Estimating Evidence Contribution in Component Network Meta-Analysis through Shortest Path and Random Walk Approaches

Estimating Evidence Contribution in Component Network Meta-Analysis through Shortest Path and Random Walk Approaches | 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 Method Article Estimating Evidence Contribution in Component Network Meta-Analysis through Shortest Path and Random Walk Approaches Qinbo Yang, Yiwen Shen, Yunhe Mao, Sheyu Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7350512/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 Background Component Network Meta-Analysis (CNMA) extends standard NMA by enabling the decomposition of multicomponent interventions into individual component-level effect estimates. Quantifying the proportional contributions of pairwise comparisons is crucial for clinical interpretation and confidence rating, yet robust methods for this quantification within CNMA are currently lacking. Methods We employed the shortest-path and random-walk approaches to utilize the hat matrix and design matrix derived from frequentist CNMA models. These methods systematically trace the composition of evidence at the component level and further quantify the proportional contribution of each pairwise comparison. A hypothetical dataset was used to illustrate the implementation process. Results This study outlines how the two approaches were adapted to address the complexity of composite interventions in CNMA. The random-walk method decomposes the CNMA network by splitting nodes that represent composite interventions, enabling precise tracking of evidence flow at the component level. In contrast, the shortest-path method bypasses conventional pathway traversal by identifying edge combinations that algebraically isolate the target components. When applied to the same dataset, the two methods generated distinct contribution profiles, reflecting their differing theoretical underpinnings. Conclusions Both the shortest-path and random-walk approaches are theoretically applicable in CNMA contexts. However, the shortest-path approach is preferable for quantifying component-level evidence contributions due to its superior computational efficiency and robustness, making it the recommended choice for practical applications. Component network meta-analysis Multicomponent interventions Contribution Full Text Additional Declarations The authors declare no competing interests. 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 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-7350512","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":499091365,"identity":"cefe74eb-6e05-4d05-8c80-8856f5f1d6f3","order_by":0,"name":"Qinbo Yang","email":"","orcid":"","institution":"Department of Nephrology, West China Hospital, Sichuan University, Chengdu, China","correspondingAuthor":false,"prefix":"","firstName":"Qinbo","middleName":"","lastName":"Yang","suffix":""},{"id":499091366,"identity":"753344fb-0d96-4a2d-886f-4afbe0ff1862","order_by":1,"name":"Yiwen Shen","email":"","orcid":"","institution":"Department of Information Systems, Business Statistics, and Operations Management, School of Business and Management, Hong Kong University of Science and Technology, Hong Kong, China","correspondingAuthor":false,"prefix":"","firstName":"Yiwen","middleName":"","lastName":"Shen","suffix":""},{"id":499091367,"identity":"3889eb56-646f-42a2-aea8-6b7f671a9a7a","order_by":2,"name":"Yunhe Mao","email":"","orcid":"","institution":"Department of Orthopedics, Orthopedic Research Institute, West China Hospital, Sichuan University, Chengdu, China","correspondingAuthor":false,"prefix":"","firstName":"Yunhe","middleName":"","lastName":"Mao","suffix":""},{"id":499091368,"identity":"8f2ffdf6-8e22-4886-968f-68883f621414","order_by":3,"name":"Sheyu 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Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Component network meta-analysis, Multicomponent interventions, Contribution","lastPublishedDoi":"10.21203/rs.3.rs-7350512/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7350512/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e\u003cp\u003eComponent Network Meta-Analysis (CNMA) extends standard NMA by enabling the decomposition of multicomponent interventions into individual component-level effect estimates. Quantifying the proportional contributions of pairwise comparisons is crucial for clinical interpretation and confidence rating, yet robust methods for this quantification within CNMA are currently lacking.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e\u003cp\u003eWe employed the shortest-path and random-walk approaches to utilize the hat matrix and design matrix derived from frequentist CNMA models. These methods systematically trace the composition of evidence at the component level and further quantify the proportional contribution of each pairwise comparison. A hypothetical dataset was used to illustrate the implementation process.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e\u003cp\u003eThis study outlines how the two approaches were adapted to address the complexity of composite interventions in CNMA. The random-walk method decomposes the CNMA network by splitting nodes that represent composite interventions, enabling precise tracking of evidence flow at the component level. In contrast, the shortest-path method bypasses conventional pathway traversal by identifying edge combinations that algebraically isolate the target components. When applied to the same dataset, the two methods generated distinct contribution profiles, reflecting their differing theoretical underpinnings.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e\u003cp\u003eBoth the shortest-path and random-walk approaches are theoretically applicable in CNMA contexts. However, the shortest-path approach is preferable for quantifying component-level evidence contributions due to its superior computational efficiency and robustness, making it the recommended choice for practical applications.\u003c/p\u003e","manuscriptTitle":"Estimating Evidence Contribution in Component Network Meta-Analysis through Shortest Path and Random Walk Approaches","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-13 03:06:23","doi":"10.21203/rs.3.rs-7350512/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"bcf6ded5-b083-4347-a526-19fb763e1f33","owner":[],"postedDate":"August 13th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-13T03:06:23+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-13 03:06:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7350512","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7350512","identity":"rs-7350512","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}