Post-matching analysis after coarsened exact matching: implications of coarsening for residual confounding and model dependence

Post-matching analysis after coarsened exact matching: implications of coarsening for residual confounding and model dependence | 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 Post-matching analysis after coarsened exact matching: implications of coarsening for residual confounding and model dependence Fei Wan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9076964/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract Background Coarsened Exact Matching (CEM) is a widely used design strategy aimed at reducing confounding in observational studies by matching treated and control units within strata of coarsened covariates. It is often promoted as a method that mimics a randomized block design, which has led many researchers to apply simple, unadjusted statistical methods—such as paired t -tests or McNemar’s test—originally developed for blocked randomized designs. However, CEM only ensures balance on the coarsened scale, and residual imbalances may remain on the original covariate scale, raising questions about the appropriateness of unadjusted analyses as the primary analytic approach. Methods We examine the implications of this coarsening process for post-matching analysis using literature review, conceptual arguments, and simulation studies. In particular, we evaluate how within-stratum heterogeneity in the original covariates affects residual confounding and the dependence of treatment effect estimates on outcome model specification. Results Our results show that matching on coarsened covariates can leave systematic differences between treated and control subjects within matched strata. These differences introduce residual confounding that does not disappear with increasing sample size. Simulation results further demonstrate a bias–variance trade-off induced by coarsening: fine coarsening may reduce residual confounding but can result in substantial data loss, whereas coarse binning preserves sample size at the cost of increased bias and greater reliance on outcome model specification. Conclusions CEM should be regarded primarily as a preprocessing tool for improving covariate overlap rather than as a stand-alone solution for confounding control. Valid causal inference following CEM generally requires regression adjustment using the original, uncoarsened covariates, and unadjusted analyses of matched data may yield biased treatment effect estimates. Coarsened exact matching Propensity score matching Model dependence Residual confounding Bias Curse of dimensionality Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 25 Apr, 2026 Reviewers agreed at journal 15 Apr, 2026 Reviewers agreed at journal 07 Apr, 2026 Reviewers invited by journal 07 Apr, 2026 Editor assigned by journal 06 Apr, 2026 Editor invited by journal 12 Mar, 2026 Submission checks completed at journal 12 Mar, 2026 First submitted to journal 11 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-9076964","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":607786123,"identity":"c170bbfe-8f59-4d32-afa6-f5d769dc17a9","order_by":0,"name":"Fei Wan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxUlEQVRIie3OIQ7CMBTG8Ue4RCeAK7RZsiAIXKULCTUdeoKQKXBg4RZTWB4hAVOCrSwKMzEuAKwoXItD9K8qvl/6AEKhfy0H0v08DECr8CIKSAx2zX8gkBbehJ4vCJj3RanF3XAYdEp0ETXlgIpkpZas+WUSO0mCkrYfC5LttLSHHVM3uVYUDk8iEi1uDXl5EC0bUhCeaG4PQzcZ6Yoingjbq4ptOB3HWxeJ1pIZnM170VKYus6HnZWL2L421GMeCoVCIXdvvCRL6pnHgzEAAAAASUVORK5CYII=","orcid":"","institution":"Washington University School of Medicine","correspondingAuthor":true,"prefix":"","firstName":"Fei","middleName":"","lastName":"Wan","suffix":""}],"badges":[],"createdAt":"2026-03-09 21:38:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9076964/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9076964/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106094616,"identity":"53f0014b-9c30-4216-90f4-e17e4319c13a","added_by":"auto","created_at":"2026-04-03 11:43:00","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":441992,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9076964/v1_covered_37aa9d4e-e5dd-43d5-8924-c22340770a7b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Post-matching analysis after coarsened exact matching: implications of coarsening for residual confounding and model dependence","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"[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},"keywords":"Coarsened exact matching, Propensity score matching, Model dependence, Residual confounding, Bias, Curse of dimensionality","lastPublishedDoi":"10.21203/rs.3.rs-9076964/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9076964/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eCoarsened Exact Matching (CEM) is a widely used design strategy aimed at reducing confounding in observational studies by matching treated and control units within strata of coarsened covariates. It is often promoted as a method that mimics a randomized block design, which has led many researchers to apply simple, unadjusted statistical methods\u0026mdash;such as paired \u003cem\u003et\u003c/em\u003e-tests or McNemar\u0026rsquo;s test\u0026mdash;originally developed for blocked randomized designs. However, CEM only ensures balance on the coarsened scale, and residual imbalances may remain on the original covariate scale, raising questions about the appropriateness of unadjusted analyses as the primary analytic approach.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eWe examine the implications of this coarsening process for post-matching analysis using literature review, conceptual arguments, and simulation studies. In particular, we evaluate how within-stratum heterogeneity in the original covariates affects residual confounding and the dependence of treatment effect estimates on outcome model specification.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eOur results show that matching on coarsened covariates can leave systematic differences between treated and control subjects within matched strata. These differences introduce residual confounding that does not disappear with increasing sample size. Simulation results further demonstrate a bias\u0026ndash;variance trade-off induced by coarsening: fine coarsening may reduce residual confounding but can result in substantial data loss, whereas coarse binning preserves sample size at the cost of increased bias and greater reliance on outcome model specification.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eCEM should be regarded primarily as a preprocessing tool for improving covariate overlap rather than as a stand-alone solution for confounding control. Valid causal inference following CEM generally requires regression adjustment using the original, uncoarsened covariates, and unadjusted analyses of matched data may yield biased treatment effect estimates.\u003c/p\u003e","manuscriptTitle":"Post-matching analysis after coarsened exact matching: implications of coarsening for residual confounding and model dependence","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-03 02:59:34","doi":"10.21203/rs.3.rs-9076964/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-04-25T10:00:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"90592092003822292731797255296779734786","date":"2026-04-16T00:25:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"240001216236042303041195630810746198640","date":"2026-04-07T10:06:27+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-07T09:26:38+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-06T10:24:54+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-03-12T11:59:38+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-12T11:31:24+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Medical Research Methodology","date":"2026-03-11T20:02:50+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":"1f2c8aa0-097d-4132-b778-1d551808841d","owner":[],"postedDate":"April 3rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-07T09:38:20+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-03 02:59:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9076964","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9076964","identity":"rs-9076964","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}