{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T02:40:59Z","timestamp":1791513659492,"version":"4.3.4"},"reference-count":13,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2019,7,24]],"date-time":"2019-07-24T00:00:00Z","timestamp":1563926400000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","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":[[2019,12,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>Doubly truncated survival data arise if failure times are observed only within certain time intervals. The nonparametric maximum likelihood estimator is widely used to estimate the underlying failure time distribution. Using a directed graph representation of the data suggested by Vardi (1985), a certain graphical condition holds if and only if the nonparametric maximum likelihood estimate exists and is unique. If this condition does not hold, then such an estimate may exist but need not be unique, so another graphical condition is proposed to check whether such an estimate exists. The conditions are simple to check using existing graphical software. Reanalysis of an AIDS incubation time dataset shows that a nonparametric maximum likelihood estimate does not exist for these data.<\/jats:p>","DOI":"10.1093\/biomet\/asz038","type":"journal-article","created":{"date-parts":[[2019,6,25]],"date-time":"2019-06-25T14:01:15Z","timestamp":1561471275000},"page":"989-996","source":"Crossref","is-referenced-by-count":10,"title":["On nonparametric maximum likelihood estimation with double truncation"],"prefix":"10.1093","volume":"106","author":[{"given":"J","family":"Xiao","sequence":"first","affiliation":[{"name":"SPHERE Institute, 500 Airport Blvd #340, Burlingame, California 94010, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M G","family":"Hudgens","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,7,23]]},"reference":[{"key":"2019111117235867300_B1","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s10985-013-9287-z","article-title":"Computationally simple estimation and improved efficiency for special cases of double truncation","volume":"20","author":"Austin,","year":"2014","journal-title":"Lifetime Data Anal."},{"key":"2019111117235867300_B2","article-title":"The igraph software package for complex network research","author":"Csardi,","year":"2006","journal-title":"Inter J. 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