{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T19:29:16Z","timestamp":1757618956171,"version":"3.44.0"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2025,7,17]],"date-time":"2025-07-17T00:00:00Z","timestamp":1752710400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,7,17]],"date-time":"2025-07-17T00:00:00Z","timestamp":1752710400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["628.011.212"],"award-info":[{"award-number":["628.011.212"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Federated learning allows us to run machine learning algorithms on decentralized data when data sharing is not permitted due to privacy concerns. Various models have been adapted to use in a federated setting. Among these models is Verticox, a federated implementation of Cox proportional hazards models, which can be used in a vertically partitioned setting. However, Verticox assumes that the survival outcome is known locally by all parties involved in the federated setting. Realistically speaking, this is not the case in most settings and thus would require the outcome to be shared. However, sharing the survival outcome would in many cases be a breach of privacy which federated learning aims to prevent. Our extension to Verticox, dubbed Verticox+, solves this problem by incorporating a privacy preserving 2-party scalar product protocol at different stages. This allows it to be used in scenarios where the survival outcome is not known at each party. In this article, we demonstrate that our algorithm achieves equivalent performance to the original Verticox implementation. We discuss the changes to the computational complexity and communication cost caused by our additions.<\/jats:p>","DOI":"10.1007\/s40747-025-02022-4","type":"journal-article","created":{"date-parts":[[2025,7,17]],"date-time":"2025-07-17T15:46:56Z","timestamp":1752767216000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Verticox+: vertically distributed Cox proportional hazards model with improved privacy guarantees"],"prefix":"10.1007","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2229-8587","authenticated-orcid":false,"given":"Florian","family":"van Daalen","sequence":"first","affiliation":[]},{"given":"Djura","family":"Smits","sequence":"additional","affiliation":[]},{"given":"Lianne","family":"Ippel","sequence":"additional","affiliation":[]},{"given":"Andre","family":"Dekker","sequence":"additional","affiliation":[]},{"given":"Inigo","family":"Bermejo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,17]]},"reference":[{"key":"2022_CR1","doi-asserted-by":"crossref","unstructured":"Kairouz P, McMahan HB, Avent B, Bellet A, Bennis M, Bhagoji AN, Bonawitz K, Charles Z, Cormode G, Cummings R, D\u2019Oliveira RGL, Rouayheb SE, Evans D, Gardner J, Garrett Z, Gasc\u00f3n A, Ghazi B, Gibbons PB, Gruteser M, Harchaoui Z, He C, He L, Huo Z, Hutchinson B, Hsu J, Jaggi M, Javidi T, Joshi G, Khodak M, Kone\u010dn\u00fd J, Korolova A, Koushanfar F, Koyejo S, Lepoint T, Liu Y, Mittal P, Mohri M, Nock R, \u00d6zg\u00fcr A, Pagh R, Raykova M, Qi H, Ramage D, Raskar R, Song D, Song W, Stich SU, Sun Z, Suresh AT, Tram\u00e8r F, Vepakomma P, Wang J, Xiong L, Xu Z, Yang Q, Yu FX, Yu H, Zhao S (2019) Advances and Open Problems in Federated Learning. arXiv:1912.04977 [cs, stat]. arXiv: 1912.04977. Accessed 2021-03-02","DOI":"10.1561\/9781680837896"},{"key":"2022_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2020.106854","volume":"149","author":"L Li","year":"2020","unstructured":"Li L, Fan Y, Tse M, Lin K-Y (2020) A review of applications in federated learning. Comput Ind Eng 149:106854. https:\/\/doi.org\/10.1016\/j.cie.2020.106854. (Accessed 2021-03-03)","journal-title":"Comput Ind Eng"},{"key":"2022_CR3","doi-asserted-by":"publisher","unstructured":"Dai W, Jiang X, Bonomi L, Li Y, Xiong H, Ohno-Machado L (2020) VERTICOX: vertically distributed Cox proportional hazards model using the alternating direction method of multipliers. IEEE Trans Knowl Data Eng. https:\/\/doi.org\/10.1109\/TKDE.2020.2989301. Accessed 2021-05-26. (Accessed 2021-05-26)","DOI":"10.1109\/TKDE.2020.2989301"},{"key":"2022_CR4","doi-asserted-by":"publisher","unstructured":"Cox DR (1972) Regression models and life-tables. J Roy Stat Soc: Ser B (Methodol) 34(2):187\u2013202. https:\/\/doi.org\/10.1111\/j.2517-6161.1972.tb00899.x. (Accessed 2024-05-22)","DOI":"10.1111\/j.2517-6161.1972.tb00899.x"},{"issue":"1","key":"2022_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000016","volume":"3","author":"S Boyd","year":"2011","unstructured":"Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1\u2013122. https:\/\/doi.org\/10.1561\/2200000016. (Accessed 2024-05-21)","journal-title":"Found Trends Mach Learn"},{"key":"2022_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbi.2023.104581","volume":"149","author":"G Miao","year":"2024","unstructured":"Miao G, Yu L, Yang J, Bennett DA, Zhao J, Wu SS (2024) Learning from vertically distributed data across multiple sites: an efficient privacy-preserving algorithm for Cox proportional hazards model with variable selection. J Biomed Inform 149:104581. https:\/\/doi.org\/10.1016\/j.jbi.2023.104581","journal-title":"J Biomed Inform"},{"issue":"1","key":"2022_CR7","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1186\/s12911-022-01771-3","volume":"22","author":"B Kamphorst","year":"2022","unstructured":"Kamphorst B, Rooijakkers T, Veugen T, Cellamare M, Knoors D (2022) Accurate training of the Cox proportional hazards model on vertically-partitioned data while preserving privacy. BMC Med Inform Decis Mak 22(1):49. https:\/\/doi.org\/10.1186\/s12911-022-01771-3","journal-title":"BMC Med Inform Decis Mak"},{"key":"2022_CR8","doi-asserted-by":"publisher","unstructured":"Yao AC (1982) Protocols for secure computations. In: 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982), pp. 160\u2013164. https:\/\/doi.org\/10.1109\/SFCS.1982.38 . ISSN: 0272-5428","DOI":"10.1109\/SFCS.1982.38"},{"issue":"9","key":"2022_CR9","doi-asserted-by":"publisher","first-page":"3310","DOI":"10.1109\/JBHI.2021.3071270","volume":"25","author":"Y Lu","year":"2021","unstructured":"Lu Y, Tian Y, Zhou T, Zhu S, Li J (2021) Multicenter privacy-preserving cox analysis based on homomorphic encryption. IEEE J Biomed Health Inform 25(9):3310\u20133320","journal-title":"IEEE J Biomed Health Inform"},{"key":"2022_CR10","unstructured":"Du W, Zhan Z (2002) Building decision tree classifier on private data. In: Proceedings of the IEEE International Conference on Privacy, Security and Data Mining - Volume 14. CRPIT \u201914, pp. 1\u20138. Australian Computer Society, Inc., AUS"},{"key":"2022_CR11","first-page":"870","volume":"2020","author":"A Moncada-Torres","year":"2021","unstructured":"Moncada-Torres A, Martin F, Sieswerda M, Van Soest J, Geleijnse G (2021) VANTAGE6: an open source priVAcy preserviNg federaTed leArninG infrastructurE for Secure Insight eXchange. AMIA Ann Symp Proc 2020:870\u2013877","journal-title":"AMIA Ann Symp Proc"},{"issue":"4","key":"2022_CR12","doi-asserted-by":"publisher","first-page":"1060","DOI":"10.1109\/TPDS.2023.3238768","volume":"34","author":"F Daalen","year":"2023","unstructured":"Daalen F, Ippel L, Dekker A, Bermejo I (2023) Privacy Preserving n-Party Scalar Product Protocol. IEEE Trans Parallel Distrib Syst 34(4):1060\u20131066. https:\/\/doi.org\/10.1109\/TPDS.2023.3238768. (Conference Name: IEEE Transactions on Parallel and Distributed Systems)","journal-title":"IEEE Trans Parallel Distrib Syst"},{"key":"2022_CR13","doi-asserted-by":"publisher","unstructured":"Shmueli E, Tassa T Mediated secure multi-party protocols for collaborative filtering. 11(2), 1\u201325 https:\/\/doi.org\/10.1145\/3375402. (Accessed 2022-10-26)","DOI":"10.1145\/3375402"},{"key":"2022_CR14","doi-asserted-by":"publisher","unstructured":"Goethals B, Laur S, Lipmaa H, Mielik\u00e4inen T (2005) On Private Scalar Product Computation for Privacy-Preserving Data Mining. In: Hutchison D, Kanade T, Kittler J, Kleinberg JM, Mattern F, Mitchell JC, Naor M, Nierstrasz O, Pandu\u00a0Rangan C, Steffen B, Sudan M, Terzopoulos D, Tygar D, Vardi MY, Weikum G, Park C-s, Chee S (eds) Information Security and Cryptology ICISC 2004 vol. 3506, pp. 104\u2013120. Springer, Berlin, Heidelberg. https:\/\/doi.org\/10.1007\/11496618_9 . Series Title: Lecture Notes in Computer Science. Accessed 2021-06-28","DOI":"10.1007\/11496618_9"},{"key":"2022_CR15","doi-asserted-by":"publisher","unstructured":"Atallah MJ, Du W (2001) Secure Multi-party Computational Geometry. In: Goos, G, Hartmanis J, Leeuwen J, Dehne F, Sack J-R, Tamassia R (eds) Algorithms and Data Structures vol. 2125, pp. 165\u2013179. Springer, Berlin, Heidelberg.https:\/\/doi.org\/10.1007\/3-540-44634-6_16 . Series Title: Lecture Notes in Computer Science. Accessed 2021-07-19","DOI":"10.1007\/3-540-44634-6_16"},{"key":"2022_CR16","doi-asserted-by":"publisher","unstructured":"Du W, Atallah MJ (2001) Privacy-preserving cooperative statistical analysis. In: Seventeenth Annual Computer Security Applications Conference, pp. 102\u2013110. IEEE Comput. Soc, New Orleans, LA, USA. https:\/\/doi.org\/10.1109\/ACSAC.2001.991526. Accessed 2021-06-16","DOI":"10.1109\/ACSAC.2001.991526"},{"key":"2022_CR17","doi-asserted-by":"publisher","unstructured":"Vaidya J, Clifton C (2002) Privacy preserving association rule mining in vertically partitioned data. In: Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data mining. KDD \u201902, pp. 639\u2013644. Association for Computing Machinery, New York, NY, USA. https:\/\/doi.org\/10.1145\/775047.775142. Accessed 2021-06-16","DOI":"10.1145\/775047.775142"},{"key":"2022_CR18","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.5120960","author":"Z Sembay","year":"2021","unstructured":"Sembay Z (2021) Seer breast cancer data. Zenodo. https:\/\/doi.org\/10.5281\/zenodo.5120960","journal-title":"Zenodo"},{"key":"2022_CR19","doi-asserted-by":"crossref","unstructured":"Harrell FE Jr, Lee KL, Mark DB (1996) Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Stat Med 15(4):361\u2013387","DOI":"10.1002\/(SICI)1097-0258(19960229)15:4<361::AID-SIM168>3.0.CO;2-4"},{"key":"2022_CR20","doi-asserted-by":"publisher","unstructured":"Wang J, Guo S, Xie X, Qi H (2022) Protect privacy from gradient leakage attack in federated learning. In: IEEE INFOCOM 2022\u2014IEEE Conference on Computer Communications, pp. 580\u2013589. IEEE, London, United Kingdom. https:\/\/doi.org\/10.1109\/INFOCOM48880.2022.9796841. Accessed 2024-05-21","DOI":"10.1109\/INFOCOM48880.2022.9796841"},{"key":"2022_CR21","unstructured":"Jin X, Chen P-Y, Hsu C-Y, Yu C-M, Chen T (2021) CAFE: catastrophic data leakage in vertical federated learning. In: Advances in Neural Information Processing Systems, vol. 34, pp. 994\u20131006. Curran Associates, Inc., https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2021\/hash\/08040837089cdf46631a10aca5258e16-Abstract.html. Accessed 2024-05-21"},{"key":"2022_CR22","doi-asserted-by":"publisher","unstructured":"Wei W, Liu L, Loper M, Chow K-H, Gursoy ME, Truex S, Wu Y (2020) A framework for evaluating gradient leakage attacks in federated learning. arXiv. arXiv:2004.10397 [cs, stat]. https:\/\/doi.org\/10.48550\/arXiv.2004.10397 . arxiv:2004.10397 Accessed 2024-05-21","DOI":"10.48550\/arXiv.2004.10397"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-02022-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-025-02022-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-02022-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,7]],"date-time":"2025-09-07T13:12:35Z","timestamp":1757250755000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-025-02022-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,17]]},"references-count":22,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["2022"],"URL":"https:\/\/doi.org\/10.1007\/s40747-025-02022-4","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"type":"print","value":"2199-4536"},{"type":"electronic","value":"2198-6053"}],"subject":[],"published":{"date-parts":[[2025,7,17]]},"assertion":[{"value":"4 February 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 July 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 July 2025","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 have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"Not applicable.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"388"}}