{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T08:03:16Z","timestamp":1791446596095,"version":"4.3.3"},"reference-count":70,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2019,6,5]],"date-time":"2019-06-05T00:00:00Z","timestamp":1559692800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,9,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>To identify the estimand in missing data problems and observational studies, it is common to base the statistical estimation on the \u2018missingness at random\u2019 and \u2018no unmeasured confounder\u2019 assumptions. However, these assumptions are unverifiable by using empirical data and pose serious threats to the validity of the qualitative conclusions of statistical inference. A sensitivity analysis asks how the conclusions may change if the unverifiable assumptions are violated to a certain degree. We consider a marginal sensitivity model which is a natural extension of Rosenbaum\u2019s sensitivity model that is widely used for matched observational studies. We aim to construct confidence intervals based on inverse probability weighting estimators, such that asymptotically the intervals have at least nominal coverage of the estimand whenever the data-generating distribution is in the collection of marginal sensitivity models. We use a percentile bootstrap and a generalized minimax\u2013maximin inequality to transform this intractable problem into a linear fractional programming problem, which can be solved very efficiently. We illustrate our method by using a real data set to estimate the causal effect of fish consumption on blood mercury level.<\/jats:p>","DOI":"10.1111\/rssb.12327","type":"journal-article","created":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T00:38:51Z","timestamp":1559781531000},"page":"735-761","source":"Crossref","is-referenced-by-count":87,"title":["Sensitivity Analysis for Inverse Probability Weighting Estimators via the Percentile Bootstrap"],"prefix":"10.1093","volume":"81","author":[{"given":"Qingyuan","family":"Zhao","sequence":"first","affiliation":[{"name":"University of Pennsylvania , Philadelphia , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dylan S.","family":"Small","sequence":"additional","affiliation":[{"name":"University of Pennsylvania , Philadelphia , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bhaswar B.","family":"Bhattacharya","sequence":"additional","affiliation":[{"name":"University of Pennsylvania , Philadelphia , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,6,5]]},"reference":[{"key":"2023022002405933600_","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1056\/NEJM199404143301501","article-title":"The effect of vitamin E and beta carotene on the incidence of lung cancer and other cancers in male smokers","volume":"330","author":"Alpha-Tocopherol Beta Carotene Cancer Prevention Study Group","year":"1994","journal-title":"New Engl. 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