{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T13:05:39Z","timestamp":1777727139399,"version":"3.51.4"},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2019,8,22]],"date-time":"2019-08-22T00:00:00Z","timestamp":1566432000000},"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":[[2019,11,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>An important research topic in survival analysis is related to the modelling and estimation of the cure rate, i.e. the proportion of subjects who will never experience the event of interest. However, most estimation methods proposed so far in the literature do not handle the case of insufficient follow-up, i.e. when the right end point of the support of the censoring time is strictly less than that of the survival time of the susceptible subjects, and consequently these estimators overestimate the cure rate in that case. We fill this gap by proposing a new estimator of the cure rate that makes use of extrapolation techniques from the area of extreme value theory. We establish the asymptotic normality of the estimator proposed and show how the estimator works for small samples by means of a simulation study. We also illustrate its practical applicability through the analysis of data on the survival of breast cancer patients.<\/jats:p>","DOI":"10.1111\/rssb.12334","type":"journal-article","created":{"date-parts":[[2019,8,23]],"date-time":"2019-08-23T05:25:02Z","timestamp":1566537902000},"page":"861-880","source":"Crossref","is-referenced-by-count":9,"title":["Non-Parametric Cure Rate Estimation Under Insufficient Follow-Up by Using Extremes"],"prefix":"10.1093","volume":"81","author":[{"given":"Mikael","family":"Escobar-Bach","sequence":"first","affiliation":[{"name":"KU Leuven \u00a0 Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ingrid Van","family":"Keilegom","sequence":"additional","affiliation":[{"name":"KU Leuven \u00a0 Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2019,8,22]]},"reference":[{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"1400","DOI":"10.2105\/AJPH.76.12.1400","article-title":"Social class and black-white differences in breast cancer survival","volume":"76","author":"Bassett","year":"1986","journal-title":"Am. J. Publ. Hlth"},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1080\/03461230152592764","article-title":"Pareto index estimation under moderate right censoring","author":"Beirlant","year":"2001","journal-title":"Scand. Act. J."},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"1158","DOI":"10.1080\/03610920902859599","article-title":"Peaks-over-threshold modeling under random censoring. Communs Statist","volume":"39","author":"Beirlant","year":"2010","journal-title":"Theory Meth."},{"key":"2023022002413429600_","volume-title":"The nonparametric location-scale mixture cure model","author":"Chown","year":"2018"},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"31","DOI":"10.3322\/caac.21320","article-title":"Breast cancer statistics, 2015: convergence of incidence rates between black and white women","volume":"66","author":"DeSantis","year":"2016","journal-title":"Cancer J. Clinicns"},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"439","DOI":"10.3322\/caac.21412","article-title":"Breast cancer statistics, 2017, racial disparity in mortality by state","volume":"67","author":"DeSantis","year":"2017","journal-title":"Cancer J. Clinicns"},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"207","DOI":"10.3150\/07-BEJ104","article-title":"Statistics of extremes under random censoring","volume":"14","author":"Einmahl","year":"2008","journal-title":"Bernoulli"},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1001\/jama.1994.03520120057031","article-title":"Racial differences in survival from breast cancer: results of the National Cancer Institute black\/white cancer survival study","volume":"272","author":"Eley","year":"1994","journal-title":"J. Am. Med. Ass."},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BFb0073873","volume-title":"Lectures on Probability Theory (Saint-Flour, 1992)","author":"Gill","year":"1994"},{"key":"2023022002413429600_","first-page":"1","article-title":"Estimation of the extreme value index for randomly censored data","volume":"48","author":"Gomes","year":"2011","journal-title":"Biometr. Lett."},{"key":"2023022002413429600_","volume-title":"Extreme Value Theory: an Introduction","author":"de Haan","year":"2007"},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.canep.2013.09.009","article-title":"Increasing black:white disparities in breast cancer mortality in the 50 largest cities in the United States","volume":"38","author":"Hunt","year":"2014","journal-title":"Cancer Epidem."},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1080\/01621459.1958.10501452","article-title":"Nonparametric estimation from incomplete observations","volume":"53","author":"Kaplan","year":"1958","journal-title":"J. Am. Statist. Ass."},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.csda.2016.08.002","article-title":"Nonparametric incidence estimation and bootstrap bandwidth selection in mixture cure models","volume":"105","author":"L\u00f3pez-Cheda","year":"2017","journal-title":"Computnl Statist. Data Anal."},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s11749-016-0515-1","article-title":"Nonparametric latency estimation for mixture cure models","volume":"26","author":"L\u00f3pez-Cheda","year":"2017","journal-title":"Test"},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1093\/biomet\/79.4.731","article-title":"Estimating the proportion of immunes in a censored sample","volume":"79","author":"Maller","year":"1992","journal-title":"Biometrika"},{"key":"2023022002413429600_","volume-title":"Survival Analysis with Long-term Survivors","author":"Maller","year":"1996"},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1111\/j.0006-341X.2000.00237.x","article-title":"A nonparametric mixture model for cure rate estimation","volume":"56","author":"Peng","year":"2000","journal-title":"Biometrics"},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jmva.2015.10.015","article-title":"Estimating the conditional extreme-value index under random right-censoring","volume":"144","author":"Stupfler","year":"2016","journal-title":"J. Multiv. Anal."},{"issue":"no. 1","key":"2023022002413429600_","doi-asserted-by":"crossref","DOI":"10.1186\/1471-2407-5-48","article-title":"Minimum follow-up time required for the estimation of statistical cure of cancer patients: verification using data from 42 cancer sites in the SEER database","volume":"5","author":"Tai","year":"2005","journal-title":"BMC Cancer"},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s10687-014-0189-6","article-title":"New estimators of the extreme value index under random right censoring, for heavy-tailed distributions","volume":"17","author":"Worms","year":"2014","journal-title":"Extremes"},{"key":"2023022002413429600_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/cjs.11197","article-title":"Nonparametric cure rate estimation with covariates","volume":"42","author":"Xu","year":"2014","journal-title":"Can. J. Statist."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Frssb.12334","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/81\/5\/861\/49270281\/jrsssb_81_5_861.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/81\/5\/861\/49270281\/jrsssb_81_5_861.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,19]],"date-time":"2023-09-19T11:08:59Z","timestamp":1695121739000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/81\/5\/861\/7048380"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,22]]},"references-count":22,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2019,8,22]]},"published-print":{"date-parts":[[2019,11,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12334","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2019,11]]},"published":{"date-parts":[[2019,8,22]]}}}