Spatial Cluster Randomized Trials - Sampling Design with Spillover Effects & Spatial Dependence

Spatial Cluster Randomized Trials - Sampling Design with Spillover Effects & Spatial 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 Spatial Cluster Randomized Trials - Sampling Design with Spillover Effects & Spatial Dependence Andrew Walther, Tonya Van Deinse, Feng-Chang Lin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8713976/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Background: Investigators designing cluster randomized trials desire insights directing treatment assignment methodology for studies involving spillover effects and spatial dependence. Methods & Simulation: Treatment assignment strategies including simple random sampling (SRS) and block stratified sampling (BSS) are defined and spatial autoregressive modeling is applied with consideration for spillover effects and spatial dependence for estimation of intervention effects. A simulation study is carried out comparing SRS and BSS sampling methods on spatial grids of varying sizes. A range of spillover effects and levels of spatial dependence were considered for estimation of the intervention effect via a spatial autoregressive (SAR) model. Results: Findings of an extensive simulation study comparing simple random sampling and block stratification methods indicate that randomly selected treatment assignments result in best case reduced Mean Squared Error (MSE) when estimating intervention effects, but block stratified treatment assignments lead to minimal variation in MSE among a series of treatment combinations, indicating that a block stratified treatment arrangement won’t achieve the minimal level of estimation error, but it remains robust across a range of selected parameters. Even though SRS is consistent and unbiased with reduced MSE, we consider variation among all possible treatment combinations to ensure a robust result. Conclusion: The relationship between spillover effects and mean squared errors (MSE) of intervention effect estimation is apparent. The MSE for the intervention effect, which is the average MSE over each of N simulation iterations, is minimized for some combinations of random sampling treatment assignment, but block stratified assignment minimizes variance among combinations of possible treatment arrangements. In short, the SRS technique may achieve minimum average MSE in some cases, but BSS achieves respectable average estimation error with minimal variation between treatment combinations. spatial autoregressive simple random sampling block stratified sampling treatment assignment clinical trials Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 20 Mar, 2026 Reviews received at journal 17 Mar, 2026 Reviewers agreed at journal 16 Feb, 2026 Reviews received at journal 11 Feb, 2026 Reviewers agreed at journal 03 Feb, 2026 Reviewers invited by journal 03 Feb, 2026 Editor invited by journal 02 Feb, 2026 Editor assigned by journal 28 Jan, 2026 Submission checks completed at journal 28 Jan, 2026 First submitted to journal 27 Jan, 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. 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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-8713976","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":585956343,"identity":"e59c177d-336c-48c7-8076-359f58abcb92","order_by":0,"name":"Andrew Walther","email":"","orcid":"","institution":"University of North Carolina at Chapel Hill","correspondingAuthor":false,"prefix":"","firstName":"Andrew","middleName":"","lastName":"Walther","suffix":""},{"id":585956344,"identity":"ca2d8dde-b521-4edb-8a5f-b72644eff496","order_by":1,"name":"Tonya Van Deinse","email":"","orcid":"","institution":"University of North Carolina at Chapel Hill","correspondingAuthor":false,"prefix":"","firstName":"Tonya","middleName":"Van","lastName":"Deinse","suffix":""},{"id":585956345,"identity":"a6641d30-30a2-4282-becc-5ae0af9945fc","order_by":2,"name":"Feng-Chang Lin","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuElEQVRIiWNgGAWjYBAC9nbGBoaPDRJwASCXAOA5zNjAOJNELQwMzLxIyojQwszc9th2h4WcfAOP2YMfDDayGw4Q1MLYbpx7RsLY4ACPuWEPQ5oxQS32zIxt0rltEokbGHjMpBkYDicSY0ubtCVQy/wGsJb/RGphBGppOADWcoA4LZK9IL8cZiuT7DFINp5JUAt7+zOJnzvq5OTbm7dJ/Kiwk+0jpAUBmEGEAdHKR8EoGAWjYBTgAwCLnzc/GZlQUQAAAABJRU5ErkJggg==","orcid":"","institution":"University of North Carolina at Chapel Hill","correspondingAuthor":true,"prefix":"","firstName":"Feng-Chang","middleName":"","lastName":"Lin","suffix":""}],"badges":[],"createdAt":"2026-01-27 19:53:45","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8713976/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8713976/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101943740,"identity":"fe7eb95b-62ab-4a95-8885-d47ff012c547","added_by":"auto","created_at":"2026-02-05 09:43:10","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":786346,"visible":true,"origin":"","legend":"","description":"","filename":"WaltherSpatialCRTLaTeXV2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8713976/v1_covered_ce05ead1-f392-45b2-b930-1a8344138c59.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Spatial Cluster Randomized Trials - Sampling Design with Spillover Effects \u0026 Spatial Dependence","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":"[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":"spatial autoregressive, simple random sampling, block stratified sampling, treatment assignment, clinical trials","lastPublishedDoi":"10.21203/rs.3.rs-8713976/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8713976/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Background: Investigators designing cluster randomized trials desire insights directing treatment assignment methodology for studies involving spillover effects and spatial dependence.\n\nMethods \u0026 Simulation: Treatment assignment strategies including simple random sampling (SRS) and block stratified sampling (BSS) are defined and spatial autoregressive modeling is applied with consideration for spillover effects and spatial dependence for estimation of intervention effects. 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