{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T20:58:16Z","timestamp":1781643496321,"version":"3.54.5"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T00:00:00Z","timestamp":1774224000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T00:00:00Z","timestamp":1777507200000},"content-version":"vor","delay-in-days":38,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["82373682"],"award-info":[{"award-number":["82373682"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Med Res Methodol"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>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.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>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.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>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.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusions<\/jats:title>\n                    <jats:p>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.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1186\/s12874-026-02827-y","type":"journal-article","created":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T01:04:57Z","timestamp":1774227897000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Variational biomarker pooling with calibration for time-to-event outcomes across multiple clinical studies"],"prefix":"10.1186","volume":"26","author":[{"given":"Jiali","family":"Song","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiwei","family":"Rong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yan","family":"Hou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,3,23]]},"reference":[{"key":"2827_CR1","unstructured":"U.S. Food and Drug Administration. FDA Facts: Biomarkers and Surrogate Endpoints 2017 [updated December 21, 2017. Available from: https:\/\/www.fda.gov\/about-fda\/innovation-fda\/fda-facts-biomarkers-and-surrogate-endpoints."},{"issue":"2","key":"2827_CR2","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1602\/neurorx.1.2.189","volume":"1","author":"R Katz","year":"2004","unstructured":"Katz R. Biomarkers and surrogate markers: an FDA perspective. NeuroRx. 2004;1(2):189\u201395.","journal-title":"NeuroRx"},{"issue":"1","key":"2827_CR3","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1002\/cpt.136","volume":"98","author":"S Amur","year":"2015","unstructured":"Amur S, LaVange L, Zineh I, Buckman\u2010Garner S, Woodcock J. Biomarker qualification: toward a multiple stakeholder framework for biomarker development, regulatory acceptance, and utilization. Clin Pharmacol Ther. 2015;98(1):34\u201346.","journal-title":"Clin Pharmacol Ther"},{"key":"2827_CR4","unstructured":"U.S. Food and Drug Administration. Biomarker Qualification: Evidentiary Framework 2018 [updated May 7, 2020. Available from: https:\/\/www.fda.gov\/regulatory-information\/search-fda-guidance-documents\/biomarker-qualification-evidentiary-framework."},{"issue":"3","key":"2827_CR5","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1093\/biostatistics\/kxz051","volume":"22","author":"A Sloan","year":"2021","unstructured":"Sloan A, Smith-Warner SA, Ziegler RG, Wang M. Statistical methods for biomarker data pooled from multiple nested case\u2013control studies. Biostatistics. 2021;22(3):541\u201357.","journal-title":"Biostatistics"},{"issue":"8","key":"2827_CR6","doi-asserted-by":"publisher","first-page":"1303","DOI":"10.1002\/sim.8052","volume":"38","author":"A Sloan","year":"2019","unstructured":"Sloan A, Song Y, Gail MH, Betensky R, Rosner B, Ziegler RG, et al. Design and analysis considerations for combining data from multiple biomarker studies. Stat Med. 2019;38(8):1303\u201320.","journal-title":"Stat Med"},{"issue":"1","key":"2827_CR7","first-page":"51","volume":"3","author":"SE Hankinson","year":"1994","unstructured":"Hankinson SE, Manson JE, London SJ, Willett WC, Speizer FE. Laboratory reproducibility of endogenous hormone levels in postmenopausal women. Cancer Epidemiol Biomarkers Prev. 1994;3(1):51\u20136.","journal-title":"Cancer Epidemiol Biomarkers Prev"},{"issue":"4","key":"2827_CR8","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1177\/1040638714535402","volume":"26","author":"MM Reising","year":"2014","unstructured":"Reising MM, Schumann KR, Crossley BM, Glas PS, Jacobson RH, Toohey-Kurth KL, et al. Methods comparison: An alternative approach for evaluating the impact of a modification to a validated assay. J Vet Diagn Invest. 2014;26(4):480\u20137.","journal-title":"J Vet Diagn Invest"},{"issue":"27","key":"2827_CR9","doi-asserted-by":"publisher","first-page":"5077","DOI":"10.1002\/sim.10218","volume":"43","author":"S Byers","year":"2024","unstructured":"Byers S, Song X. Nonparametric biomarker based treatment selection with reproducibility data. Stat Med. 2024;43(27):5077\u201387.","journal-title":"Stat Med"},{"issue":"1","key":"2827_CR10","doi-asserted-by":"publisher","first-page":"e78644","DOI":"10.1371\/journal.pone.0078644","volume":"9","author":"SR Zhao","year":"2014","unstructured":"Zhao SR, Fung-Leung WP, Bittner A, Ngo K, Liu XJ. Comparison of RNA-Seq and microarray in transcriptome profiling of activated T cells. PLoS One. 2014;9(1):e78644.","journal-title":"PLoS One"},{"issue":"1","key":"2827_CR11","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1038\/nrg2484","volume":"10","author":"Z Wang","year":"2009","unstructured":"Wang Z, Gerstein M, Snyder M. RNA-Seq: a revolutionary tool for transcriptomics. Nat Rev Genet. 2009;10(1):57\u201363.","journal-title":"Nat Rev Genet"},{"issue":"2","key":"2827_CR12","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1093\/biomet\/69.2.331","volume":"69","author":"RL Prentice","year":"1982","unstructured":"Prentice RL. Covariate measurement errors and parameter-estimation in a failure time regression-model. Biometrika. 1982;69(2):331\u201342.","journal-title":"Biometrika"},{"key":"2827_CR13","doi-asserted-by":"crossref","unstructured":"Wang CY, Hwang WH, Song X. Biomarker data with measurement error in medical research: a literature review. Wires Comput Stat. 2024;16(1):e1641.","DOI":"10.1002\/wics.1641"},{"key":"2827_CR14","doi-asserted-by":"crossref","unstructured":"Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM. Measurement error in nonlinear models: a modern perspective. 2nd ed. Chapman & Hall; 2006.","DOI":"10.1201\/9781420010138"},{"issue":"4","key":"2827_CR15","doi-asserted-by":"publisher","first-page":"1179","DOI":"10.1093\/ajcn\/65.4.1179S","volume":"65","author":"D Spiegelman","year":"1997","unstructured":"Spiegelman D, McDermott A, Rosner B. Regression calibration method for correcting measurement-error bias in nutritional epidemiology. Am J Clin Nutr. 1997;65(4):1179\u201386.","journal-title":"Am J Clin Nutr"},{"key":"2827_CR16","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1111\/1467-9868.00317","volume":"63","author":"SX Xie","year":"2001","unstructured":"Xie SX, Wang CY, Prentice RL. A risk set calibration method for failure time regression by using a covariate reliability sample. J R Stat Soc Ser B Stat Methodol. 2001;63:855\u201370.","journal-title":"J R Stat Soc Ser B Stat Methodol"},{"issue":"428","key":"2827_CR17","doi-asserted-by":"publisher","first-page":"1314","DOI":"10.1080\/01621459.1994.10476871","volume":"89","author":"JR Cook","year":"1994","unstructured":"Cook JR, Stefanski LA. Simulation-extrapolation estimation in parametric measurement error models. J Am Stat Assoc. 1994;89(428):1314\u201328.","journal-title":"J Am Stat Assoc"},{"issue":"1","key":"2827_CR18","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1093\/biomet\/77.1.127","volume":"77","author":"T Nakamura","year":"1990","unstructured":"Nakamura T. Corrected Score Function for Errors-in-Variables Models - Methodology and Application to Generalized Linear-Models. Biometrika. 1990;77(1):127\u201337.","journal-title":"Biometrika"},{"issue":"4","key":"2827_CR19","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1111\/1467-9469.00310","volume":"29","author":"CC Hu","year":"2002","unstructured":"Hu CC, Lin DY. Cox regression with covariate measurement error. Scand J Stat. 2002;29(4):637\u201355.","journal-title":"Scand J Stat"},{"issue":"2","key":"2827_CR20","doi-asserted-by":"publisher","first-page":"1485","DOI":"10.1111\/biom.13618","volume":"79","author":"A Sloan","year":"2023","unstructured":"Sloan A, Cheng C, Rosner B, Ziegler RG, Smith-Warner SA, Wang ML. A repeated measures approach to pooled and calibrated biomarker data. Biometrics. 2023;79(2):1485\u201395.","journal-title":"Biometrics"},{"key":"2827_CR21","doi-asserted-by":"crossref","unstructured":"Rong ZW, Song JL, Sun FY, Zhang CB, Mi L, Song YQ, et al. Bayesian biomarker effect estimate for combining data from multiple biomarker studies. J Appl Stat. 2026;53(4):614\u201332.","DOI":"10.1080\/02664763.2025.2528362"},{"issue":"2","key":"2827_CR22","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1111\/j.2517-6161.1984.tb01288.x","volume":"46","author":"PJ Green","year":"1984","unstructured":"Green PJ. Iteratively Reweighted Least-Squares for Maximum-Likelihood Estimation, and Some Robust and Resistant Alternatives. J Roy Stat Soc B. 1984;46(2):149\u201392.","journal-title":"J Roy Stat Soc B"},{"issue":"3","key":"2827_CR23","doi-asserted-by":"publisher","first-page":"370","DOI":"10.2307\/2344614","volume":"135","author":"JA Nelder","year":"1972","unstructured":"Nelder JA, Wedderburn RWM. Generalized linear models. J R Stat Soc Series A (General). 1972;135(3):370\u201384.","journal-title":"J R Stat Soc Series A (General)"},{"issue":"518","key":"2827_CR24","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","volume":"112","author":"DM Blei","year":"2017","unstructured":"Blei DM, Kucukelbir A, McAuliffe JD. Variational inference: a review for statisticians. J Am Stat Assoc. 2017;112(518):859\u201377.","journal-title":"J Am Stat Assoc"},{"issue":"2","key":"2827_CR25","doi-asserted-by":"publisher","first-page":"790","DOI":"10.1016\/j.csda.2006.10.028","volume":"52","author":"G Consonni","year":"2007","unstructured":"Consonni G, Marin JM. Mean-field variational approximate Bayesian inference for latent variable models. Comput Stat Data Anal. 2007;52(2):790\u20138.","journal-title":"Comput Stat Data Anal"},{"issue":"1","key":"2827_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1214\/aos\/1176344552","volume":"7","author":"B Efron","year":"1979","unstructured":"Efron B. Bootstrap methods: another look at the jackknife. Ann Stat. 1979;7(1):1\u201326.","journal-title":"Ann Stat"},{"issue":"4","key":"2827_CR27","doi-asserted-by":"publisher","first-page":"734","DOI":"10.1093\/oxfordjournals.aje.a115715","volume":"132","author":"B Rosner","year":"1990","unstructured":"Rosner B, Spiegelman D, Willett WC. Correction of logistic-regression relative risk estimates and confidence-intervals for measurement error - the case of multiple covariates measured with error. Am J Epidemiol. 1990;132(4):734\u201345.","journal-title":"Am J Epidemiol"},{"issue":"24","key":"2827_CR28","doi-asserted-by":"publisher","first-page":"4279","DOI":"10.1002\/sim.2673","volume":"25","author":"A Burton","year":"2006","unstructured":"Burton A, Altman DG, Royston P, Holder RL. The design of simulation studies in medical statistics. Stat Med. 2006;25(24):4279\u201392.","journal-title":"Stat Med"},{"key":"2827_CR29","doi-asserted-by":"crossref","unstructured":"Wang L, Wei L, Miao SX, Zhang W. Clinical value of serum DJ-1 in lung adenocarcinoma. Peerj. 2024;12:e16845.","DOI":"10.7717\/peerj.16845"},{"key":"2827_CR30","doi-asserted-by":"crossref","unstructured":"Jin W. Novel insights into PARK7 (DJ-1), a potential anti-cancer therapeutic target, and implications for cancer progression. J Clin Med. 2020;9(5):1256.","DOI":"10.3390\/jcm9051256"}],"container-title":["BMC Medical Research Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s12874-026-02827-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12874-026-02827-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12874-026-02827-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T20:40:00Z","timestamp":1781642400000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s12874-026-02827-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,23]]},"references-count":30,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["2827"],"URL":"https:\/\/doi.org\/10.1186\/s12874-026-02827-y","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-8764450\/v1","asserted-by":"object"}]},"ISSN":["1471-2288"],"issn-type":[{"value":"1471-2288","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,23]]},"assertion":[{"value":"2 February 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 March 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 March 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Since the simulated datasets did not involve any human data, ethics approval was not applicable; and the real data is publicly available, thus ethics approval was not required.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare no competing interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"97"}}