Bias from cluster-specific time trajectories in cluster-randomized stepped wedge trials

Bias from cluster-specific time trajectories in cluster-randomized stepped wedge trials | 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 Bias from cluster-specific time trajectories in cluster-randomized stepped wedge trials Kevin Dobbin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8978583/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 12 You are reading this latest preprint version Abstract Cluster-randomized stepped-wedge trials (SWT's) randomize each cluster to the time at which it crosses over from control to intervention. Commonly used models for SWT's assume that all clusters share a common time trajectory, meaning that the effect of time is the same across all clusters. But, the time effects may vary by cluster, resulting in cluster-specific time trajectories (CSTT's). This paper explores the bias induced in treatment effect estimatees is CSTT's exist but are ignored. A formula for estimating the bias is derived. To correct for the bias, two models with less restrictive assumptions are proposed that allow time trajectories to be cluster-specific, estimated using polynomials. It is shown using simulations that the bias formula is accurate, and that the proposed CSTT models reduce the bias. The bias seems particularly problematic when CSTT patterns are nonlinear. These methods are applied to two cluster-randomized SWT datasets. Full Text Additional Declarations No competing interests reported. Supplementary Files supplementdraft.pdf Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 29 Apr, 2026 Reviews received at journal 16 Apr, 2026 Reviews received at journal 13 Apr, 2026 Reviewers agreed at journal 10 Apr, 2026 Reviews received at journal 08 Apr, 2026 Reviewers agreed at journal 06 Apr, 2026 Reviewers agreed at journal 03 Apr, 2026 Reviewers invited by journal 02 Apr, 2026 Editor assigned by journal 31 Mar, 2026 Editor invited by journal 09 Mar, 2026 Submission checks completed at journal 09 Mar, 2026 First submitted to journal 04 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-8978583","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":615114018,"identity":"18a639f1-35a5-45e6-b849-02a1566b8280","order_by":0,"name":"Kevin Dobbin","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYBACCYYENmYGAwY5JLEE4rQYI6kmSgsDQ2ID0Vok25OPPS4ouJPePyP9muTPH3YM/Ow5Bni1SPM8SzeeYfAsd8aNnDJpnoRkBsmeN/i1yEnkmEnzGBzObbiRkybNkAD01w0CtsC0pMsDtUj+SKhnsCekRRqqJcHgRvoxCZ6EwwwGEgS0SPaA/XLYcOOZN8zWPGnHeSTOPCvAq0XiOCjE/hyWlzue/vDmD5tqOf725A14tSABHrB7eIhVDgLsD0hRPQpGwSgYBSMIAAB6+EPskUdzwAAAAABJRU5ErkJggg==","orcid":"","institution":"Augusta University","correspondingAuthor":true,"prefix":"","firstName":"Kevin","middleName":"","lastName":"Dobbin","suffix":""}],"badges":[],"createdAt":"2026-02-26 14:09:03","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8978583/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8978583/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106001074,"identity":"3a72e206-1b83-4b1f-bf13-795058a56485","added_by":"auto","created_at":"2026-04-02 09:57:45","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":861016,"visible":true,"origin":"","legend":"","description":"","filename":"LatexForZipTry3.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8978583/v1_covered_ecb1f3f3-ece1-4413-9246-2cd208648b8f.pdf"},{"id":106000569,"identity":"58a7c87d-9551-423f-8950-f410f2474ee1","added_by":"auto","created_at":"2026-04-02 09:56:38","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":63721,"visible":true,"origin":"","legend":"","description":"","filename":"supplementdraft.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8978583/v1/823923d463b02f9a43d64338.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bias from cluster-specific time trajectories in cluster-randomized stepped wedge trials","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":"","lastPublishedDoi":"10.21203/rs.3.rs-8978583/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8978583/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Cluster-randomized stepped-wedge trials (SWT's) randomize each cluster to the time at which it crosses over from control to intervention. 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