Revisiting VERTIGO and VERTIGO-CI:  Identifying confidentiality breaches and introducing a statistically sound, efficient alternative

Revisiting VERTIGO and VERTIGO-CI: Identifying confidentiality breaches and introducing a statistically sound, efficient alternative | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Revisiting VERTIGO and VERTIGO-CI: Identifying confidentiality breaches and introducing a statistically sound, efficient alternative Marie-Pier Domingue, Jean-François Ethier, Jean-Philippe Morissette, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6933988/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Background: Health Data Research Network Canada is tasked with facilitating large-scale health data research, such as statistical analyses that integrate, within a single model, data collected by different organizations, each holding distinct subsets of features corresponding to the same individuals, thereby forming a vertical data partition. To support logistic regression analyses in this setting, we assessed two recently proposed algorithms, VERTIGO and VERTIGO-CI, which enable parameter estimation and confidence interval computation, respectively, with respect to three aspects: the risk of re-identifying patient feature data, communication efficiency, and the extent to which model interpretability is preserved. This study has three main objectives: (1) highlighting confidentiality issues that arise with VERTIGO-CI, as well as those that may occur with VERTIGO when a data node holds only binary covariates; (2) reducing the number of required communication rounds; and (3) proposing an alternative (RidgeLog-V) to VERTIGO that excludes the intercept from the penalty term, which VERTIGO otherwise includes. Methods: We inspected the quantities exchanged in the original algorithms and used linear algebra to identify reverse-engineering procedures that the coordinating center could employ to reconstruct raw data. We also analyzed the objective function of the optimization problem, leading to the proposal of an alternative formulation that requires only a single round of communication while allowing the intercept to be excluded from the penalty term. Results: We showed that, when the VERTIGO-CI algorithm is executed, the coordinating center can reconstruct all individual-level data using simple vector-matrix operations. When the VERTIGO algorithm is executed and a data node has binary covariates only, the coordinating center may be able to recover individual data when parameter estimates are shared. We adapted the VERTIGO algorithm to reduce the number of communications and proposed a variant that excludes the intercept from the penalty term. Conclusions: While the use of VERTIGO-CI, or of VERTIGO with binary covariates does not involve directly sharing raw data, confidentiality breaches may arise through reverse-engineering, illustrating that that the distributed nature of an algorithm does not inherently guarantee data privacy. This work also proposed a new algorithm (RidgeLog-V) that reduces operational costs and enhances model interpretability. Vertically partitioned data Data privacy Distributed analysis Logistic regression model Distributed algorithm Full Text Additional Declarations No competing interests reported. Supplementary Files AdditionalFile1REVISITINGVERTIGOANDVERTIGOC.pdf Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 21 Oct, 2025 Reviewers agreed at journal 07 Oct, 2025 Reviewers agreed at journal 10 Aug, 2025 Reviewers agreed at journal 04 Jul, 2025 Reviewers invited by journal 29 Jun, 2025 Editor invited by journal 23 Jun, 2025 Editor assigned by journal 20 Jun, 2025 Submission checks completed at journal 20 Jun, 2025 First submitted to journal 19 Jun, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6933988","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":474034354,"identity":"1364bec3-6af0-4204-866f-0989b712f243","order_by":0,"name":"Marie-Pier Domingue","email":"","orcid":"","institution":"Université de Sherbrooke","correspondingAuthor":false,"prefix":"","firstName":"Marie-Pier","middleName":"","lastName":"Domingue","suffix":""},{"id":474034356,"identity":"37feceb2-efd6-463c-9795-950a58818448","order_by":1,"name":"Jean-François 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To support logistic regression analyses in this setting, we assessed two recently proposed algorithms, VERTIGO and VERTIGO-CI, which enable parameter estimation and confidence interval computation, respectively, with respect to three aspects: the risk of re-identifying patient feature data, communication efficiency, and the extent to which model interpretability is preserved. 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We also analyzed the objective function of the optimization problem, leading to the proposal of an alternative formulation that requires only a single round of communication while allowing the intercept to be excluded from the penalty term.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults:\u003c/strong\u003e We showed that, when the VERTIGO-CI algorithm is executed, the coordinating center can reconstruct all individual-level data using simple vector-matrix operations. When the VERTIGO algorithm is executed and a data node has binary covariates only, the coordinating center may be able to recover individual data when parameter estimates are shared. 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This work also proposed a new algorithm (RidgeLog-V) that reduces operational costs and enhances model interpretability.\u003c/p\u003e","manuscriptTitle":"Revisiting VERTIGO and VERTIGO-CI: Identifying confidentiality breaches and introducing a statistically sound, efficient alternative","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-23 04:11:52","doi":"10.21203/rs.3.rs-6933988/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2025-10-21T04:25:40+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"250802874490610504304563132240080306942","date":"2025-10-08T02:43:33+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"146712432825268247446629150938215439485","date":"2025-08-10T11:32:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"186457473293504522230706272312548298665","date":"2025-07-04T11:33:39+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-06-29T11:23:24+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-06-23T09:08:31+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-06-20T09:49:45+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-06-20T09:47:25+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Medical Research Methodology","date":"2025-06-19T23:29:12+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-medical-research-methodology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmrm","sideBox":"Learn more about [BMC Medical Research Methodology](http://bmcmedresmethodol.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/bmrm/default.aspx","title":"BMC Medical Research Methodology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"372278b5-d91b-461a-8285-a207049a1a0c","owner":[],"postedDate":"June 23rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-07-13T16:56:17+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-23 04:11:52","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6933988","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6933988","identity":"rs-6933988","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}