{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T06:18:27Z","timestamp":1772000307167,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T00:00:00Z","timestamp":1771804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Zhejiang Provincial Philosophy and Social Sciences Planning Project","award":["25NDJC126YBMS"],"award-info":[{"award-number":["25NDJC126YBMS"]}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["LMS25G010001"],"award-info":[{"award-number":["LMS25G010001"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009376","name":"National Bureau of Statistics of China","doi-asserted-by":"publisher","award":["2025LZ023"],"award-info":[{"award-number":["2025LZ023"]}],"id":[{"id":"10.13039\/100009376","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100022955","name":"Fundamental Research Funds for the Provincial Universities of Zhejiang","doi-asserted-by":"crossref","award":["2025ZDPY06"],"award-info":[{"award-number":["2025ZDPY06"]}],"id":[{"id":"10.13039\/100022955","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>In large-scale medical data, the connection between hospital length of stay and medical expenses shows a complex and nonlinear relationship instead of a straightforward positive link. This study proposes a Cox\u2013Log-Logistic\u2013Copula joint modeling framework to describe the marginal distributions and latent dependence between the two variables. Specifically, a semi-parametric Cox proportional hazards model is used for hospitalization duration, while a Log-Logistic model handles medical costs. The two margins are flexibly coupled through a Copula function to capture dynamic variations in cost levels during different hospitalization stages. To address computational challenges in large datasets, this study also includes subsample correction and one-step adjustment algorithms, combined with parallel computing strategies, to enhance estimation efficiency and accuracy. Empirical results show that the length of hospital stays and medical costs are not always positively related. In some cases, higher medical expenses occur during shorter stays, suggesting possible over-treatment or uneven resource distribution. The proposed framework proves to have strong explanatory power in identifying nonlinear patterns in healthcare behavior and offers a new quantitative tool for optimizing medical resource allocation and controlling costs.<\/jats:p>","DOI":"10.3390\/systems14020226","type":"journal-article","created":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T10:00:52Z","timestamp":1771840852000},"page":"226","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Copula-Based Joint Modeling Framework for Hospitalization Costs and Length of Stay in Massive Healthcare Data"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-4687-0409","authenticated-orcid":false,"given":"Xuan","family":"Xu","sequence":"first","affiliation":[{"name":"Asset and Laboratory Management Office, Zhejiang University of Finance and Economics, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yijun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, Zhejiang Gongshang University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,23]]},"reference":[{"key":"ref_1","first-page":"489","article-title":"Is patient length of stay related to quality of care?","volume":"42","author":"Thomas","year":"1997","journal-title":"J. Healthc. Manag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1097\/00005650-199103000-00007","article-title":"The effects of patient, hospital, and physician characteristics on length of stay and mortality","volume":"29","author":"Burns","year":"1991","journal-title":"Med. Care"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1097\/01.MLR.0000053021.93198.96","article-title":"Length of stay data as a guide to hospital economic performance for ICU patients","volume":"41","author":"Rapoport","year":"2003","journal-title":"Med. Care"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1075","DOI":"10.1001\/jama.1996.03540130073033","article-title":"The effect of managed care on ICU length of stay: Implications for medicare","volume":"276","author":"Angus","year":"1996","journal-title":"JAMA"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"e230080","DOI":"10.57264\/cer-2023-0080","article-title":"Impact of surgical complications on hospital costs and revenues: Retrospective database study of Medicare claims","volume":"12","author":"Haidar","year":"2023","journal-title":"J. Comp. Eff. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1093\/gerona\/61.5.495","article-title":"Gender differences in functioning after hip fracture","volume":"61","author":"Hawkes","year":"2006","journal-title":"J. Gerontol. Ser. A Biol. Sci. Med. Sci."},{"key":"ref_7","first-page":"mzab160","article-title":"Evaluation of the association of length of stay in hospital and outcomes","volume":"34","author":"Han","year":"2022","journal-title":"Int. J. Qual. Health Care"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zhao, X., Xia, Y., and Xu, X. (2025). Sufficient dimension reduction on partially nonlinear index models with applications to medical costs analysis. PLoS ONE, 20.","DOI":"10.1371\/journal.pone.0321796"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"e4839","DOI":"10.1097\/MD.0000000000004839","article-title":"Impact of payment system change from per-case to per-diem on high severity patient\u2019s length of stay","volume":"95","author":"Jang","year":"2016","journal-title":"Medicine"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1257\/jep.6.3.3","article-title":"Medical care costs: How much welfare loss?","volume":"6","author":"Newhouse","year":"1992","journal-title":"J. Econ. Perspect."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1017\/S1748499500000518","article-title":"Individual claim loss reserving conditioned by case estimates","volume":"3","author":"Taylor","year":"2008","journal-title":"Ann. Actuar. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1002\/hec.774","article-title":"Estimating mean hospital cost as a function of length of stay and patient characteristics","volume":"12","author":"Polverejan","year":"2003","journal-title":"Health Econ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2020","DOI":"10.1111\/1475-6773.12460","article-title":"Using length of stay to control for unobserved heterogeneity when estimating treatment effect on hospital costs with observational data: Issues of reliability, robustness, and usefulness","volume":"51","author":"May","year":"2016","journal-title":"Health Serv. Res."},{"key":"ref_14","unstructured":"Lorenzoni, A.M.L., and Marino, A. (2017). Understanding Variations in Hospital Length of Stay and Cost, OECD."},{"key":"ref_15","first-page":"229","article-title":"Fonctions de r\u00e9partition \u00e0 n dimensions et leurs marges","volume":"8","author":"Sklar","year":"1959","journal-title":"Ann. l\u2019ISUP"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1111\/1368-423X.00101","article-title":"Modelling sample selection using Archimedean copulas","volume":"6","author":"Smith","year":"2003","journal-title":"Econom. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1198\/073500105000000153","article-title":"Using trivariate copulas to model sample selection and treatment effects: Application to family health care demand","volume":"24","author":"Zimmer","year":"2006","journal-title":"J. Bus. Econ. Stat."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1015","DOI":"10.1002\/hec.1379","article-title":"Infant mortality and child nutrition in Bangladesh","volume":"17","author":"Dancer","year":"2008","journal-title":"Health Econ."},{"key":"ref_19","unstructured":"Quinn, C. (2007). Using Copulas to Estimate Reduced-Form Systems of Equations, Department of Economics, University of York. Technical Report, HEDG, c\/o."},{"key":"ref_20","first-page":"182","article-title":"Gaussian copula\u2013based regression models for the analysis of mixed outcomes: An application on household\u2019s utilization of health services data","volume":"18","author":"Ghahroodi","year":"2019","journal-title":"J. Stat. Theory Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1093\/biostatistics\/kxt043","article-title":"High-dimensional, massive sample-size Cox proportional hazards regression for survival analysis","volume":"15","author":"Mittal","year":"2014","journal-title":"Biostatistics"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wang, W., Wang, Y., and Zhao, X. (2026). Estimation and inference for fixed center effects on panel count data. Stat. Pap., 67.","DOI":"10.1007\/s00362-026-01807-0"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1080\/01621459.2022.2161387","article-title":"Copula based Cox proportional hazards models for dependent censoring","volume":"119","author":"Deresa","year":"2024","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1111\/j.2517-6161.1972.tb00899.x","article-title":"Regression models and life-tables","volume":"34","author":"Cox","year":"1972","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1136\/bmj.320.7243.1197","article-title":"How should cost data in pragmatic randomised trials be analysed?","volume":"320","author":"Thompson","year":"2000","journal-title":"BMJ"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1177\/135581969800300410","article-title":"The distribution of health care costs and their statistical analysis for economic evaluation","volume":"3","author":"Briggs","year":"1998","journal-title":"J. Health Serv. Res. Policy"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1610","DOI":"10.1080\/13696998.2020.1839272","article-title":"Hospitalization charges for extremely preterm infants: A ten-year analysis in Shanghai, China","volume":"23","author":"Zhu","year":"2020","journal-title":"J. Med Econ."},{"key":"ref_28","first-page":"974","article-title":"Evaluate the Medical Insurance Premium under Heavy-tailed Distribution: Empirical Research on NCMS of minhang (Shanghai)","volume":"32","author":"Qiu","year":"2013","journal-title":"J. Appl. Stat. Manag."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4306","DOI":"10.1002\/sim.5838","article-title":"A flexible model for the mean and variance functions, with application to medical cost data","volume":"32","author":"Chen","year":"2013","journal-title":"Stat. Med."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Tang, X., Luo, Z., and Gardiner, J.C. (2016). A Bivariate Random-Effects Copula Model for Length of Stay and Cost. Statistical Applications from Clinical Trials and Personalized Medicine to Finance and Business Analytics: Selected Papers from the 2015 ICSA\/Graybill Applied Statistics Symposium, Colorado State University, Fort Collins, Springer.","DOI":"10.1007\/978-3-319-42568-9_25"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1111\/j.2517-6161.1982.tb01222.x","article-title":"A model for association in bivariate survival data","volume":"44","author":"Oakes","year":"1982","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Di Clemente, A., and Romano, C. (2021). Calibrating and simulating copula functions in financial applications. Front. Appl. Math. Stat., 7.","DOI":"10.3389\/fams.2021.642210"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1111\/j.1539-6975.2009.01321.x","article-title":"Number of accidents or number of claims? An approach with zero-inflated Poisson models for panel data","volume":"76","author":"Boucher","year":"2009","journal-title":"J. Risk Insur."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1002\/cjs.5550350205","article-title":"Nonparametric estimation of copula functions for dependence modelling","volume":"35","author":"Chen","year":"2007","journal-title":"Can. J. Stat."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1228","DOI":"10.1198\/016214506000000311","article-title":"Efficient estimation of semiparametric multivariate copula models","volume":"101","author":"Chen","year":"2006","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1111\/j.1467-9868.2007.00607.x","article-title":"L 1-regularization path algorithm for generalized linear models","volume":"69","author":"Park","year":"2007","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"14","DOI":"10.2202\/1544-6115.1423","article-title":"Survival analysis with high-dimensional covariates: An application in microarray studies","volume":"8","author":"Engler","year":"2009","journal-title":"Stat. Appl. Genet. Mol. Biol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"ujae018","DOI":"10.1093\/biomtc\/ujae018","article-title":"Fitting the Cox proportional hazards model to big data","volume":"80","author":"Wang","year":"2024","journal-title":"Biometrics"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Ruppert, D., Wand, M.P., and Carroll, R.J. (2003). Semiparametric Regression, Cambridge University Press.","DOI":"10.1017\/CBO9780511755453"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.eswa.2016.07.041","article-title":"Dimensionality reduction in data mining: A Copula approach","volume":"64","author":"Houari","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"2003","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1002\/hec.800","article-title":"Analysis of hospital length of stay and discharge destination using hazard functions with unmeasured heterogeneity","volume":"12","author":"Picone","year":"2003","journal-title":"Health Econ."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1111\/sjos.70031","article-title":"Recursive Bayesian prediction of remaining useful life for gamma degradation process under conjugate priors","volume":"53","author":"Xu","year":"2025","journal-title":"Scand. J. Stat."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1111\/sjos.70049","article-title":"Kernel-based marginal testing for covariate effects in high-dimensional settings","volume":"53","author":"Yin","year":"2026","journal-title":"Scand. J. Stat."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1109\/TR.2025.3647489","article-title":"An Online Bayesian Framework for Identifying Latent System Degradation States","volume":"75","author":"Zhu","year":"2026","journal-title":"IEEE Trans. Reliab."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/2\/226\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T05:19:24Z","timestamp":1771996764000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/2\/226"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,23]]},"references-count":45,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["systems14020226"],"URL":"https:\/\/doi.org\/10.3390\/systems14020226","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,23]]}}}