034"},{"key":"e_1_2_1_18_2","volume-title":"Large Sample Estimation and Hypothesis Testing. Hand\u2010book of Econometrics","author":"Newey WK","year":"1994"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.1657","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.1657","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,15]],"date-time":"2024-12-15T11:14:15Z","timestamp":1734261255000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.1657"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,2,11]]},"references-count":17,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2004,3,15]]}},"alternative-id":["10.1002\/sim.1657"],"URL":"https:\/\/doi.org\/10.1002\/sim.1657","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,2,11]]}}}