{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T23:43:19Z","timestamp":1773013399337,"version":"3.50.1"},"reference-count":38,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T00:00:00Z","timestamp":1770595200000},"content-version":"vor","delay-in-days":8,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T00:00:00Z","timestamp":1769904000000},"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":["12301348"],"award-info":[{"award-number":["12301348"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Stat Anal Data Min: An ASA Data Sci Journal"],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>With the advancement of precision medicine, it is of great significance to identify potential patient types based on heterogeneous data and carry out risk assessment and measurement. The Cox mixture model is a highly significant tool for addressing such issues. However, as manifested in our numerical studies, the estimation of a Cox mixture model demands sufficient sample size; otherwise, it might lead to inferior classification accuracy and survival prediction. Motivated by the problem of insufficient sample sizes in estimating mixture models, this paper leverages a transfer learning framework and proposes a likelihood\u2010based approach incorporating an L\u20101 penalty to improve the estimation efficiency and prediction accuracy. The asymptotic properties of the proposed estimators have been established. The numerical studies show that our proposed method possesses good performance under finite samples. Finally, two primary breast cancer datasets have been employed to illustrate the practical utility of our proposed method.<\/jats:p>","DOI":"10.1002\/sam.70059","type":"journal-article","created":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T04:28:31Z","timestamp":1770697711000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Transfer Learning Analysis of the Cox Mixture Model"],"prefix":"10.1002","volume":"19","author":[{"given":"Kangyi","family":"Liu","sequence":"first","affiliation":[{"name":"Zhongtai Securities Institute for Financial Studies Shandong University  Jinan China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yue","family":"Kong","sequence":"additional","affiliation":[{"name":"School of Mathematics Shandong University  Jinan China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7121-6341","authenticated-orcid":false,"given":"Wei","family":"Zhao","sequence":"additional","affiliation":[{"name":"Zhongtai Securities Institute for Financial Studies Shandong University  Jinan China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,2,9]]},"reference":[{"key":"e_1_2_12_2_1","article-title":"Deep Representation Learning for Clustering Longitudinal Survival Data From Electronic Health Records","author":"Qiu J.","year":"2024","journal-title":"medRxiv"},{"key":"e_1_2_12_3_1","volume-title":"Finite Mixture Models","author":"Peel D.","year":"2000"},{"key":"e_1_2_12_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12499"},{"key":"e_1_2_12_5_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214502753479220"},{"key":"e_1_2_12_6_1","doi-asserted-by":"publisher","DOI":"10.1214\/21-AOS2117"},{"key":"e_1_2_12_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2015.05.007"},{"key":"e_1_2_12_8_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280212445839"},{"key":"e_1_2_12_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1972.tb00899.x"},{"key":"e_1_2_12_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/sjos.12213"},{"key":"e_1_2_12_11_1","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/btu065"},{"key":"e_1_2_12_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/biom.12843"},{"key":"e_1_2_12_13_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12874-020-01063-2"},{"key":"e_1_2_12_14_1","first-page":"674","article-title":"Deep Cox Mixtures for Survival Regression","volume":"149","author":"Nagpal C.","year":"2021","journal-title":"Proceedings of the 6th Machine Learning for Healthcare Conference"},{"key":"e_1_2_12_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2022.08.009"},{"key":"e_1_2_12_16_1","doi-asserted-by":"publisher","DOI":"10.4018\/978-1-60566-766-9.ch011"},{"key":"e_1_2_12_17_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2022.2044333"},{"key":"e_1_2_12_18_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2023.2210336"},{"key":"e_1_2_12_19_1","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.2020.3729"},{"key":"e_1_2_12_20_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12479"},{"key":"e_1_2_12_21_1","doi-asserted-by":"publisher","DOI":"10.1214\/20-AOS1949"},{"key":"e_1_2_12_22_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asad029"},{"key":"e_1_2_12_23_1","doi-asserted-by":"publisher","DOI":"10.1214\/21-AOS2102"},{"key":"e_1_2_12_24_1","doi-asserted-by":"publisher","DOI":"10.1214\/23-AOAS1747"},{"key":"e_1_2_12_25_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2023.2184373"},{"key":"e_1_2_12_26_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2022.2071278"},{"key":"e_1_2_12_27_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asad038"},{"key":"e_1_2_12_28_1","first-page":"1","article-title":"Efficient and Robust Transfer Learning of Optimal Individualized Treatment Regimes With Right\u2010Censored Survival Data","volume":"26","author":"Zhao P.","year":"2023","journal-title":"arXiv:2301.05491"},{"key":"e_1_2_12_29_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2016.0034"},{"key":"e_1_2_12_30_1","doi-asserted-by":"publisher","DOI":"10.1002\/sam.11680"},{"key":"e_1_2_12_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ctrv.2011.11.005"},{"key":"e_1_2_12_32_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11033-022-07571-2"},{"key":"e_1_2_12_33_1","first-page":"985","article-title":"Covariate Shift Adaptation by Importance Weighted Cross Validation","volume":"8","author":"Sugiyama M.","year":"2007","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_12_34_1","doi-asserted-by":"publisher","DOI":"10.1002\/wics.199"},{"key":"e_1_2_12_35_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344136"},{"key":"e_1_2_12_36_1","first-page":"20","article-title":"On Ranking in Survival Analysis: Bounds on the Concordance Index","author":"Steck H.","year":"2007","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_2_12_37_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2000.00337.x"},{"key":"e_1_2_12_38_1","doi-asserted-by":"publisher","DOI":"10.1200\/jco.2010.28.15_suppl.e11004"},{"key":"e_1_2_12_39_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0140-6736(19)31901-4"}],"container-title":["Statistical Analysis and Data Mining: An ASA Data Science Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sam.70059","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/sam.70059","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sam.70059","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T22:26:47Z","timestamp":1773008807000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sam.70059"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["10.1002\/sam.70059"],"URL":"https:\/\/doi.org\/10.1002\/sam.70059","archive":["Portico"],"relation":{},"ISSN":["1932-1864","1932-1872"],"issn-type":[{"value":"1932-1864","type":"print"},{"value":"1932-1872","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2]]},"assertion":[{"value":"2025-06-29","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-12-29","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-02-09","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70059"}}