{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T03:25:23Z","timestamp":1778297123882,"version":"3.51.4"},"reference-count":23,"publisher":"Wiley","issue":"19-20","license":[{"start":{"date-parts":[[2006,10,15]],"date-time":"2006-10-15T00:00:00Z","timestamp":1160870400000},"content-version":"vor","delay-in-days":4383,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[1994,10,15]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In many epidemiologic studies of human immunodeficiency virus (HIV) disease, interest focuses on the distribution of the length of the interval of time between two events. In many such cases, statistical estimation of properties of this distribution is complicated by the fact that observation of the times of both events is subject to intervalcensoring so that the length of time between the events is never observed exactly. Following DeGruttola and Lagakos, we call such data <jats:italic>doubly\u2010censored.<\/jats:italic> Jewell, Malani and Vittinghoff showed that, with certain assumptions and for a particular doubly\u2010censored data structure, non\u2010parametric maximum likelihood estimation of the interval length distribution is equivalent to non\u2010parametric estimation of a mixing distribution. Here, we extend these ideas to various other kinds of doubly\u2010censored data. We consider application of the methods to various studies generated by investigations into the natural history of HIV disease with particular attention given to estimation of the distribution of time between infection of an individual (an <jats:italic>index case<\/jats:italic>) and transmission of HIV to their sexual partner.<\/jats:p>","DOI":"10.1002\/sim.4780131917","type":"journal-article","created":{"date-parts":[[2007,4,28]],"date-time":"2007-04-28T14:16:42Z","timestamp":1177769802000},"page":"2081-2095","source":"Crossref","is-referenced-by-count":11,"title":["Non\u2010parametric estimation and doubly\u2010censored data: General ideas and applications to AIDS"],"prefix":"10.1002","volume":"13","author":[{"given":"Nicholas P.","family":"Jewell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,15]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.2307\/2532030"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346059"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1080\/01621459.1994.10476441","article-title":"Nonparametric estimation for a form of doubly\u2010censored data with application to two problems in AIDS","volume":"89","author":"Jewell N. P.","year":"1994","journal-title":"Journal of the American Statistical Association"},{"key":"e_1_2_1_5_2","unstructured":"Jewell N. P.\u2018Double\u2010censoring and all that: Problems in biostatistical inference\u2019 Proceedings of CIMAT Conference on Biostatistics and Statistical Inference Perez\u2010Abren V. and Sprott D. (eds) to appear (1994)."},{"key":"e_1_2_1_6_2","volume-title":"Demographic Applications of Event History Analysis","author":"Diamond I. D.","year":"1991"},{"key":"e_1_2_1_7_2","volume-title":"Methodological Issues of AIDS Behavioral Research","author":"Jewell N. P.","year":"1993"},{"key":"e_1_2_1_8_2","volume-title":"Modeling the AIDS Epidemic","author":"Shiboski S.","year":"1994"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1001\/jama.1987.03400060064030","article-title":"Male\u2010to\u2010female transmission of human immunodeficiency virus","volume":"258","author":"Padian N.","year":"1987","journal-title":"Journal of the American Medical Association"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/2532454"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1992.10475215"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1046\/j.1537-2995.1994.34494233574.x"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.2307\/2532057"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.7326\/0003-4819-103-2-210"},{"key":"e_1_2_1_15_2","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1001\/jama.1987.03390030051019","article-title":"Sexual practices and risk of infection by the human immunodeficiency virus. The San Francisco Men's Health Study","volume":"257","author":"Winkelstein W.","year":"1987","journal-title":"Journal of the American Medical Association"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1136\/bmj.296.6624.745"},{"key":"e_1_2_1_17_2","doi-asserted-by":"crossref","first-page":"1050","DOI":"10.1093\/oxfordjournals.aje.a115814","article-title":"Estimating the AIDS incubation period from a prevalent cohort","volume":"133","author":"Kuo J. M.","year":"1990","journal-title":"American Journal of Epidemiology"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.2307\/2532651"},{"key":"e_1_2_1_19_2","doi-asserted-by":"crossref","unstructured":"Efron B.The Jackknfe the Bootstrap and other Resampling Plans Society for Industrial and Applied Mathematics Philadelphia 1982.","DOI":"10.1137\/1.9781611970319"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177728423"},{"key":"e_1_2_1_21_2","volume-title":"Statistical Inference Under Order Restrictions","author":"Barlow R. E.","year":"1972"},{"key":"e_1_2_1_22_2","volume-title":"Information Bounds and Nonparametric Maximum Likelihood Estimation, DMV Seminar","author":"Groeneboom P."},{"key":"e_1_2_1_23_2","unstructured":"Rabinowitz D. Tsiatis A.andAragon J.\u2018Regression with current status data\u2019 Biometrika (1994)."},{"key":"e_1_2_1_24_2","unstructured":"Rabinowitz D.andJewell N. P.\u2018Regression with doubly censored current status data\u2019 submitted for publication (1994)."}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.4780131917","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.4780131917","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T13:13:45Z","timestamp":1693487625000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.4780131917"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,10,15]]},"references-count":23,"journal-issue":{"issue":"19-20","published-print":{"date-parts":[[1994,10,15]]}},"alternative-id":["10.1002\/sim.4780131917"],"URL":"https:\/\/doi.org\/10.1002\/sim.4780131917","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,10,15]]}}}