Optimum Strata Boundaries for Breast Cancer Patients Using Dynamic Programming Approach

Optimum Strata Boundaries for Breast Cancer Patients Using Dynamic Programming Approach | 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 Help Center Sign In Submit a Preprint Cite Share Download PDF Article Optimum Strata Boundaries for Breast Cancer Patients Using Dynamic Programming Approach Faizan Danish This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4331035/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The study examines the determination of stratification points for two study variables within the framework of simple random sampling, particularly focusing on calculating the population mean using a closely associated variable. Utilizing a superpopulation model, the investigation seeks to derive minimal equations by minimizing aggregated variance with the assistance of the variables under scrutiny. In order to improve the accuracy of estimating population parameters within a stratified sampling framework, it is suggested in the article to establish optimal strata boundaries (OSB) instead of categorizing variables, the study focuses on continuous variables for analysis. The creation of homogeneous units within each stratum, facilitated by optimally constructed OSB, leads to more effective sample sizes (SS) and consequently enhances precision in estimation. However, it's noted that the OSB and SS may not remain optimal in cases where a fixed total sample size is mandated, particularly in survey designs constrained by a fixed budget. To address this challenge, the article outlines a methodology for calculating the OSB and SS under the condition that the survey's per-unit stratum measurement costs or its probability density function is understood. An empirical demonstration of a design-based stratification approach is showcased using breast cancer data, where the mean perimeter is estimated based on mean radius and mean texture. Furthermore, numerical examples are provided for hypothetical study variables following Cauchy and standard power distributions. The novel approach has been integrated into the revised stratifyR package and LINGO software. The research outcomes indicate that the newly introduced method demonstrates superior efficiency or comparable performance when aiming to refine the precision of population parameter estimations. Physical sciences/Mathematics and computing/Statistics Health sciences/Health care/Health services Optimum Strata Boundaries Sample Size Dynamic programming Breast Cancer Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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 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-4331035","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":298967744,"identity":"53d375a4-f7ed-46e1-8597-a53eaca7c2ff","order_by":0,"name":"Faizan Danish","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEElEQVRIiWNgGAWjYBAC9gbGBhANJBkbmBkqGHhgMjy4tPAcQNFyhoGHh7AWCA3WyMzYhkcpXAv74eYPP3cwyPbPbm7+XDjvsIw9+9kDDD9qGGTMcWnhSWww7D3DYDzjzsE26ZnbDvPw8OQlMPYcY+CxbMCuxZ4hsSGBtw1I3khsY+bdlgb0S44BA28DA4/BARy28D9sOPgXqGX+jcTmz7xzgFr43xgw/sWnRSKxsRlky4YbiQ3SvA02PDwSOQbMeG2ReNjMLNsmYbwR6DBpnmNALTfeJRyWOSaBx2Hpjz++bbORnXcj/fFnnhoJe/b+3IMP39TY2OPSAgUSKMYwHEATIQgIRuYoGAWjYBSMMAAAip1V47jRArIAAAAASUVORK5CYII=","orcid":"","institution":"VIT-AP University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Faizan","middleName":"","lastName":"Danish","suffix":""}],"badges":[],"createdAt":"2024-04-26 17:29:49","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4331035/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4331035/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":63235116,"identity":"9f8ed250-5cce-43a8-bb7f-821ff87083de","added_by":"auto","created_at":"2024-08-26 02:52:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":460945,"visible":true,"origin":"","legend":"","description":"","filename":"problemofstratification.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4331035/v1_covered_9f9357d6-2380-4935-b500-272ed30dc21f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eOptimum Strata Boundaries for Breast Cancer Patients Using Dynamic Programming Approach\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Optimum Strata Boundaries, Sample Size, Dynamic programming, Breast Cancer","lastPublishedDoi":"10.21203/rs.3.rs-4331035/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4331035/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe study examines the determination of stratification points for two study variables within the framework of simple random sampling, particularly focusing on calculating the population mean using a closely associated variable. 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