A general framework for using two-stage meta-analysis with individual participant data to predict individualized treatment effects

A general framework for using two-stage meta-analysis with individual participant data to predict individualized treatment effects | 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 A general framework for using two-stage meta-analysis with individual participant data to predict individualized treatment effects Marta Mainetti, Konstantina Chalkou, Frederik Luca Philipona, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9422615/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract Background A key application of an individual participant data meta-analysis (IPD-MA) of randomized controlled trials is to predict individualized treatment effects (ITEs). A two-stage approach is often employed, for example when data from trials reside in different servers; however, analyses are typically limited to regression-based models. We hereby present a general framework for two-stage IPD-MA for predicting ITE for a continuous outcome, applicable to any type of statistical or machine learning model. We also present a simulation study to assess the performance of the methods described here. Methods We outline different types of models that can be used for trial-specific analyses at the first stage, including ordinary least squares (OLS) and penalized regressions, machine learning (ML) models, and Bayesian models. Subsequently, we describe alternative methods to synthesize results at the second stage and predict treatment effects on new individuals. The second-stage methods were chosen based on the first-stage model used, and include: (a) multivariate meta-analyses of regression coefficients, applicable to OLS; (b) weighted average of predicted ITEs, applicable to all models, with weights obtained via either bootstrapping or via auxiliary OLS models; (c) multivariate Bayesian meta-analysis, applicable to Bayesian regressions; (d) weighted mixing of posterior distributions, applicable to all Bayesian models. A simulation study assessed the performance of all feasible combinations of first- and second-stage approaches under various scenarios in terms of median absolute error of predicted ITEs. Results The performance of methods in simulations depended on the sample size, the heterogeneity of treatment effects, and the assumed form of effect modification. In scenarios with complex treatment-covariate interactions and large samples, ML models substantially outperformed regression methods. Conversely, in scenarios with linear effect modification, regression models performed better. Among second-stage methods for pooling ML models, we found that weighting based on an auxiliary OLS model was better than bootstrapping. We found no important differences between frequentist and Bayesian regression-based methods. Shrinkage models provided only modest improvements over unpenalized regression. Conclusions Our framework for predicting patient-level treatment effects using two-stage IPD-MA can accommodate any type of statistical or machine learning model. The optimal method to use depends on the data generating mechanism, which in practice is unknown, and should be decided following internal validation. Individualized treatment effect Individual participant data meta-analysis personalized medicine clinical prediction modelling Full Text Additional Declarations No competing interests reported. Supplementary Files supplementalmaterial.docx Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 12 May, 2026 Reviewers agreed at journal 07 May, 2026 Reviewers agreed at journal 05 May, 2026 Reviewers invited by journal 05 May, 2026 Editor invited by journal 17 Apr, 2026 Editor assigned by journal 17 Apr, 2026 Submission checks completed at journal 17 Apr, 2026 First submitted to journal 15 Apr, 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-9422615","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":638864706,"identity":"c864d214-0642-4b85-a579-7cac801f248d","order_by":0,"name":"Marta 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A two-stage approach is often employed, for example when data from trials reside in different servers; however, analyses are typically limited to regression-based models. We hereby present a general framework for two-stage IPD-MA for predicting ITE for a continuous outcome, applicable to any type of statistical or machine learning model. We also present a simulation study to assess the performance of the methods described here.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eWe outline different types of models that can be used for trial-specific analyses at the first stage, including ordinary least squares (OLS) and penalized regressions, machine learning (ML) models, and Bayesian models. Subsequently, we describe alternative methods to synthesize results at the second stage and predict treatment effects on new individuals. The second-stage methods were chosen based on the first-stage model used, and include: (a) multivariate meta-analyses of regression coefficients, applicable to OLS; (b) weighted average of predicted ITEs, applicable to all models, with weights obtained via either bootstrapping or via auxiliary OLS models; (c) multivariate Bayesian meta-analysis, applicable to Bayesian regressions; (d) weighted mixing of posterior distributions, applicable to all Bayesian models. A simulation study assessed the performance of all feasible combinations of first- and second-stage approaches under various scenarios in terms of median absolute error of predicted ITEs.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eThe performance of methods in simulations depended on the sample size, the heterogeneity of treatment effects, and the assumed form of effect modification. In scenarios with complex treatment-covariate interactions and large samples, ML models substantially outperformed regression methods. Conversely, in scenarios with linear effect modification, regression models performed better. Among second-stage methods for pooling ML models, we found that weighting based on an auxiliary OLS model was better than bootstrapping. We found no important differences between frequentist and Bayesian regression-based methods. Shrinkage models provided only modest improvements over unpenalized regression.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eOur framework for predicting patient-level treatment effects using two-stage IPD-MA can accommodate any type of statistical or machine learning model. The optimal method to use depends on the data generating mechanism, which in practice is unknown, and should be decided following internal validation.\u003c/p\u003e","manuscriptTitle":"A general framework for using two-stage meta-analysis with individual participant data to predict individualized treatment effects","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-14 16:44:01","doi":"10.21203/rs.3.rs-9422615/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-05-12T08:58:01+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"274082754549457959399076711647011855286","date":"2026-05-07T16:49:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"72175407005789720729031947371877862509","date":"2026-05-06T03:43:03+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-05-05T15:59:14+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-04-17T19:19:59+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-17T14:58:58+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-17T14:58:00+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Medical Research Methodology","date":"2026-04-15T06:06:49+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":"355cc292-ca25-4971-8338-c6f7fbaba0c8","owner":[],"postedDate":"May 14th, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"","date":"2026-05-12T08:58:01+00:00","index":54,"fulltext":""},{"type":"reviewerAgreed","content":"274082754549457959399076711647011855286","date":"2026-05-07T16:49:05+00:00","index":49,"fulltext":""},{"type":"reviewerAgreed","content":"72175407005789720729031947371877862509","date":"2026-05-06T03:43:03+00:00","index":44,"fulltext":""},{"type":"reviewersInvited","content":"20","date":"2026-05-05T15:59:14+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-14T16:44:01+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-14 16:44:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9422615","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9422615","identity":"rs-9422615","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}