When to Use Precision-Weighted Cross-Validation in Meta-Regression: A Simulation Study and Empirical Comparison for consideration as a Methodology article in Systematic Reviews

When to Use Precision-Weighted Cross-Validation in Meta-Regression: A Simulation Study and Empirical Comparison for consideration as a Methodology article in Systematic Reviews | 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 When to Use Precision-Weighted Cross-Validation in Meta-Regression: A Simulation Study and Empirical Comparison for consideration as a Methodology article in Systematic Reviews Mahmood Ahmad, Lucia Lucia Garcia Perez This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7852293/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Background: Cross-validation is regularly used for assessing predictive performance while doing meta-regression. There is however no consensus on which predictions should be evaluated using precision weights (inversely proportional to total study variance) or alternatively equal weights. This choice can affect cross-validated R² estimates and the also downstream inferences about model performance. Methods: We coded a leave-one-out cross-validation for meta-regression with both precision-weighted and unweighted evaluation metrics which usedmoment-based estimators for between-study heterogeneity. Performance was then evaluated across 32 simulated scenarios (300 replications each) which varied in sample size (k=10-40), the number of moderators (p=1-2), heterogeneity (τ²=0.05-0.20), true R²het (0%-25%), and the sampling variance structure (this was homogeneous gamma-distributed vs. heterogeneous with "anchor" studies then having extreme precision). We also tried analysing seven real meta-analytic datasets from education, medicine, and public health from R. Our diagnostic criteria were based on I² statistics and weight dispersion (coefficient of variation, Gini coefficient) which were developed to guide the method selection. Results: In our simulations with homogeneous sampling variances, weighted and unweighted cross-validation were closely in agreement(mean |ΔCV|=2.6 percentage points). Theheterogeneous variances including anchor studies, unweighted cross-validation then produced implausible estimates exceeding apparent R² by >20 percentage points in 81% of scenarios (vs. 0% for weighted). In our seven empirical datasets, the mean absolute difference resulted in 14.8pp (range: 0-81pp). In the datasets the Passive Smoking dataset showed the widest discrepancy: unweighted CV estimated 81.8% R² vs. 0.6% for weighted CV (apparent R² = 45.5%). The truncation of negative τ²CV estimates to zero occurred in 23% of weighted and 8% of unweighted scenarios. We recommended precision-weighted cross-validation for 6 of 7 datasets based on diagnostic criteria (I² > 50% or weight CV > 0.6). Conclusions: We suggest Precision-weighted cross-validation should be considered as an approach in meta-regression, especially when I² > 50% or weight dispersion is high (CV > 0.6). Unweighted cross-validation can often produce inflated estimates when sampling variances are heterogeneous, this could lead to in turn incorrect conclusions about predictive performance. The choice of evaluation metric may have important implications for model assessment in many meta-analysis. Meta-regression cross-validation predictive performance heterogeneity precision weighting model validation leave-one-out cross-validation Figures Figure 1 Figure 2 Figure 3 Figure 4 Full Text Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 03 Dec, 2025 Reviewers invited by journal 02 Dec, 2025 Editor assigned by journal 25 Nov, 2025 First submitted to journal 27 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. 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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-7852293","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":554273806,"identity":"68091acb-4bf6-48d5-8ad0-4dc6655a741c","order_by":0,"name":"Mahmood 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4","display":"","copyAsset":false,"role":"figure","size":836088,"visible":true,"origin":"","legend":"\u003cp\u003eFifteen meta-analysis\u003c/p\u003e","description":"","filename":"Fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-7852293/v1/0c728891189b1ac910b341af.png"},{"id":97677839,"identity":"1bf952a1-8eb4-4701-a14e-efd30309ee41","added_by":"auto","created_at":"2025-12-08 09:54:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2960850,"visible":true,"origin":"","legend":"","description":"","filename":"MetaRegressionCVManuscriptRevised5.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7852293/v1_covered_0146054e-ba45-42c0-a61c-cc99fda9b165.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eWhen to Use Precision-Weighted Cross-Validation in Meta-Regression: A Simulation Study and Empirical Comparison for consideration as a Methodology article in Systematic Reviews\u003c/p\u003e","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":"systematic-reviews","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"sysr","sideBox":"Learn more about [Systematic Reviews](http://systematicreviewsjournal.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/sysr/default.aspx","title":"Systematic Reviews","twitterHandle":"@MedicalEvidence","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Meta-regression, cross-validation, predictive performance, heterogeneity, precision weighting, model validation, leave-one-out cross-validation","lastPublishedDoi":"10.21203/rs.3.rs-7852293/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7852293/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBackground: Cross-validation is regularly used for assessing predictive performance while doing meta-regression. There is however no consensus on which predictions should be evaluated using precision weights (inversely proportional to total study variance) or alternatively equal weights. This choice \u0026nbsp;can affect cross-validated R² estimates and the also downstream inferences about model performance.\u003c/p\u003e\n\u003cp\u003eMethods: We coded a \u0026nbsp;leave-one-out cross-validation for meta-regression with both precision-weighted and unweighted evaluation metrics which usedmoment-based estimators for between-study heterogeneity. Performance was then evaluated across 32 simulated scenarios (300 replications each) which varied in sample size (k=10-40), the number of moderators (p=1-2), heterogeneity (τ²=0.05-0.20), true R²het (0%-25%), and the sampling variance structure (this was homogeneous gamma-distributed vs. heterogeneous with \"anchor\" studies then having extreme precision). We also tried analysing seven real meta-analytic datasets from education, medicine, and public health from R. Our diagnostic criteria were based on I² statistics and weight dispersion (coefficient of variation, Gini coefficient) which were developed to guide the method selection.\u003c/p\u003e\n\u003cp\u003eResults: In our simulations with homogeneous sampling variances, weighted and unweighted cross-validation were closely in agreement(mean |ΔCV|=2.6 percentage points). Theheterogeneous variances including anchor studies, unweighted cross-validation then produced implausible estimates exceeding apparent R² by \u0026gt;20 percentage points in 81% of scenarios (vs. 0% for weighted). In our seven empirical datasets, the mean absolute difference resulted in \u0026nbsp;14.8pp (range: 0-81pp). In the datasets the Passive Smoking dataset showed the widest discrepancy: unweighted CV estimated 81.8% R² vs. 0.6% for weighted CV (apparent R² = 45.5%). The truncation of negative τ²CV estimates to zero occurred in 23% of weighted and 8% of unweighted scenarios. We recommended precision-weighted cross-validation \u0026nbsp;for 6 of 7 datasets based on diagnostic criteria (I² \u0026gt; 50% or weight CV \u0026gt; 0.6).\u003c/p\u003e\n\u003cp\u003eConclusions: We suggest Precision-weighted cross-validation should be considered as an \u0026nbsp;approach in meta-regression, especially when I² \u0026gt; 50% or weight dispersion is high (CV \u0026gt; 0.6). Unweighted cross-validation can often produce inflated estimates when sampling variances are heterogeneous, this could lead to in turn \u0026nbsp;incorrect conclusions about predictive performance. The \u0026nbsp;choice of evaluation metric may have important implications for model assessment in many meta-analysis.\u003c/p\u003e","manuscriptTitle":"When to Use Precision-Weighted Cross-Validation in Meta-Regression: A Simulation Study and Empirical Comparison for consideration as a Methodology article in Systematic Reviews","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-04 23:22:14","doi":"10.21203/rs.3.rs-7852293/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2025-12-03T05:30:21+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-02T20:20:36+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-25T06:26:42+00:00","index":"","fulltext":""},{"type":"submitted","content":"Systematic Reviews","date":"2025-10-27T09:41:31+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"systematic-reviews","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"sysr","sideBox":"Learn more about [Systematic Reviews](http://systematicreviewsjournal.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/sysr/default.aspx","title":"Systematic Reviews","twitterHandle":"@MedicalEvidence","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"44093271-68e6-4149-b798-0dd319dc93d2","owner":[],"postedDate":"December 4th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-12-04T23:22:15+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-04 23:22:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7852293","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7852293","identity":"rs-7852293","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}