{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T19:50:25Z","timestamp":1774468225185,"version":"3.50.1"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T00:00:00Z","timestamp":1697760000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T00:00:00Z","timestamp":1697760000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["14302220, 14303622"],"award-info":[{"award-number":["14302220, 14303622"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2024,2]]},"DOI":"10.1007\/s11222-023-10306-3","type":"journal-article","created":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T04:02:13Z","timestamp":1697774533000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Transformation models with informative partly interval-censored data"],"prefix":"10.1007","volume":"34","author":[{"given":"Jingjing","family":"Jiang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunjie","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deng","family":"Pan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyuan","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,10,20]]},"reference":[{"issue":"3","key":"10306_CR1","first-page":"303","volume":"11","author":"B Aljawadi","year":"2017","unstructured":"Aljawadi, B.: Approximation of survival function by Taylor series for general partly interval censored data. Malays. J. Math. Sci. 11(3), 303\u2013315 (2017)","journal-title":"Malays. J. Math. Sci."},{"issue":"2","key":"10306_CR2","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s10985-007-9035-3","volume":"13","author":"T Banerjee","year":"2007","unstructured":"Banerjee, T., Chen, M., Dey, D., Kim, S.: Bayesian analysis of generalized odds-rate hazards models for survival data. Lifetime Data Anal. 13(2), 241\u2013260 (2007)","journal-title":"Lifetime Data Anal."},{"issue":"1","key":"10306_CR3","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1111\/j.0006-341X.2002.00058.x","volume":"58","author":"R Betensky","year":"2002","unstructured":"Betensky, R., Finkelstein, D.: Testing for dependence between failure time and visit compliance with interval-censored data. Biometrics 58(1), 58\u201363 (2002)","journal-title":"Biometrics"},{"issue":"2","key":"10306_CR4","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1093\/biomet\/91.2.277","volume":"91","author":"T Cai","year":"2004","unstructured":"Cai, T., Cheng, S.: Semiparametric regression analysis for doubly censored data. Biometrika 91(2), 277\u2013290 (2004)","journal-title":"Biometrika"},{"issue":"9","key":"10306_CR5","doi-asserted-by":"crossref","first-page":"2644","DOI":"10.1016\/j.csda.2011.03.013","volume":"55","author":"B Cai","year":"2011","unstructured":"Cai, B., Lin, X., Wang, L.: Bayesian proportional hazards model for current status data with monotone splines. Comput. Stat. Data Anal. 55(9), 2644\u20132651 (2011)","journal-title":"Comput. Stat. Data Anal."},{"issue":"1","key":"10306_CR6","first-page":"1","volume":"15","author":"D Dabrowska","year":"1988","unstructured":"Dabrowska, D., Doksum, K.: Partial likelihood in transformation models with censored data. Scand. J. Stat. 15(1), 1\u201323 (1988)","journal-title":"Scand. J. Stat."},{"issue":"5","key":"10306_CR7","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1080\/02664763.2020.1752633","volume":"48","author":"M Du","year":"2021","unstructured":"Du, M., Zhou, Q., Zhao, S., Sun, J.: Regression analysis of case-cohort studies in the presence of dependent interval censoring. J. Appl. Stat. 48(5), 846\u2013865 (2021)","journal-title":"J. Appl. Stat."},{"issue":"2","key":"10306_CR8","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1111\/j.0006-341X.2002.00298.x","volume":"58","author":"D Finkelstein","year":"2002","unstructured":"Finkelstein, D., Goggins, W., Schoenfeld, D.: Analysis of failure time data with dependent interval censoring. Biometrics 58(2), 298\u2013304 (2002)","journal-title":"Biometrics"},{"issue":"4","key":"10306_CR9","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1111\/biom.12700","volume":"73","author":"F Gao","year":"2017","unstructured":"Gao, F., Zeng, D., Lin, D.: Semiparametric estimation of the accelerated failure time model with partly interval-censored data. Biometrics 73(4), 1161\u20131168 (2017)","journal-title":"Biometrics"},{"issue":"4","key":"10306_CR10","doi-asserted-by":"crossref","first-page":"455","DOI":"10.2307\/2986138","volume":"44","author":"W Gilks","year":"1995","unstructured":"Gilks, W., Best, N., Tan, K.: Adaptive rejection metropolis sampling within Gibbs sampling. Appl. Stat. 44(4), 455\u2013472 (1995)","journal-title":"Appl. Stat."},{"key":"10306_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1304-8","volume-title":"Analysis of Multivariate Survival Data","author":"P Hougaard","year":"2000","unstructured":"Hougaard, P.: Analysis of Multivariate Survival Data. Springer, New York (2000)"},{"issue":"2","key":"10306_CR12","first-page":"501","volume":"9","author":"J Huang","year":"1999","unstructured":"Huang, J.: Asymptotic properties of nonparametric estimation based on partly interval-censored data. Stat. Sin. 9(2), 501\u2013519 (1999)","journal-title":"Stat. Sin."},{"key":"10306_CR13","doi-asserted-by":"crossref","DOI":"10.1002\/9781118032985","volume-title":"The Statistical Analysis of Failure Time Data","author":"J Kalbfleisch","year":"2002","unstructured":"Kalbfleisch, J., Prentice, R.: The Statistical Analysis of Failure Time Data. Wiley, Hoboken (2002)"},{"issue":"2","key":"10306_CR14","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1111\/1467-9868.00398","volume":"65","author":"J Kim","year":"2003","unstructured":"Kim, J.: Maximum likelihood estimation for the proportional hazards model with partly interval-censored data. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 65(2), 489\u2013502 (2003)","journal-title":"J. R. Stat. Soc. Ser. B (Stat. Methodol.)"},{"issue":"1","key":"10306_CR15","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.jkss.2015.09.002","volume":"45","author":"J Kim","year":"2016","unstructured":"Kim, J., Kim, Y., Kim, S.: Frailty model approach for the clustered interval-censored data with informative censoring. J. Korean Stat. Soc. 45(1), 156\u2013165 (2016)","journal-title":"J. Korean Stat. Soc."},{"key":"10306_CR16","doi-asserted-by":"crossref","DOI":"10.1002\/9780470024737","volume-title":"Structural Equation Modeling: A Bayesian Approach","author":"S Lee","year":"2007","unstructured":"Lee, S.: Structural Equation Modeling: A Bayesian Approach. Wiley, Hoboken (2007)"},{"issue":"9","key":"10306_CR17","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.csda.2019.02.010","volume":"137","author":"J Li","year":"2019","unstructured":"Li, J., Ma, J.: Maximum penalized likelihood estimation of additive hazards models with partly interval censoring. Comput. Stat. Data Anal. 137(9), 170\u2013180 (2019)","journal-title":"Comput. Stat. Data Anal."},{"issue":"12","key":"10306_CR18","doi-asserted-by":"crossref","first-page":"3804","DOI":"10.1177\/0962280220942555","volume":"29","author":"J Li","year":"2020","unstructured":"Li, J., Ma, J.: On hazard-based penalized likelihood estimation of accelerated failure time model with partly interval censoring. Stat. Methods Med. Res. 29(12), 3804\u20133817 (2020)","journal-title":"Stat. Methods Med. Res."},{"issue":"4","key":"10306_CR19","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1080\/10485252.2012.720256","volume":"24","author":"J Li","year":"2012","unstructured":"Li, J., Wang, C., Sun, J.: Regression analysis of clustered interval-censored failure time data with the additive hazards model. J. Nonparametr. Stat. 24(4), 1041\u20131050 (2012)","journal-title":"J. Nonparametr. Stat."},{"issue":"3","key":"10306_CR20","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1007\/s10985-014-9305-9","volume":"21","author":"X Lin","year":"2015","unstructured":"Lin, X., Cai, B., Wang, L., Zhang, Z.: A Bayesian proportional hazards model for general interval-censored data. Lifetime Data Anal. 21(3), 470\u2013490 (2015)","journal-title":"Lifetime Data Anal."},{"issue":"3","key":"10306_CR21","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1111\/j.0006-341X.2004.00225.x","volume":"60","author":"L Liu","year":"2004","unstructured":"Liu, L., Wolfe, R., Huang, X.: Shared frailty models for recurrent events and a terminal event. Biometrics 60(3), 747\u2013756 (2004)","journal-title":"Biometrics"},{"issue":"9","key":"10306_CR22","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.csda.2016.04.011","volume":"103","author":"L Ma","year":"2016","unstructured":"Ma, L., Hu, T., Sun, J.: Cox regression analysis of dependent interval-censored failure time data. Comput. Stat. Data Anal. 103(9), 79\u201390 (2016)","journal-title":"Comput. Stat. Data Anal."},{"key":"10306_CR23","volume-title":"An Introduction to Copulas","author":"R Nelsen","year":"2006","unstructured":"Nelsen, R.: An Introduction to Copulas, 2nd edn. Springer, New York (2006)","edition":"2"},{"issue":"3","key":"10306_CR24","doi-asserted-by":"crossref","first-page":"951","DOI":"10.2307\/2532360","volume":"48","author":"P Odell","year":"1992","unstructured":"Odell, P., Anderson, K., D\u2019Agostino, R.: Maximum likelihood estimation for interval-censored data using a Weibull-based accelerated failure time model. Biometrics 48(3), 951\u2013959 (1992)","journal-title":"Biometrics"},{"issue":"511","key":"10306_CR25","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1080\/01621459.2014.950083","volume":"110","author":"D Pan","year":"2015","unstructured":"Pan, D., He, H., Song, X., Sun, L.: Regression analysis of additive hazards model with latent variables. J. Am. Stat. Assoc. 110(511), 1148\u20131159 (2015)","journal-title":"J. Am. Stat. Assoc."},{"issue":"11","key":"10306_CR26","doi-asserted-by":"crossref","first-page":"3192","DOI":"10.1177\/0962280220921552","volume":"29","author":"C Pan","year":"2020","unstructured":"Pan, C., Cai, B., Wang, L.: A bayesian approach for analyzing partly interval-censored data under the proportional hazards model. Stat. Methods Med. Res. 29(11), 3192\u20133204 (2020)","journal-title":"Stat. Methods Med. Res."},{"issue":"482","key":"10306_CR27","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1198\/016214508000000337","volume":"103","author":"T Park","year":"2008","unstructured":"Park, T., Casella, G.: The Bayesian lasso. J. Am. Stat. Assoc. 103(482), 681\u2013686 (2008)","journal-title":"J. Am. Stat. Assoc."},{"issue":"4","key":"10306_CR28","first-page":"425","volume":"3","author":"J Ramsay","year":"1988","unstructured":"Ramsay, J.: Monotone regression splines in action. Stat. Sci. 3(4), 425\u2013461 (1988)","journal-title":"Stat. Sci."},{"issue":"3","key":"10306_CR29","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1093\/biomet\/89.3.617","volume":"89","author":"D Scharfstein","year":"2002","unstructured":"Scharfstein, D., Robins, J.: Estimation of the failure time distribution in the presence of informative censoring. Biometrika 89(3), 617\u2013634 (2002)","journal-title":"Biometrika"},{"issue":"4","key":"10306_CR30","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1023\/A:1009634103154","volume":"4","author":"D Scharfstein","year":"1998","unstructured":"Scharfstein, D., Tsiatis, A., Gilbert, P.: Semiparametric efficient estimation in the generalized odds-rate class of regression models for right-censored time-to-event data. Lifetime Data Anal. 4(4), 355\u2013391 (1998)","journal-title":"Lifetime Data Anal."},{"key":"10306_CR31","doi-asserted-by":"crossref","DOI":"10.1002\/9781118358887","volume-title":"Basic and Advanced Bayesian Structural Equation Modeling: With Applications in the Medical and Behavioral Sciences","author":"X Song","year":"2012","unstructured":"Song, X., Lee, S.: Basic and Advanced Bayesian Structural Equation Modeling: With Applications in the Medical and Behavioral Sciences. Wiley, Hoboken (2012)"},{"key":"10306_CR32","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1007\/s11222-011-9280-x","volume":"22","author":"X Song","year":"2012","unstructured":"Song, X., Lu, Z.: Semiparametric transformation models with Bayesian p-splines. Stat. Comput. 22, 1085\u20131098 (2012)","journal-title":"Stat. Comput."},{"issue":"8","key":"10306_CR33","doi-asserted-by":"crossref","first-page":"1543","DOI":"10.1007\/s00125-009-1400-1","volume":"52","author":"X Song","year":"2009","unstructured":"Song, X., Lee, S., Ma, R., So, W., Cai, J., Tam, C., Lam, V., Ying, W., Ng, M., Chan, J.: Phenotype-genotype interactions on renal function in type2 diabetes: an analysis using structural equation modelling. Diabetologia 52(8), 1543\u20131553 (2009)","journal-title":"Diabetologia"},{"issue":"7","key":"10306_CR34","doi-asserted-by":"crossref","first-page":"473","DOI":"10.7326\/0003-4819-143-7-200510040-00005","volume":"143","author":"R Vasan","year":"2005","unstructured":"Vasan, R., Pencina, M., Cobain, M., Freiberg, M., D\u2019Agostino, R.: Estimated risks for developing obesity in the Framingham heart study. Ann. Intern. Med. 143(7), 473\u2013480 (2005)","journal-title":"Ann. Intern. Med."},{"issue":"4","key":"10306_CR35","first-page":"1709","volume":"20","author":"L Wang","year":"2010","unstructured":"Wang, L., Sun, J., Tong, X.: Regression analysis of case ii interval-censored failure time data with the additive hazards model. Stat. Sin. 20(4), 1709\u20131723 (2010)","journal-title":"Stat. Sin."},{"issue":"1","key":"10306_CR36","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1111\/biom.12389","volume":"72","author":"L Wang","year":"2016","unstructured":"Wang, L., McMahan, C., Hudgens, M., Qureshi, Z.: A flexible, computationally efficient method for fitting the proportional hazards model to interval-censored data. Biometrics 72(1), 222\u2013231 (2016)","journal-title":"Biometrics"},{"issue":"7","key":"10306_CR37","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1002\/sim.9271","volume":"41","author":"C Wang","year":"2022","unstructured":"Wang, C., Jiang, J., Song, X.: Bayesian transformation models with partly interval-censored data. Stat. Med. 41(7), 1263\u20131279 (2022)","journal-title":"Stat. Med."},{"issue":"3","key":"10306_CR38","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1007\/s10985-018-9445-4","volume":"25","author":"Y Wu","year":"2019","unstructured":"Wu, Y., Chambers, C., Xu, R.: Semiparametric sieve maximum likelihood estimation under cure model with partly interval censored and left truncated data for application to spontaneous abortion. Lifetime Data Anal. 25(3), 507\u2013528 (2019)","journal-title":"Lifetime Data Anal."},{"issue":"3\/4","key":"10306_CR39","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1080\/10485252.2019.1626383","volume":"31","author":"D Xu","year":"2019","unstructured":"Xu, D., Zhao, S., Hu, T., Sun, J.: Regression analysis of informatively interval-censored failure time data with semiparametric linear transformation model. J. Nonparametr. Stat. 31(3\/4), 663\u2013679 (2019)","journal-title":"J. Nonparametr. Stat."},{"issue":"4","key":"10306_CR40","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1111\/j.1369-7412.2007.00606.x","volume":"69","author":"D Zeng","year":"2007","unstructured":"Zeng, D., Lin, D.: Maximum likelihood estimation in semiparametric regression models with censored data. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 69(4), 507\u2013564 (2007)","journal-title":"J. R. Stat. Soc. Ser. B (Stat. Methodol.)"},{"issue":"474","key":"10306_CR41","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1198\/016214505000001122","volume":"101","author":"D Zeng","year":"2006","unstructured":"Zeng, D., Yin, G., Ibrahim, J.: Semiparametric transformation models for survival data with a cure fraction. J. Am. Stat. Assoc. 101(474), 670\u2013684 (2006)","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"10306_CR42","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1093\/biomet\/asw013","volume":"103","author":"D Zeng","year":"2016","unstructured":"Zeng, D., Mao, L., Lin, D.: Maximum likelihood estimation for semiparametric transformation models with interval-censored data. Biometrika 103(2), 253\u2013271 (2016)","journal-title":"Biometrika"},{"issue":"12","key":"10306_CR43","doi-asserted-by":"crossref","first-page":"2533","DOI":"10.1002\/sim.2721","volume":"26","author":"Z Zhang","year":"2007","unstructured":"Zhang, Z., Sun, L., Sun, J., Finkelstein, D.: Regression analysis of failure time data with informative interval censoring. Stat. Med. 26(12), 2533\u20132546 (2007)","journal-title":"Stat. Med."},{"key":"10306_CR44","doi-asserted-by":"crossref","unstructured":"Zhao, X., Zhao, Q., Sun, J., Kim, J.: Generalized log-rank tests for partly interval-censored failure time data. Biom. J. 50(3), 375\u2013385 (2008)","DOI":"10.1002\/bimj.200710419"},{"issue":"3","key":"10306_CR45","doi-asserted-by":"crossref","first-page":"367","DOI":"10.4310\/SII.2015.v8.n3.a10","volume":"8","author":"S Zhao","year":"2015","unstructured":"Zhao, S., Hu, T., Ma, L., Wang, P., Sun, J.: Regression analysis of interval-censored failure time data with the additive hazards model in the presence of informative censoring. Stat. Interface 8(3), 367\u2013377 (2015)","journal-title":"Stat. Interface"},{"issue":"1","key":"10306_CR46","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1093\/biomet\/82.1.127","volume":"82","author":"M Zheng","year":"1995","unstructured":"Zheng, M., Klein, J.: Estimates of marginal survival for dependent competing risk based on an assumed copula. Biometrika 82(1), 127\u2013138 (1995)","journal-title":"Biometrika"},{"issue":"20","key":"10306_CR47","doi-asserted-by":"crossref","first-page":"4376","DOI":"10.1002\/sim.9035","volume":"40","author":"Q Zhou","year":"2021","unstructured":"Zhou, Q., Sun, Y., Gilbert, P.: Semiparametric regression analysis of partly interval-censored failure time data with application to an aids clinical trial. Stat. Med. 40(20), 4376\u20134394 (2021)","journal-title":"Stat. Med."},{"issue":"6","key":"10306_CR48","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1002\/sim.2255","volume":"25","author":"D Zucker","year":"2006","unstructured":"Zucker, D., Yang, S.: Inference for a family of survival models encompassing the proportional hazards and proportional odds models. Stat. Med. 25(6), 995\u20131014 (2006)","journal-title":"Stat. Med."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-023-10306-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-023-10306-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-023-10306-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,20]],"date-time":"2024-01-20T10:11:56Z","timestamp":1705745516000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-023-10306-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,20]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["10306"],"URL":"https:\/\/doi.org\/10.1007\/s11222-023-10306-3","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,20]]},"assertion":[{"value":"2 March 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 October 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"8"}}