{"paper_id":"3f9d1ee3-185d-4eaf-ae2b-443704e149ce","body_text":"IONE: Incoherence-Oriented Neutralisation and Extraction for Detecting Hidden Population Structure in Observational Studies | 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 IONE: Incoherence-Oriented Neutralisation and Extraction for Detecting Hidden Population Structure in Observational Studies Onishi Tatsuki This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9271445/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 13 You are reading this latest preprint version Abstract Background Observational studies are susceptible to multiple biases arising from hidden population structure, including confounding, Simpson's paradox, undetected effect modification, the ecological fallacy, and non-collapsibility. Existing adjustment methods such as propensity scores and prognostic scores address only measured confounders and provide no mechanism for detecting subgroup structure driven by unmeasured variables. We propose IONE (Incoherence-Oriented Neutralisation and Extraction), a framework that quantifies population incoherence and extracts coherent subpopulations using routinely measured variables alone. Methods We conducted a Monte Carlo simulation study following the ADEMP framework. Data were generated from a causal directed acyclic graph with three intentionally withheld variables (age, sex, BMI) influencing ten measured variables and a binary outcome. We evaluated six stratification methods in two families: decision power-based methods (predicted probability, residual, cross-validated, machine learning uncertainty) exploiting the outcome, and feature score-based methods (principal component analysis, clustering) operating in the covariate space alone. Performance was assessed by the Adjusted Rand Index (ARI), eta-squared (η²), and a coherence indicator (C1) derived from the I² heterogeneity statistic. Phase 1 comprised 18,000 evaluations across 1,200 scenarios; sensitivity analyses comprised 48,600 evaluations across 8,100 scenarios. We additionally applied IONE to five published instances of Simpson's paradox: COVID-19 case fatality rates, kidney stone treatments, UC Berkeley admissions, Israeli vaccine effectiveness, and the smoking–mortality paradox. Results In simulations, all proposed methods significantly outperformed random stratification (best ARI = 0.020 vs. 0.000, p < 0.001). Decision power-based methods consistently outperformed feature score-based methods. The strength of the hidden variable’s influence on measured variables (Z→X influence) was the primary determinant of performance, with ARI increasing up to 18-fold from weak to strong influence conditions. The coherence indicator C1 clearly distinguished incoherent from coherent populations (proposed methods C1 = 0.001 vs. random C1 = 0.863). In empirical validation, C1 correctly detected incoherence in all five examples (C1 = 0.001–0.034 vs. random C1 = 0.695–1.000). For two-group structures, stratification achieved high accuracy (kidney stone ARI = 0.851; Israeli vaccine ARI = 0.746). For multi-group structures, detection power was limited (COVID-19 ARI = 0.064; Berkeley ARI = 0.082). Conclusions IONE provides a two-tier contribution: first, the C1 coherence indicator reliably detects population incoherence regardless of subgroup complexity; second, stratification-based extraction of coherent subpopulations is effective when hidden variables leave sufficiently strong traces in measured variables (η² > 0.4) and the subgroup structure is discrete. We recommend that coherence assessment be incorporated as a standard step in observational study reporting. Simpson’s paradox confounding population heterogeneity coherence stratification unmeasured confounders observational studies causal inference Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 19 May, 2026 Reviews received at journal 18 May, 2026 Reviewers agreed at journal 18 May, 2026 Reviewers agreed at journal 17 May, 2026 Reviewers agreed at journal 15 May, 2026 Reviewers agreed at journal 15 May, 2026 Reviewers agreed at journal 15 May, 2026 Reviews received at journal 11 May, 2026 Reviewers agreed at journal 05 May, 2026 Reviewers invited by journal 08 Apr, 2026 Editor assigned by journal 31 Mar, 2026 Submission checks completed at journal 31 Mar, 2026 First submitted to journal 30 Mar, 2026 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. 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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-9271445\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":623059407,\"identity\":\"a97ff12b-64fb-4b3b-afc4-20ecac3bd112\",\"order_by\":0,\"name\":\"Onishi Tatsuki\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYBACAwglwcAPohIKiNVyAKhFsgGkxYB4LUDGASRL8QJz9h7j1x8qLPKNz69O/PDAgEGeX+wAfi2WPWfMLA6ckbDcduPtZgmgwwxnzk4g4LAbOWYGB9skDMxunN0A0pJgcJtYLcYzzm7+QawW4wcgLQb8vduIs8Wy51gZw5kzEgYSN3i3WSQYSBD2izl78+YPFRV1Bvz9Zzff/FFhI88vTUALELBJgCkJsEoJgspBgPkDmOI/QJTqUTAKRsEoGIEAAJeoRVkFK/y3AAAAAElFTkSuQmCC\",\"orcid\":\"\",\"institution\":\"Shiga University\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Onishi\",\"middleName\":\"\",\"lastName\":\"Tatsuki\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2026-03-30 19:09:51\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-9271445/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-9271445/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":107480868,\"identity\":\"8fb35634-789f-4963-8e18-e1248fdc065d\",\"added_by\":\"auto\",\"created_at\":\"2026-04-22 02:14:02\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":1074583,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"IONEmanuscript1.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-9271445/v1_covered_187c42c1-16b4-41f4-a820-13c53e65cd13.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"IONE: Incoherence-Oriented Neutralisation and Extraction for Detecting Hidden Population Structure in Observational Studies\",\"fulltext\":[],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":false,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":true,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":true,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"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},\"keywords\":\"Simpson’s paradox, confounding, population heterogeneity, coherence, stratification, unmeasured confounders, observational studies, causal inference\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-9271445/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-9271445/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003ch2\\u003eBackground\\u003c/h2\\u003e \\u003cp\\u003eObservational studies are susceptible to multiple biases arising from hidden population structure, including confounding, Simpson's paradox, undetected effect modification, the ecological fallacy, and non-collapsibility. Existing adjustment methods such as propensity scores and prognostic scores address only measured confounders and provide no mechanism for detecting subgroup structure driven by unmeasured variables. We propose IONE (Incoherence-Oriented Neutralisation and Extraction), a framework that quantifies population incoherence and extracts coherent subpopulations using routinely measured variables alone.\\u003c/p\\u003e\\u003ch2\\u003eMethods\\u003c/h2\\u003e \\u003cp\\u003eWe conducted a Monte Carlo simulation study following the ADEMP framework. Data were generated from a causal directed acyclic graph with three intentionally withheld variables (age, sex, BMI) influencing ten measured variables and a binary outcome. We evaluated six stratification methods in two families: decision power-based methods (predicted probability, residual, cross-validated, machine learning uncertainty) exploiting the outcome, and feature score-based methods (principal component analysis, clustering) operating in the covariate space alone. Performance was assessed by the Adjusted Rand Index (ARI), eta-squared (η\\u0026sup2;), and a coherence indicator (C1) derived from the I\\u0026sup2; heterogeneity statistic. Phase 1 comprised 18,000 evaluations across 1,200 scenarios; sensitivity analyses comprised 48,600 evaluations across 8,100 scenarios. We additionally applied IONE to five published instances of Simpson's paradox: COVID-19 case fatality rates, kidney stone treatments, UC Berkeley admissions, Israeli vaccine effectiveness, and the smoking\\u0026ndash;mortality paradox.\\u003c/p\\u003e\\u003ch2\\u003eResults\\u003c/h2\\u003e \\u003cp\\u003eIn simulations, all proposed methods significantly outperformed random stratification (best ARI\\u0026thinsp;=\\u0026thinsp;0.020 vs. 0.000, p\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.001). Decision power-based methods consistently outperformed feature score-based methods. The strength of the hidden variable\\u0026rsquo;s influence on measured variables (Z\\u0026rarr;X influence) was the primary determinant of performance, with ARI increasing up to 18-fold from weak to strong influence conditions. The coherence indicator C1 clearly distinguished incoherent from coherent populations (proposed methods C1\\u0026thinsp;=\\u0026thinsp;0.001 vs. random C1\\u0026thinsp;=\\u0026thinsp;0.863). In empirical validation, C1 correctly detected incoherence in all five examples (C1\\u0026thinsp;=\\u0026thinsp;0.001\\u0026ndash;0.034 vs. random C1\\u0026thinsp;=\\u0026thinsp;0.695\\u0026ndash;1.000). For two-group structures, stratification achieved high accuracy (kidney stone ARI\\u0026thinsp;=\\u0026thinsp;0.851; Israeli vaccine ARI\\u0026thinsp;=\\u0026thinsp;0.746). For multi-group structures, detection power was limited (COVID-19 ARI\\u0026thinsp;=\\u0026thinsp;0.064; Berkeley ARI\\u0026thinsp;=\\u0026thinsp;0.082).\\u003c/p\\u003e\\u003ch2\\u003eConclusions\\u003c/h2\\u003e \\u003cp\\u003eIONE provides a two-tier contribution: first, the C1 coherence indicator reliably detects population incoherence regardless of subgroup complexity; second, stratification-based extraction of coherent subpopulations is effective when hidden variables leave sufficiently strong traces in measured variables (η\\u0026sup2; \\u0026gt; 0.4) and the subgroup structure is discrete. We recommend that coherence assessment be incorporated as a standard step in observational study reporting.\\u003c/p\\u003e\",\"manuscriptTitle\":\"IONE: Incoherence-Oriented Neutralisation and Extraction for Detecting Hidden Population Structure in Observational Studies\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2026-04-15 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