{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T12:31:33Z","timestamp":1762950693530,"version":"3.45.0"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T00:00:00Z","timestamp":1762905600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T00:00:00Z","timestamp":1762905600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/100000057","name":"National Institute of General Medical Sciences","doi-asserted-by":"publisher","award":["T32 GM008721-24","R01 GM110240","R01 GM149657","R01 NS131606","OT2 OD032701"],"award-info":[{"award-number":["T32 GM008721-24","R01 GM110240","R01 GM149657","R01 NS131606","OT2 OD032701"]}],"id":[{"id":"10.13039\/100000057","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000133","name":"Agency for Healthcare Research and Quality","doi-asserted-by":"publisher","award":["T32-HS026121"],"award-info":[{"award-number":["T32-HS026121"]}],"id":[{"id":"10.13039\/100000133","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Frederick Thomas Advanced Medical Analytics Fund"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["npj Digit. Med."],"DOI":"10.1038\/s41746-025-02013-2","type":"journal-article","created":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T12:29:12Z","timestamp":1762950552000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Equipping mathematical models for hospital dynamics using information theory"],"prefix":"10.1038","volume":"8","author":[{"given":"Jeremy A.","family":"Balch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jackson G.","family":"Brandberg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert T.","family":"Andris","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ian G.","family":"Mesner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel C.","family":"Nametz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Murad","family":"Megjhani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthew M.","family":"Ruppert","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Die","family":"Hu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthew T.","family":"Clark","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benjamin","family":"Shickel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benjamin L.","family":"Ranard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John B.","family":"Delos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David J.","family":"Albers","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tyler J.","family":"Loftus","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Soojin","family":"Park","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Randall Moorman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,11,12]]},"reference":[{"key":"2013_CR1","doi-asserted-by":"crossref","unstructured":"Agniel, D., Kohane, I. S. & Weber, G. M. Biases in electronic health record data due to processes within the healthcare system: Retrospective observational study. BMJ 361, 1\u20139 (2018).","DOI":"10.1136\/bmj.k1479"},{"key":"2013_CR2","doi-asserted-by":"publisher","first-page":"1159","DOI":"10.1016\/j.physleta.2009.12.067","volume":"374","author":"DJ Albers","year":"2010","unstructured":"Albers, D. J. & Hripcsak, G. A statistical dynamics approach to the study of human health data: resolving population scale diurnal variation in laboratory data. Phys. Lett. A 374, 1159\u20131164 (2010).","journal-title":"Phys. Lett. A"},{"key":"2013_CR3","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1136\/amiajnl-2012-001145","volume":"20","author":"G Hripcsak","year":"2013","unstructured":"Hripcsak, G. & Albers, D. J. Next-generation phenotyping of electronic health records. J. Am. Med. Inform. Assoc. 20, 117\u2013121 (2013).","journal-title":"J. Am. Med. Inform. Assoc."},{"key":"2013_CR4","unstructured":"Petersen, K. E. & Petersen, K. Ergodic Theory. (Cambridge University Press, 1989)."},{"key":"2013_CR5","doi-asserted-by":"publisher","DOI":"10.1186\/s12913-019-4627-7","volume":"19","author":"R Cassidy","year":"2019","unstructured":"Cassidy, R. et al. Mathematical modelling for health systems research: a systematic review of system dynamics and agent-based models. BMC Health Serv. Res. 19, 845 (2019).","journal-title":"BMC Health Serv. Res."},{"key":"2013_CR6","doi-asserted-by":"crossref","unstructured":"\u00c7\u00f6mez, D. in Handbook of the Mathematics of the Arts and Sciences 1969\u20131992 (2021).","DOI":"10.1007\/978-3-319-57072-3_31"},{"key":"2013_CR7","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1001\/jama.2012.7551","volume":"308","author":"LA Lipsitz","year":"2012","unstructured":"Lipsitz, L. A. Understanding health care as a complex system: the foundation for unintended consequences. JAMA 308, 243\u2013244 (2012).","journal-title":"JAMA"},{"key":"2013_CR8","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1111\/j.1365-2753.2011.01792.x","volume":"18","author":"JP Sturmberg","year":"2012","unstructured":"Sturmberg, J. P., O\u2019Halloran, D. M. & Martin, C. M. Understanding health system reform\u2013a complex adaptive systems perspective. J. Eval. Clin. Pract. 18, 202\u2013208 (2012).","journal-title":"J. Eval. Clin. Pract."},{"key":"2013_CR9","unstructured":"Tribus, M. Thermostatics and thermodynamics: an introduction to energy, information and states of matter, with engineering applications. (1961)."},{"key":"2013_CR10","unstructured":"Kolmogorov, A. N. in Dokl. Akad. Nauk Vol. 119 861\u2013864 (Russian Academy of Sciences, 1958)."},{"key":"2013_CR11","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"CE Shannon","year":"1948","unstructured":"Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379\u2013423 (1948).","journal-title":"Bell Syst. Tech. J."},{"key":"2013_CR12","first-page":"768","volume":"124","author":"YG Sinai","year":"1959","unstructured":"Sinai, Y. G. in Dokl. Akad. Nauk SSSR 124, 768\u2013771 (1959).","journal-title":"Akad. Nauk SSSR"},{"key":"2013_CR13","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1038\/s41746-022-00611-y","volume":"5","author":"J Feng","year":"2022","unstructured":"Feng, J. et al. Clinical artificial intelligence quality improvement: towards continual monitoring and updating of AI algorithms in healthcare. NPJ Digit Med. 5, 66 (2022).","journal-title":"NPJ Digit Med."},{"key":"2013_CR14","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1056\/NEJMc2104626","volume":"385","author":"SG Finlayson","year":"2021","unstructured":"Finlayson, S. G. et al. The clinician and dataset shift in artificial intelligence. N. Engl. J. Med. 385, 283\u2013286 (2021).","journal-title":"N. Engl. J. Med."},{"key":"2013_CR15","doi-asserted-by":"publisher","first-page":"20220878","DOI":"10.1259\/bjr.20220878","volume":"96","author":"B Sahiner","year":"2023","unstructured":"Sahiner, B., Chen, W., Samala, R. K. & Petrick, N. Data drift in medical machine learning: implications and potential remedies. Br. J. Radiol. 96, 20220878 (2023).","journal-title":"Br. J. Radiol."},{"key":"2013_CR16","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-022-15245-z","volume":"12","author":"D Vela","year":"2022","unstructured":"Vela, D. et al. Temporal quality degradation in AI models. Sci. Rep. 12, 11654 (2022).","journal-title":"Sci. Rep."},{"key":"2013_CR17","unstructured":"Yang, J., Karstens, L., Ross, C. & Yala, A. AI Gone Astray: Technical Supplement. arXiv preprint arXiv:2203.16452 (2022)."},{"key":"2013_CR18","first-page":"421","volume":"2","author":"A Rajagopal","year":"2024","unstructured":"Rajagopal, A. et al. Machine learning operations in health care: A scoping review. Mayo Clin. Proc.: Digital Health 2, 421\u2013437 (2024).","journal-title":"Mayo Clin. Proc.: Digital Health"},{"key":"2013_CR19","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.jbi.2018.01.004","volume":"78","author":"DJ Albers","year":"2018","unstructured":"Albers, D. J. et al. Estimating summary statistics for electronic health record laboratory data for use in high-throughput phenotyping algorithms. J. Biomed. Inform. 78, 87\u2013101 (2018).","journal-title":"J. Biomed. Inform."},{"key":"2013_CR20","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-46142-w","volume":"15","author":"A Kore","year":"2024","unstructured":"Kore, A. et al. Empirical data drift detection experiments on real-world medical imaging data. Nat. Commun. 15, 1887 (2024).","journal-title":"Nat. Commun."},{"key":"2013_CR21","doi-asserted-by":"crossref","unstructured":"van der Vegt, A. H., Campbell, V., Wang, S., Malycha, J. & Scott, I. A. Factors underpinning the performance of implemented artificial intelligence-based patient deterioration prediction systems: reasons for selection and implications for hospitals and researchers. J. Am. Med. Inform. Assoc., ocae321, 492\u2013509 (2025).","DOI":"10.1093\/jamia\/ocae321"},{"key":"2013_CR22","doi-asserted-by":"publisher","first-page":"1294","DOI":"10.1007\/s10955-016-1456-5","volume":"162","author":"L Merchan","year":"2016","unstructured":"Merchan, L. & Nemenman, I. On the sufficiency of pairwise interactions in maximum entropy models of networks. J. Stat. Phys. 162, 1294\u20131308 (2016).","journal-title":"J. Stat. Phys."},{"key":"2013_CR23","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1109\/18.61115","volume":"37","author":"J Lin","year":"1991","unstructured":"Lin, J. Divergence measures based on the Shannon entropy. IEEE Trans. Inf. theory 37, 145\u2013151 (1991).","journal-title":"IEEE Trans. Inf. theory"},{"key":"2013_CR24","first-page":"152","volume":"62","author":"MA Raussen","year":"2015","unstructured":"Raussen, M. A. & Skau, C. Interview with Yakov Sinai. Not. Am. Math. Soc. 62, 152\u2013160 (2015).","journal-title":"Not. Am. Math. Soc."},{"key":"2013_CR25","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1097\/CCM.0000000000001738","volume":"44","author":"TJ Moss","year":"2016","unstructured":"Moss, T. J. et al. Signatures of subacute potentially catastrophic illness in the ICU: model development and validation. Crit. Care Med. 44, 1639\u20131648 (2016).","journal-title":"Crit. Care Med."},{"key":"2013_CR26","doi-asserted-by":"publisher","first-page":"e221","DOI":"10.1097\/CCM.0000000000005171","volume":"50","author":"WB Horton","year":"2022","unstructured":"Horton, W. B., Barros, A. J., Andris, R. T., Clark, M. T. & Moorman, J. R. Pathophysiologic signature of impending ICU hypoglycemia in bedside monitoring and electronic health record data: model development and external validation. Crit. Care Med. 50, e221\u2013e230 (2022).","journal-title":"Crit. Care Med."},{"key":"2013_CR27","doi-asserted-by":"publisher","unstructured":"Winasti, W., Berden, H. & van Merode, F. Hospital organizational structure and information processing: An entropy perspective. Entropy (Basel) 25, https:\/\/doi.org\/10.3390\/e25030420 (2023).","DOI":"10.3390\/e25030420"},{"key":"2013_CR28","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1093\/treephys\/25.7.825","volume":"25","author":"SA Pietsch","year":"2005","unstructured":"Pietsch, S. A. & Hausenauer, H. Using ergodic theory to assess the performance of ecosystem models. Tree Physiol. 25, 825\u2013837 (2005).","journal-title":"Tree Physiol."},{"key":"2013_CR29","doi-asserted-by":"publisher","first-page":"1216","DOI":"10.1038\/s41567-019-0732-0","volume":"15","author":"O Peters","year":"2019","unstructured":"Peters, O. The ergodicity problem in economics. Nat. Phys. 15, 1216\u20131221 (2019).","journal-title":"Nat. Phys."},{"key":"2013_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.dcn.2024.101406","volume":"68","author":"MD Hunter","year":"2024","unstructured":"Hunter, M. D., Fisher, Z. F. & Geier, C. F. What ergodicity means for you. Dev. Cogn. Neurosci. 68, 101406 (2024).","journal-title":"Dev. Cogn. Neurosci."},{"key":"2013_CR31","unstructured":"Glyde, H. R. in PHYS 813 Statistical Mechanics Lecture Notes (Department of Physics & Astronomy, University of Delaware, 2010)."},{"key":"2013_CR32","unstructured":"Kestin, J. A Course In Thermodynamics. (Taylor & Francis, 1979)."},{"key":"2013_CR33","doi-asserted-by":"publisher","DOI":"10.1186\/s12859-022-05007-z","volume":"23","author":"C Weistuch","year":"2022","unstructured":"Weistuch, C., Zhu, J., Deasy, J. O. & Tannenbaum, A. R. The maximum entropy principle for compositional data. BMC Bioinforma. 23, 449 (2022).","journal-title":"BMC Bioinforma."},{"key":"2013_CR34","doi-asserted-by":"publisher","first-page":"1121","DOI":"10.1016\/S0140-6736(13)61215-5","volume":"382","author":"JD Birkmeyer","year":"2013","unstructured":"Birkmeyer, J. D. et al. Understanding of regional variation in the use of surgery. Lancet 382, 1121\u20131129 (2013).","journal-title":"Lancet"},{"key":"2013_CR35","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1111\/j.1945-1474.2003.tb01052.x","volume":"25","author":"J Butler","year":"2003","unstructured":"Butler, J., Weingarten, J. P., Weddle, J. A. & Jain, M. K. Differences Among Hospitals in Delivery of Care for Heart Failure. J. Healthc. Qual. 25, 39 (2003).","journal-title":"J. Healthc. Qual."},{"key":"2013_CR36","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1542\/peds.2013-1569","volume":"132","author":"MI Neuman","year":"2013","unstructured":"Neuman, M. I. & Chiang, V. W. Variation in Pediatric Care at US Hospitals. Pediatrics 132, 369\u2013370 (2013).","journal-title":"Pediatrics"},{"key":"2013_CR37","volume":"2","author":"JN Blackwell","year":"2020","unstructured":"Blackwell, J. N. et al. Early detection of in-patient deterioration: one prediction model does not fit all. Crit. Care. Explor. 2, e0116 (2020).","journal-title":"Crit. Care. Explor."},{"key":"2013_CR38","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41746-021-00426-3","volume":"4","author":"BK Beaulieu-Jones","year":"2021","unstructured":"Beaulieu-Jones, B. K. et al. Machine learning for patient risk stratification: standing on, or looking over, the shoulders of clinicians?. NPJ digital Med. 4, 1\u20136 (2021).","journal-title":"NPJ digital Med."},{"key":"2013_CR39","first-page":"1571","volume":"2017","author":"E Sherman","year":"2017","unstructured":"Sherman, E., Gurm, H., Balis, U., Owens, S. & Wiens, J. Leveraging clinical time-series data for prediction: A cautionary tale. AMIA Annu. Symp. Proc. Arch. 2017, 1571 (2017).","journal-title":"AMIA Annu. Symp. Proc. Arch."},{"key":"2013_CR40","doi-asserted-by":"publisher","first-page":"AIoa2300032","DOI":"10.1056\/AIoa2300032","volume":"1","author":"F Kamran","year":"2024","unstructured":"Kamran, F. et al. Evaluation of sepsis prediction models before onset of treatment. Nejm Ai 1, AIoa2300032 (2024).","journal-title":"Nejm Ai"},{"key":"2013_CR41","doi-asserted-by":"crossref","unstructured":"Nemenman, I., Shafee, F. & Bialek, W. Entropy and inference, revisited. Adv. Neural Inf. Process. Syst. 14 (2001).","DOI":"10.7551\/mitpress\/1120.003.0065"},{"key":"2013_CR42","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1063\/1.166141","volume":"5","author":"CK Peng","year":"1995","unstructured":"Peng, C. K., Havlin, S., Stanley, H. E. & Goldberger, A. L. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos: Interdiscip. J. nonlinear Sci. 5, 82\u201387 (1995).","journal-title":"Chaos: Interdiscip. J. nonlinear Sci."},{"key":"2013_CR43","doi-asserted-by":"publisher","first-page":"H319","DOI":"10.1152\/ajpheart.00561.2010","volume":"300","author":"DE Lake","year":"2011","unstructured":"Lake, D. E. & Moorman, J. R. Accurate estimation of entropy in very short physiological time series: the problem of atrial fibrillation detection in implanted ventricular devices. Am. J. Physiol. Heart Circ. Physiol. 300, H319\u2013H325 (2011).","journal-title":"Am. J. Physiol. Heart Circ. Physiol."},{"key":"2013_CR44","doi-asserted-by":"crossref","unstructured":"Harrell, F. Regression Modeling Strategies: With Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis. (Springer International Publishing, 2015).","DOI":"10.1007\/978-3-319-19425-7"},{"key":"2013_CR45","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","volume":"12","author":"AE Hoerl","year":"1970","unstructured":"Hoerl, A. E. & Kennard, R. W. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12, 55\u201367 (1970).","journal-title":"Technometrics"},{"key":"2013_CR46","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1093\/biomet\/76.2.297","volume":"76","author":"CM Hurvich","year":"1989","unstructured":"Hurvich, C. M. & Tsai, C.-L. Regression and time series model selection in small samples. Biometrika 76, 297\u2013307 (1989).","journal-title":"Biometrika"},{"key":"2013_CR47","volume":"2","author":"AN Zimmet","year":"2020","unstructured":"Zimmet, A. N. et al. Pathophysiologic signatures of bloodstream infection in critically ill adults. Crit. Care. Explor. 2, e0191 (2020).","journal-title":"Crit. Care. Explor."}],"container-title":["npj Digital Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41746-025-02013-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41746-025-02013-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41746-025-02013-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T12:29:16Z","timestamp":1762950556000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41746-025-02013-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,12]]},"references-count":47,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["2013"],"URL":"https:\/\/doi.org\/10.1038\/s41746-025-02013-2","relation":{},"ISSN":["2398-6352"],"issn-type":[{"value":"2398-6352","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,12]]},"assertion":[{"value":"12 January 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 September 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 November 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"J.R.M. has stock in Medical Predictive Science Corporation, Charlottesville, VA, and consults for Nihon Kohden Digital Health Solutions, proceeds donated to the University of Virginia.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"652"}}