{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T11:10:07Z","timestamp":1749467407928,"version":"3.41.0"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T00:00:00Z","timestamp":1748736000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T00:00:00Z","timestamp":1748736000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s11424-025-4093-8","type":"journal-article","created":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T10:45:23Z","timestamp":1749465923000},"page":"1186-1205","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Additive Rates Model for Multivariate Recurrent Event Data with Time-Dependent Coefficients and Missing Types"],"prefix":"10.1007","volume":"38","author":[{"given":"Xiaowei","family":"Sun","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiaqi","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,9]]},"reference":[{"key":"4093_CR1","doi-asserted-by":"publisher","first-page":"1100","DOI":"10.1214\/aos\/1176345976","volume":"10","author":"P K Andersen","year":"1982","unstructured":"Andersen P K and Gill R D, Cox\u2019s regression model for counting processes: A large sample study, Annals of Statistics, 1982, 10: 1100\u20131120.","journal-title":"Annals of Statistics"},{"key":"4093_CR2","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1080\/01621459.1993.10476346","volume":"88","author":"M S Pepe","year":"1993","unstructured":"Pepe M S and Cai J, Some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates, Journal of the American Statistical Association, 1993, 88: 811\u2013820.","journal-title":"Journal of the American Statistical Association"},{"key":"4093_CR3","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1080\/00401706.1995.10484300","volume":"37","author":"J F Lawless","year":"1995","unstructured":"Lawless J F and Nadeau C, Some simple robust methods for the analysis of recurrent events, Technometrics, 1995, 37: 158\u2013168.","journal-title":"Technometrics"},{"key":"4093_CR4","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1111\/1467-9868.00259","volume":"62","author":"D Y Lin","year":"2000","unstructured":"Lin D Y, Wei L J, Yang I, et al., Semiparametric regression for the mean and rate functions of recurrent events, Journal of the Royal Statistical Society, Series B, 2000, 62: 711\u2013730.","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"4093_CR5","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/s10985-006-9017-x","volume":"12","author":"D E Schaubel","year":"2006","unstructured":"Schaubel D E, Zeng D, and Cai J, A semiparametric additive rates model for recurrent event data, Lifetime Data Analysis, 2006, 12: 389\u2013406.","journal-title":"Lifetime Data Analysis"},{"key":"4093_CR6","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1198\/016214506000001239","volume":"102","author":"D Zeng","year":"2007","unstructured":"Zeng D and Lin D, Semiparametric transformation models with random effects for recurrent events, Journal of the American Statistical Association, 2007, 102: 167\u2013180.","journal-title":"Journal of the American Statistical Association"},{"key":"4093_CR7","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1007\/s10985-010-9165-x","volume":"17","author":"L Sun","year":"2011","unstructured":"Sun L, Tong X, and Zhou X, A class of Box-Cox transformation models for recurrent event data, Lifetime Data Analysis, 2011, 17: 280\u2013301.","journal-title":"Lifetime Data Analysis"},{"key":"4093_CR8","volume-title":"The Statistical Analysis of Recurrent Events","author":"R J Cook","year":"2007","unstructured":"Cook R J and Lawless J F, The Statistical Analysis of Recurrent Events, Springer, New York, 2007."},{"key":"4093_CR9","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1023\/B:LIDA.0000030199.23383.45","volume":"10","author":"J Cai","year":"2004","unstructured":"Cai J and Schaubel D E, Marginal mean\/rates models for multiple type recurrent event data, Lifetime Data Analysis, 2004, 10: 121\u2013138.","journal-title":"Lifetime Data Analysis"},{"key":"4093_CR10","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1002\/sim.1936","volume":"24","author":"B E Chen","year":"2005","unstructured":"Chen B E, Cook R J, Lawless J F, et al., Statistical methods for multivariate interval-censored recurrent events, Statistics in Medicine, 2005, 24: 671\u2013691.","journal-title":"Statistics in Medicine"},{"key":"4093_CR11","doi-asserted-by":"publisher","first-page":"1017","DOI":"10.2307\/2532445","volume":"46","author":"H Abu-Libdeh","year":"1990","unstructured":"Abu-Libdeh H, Turnbull B W, and Clark L C, Analysis of muti-type recurrent events in longitudinal studies: Application to a skin cancer prevention trial, Biometrics, 1990, 46: 1017\u20131034.","journal-title":"Biometrics"},{"key":"4093_CR12","doi-asserted-by":"publisher","first-page":"504","DOI":"10.1007\/s10985-012-9226-4","volume":"18","author":"X Chen","year":"2012","unstructured":"Chen X, Wang Q, Cai J, et al., Semiparametric additive marginal regression models for multiple type recurrent events, Lifetime Data Analysis, 2012, 18: 504\u2013527.","journal-title":"Lifetime Data Analysis"},{"key":"4093_CR13","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1111\/j.0006-341X.1999.00805.x","volume":"55","author":"L Clegg","year":"1999","unstructured":"Clegg L, Cai J, and Sen P K, A marginal mixed baseline hazards model for multivariate failure time data, Biometrics, 1999, 55: 805\u2013812.","journal-title":"Biometrics"},{"key":"4093_CR14","doi-asserted-by":"publisher","first-page":"1164","DOI":"10.1080\/01621459.1998.10473777","volume":"93","author":"C F Spiekerman","year":"1998","unstructured":"Spiekerman C F and Lin D Y, Marginal regression models for multivariate failure time data, Journal of the American Statistical Association, 1998, 93: 1164\u20131175.","journal-title":"Journal of the American Statistical Association"},{"key":"4093_CR15","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1002\/bimj.201100194","volume":"54","author":"X Zhao","year":"2012","unstructured":"Zhao X, Liu L, Liu Y, et al., Analysis of multivariate recurrent event data with time-dependent covariates and informative censoring, Biometrical Journal, 2012, 54: 585\u2013599.","journal-title":"Biometrical Journal"},{"key":"4093_CR16","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1007\/s10985-010-9158-9","volume":"16","author":"L Zhu","year":"2010","unstructured":"Zhu L, Sun J, Tong X, et al., Regression analysis of multivariate recurrent event data with a dependent terminal event, Lifetime Data Analysis, 2010, 16: 478\u2013490.","journal-title":"Lifetime Data Analysis"},{"key":"4093_CR17","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1007\/s10255-014-0425-5","volume":"30","author":"X Chen","year":"2014","unstructured":"Chen X, Partially time-varying coefficient linear rate model for the recurrent event data, Acta Mathematicae Applicatae Sinica, English Series, 2014, 30: 681\u2013698.","journal-title":"Acta Mathematicae Applicatae Sinica, English Series"},{"key":"4093_CR18","doi-asserted-by":"publisher","first-page":"2214","DOI":"10.1016\/j.jmva.2009.08.001","volume":"100","author":"L Sun","year":"2009","unstructured":"Sun L, Zhu L, and Sun J, Regression analysis of multivariate recurrent event data with time-varying covariate effects, Journal of Multivariate Analysis, 2009, 100: 2214\u20132223.","journal-title":"Journal of Multivariate Analysis"},{"key":"4093_CR19","doi-asserted-by":"publisher","first-page":"2265","DOI":"10.1002\/sim.4260","volume":"30","author":"L Sun","year":"2011","unstructured":"Sun L, Zhou X, and Guo S, Marginal regression models with time-varying coefficients for recurrent event data, Statistics in Medicine, 2011, 30: 2265\u20132277.","journal-title":"Statistics in Medicine"},{"key":"4093_CR20","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1111\/j.1541-0420.2010.01458.x","volume":"67","author":"X Zhao","year":"2011","unstructured":"Zhao X, Zhou J, and Sun L, Semiparametric transformation models with time-varying coefficients for recurrent and terminal events, Biometrics, 2011, 67: 404\u2013414.","journal-title":"Biometrics"},{"key":"4093_CR21","first-page":"677","volume":"34","author":"D E Schaubel","year":"2006","unstructured":"Schaubel D E and Cai J, Multiple imputation methods for recurrent event data with missing event category, Scandinavian Journal of Statistics, 2006, 34: 677\u2013692.","journal-title":"Scandinavian Journal of Statistics"},{"key":"4093_CR22","doi-asserted-by":"publisher","DOI":"10.1002\/9781119013563","volume-title":"Statistical Analysis with Missing Data","author":"R J A Little","year":"2002","unstructured":"Little R J A and Rubin D B, Statistical Analysis with Missing Data, Wiley, New York, 2002."},{"key":"4093_CR23","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s10985-008-9091-3","volume":"15","author":"B E Chen","year":"2009","unstructured":"Chen B E and Cook R J, The analysis of multivariate recurrent events with partially missing event types, Lifetime Data Analysis, 2009, 15: 41\u201358.","journal-title":"Lifetime Data Analysis"},{"key":"4093_CR24","doi-asserted-by":"publisher","first-page":"727","DOI":"10.1093\/biomet\/ast016","volume":"100","author":"F Lin","year":"2013","unstructured":"Lin F, Cai J, Fine J P, et al., Nonparametric estimation of the mean function for recurrent event data with missing event category, Biometrika, 2013, 100: 727\u2013740.","journal-title":"Biometrika"},{"key":"4093_CR25","doi-asserted-by":"publisher","first-page":"2765","DOI":"10.1002\/sim.8927","volume":"40","author":"F Lin","year":"2021","unstructured":"Lin F, Cai J, Deng Y, et al., Inverse probability weighted estimation for recurrent events data with missing category, Statistics in Medicine, 2021, 40: 2765\u20132782.","journal-title":"Statistics in Medicine"},{"key":"4093_CR26","doi-asserted-by":"publisher","first-page":"4285","DOI":"10.1002\/sim.9509","volume":"41","author":"H Ma","year":"2022","unstructured":"Ma H, Pang W, Sun L, et al., Augmented weighting estimators for the additive rates model under multivariate recurrent event data with missing event type, Statistics in Medicine, 2022, 41: 4285\u20134298.","journal-title":"Statistics in Medicine"},{"key":"4093_CR27","first-page":"191","volume":"33","author":"D E Schaubel","year":"2006","unstructured":"Schaubel D E and Cai J, Rate\/mean regression for multiple-sequence recurrent event data with missing event category, Canadian Journal of Statistics, 2006, 33: 191\u2013207.","journal-title":"Canadian Journal of Statistics"},{"key":"4093_CR28","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/j.csda.2015.03.002","volume":"89","author":"P Ye","year":"2015","unstructured":"Ye P, Zhao X, Sun L, et al., A semiparametric additive rates model for multivariate recurrent events with missing event categories, Computational Statistics and Data Analysis, 2015, 89: 39\u201350.","journal-title":"Computational Statistics and Data Analysis"},{"key":"4093_CR29","doi-asserted-by":"publisher","first-page":"11631178","DOI":"10.1007\/s11425-015-5000-x","volume":"58","author":"P Ye","year":"2015","unstructured":"Ye P, Sun L, Zhao X, et al., An additive-multiplicative rates model for multivariate recurrent events with event categories missing at random, Science China Mathematics, 2015, 58: 11631178.","journal-title":"Science China Mathematics"},{"key":"4093_CR30","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032985","volume-title":"The Statistical Analysis of Failure Time Data","author":"J Kalbfleisch","year":"2002","unstructured":"Kalbfleisch J and Prentice R, The Statistical Analysis of Failure Time Data, 2nd Edition, Wiley, New York, 2002.","edition":"2nd Edition"},{"key":"4093_CR31","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1093\/biomet\/73.1.13","volume":"73","author":"K Liang","year":"1986","unstructured":"Liang K and Zeger S, Longitudinal data analysis using generalized linear models, Biometrika, 1986, 73: 13\u201322.","journal-title":"Biometrika"},{"key":"4093_CR32","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1046\/j.1365-3148.2000.00253.x","volume":"10","author":"B J Patterson","year":"2000","unstructured":"Patterson B J, Freedman J, Blanchette V, et al., Effect of premedication guidelines and leuko-reduction on the rate of febrile nonhaemolytic platelet transfusion, Transfusion Medicine, 2000, 10: 199\u2013206.","journal-title":"Transfusion Medicine"},{"key":"4093_CR33","volume-title":"Semiparametric Theory and Missing Data","author":"A A Tsiatis","year":"2006","unstructured":"Tsiatis A A, Semiparametric Theory and Missing Data, Springer, New York, 2006."},{"key":"4093_CR34","doi-asserted-by":"publisher","DOI":"10.1214\/cbms\/1462061091","volume-title":"Empirical Processes: Theory and Applications","author":"D Pollard","year":"1990","unstructured":"Pollard D, Empirical Processes: Theory and Applications, Institute of Mathematical Statistics, Hayward, California, 1990."},{"key":"4093_CR35","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2545-2","volume-title":"Weak Convergence and Empirical Processes","author":"A W van der Vaart","year":"1996","unstructured":"van der Vaart A W and Wellner J A, Weak Convergence and Empirical Processes, Springer, New York, 1996."}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-025-4093-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11424-025-4093-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-025-4093-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T10:45:24Z","timestamp":1749465924000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11424-025-4093-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["4093"],"URL":"https:\/\/doi.org\/10.1007\/s11424-025-4093-8","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6]]},"assertion":[{"value":"17 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 September 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no conflict of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}]}}