{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T10:49:01Z","timestamp":1782211741016,"version":"3.54.5"},"reference-count":41,"publisher":"Wiley","issue":"13-14","license":[{"start":{"date-parts":[[2026,6,7]],"date-time":"2026-06-07T00:00:00Z","timestamp":1780790400000},"content-version":"vor","delay-in-days":6,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11601307"],"award-info":[{"award-number":["11601307"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12571299"],"award-info":[{"award-number":["12571299"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["CXJJ\u20102024\u2010447"],"award-info":[{"award-number":["CXJJ\u20102024\u2010447"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>In many clinical trials, subjects often experience recurrent events, and some individuals may have their follow\u2010up terminated by a dependent terminal event, such as death. We are particularly interested in the effect of covariates on recurrent gap times and correlations among recurrent gap times and the terminal event. In this article, we propose a novel nested copula model with a two\u2010layer structure: the inner layer uses an Archimedean copula to capture the internal correlations among recurrent gap times, while the outer layer employs a general bivariate copula to model the dependence between recurrent events and the terminal event. The nested copula framework serves as a copula\u2010based counterpart to the frailty model, providing improved interpretability and enabling straightforward extensions to accommodate heterogeneous dependence structures. Both parametric and semiparametric methods are developed for parameter estimation, and the resulting estimators are shown to be consistent and asymptotically normal. In addition, a likelihood\u2010based copula selection procedure is provided to select a suitable model for a given dataset. Extensive simulation studies are conducted to investigate the finite sample properties of the proposed methods. Finally, an application to colorectal cancer data from a clinical study conducted at Bellvitge Hospital is presented.<\/jats:p>","DOI":"10.1002\/sim.70626","type":"journal-article","created":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T05:58:20Z","timestamp":1780898300000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Nested Copula Model for Recurrent Gap Times With a Dependent Terminal Event"],"prefix":"10.1002","volume":"45","author":[{"given":"Yuanjia","family":"Duan","sequence":"first","affiliation":[{"name":"School of Statistics and Data Science Shanghai University of Finance and Economics  Shanghai P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miao","family":"Han","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science Shanghai University of Finance and Economics  Shanghai P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8816-942X","authenticated-orcid":false,"given":"Liuquan","family":"Sun","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mathematical Sciences Academy of Mathematics and Systems Science, Chinese Academy of Sciences  Beijing P.R. China"},{"name":"School of Mathematical Sciences University of Chinese Academy of Sciences  Beijing P.R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,6,7]]},"reference":[{"key":"e_1_2_12_2_1","volume-title":"The Statistical Analysis of Recurrent Events","author":"Cook R. J.","year":"2007"},{"key":"e_1_2_12_3_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345976"},{"key":"e_1_2_12_4_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/93.3.627"},{"key":"e_1_2_12_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00259"},{"key":"e_1_2_12_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10985-006-9017-x"},{"key":"e_1_2_12_7_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/86.1.59"},{"key":"e_1_2_12_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.13014"},{"key":"e_1_2_12_9_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1989.10478873"},{"key":"e_1_2_12_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19970430)16:8<911::AID-SIM544>3.0.CO;2-I"},{"key":"e_1_2_12_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19970430)16:8<925::AID-SIM545>3.0.CO;2-2"},{"issue":"3","key":"e_1_2_12_12_1","first-page":"663","article-title":"Marginal Regression Models for Recurrent and Terminal Events","volume":"12","author":"Ghosh D.","year":"2002","journal-title":"Statistica Sinica"},{"key":"e_1_2_12_13_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2003.00102.x"},{"key":"e_1_2_12_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2010.01497.x"},{"key":"e_1_2_12_15_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2010.01458.x"},{"key":"e_1_2_12_16_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214501753209031"},{"key":"e_1_2_12_17_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214504000001033"},{"key":"e_1_2_12_18_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2004.00225.x"},{"key":"e_1_2_12_19_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2006.00719.x"},{"key":"e_1_2_12_20_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.6853"},{"key":"e_1_2_12_21_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.13242"},{"key":"e_1_2_12_22_1","doi-asserted-by":"publisher","DOI":"10.1080\/02664760802271389"},{"issue":"3","key":"e_1_2_12_23_1","first-page":"229","article-title":"Fonctions de r\u00e9partition \u00e0n dimensions et leurs marges","volume":"8","author":"Sklar M.","year":"1959","journal-title":"Publications de L'institut Statistique de L'universit\u00e9 Paris"},{"key":"e_1_2_12_24_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3830"},{"key":"e_1_2_12_25_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssc.12382"},{"key":"e_1_2_12_26_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280215604510"},{"key":"e_1_2_12_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/s42081-020-00087-8"},{"key":"e_1_2_12_28_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2021.1990766"},{"key":"e_1_2_12_29_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/88.4.907"},{"key":"e_1_2_12_30_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2009.01340.x"},{"key":"e_1_2_12_31_1","volume-title":"An Introduction to Copulas","author":"Nelsen R. B.","year":"2006"},{"key":"e_1_2_12_32_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.3449"},{"key":"e_1_2_12_33_1","volume-title":"Asymptotic Statistics","author":"Vaart A. W.","year":"2000"},{"key":"e_1_2_12_34_1","doi-asserted-by":"publisher","DOI":"10.2307\/2533269"},{"key":"e_1_2_12_35_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12174"},{"key":"e_1_2_12_36_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00322"},{"key":"e_1_2_12_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2011.02.008"},{"key":"e_1_2_12_38_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v039.i09"},{"key":"e_1_2_12_39_1","doi-asserted-by":"publisher","DOI":"10.1136\/jech.2004.028902"},{"key":"e_1_2_12_40_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v047.i04"},{"key":"e_1_2_12_41_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201000131"},{"key":"e_1_2_12_42_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1998.10473777"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70626","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sim.70626","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.70626","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T10:19:17Z","timestamp":1782209957000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.70626"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":41,"journal-issue":{"issue":"13-14","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["10.1002\/sim.70626"],"URL":"https:\/\/doi.org\/10.1002\/sim.70626","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"2025-03-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-05-19","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-06-07","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70626"}}