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This article proposes a novel bivariate time\u2010varying coefficients logistic regression model for addressing the combined longitudinal biomarkers. Using the B\u2010splines method to estimate the proposed model, we can effectively combine multiple longitudinal biomarkers and improve diagnostic accuracy. We show that the proposed method is theoretically consistent. And it exhibits superior performance compared to the existing method, as presented through numerical results. The proposed method is verified in a study on predicting the probability of onset of future cardiovascular events for type 2 diabetic patients. The longitudinal biomarkers, HbA1c and LDL\u2010C, are considered in this study. We demonstrate that the combined longitudinal biomarkers significantly improved disease diagnostic accuracy over only a combination of the latest measured biomarkers in most cases.<\/jats:p>","DOI":"10.1002\/sim.10318","type":"journal-article","created":{"date-parts":[[2025,2,6]],"date-time":"2025-02-06T05:06:51Z","timestamp":1738818411000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Time\u2010Dependent\n                    <scp>ROC<\/scp>\n                    Curve for Multiple Longitudinal Biomarkers and Its Application in Diagnosing Cardiovascular Events"],"prefix":"10.1002","volume":"44","author":[{"given":"Lizhe","family":"Sun","sequence":"first","affiliation":[{"name":"School of Statistics Shanxi University of Finance and Economics  Taiyuan Shanxi People's Republic of China"},{"name":"Beijing International Center for Mathematical Research Peking University  Beijing People's Republic of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pingyuan","family":"Wei","sequence":"additional","affiliation":[{"name":"Beijing International Center for Mathematical Research Peking University  Beijing People's Republic of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5061-4367","authenticated-orcid":false,"given":"Jie","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences Capital Normal University  Beijing People's Republic of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiao\u2010Hua","family":"Zhou","sequence":"additional","affiliation":[{"name":"Beijing International Center for Mathematical Research Peking University  Beijing People's Republic of China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,2,6]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12933-018-0728-6"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0140-6736(10)60484-9"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00125-011-2404-1"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.18203\/2320-6012.ijrms20172998"},{"key":"e_1_2_10_6_1","first-page":"1","article-title":"Comparative Effectiveness of Statins on Non\u2010High Density Lipoprotein Cholesterol in People With Diabetes and at Risk of Cardiovascular Disease: Systematic Review and Network Meta\u2010Analysis","volume":"376","author":"Alex H.","year":"2022","journal-title":"BMJ"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2000.00337.x"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2005.030814.x"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.4178"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.1177\/0962280216680239"},{"key":"e_1_2_10_11_1","volume-title":"Statistical Methods in Diagnostic Medicine","author":"Xiao\u2010Hua Z.","year":"2011"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1186\/s12874-017-0332-6"},{"key":"e_1_2_10_13_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2006.00726.x"},{"key":"e_1_2_10_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.9180"},{"key":"e_1_2_10_15_1","first-page":"1102","article-title":"Kernel Estimation of Bivariate Time\u2010Varying Coefficient Model for Longitudinal Data With Terminal Event","volume":"119","author":"Yue W.","year":"2023","journal-title":"Journal of the American Statistical Association"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2005.00441.x"},{"key":"e_1_2_10_17_1","doi-asserted-by":"publisher","DOI":"10.1056\/NEJMoa1603827"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10985-013-9251-y"},{"key":"e_1_2_10_19_1","doi-asserted-by":"publisher","DOI":"10.1002\/cjs.11498"},{"issue":"4","key":"e_1_2_10_20_1","first-page":"530","article-title":"Comparison of Two Frameworks for Analyzing Longitudinal Data","volume":"36","author":"Jie Z.","year":"2021","journal-title":"Statistical Science"},{"key":"e_1_2_10_21_1","volume-title":"Stochastic Processes","author":"Ross S. 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