{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T16:10:05Z","timestamp":1784909405795,"version":"3.55.0"},"reference-count":29,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T00:00:00Z","timestamp":1766966400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T00:00:00Z","timestamp":1766966400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100000049","name":"National Institute on Aging","doi-asserted-by":"publisher","award":["1RF1AG075107"],"award-info":[{"award-number":["1RF1AG075107"]}],"id":[{"id":"10.13039\/100000049","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000049","name":"National Institute on Aging","doi-asserted-by":"publisher","award":["P30AG066519"],"award-info":[{"award-number":["P30AG066519"]}],"id":[{"id":"10.13039\/100000049","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Biometrical J"],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Prediction model selection and assessment are primary objectives of many statistical analyses. Covariance\u2010based penalty estimators provide analytic estimates of the optimism associated with naive training error estimates for multiple classes of prediction models and error assessment rules. While the majority of work on covariance\u2010based penalties has focused on prediction for uncensored data, little attention has been given to time\u2010to\u2010event data. In this article, we consider estimating the optimism for survival prediction models assessed via the Brier score. We first analytically derive an expression of the optimism in a single group scenario with uncensored data based on a reformulation of the optimism. With the same reformulation, we propose an algorithm to estimate the optimism for Cox's proportional hazards regression under a general prediction setting involving covariates and right censoring. We verify the derived theory and demonstrate the applicability of the proposed algorithm via simulation studies. Finally, we illustrate the utility of our new covariance\u2010based penalty estimator through an application predicting time to hemodialysis access failure among patients with end\u2010stage renal disease using data from the United States Renal Data\u00a0System.<\/jats:p>","DOI":"10.1002\/bimj.70103","type":"journal-article","created":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T11:53:02Z","timestamp":1767009182000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Covariance\u2010Based Penalty Estimator for Model Assessment With Censored Data"],"prefix":"10.1002","volume":"68","author":[{"given":"Zhuoran","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Statistics University of California Irvine  Irvine California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel L.","family":"Gillen","sequence":"additional","affiliation":[{"name":"Department of Statistics University of California Irvine  Irvine California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,12,29]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1974.1100705"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1974.10489157"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0493(1950)078<0001:VOFEIT>2.0.CO;2"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1972.tb00899.x"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1983.10477973"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1986.10478291"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1198\/016214504000000692"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1201\/9780429246593"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.2307\/2965703"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1975.10479865"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1067\/mva.2001.117890"},{"key":"e_1_2_10_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19990915\/30)18:17\/18<2529::AID-SIM274>3.0.CO;2-5"},{"key":"e_1_2_10_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.200610301"},{"key":"e_1_2_10_15_1","doi-asserted-by":"publisher","DOI":"10.1001\/jama.1982.03320430047030"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-84858-7"},{"key":"e_1_2_10_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/cjs.11527"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOAS169"},{"key":"e_1_2_10_19_1","doi-asserted-by":"publisher","DOI":"10.1053\/j.ajkd.2021.01.002"},{"key":"e_1_2_10_20_1","volume-title":"The Statistical Analysis of Failure Time Data","author":"Kalbfleisch J.","year":"2011"},{"key":"e_1_2_10_21_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1958.10501452"},{"key":"e_1_2_10_22_1","first-page":"1","article-title":"The Brier Score Under Administrative Censoring: Problems and a Solution","volume":"24","author":"Kvamme H.","year":"2023","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_10_23_1","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v32i1.11842"},{"key":"e_1_2_10_24_1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.2000.10485984"},{"key":"e_1_2_10_25_1","doi-asserted-by":"publisher","DOI":"10.3348\/kjr.2021.0223"},{"key":"e_1_2_10_26_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176344136"},{"key":"e_1_2_10_27_1","unstructured":"Shiao H. andV.Cherkassky.2013. \u201cSVM\u2010Based Approaches for Predictive Modeling of Survival Data.\u201d InProceedings of the International Conference on Data Science (ICDATA) 1. IEEE Computer Society."},{"key":"e_1_2_10_28_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345632"},{"key":"e_1_2_10_29_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1974.tb00994.x"},{"key":"e_1_2_10_30_1","unstructured":"United States Renal Data System.2022. \u201c2022 USRDS Annual Data Report: Epidemiology of Kidney Disease in the United States.\u201dNational Institutes of Health National Institute of Diabetes and Digestive and Kidney Diseases."}],"container-title":["Biometrical Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/bimj.70103","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/bimj.70103","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/bimj.70103","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T19:27:18Z","timestamp":1772998038000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/bimj.70103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,29]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["10.1002\/bimj.70103"],"URL":"https:\/\/doi.org\/10.1002\/bimj.70103","archive":["Portico"],"relation":{},"ISSN":["0323-3847","1521-4036"],"issn-type":[{"value":"0323-3847","type":"print"},{"value":"1521-4036","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,29]]},"assertion":[{"value":"2024-09-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-17","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-12-29","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70103"}}