Network meta-analysis with dose-response relationships

Network meta-analysis with dose-response relationships | 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 Network meta-analysis with dose-response relationships Maria Petropoulou, Gerta Rücker, Guido Schwarzer This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7903334/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Jan, 2026 Read the published version in BMC Medical Research Methodology → Version 1 posted 10 You are reading this latest preprint version Abstract Background: Network meta-analysis (NMA) is a widely used method for synthesizing evidence from multiple interventions for a medical condition. However, NMA applications typically ignore the crucial role of drug dosage on intervention effects. Traditional NMAs either consider each intervention dose as an independent node or ignore the intervention dose, which may impact heterogeneity, inconsistency, or sparsity. Methods: This paper introduces a novel frequentist approach, termed dose-response network meta-analysis (DR-NMA), which explicitly models dose-response relationships across multiple interventions. The DR-NMA approach incorporates both linear and nonlinear dose-response relationships, including exponential, quadratic, fractional polynomials, and restricted cubic splines. DR-NMA allows for dose-dependent estimation and prediction of treatment effects across dose ranges, even in disconnected networks if common agents exist. The proposed methods are implemented in the R package netdose, enhancing accessibility and reproducibility. We illustrate the approach using clinical datasets on postoperative nausea and vomiting, as well as antidepressant treatments. Results: Our findings indicate that some dose-response NMA models yield substantially different results compared to standard NMA, emphasizing the critical importance of dose-response function selection in model performance. Conclusions: DR-NMA provides valuable insights into the dose-dependent effects of interventions, enhancing decision-making and offering perspectives beyond traditional methods. dose-response relationship Network meta-analysis Fractional polynomials Restricted cubic splines Full Text Additional Declarations No competing interests reported. Supplementary Files Additionalfile1.txt Additionalfile2.pdf Additionalfile3.pdf Additionalfile4.pdf Additionalfile5.pdf Additionalfile6.pdf Additionalfile7.pdf Cite Share Download PDF Status: Published Journal Publication published 13 Jan, 2026 Read the published version in BMC Medical Research Methodology → Version 1 posted Editorial decision: Revision requested 12 Nov, 2025 Reviews received at journal 11 Nov, 2025 Reviews received at journal 11 Nov, 2025 Reviewers agreed at journal 28 Oct, 2025 Reviewers agreed at journal 28 Oct, 2025 Reviewers invited by journal 24 Oct, 2025 Editor invited by journal 23 Oct, 2025 Editor assigned by journal 23 Oct, 2025 Submission checks completed at journal 23 Oct, 2025 First submitted to journal 20 Oct, 2025 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-7903334","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":539000300,"identity":"d95808bf-cadc-4883-9e84-d21e4db03732","order_by":0,"name":"Maria Petropoulou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYHAD5gYQKQciDjwgpPgAmGQEazEGCySQoiURTOLTotvAe/Dxxz02efwSiY2PeRjs0ueHHX4ItMVOTrcBuxazA3zJBgeepRVLzkhsNuZhSM7deDvNAKgl2djsAC4tPGYSBw4cTtxwI7FNmoeBOXfj7ASQlgOJ23BrMf+BpKU+3XB2+gdCWswYkLQcTpCXziFgy2G+ZIkzB4B+6XnYbDjH4LjhBumcggMJBnj8crz34IeKA8AQY08++OBNRbW8/Oz0zR8+VNjJ4dLCwMwDphIgPAMgOgBl4AYoWoBAvgGf6lEwCkbBKBiJAACYEmOztp0r0AAAAABJRU5ErkJggg==","orcid":"","institution":"University of Freiburg","correspondingAuthor":true,"prefix":"","firstName":"Maria","middleName":"","lastName":"Petropoulou","suffix":""},{"id":539000307,"identity":"4fa271c3-7e4e-4508-bd2e-48406609aec9","order_by":1,"name":"Gerta Rücker","email":"","orcid":"","institution":"University of Freiburg","correspondingAuthor":false,"prefix":"","firstName":"Gerta","middleName":"","lastName":"Rücker","suffix":""},{"id":539000309,"identity":"16023df8-0437-456f-8c56-e96616d36213","order_by":2,"name":"Guido Schwarzer","email":"","orcid":"","institution":"University of Freiburg","correspondingAuthor":false,"prefix":"","firstName":"Guido","middleName":"","lastName":"Schwarzer","suffix":""}],"badges":[],"createdAt":"2025-10-20 07:53:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7903334/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7903334/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s12874-025-02754-4","type":"published","date":"2026-01-13T16:29:56+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":95166414,"identity":"53478f4b-bc04-4a1c-9e9d-ea9f3a0ca738","added_by":"auto","created_at":"2025-11-05 05:13:00","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5356,"visible":true,"origin":"","legend":"","description":"","filename":"3a5f77888ebb4c8f90d1a329c606ff9c.json","url":"https://assets-eu.researchsquare.com/files/rs-7903334/v1/205b46f617cfaaf09c50c42f.json"},{"id":100614759,"identity":"b175166f-941e-4e8b-afe9-795f82594b40","added_by":"auto","created_at":"2026-01-19 17:24:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":903355,"visible":true,"origin":"","legend":"","description":"","filename":"DRNMA.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7903334/v1_covered_e67cee2b-8ee4-48d3-b5fe-ed340eba0279.pdf"},{"id":95226410,"identity":"af18daaa-c2b4-4189-a5dc-93376a7a3f1e","added_by":"auto","created_at":"2025-11-05 16:31:04","extension":"txt","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":14807,"visible":true,"origin":"","legend":"","description":"","filename":"Additionalfile1.txt","url":"https://assets-eu.researchsquare.com/files/rs-7903334/v1/8142b52de20b464adb9b4e80.txt"},{"id":95166411,"identity":"459d8722-de43-4233-8ae8-e6675c5d05c6","added_by":"auto","created_at":"2025-11-05 05:13:00","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":10717,"visible":true,"origin":"","legend":"","description":"","filename":"Additionalfile2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7903334/v1/506fbeff805ffd83c67ab04e.pdf"},{"id":95226159,"identity":"37260ca1-974f-47a8-a23e-a37dae87423e","added_by":"auto","created_at":"2025-11-05 16:26:47","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":29168,"visible":true,"origin":"","legend":"","description":"","filename":"Additionalfile3.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7903334/v1/2251b99d62e95f4dd30c3107.pdf"},{"id":95166417,"identity":"a1ceaace-fdda-47fe-9502-4ef0452870c9","added_by":"auto","created_at":"2025-11-05 05:13:01","extension":"pdf","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":34638,"visible":true,"origin":"","legend":"","description":"","filename":"Additionalfile4.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7903334/v1/4cd649fc3494c0dda2694cbe.pdf"},{"id":95227875,"identity":"9d96856b-23b3-4da9-ae04-00d85546ce31","added_by":"auto","created_at":"2025-11-05 16:33:03","extension":"pdf","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":56363,"visible":true,"origin":"","legend":"","description":"","filename":"Additionalfile5.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7903334/v1/4992322126c48f3e37ac880f.pdf"},{"id":95227077,"identity":"030fc573-3163-4b95-a156-c0fa5d6e7369","added_by":"auto","created_at":"2025-11-05 16:32:04","extension":"pdf","order_by":5,"title":"","display":"","copyAsset":false,"role":"supplement","size":9357,"visible":true,"origin":"","legend":"","description":"","filename":"Additionalfile6.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7903334/v1/03b4022dcd01e2a87315f903.pdf"},{"id":95166418,"identity":"1f20e6fa-8960-40c4-8d60-cb4f1e34c7c9","added_by":"auto","created_at":"2025-11-05 05:13:01","extension":"pdf","order_by":6,"title":"","display":"","copyAsset":false,"role":"supplement","size":72868,"visible":true,"origin":"","legend":"","description":"","filename":"Additionalfile7.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7903334/v1/44b4b79fa8f5c7594b1b767b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Network meta-analysis with dose-response relationships","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"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":"dose-response relationship, Network meta-analysis, Fractional polynomials, Restricted cubic splines","lastPublishedDoi":"10.21203/rs.3.rs-7903334/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7903334/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground:\u003c/strong\u003e Network meta-analysis (NMA) is a widely used method for synthesizing evidence from multiple interventions for a medical condition. However, NMA applications typically ignore the crucial role of drug dosage on intervention effects. Traditional NMAs either consider each intervention dose as an independent node or ignore the intervention dose, which may impact heterogeneity, inconsistency, or sparsity.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods: \u003c/strong\u003eThis paper introduces a novel frequentist approach, termed dose-response network meta-analysis (DR-NMA), which explicitly models dose-response relationships across multiple interventions. The DR-NMA approach incorporates both linear and nonlinear dose-response relationships, including exponential, quadratic, fractional polynomials, and restricted cubic splines. DR-NMA allows for dose-dependent estimation and prediction of treatment effects across dose ranges, even in disconnected networks if common agents exist. The proposed methods are implemented in the R package netdose, enhancing accessibility and reproducibility. We illustrate the approach using clinical datasets on postoperative nausea and vomiting, as well as antidepressant treatments.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults:\u003c/strong\u003e Our findings indicate that some dose-response NMA models yield substantially different results compared to standard NMA, emphasizing the critical importance of dose-response function selection in model performance.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusions:\u003c/strong\u003e DR-NMA provides valuable insights into the dose-dependent effects of interventions, enhancing decision-making and offering perspectives beyond traditional methods.\u003c/p\u003e","manuscriptTitle":"Network meta-analysis with dose-response relationships","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-05 05:12:56","doi":"10.21203/rs.3.rs-7903334/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-12T16:56:42+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-11T19:20:26+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-11T09:21:40+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"228398113106316016909611501816795606315","date":"2025-10-28T13:18:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"139857526666610334174351143725948053043","date":"2025-10-28T07:47:02+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-24T07:43:49+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-10-23T21:13:29+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-23T05:59:29+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-23T05:58:39+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Medical Research Methodology","date":"2025-10-20T07:50:01+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":"ce4642e5-734f-4767-8af1-98e863cd969d","owner":[],"postedDate":"November 5th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-01-19T16:49:07+00:00","versionOfRecord":{"articleIdentity":"rs-7903334","link":"https://doi.org/10.1186/s12874-025-02754-4","journal":{"identity":"bmc-medical-research-methodology","isVorOnly":false,"title":"BMC Medical Research Methodology"},"publishedOn":"2026-01-13 16:29:56","publishedOnDateReadable":"January 13th, 2026"},"versionCreatedAt":"2025-11-05 05:12:56","video":"","vorDoi":"10.1186/s12874-025-02754-4","vorDoiUrl":"https://doi.org/10.1186/s12874-025-02754-4","workflowStages":[]},"version":"v1","identity":"rs-7903334","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7903334","identity":"rs-7903334","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}