Variational biomarker pooling with calibration for time-to-event outcomes across multiple clinical studies

Variational biomarker pooling with calibration for time-to-event outcomes across multiple clinical studies | 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 Variational biomarker pooling with calibration for time-to-event outcomes across multiple clinical studies Jiali Song, Zhiwei Rong, Yan Hou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8764450/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 Mar, 2026 Read the published version in BMC Medical Research Methodology → Version 1 posted 10 You are reading this latest preprint version Abstract Background Biomarkers are widely used in oncology research to study disease progression and predict survival outcomes. Pooling biomarker data across studies can improve precision, but pooled analyses are often affected by assay heterogeneity. Many studies use calibration designs because re-assaying all biospecimens on a reference platform is impractical. In pooled analyses, calibration can be incomplete when some studies have no reference measurements. This setting can be viewed as covariate measurement error in time-to-event models. Most existing methods were developed for single-cohort designs with validation or replicate measurements, and they do not directly accommodate study-specific calibration with incomplete reference data in pooled survival analyses. Methods In this paper, we propose Variational Inference-Based Biomarker Pooling (VIBP) for censored survival data. VIBP treats the target biomarker as latent and jointly models study-specific calibration and the survival outcome using parametric survival models. Variational inference provides scalable estimation, and uncertainty is quantified using bootstrap. Results Through extensive simulation studies for exponential and Weibull survival data, we find that VIBP consistently provides estimates with lower bias, smaller mean squared error, and near-nominal 95% coverage across a wide range of effect sizes and censoring rates. We further apply VIBP to a real-world dataset to evaluate the association between DJ-1 protein levels and overall survival in lung squamous cell carcinoma. The results highlight the ability of VIBP to recover meaningful survival associations under sparse and heterogeneous calibration information. Conclusions The proposed method provides accurate and robust estimation in the presence of inter-study variability and partially observed reference measurements, and it remains applicable even when some studies have no reference data. biomarker pooling mean-field variational inference inter-study variability calibration Full Text Additional Declarations No competing interests reported. Supplementary Files supplementary.xlsx supplementary.docx Cite Share Download PDF Status: Published Journal Publication published 23 Mar, 2026 Read the published version in BMC Medical Research Methodology → Version 1 posted Editorial decision: Revision requested 25 Feb, 2026 Reviews received at journal 24 Feb, 2026 Reviews received at journal 11 Feb, 2026 Reviewers agreed at journal 10 Feb, 2026 Reviewers agreed at journal 08 Feb, 2026 Reviewers invited by journal 08 Feb, 2026 Editor invited by journal 05 Feb, 2026 Editor assigned by journal 02 Feb, 2026 Submission checks completed at journal 02 Feb, 2026 First submitted to journal 02 Feb, 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. 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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-8764450","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":589382061,"identity":"b308ec59-3740-40ef-959d-b09a75a9e4d0","order_by":0,"name":"Jiali Song","email":"","orcid":"","institution":"Peking University","correspondingAuthor":false,"prefix":"","firstName":"Jiali","middleName":"","lastName":"Song","suffix":""},{"id":589382062,"identity":"1fece0ef-c4b8-47eb-9ef9-c6d8c58688ab","order_by":1,"name":"Zhiwei Rong","email":"","orcid":"","institution":"Tianjin Medical 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Pooling biomarker data across studies can improve precision, but pooled analyses are often affected by assay heterogeneity. Many studies use calibration designs because re-assaying all biospecimens on a reference platform is impractical. In pooled analyses, calibration can be incomplete when some studies have no reference measurements. This setting can be viewed as covariate measurement error in time-to-event models. Most existing methods were developed for single-cohort designs with validation or replicate measurements, and they do not directly accommodate study-specific calibration with incomplete reference data in pooled survival analyses.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eIn this paper, we propose Variational Inference-Based Biomarker Pooling (VIBP) for censored survival data. VIBP treats the target biomarker as latent and jointly models study-specific calibration and the survival outcome using parametric survival models. Variational inference provides scalable estimation, and uncertainty is quantified using bootstrap.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eThrough extensive simulation studies for exponential and Weibull survival data, we find that VIBP consistently provides estimates with lower bias, smaller mean squared error, and near-nominal 95% coverage across a wide range of effect sizes and censoring rates. We further apply VIBP to a real-world dataset to evaluate the association between DJ-1 protein levels and overall survival in lung squamous cell carcinoma. 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