{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T15:07:45Z","timestamp":1779376065896,"version":"3.53.1"},"reference-count":36,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T00:00:00Z","timestamp":1775692800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000049","name":"National Institute on Aging","doi-asserted-by":"publisher","award":["1-R56-AG066693"],"award-info":[{"award-number":["1-R56-AG066693"]}],"id":[{"id":"10.13039\/100000049","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,4,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Longitudinal biomarker data and health outcomes are routinely collected in many studies to assess how biomarker trajectories predict health outcomes. Existing methods primarily focus on mean biomarker profiles, treating variability as a nuisance. However, excess variability may indicate system dysregulations that may be associated with poor outcomes. In this paper, we address the long-standing problem of using variability information of multiple longitudinal biomarkers in time-to-event analyses by formulating and studying a Bayesian joint model. We first model multiple longitudinal biomarkers, some of which are subject to limit-of-detection censoring. We then model the survival times by incorporating random effects and variances from the longitudinal component as predictors through threshold regression that admits nonproportional hazards. We demonstrate the operating characteristics of the proposed joint model through simulations and apply it to data from the Study of Women\u2019s Health Across the Nation to investigate the impact of the mean and variability of follicle-stimulating hormone and anti-M\u00fcllerian hormone on age at the final menstrual period.<\/jats:p>","DOI":"10.1093\/biomtc\/ujag080","type":"journal-article","created":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T11:48:30Z","timestamp":1776858510000},"source":"Crossref","is-referenced-by-count":0,"title":["Joint modeling of multiple longitudinal biomarkers and survival outcomes via threshold regression: variability as a predictor"],"prefix":"10.1093","volume":"82","author":[{"given":"Mingyan","family":"Yu","sequence":"first","affiliation":[{"name":"Department of Biostatistics, University of Michigan , Ann Arbor, MI 48109 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7582-669X","authenticated-orcid":false,"given":"Zhenke","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Michigan , Ann Arbor, MI 48109 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michelle M","family":"Hood","sequence":"additional","affiliation":[{"name":"Department of Epidemiology, University of Michigan , Ann Arbor, MI 48109 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1950-5397","authenticated-orcid":false,"given":"Carrie","family":"Karvonen-Gutierrez","sequence":"additional","affiliation":[{"name":"Department of Epidemiology, University of Michigan , Ann Arbor, MI 48109 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Siob\u00e1n D","family":"Harlow","sequence":"additional","affiliation":[{"name":"Department of Epidemiology, University of Michigan , Ann Arbor, MI 48109 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael R","family":"Elliott","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Michigan , Ann Arbor, MI 48109 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,5,21]]},"reference":[{"key":"2026052110403815800_bib1","doi-asserted-by":"crossref","first-page":"1855","DOI":"10.1002\/sim.8074","article-title":"Estimating the association between blood pressure variability and cardiovascular disease: an application using the ARIC study","volume":"38","author":"Barrett","year":"2019","journal-title":"Statistics in Medicine"},{"key":"2026052110403815800_bib2","doi-asserted-by":"crossref","DOI":"10.1002\/9781119437260","volume-title":"First Hitting Time Regression Models: Lifetime Data Analysis based on Underlying Stochastic Processes","author":"Caroni","year":"2017"},{"key":"2026052110403815800_bib3","doi-asserted-by":"crossref","first-page":"1642","DOI":"10.1214\/23-AOAS1852","article-title":"Variance as a predictor of health outcomes: Subject-level trajectories and variability of sex hormones to predict body fat changes in peri-and postmenopausal women","volume":"18","author":"Chen","year":"2024","journal-title":"The Annals of Applied Statistics"},{"key":"2026052110403815800_bib4","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1111\/j.1541-0420.2005.00448.x","article-title":"Joint models for multivariate longitudinal and multivariate survival data","volume":"62","author":"Chi","year":"2006","journal-title":"Biometrics"},{"key":"2026052110403815800_bib5","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1007\/s10985-022-09553-9","article-title":"A boosting first-hitting-time model for survival analysis in high-dimensional settings","volume":"29","author":"De\u00a0Bin","year":"2023","journal-title":"Lifetime Data Analysis"},{"key":"2026052110403815800_bib6","unstructured":"de\u00a0Valpine P., Paciorek C., Turek D., Michaud N., Anderson-Bergman C., Obermeyer F. (2025). NIMBLE: MCMC, particle filtering, and programmable hierarchical modeling. R package version 1.4.2. https:\/\/cran.r-project.org\/package=nimble, 10.5281\/zenodo.1211190"},{"key":"2026052110403815800_bib7","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1080\/10618600.2016.1172487","article-title":"Programming with models: writing statistical algorithms for general model structures with NIMBLE","volume":"26","author":"de\u00a0Valpine","year":"2017","journal-title":"Journal of Computational and Graphical Statistics"},{"key":"2026052110403815800_bib8","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1007\/s11009-015-9445-8","article-title":"Bayesian threshold regression model with random effects for recurrent events","volume":"17","author":"Economou","year":"2015","journal-title":"Methodology and Computing in Applied Probability"},{"key":"2026052110403815800_bib9","doi-asserted-by":"crossref","first-page":"e1862","DOI":"10.1210\/clinem\/dgz283","article-title":"Antimullerian hormone and impending menopause in late reproductive age: the study of women\u2019s health across the nation","volume":"105","author":"Finkelstein","year":"2020","journal-title":"The Journal of Clinical Endocrinology and Metabolism"},{"key":"2026052110403815800_bib10","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s10260-010-0150-z","article-title":"A joint-modeling approach to assess the impact of biomarker variability on the risk of developing clinical outcome","volume":"20","author":"Gao","year":"2011","journal-title":"Statistical Methods and Applications"},{"key":"2026052110403815800_bib11","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1214\/06-BA117A","article-title":"Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper)","volume":"1","author":"Gelman","year":"2006","journal-title":"Bayesian Analysis"},{"key":"2026052110403815800_bib12","doi-asserted-by":"crossref","DOI":"10.1201\/b16018","volume-title":"Bayesian Data Analysis","author":"Gelman","year":"2013"},{"key":"2026052110403815800_bib13","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1214\/20-BA1237","article-title":"Bayesian estimation of correlation matrices of longitudinal data","volume":"16","author":"Ghosh","year":"2021","journal-title":"Bayesian Analysis"},{"key":"2026052110403815800_bib14","first-page":"425","article-title":"The timing of the age at which natural menopause occurs","volume":"38","author":"Gold","year":"2011","journal-title":"Obstetrics and Gynecology Clinics"},{"key":"2026052110403815800_bib15","doi-asserted-by":"crossref","first-page":"257","DOI":"10.2307\/2344321","article-title":"A stochastic model for the duration of a strike","volume":"135","author":"Lancaster","year":"1972","journal-title":"Journal of the Royal Statistical Society: Series A (General)"},{"key":"2026052110403815800_bib16","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1080\/10543400802398524","article-title":"A threshold regression mixture model for assessing treatment efficacy in a multiple myeloma clinical trial","volume":"18","author":"Lee","year":"2008","journal-title":"Journal of Biopharmaceutical Statistics"},{"key":"2026052110403815800_bib17","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1214\/088342306000000330","article-title":"Threshold regression for survival analysis: modeling event times by a stochastic process reaching a boundary","volume":"21","author":"Lee","year":"2006","journal-title":"Statistical Science"},{"key":"2026052110403815800_bib18","doi-asserted-by":"crossref","first-page":"896","DOI":"10.1002\/sim.3808","article-title":"Threshold regression for survival data with time-varying covariates","volume":"29","author":"Lee","year":"2010","journal-title":"Statistics in Medicine"},{"key":"2026052110403815800_bib19","doi-asserted-by":"crossref","first-page":"1989","DOI":"10.1016\/j.jmva.2009.04.008","article-title":"Generating random correlation matrices based on vines and extended onion method","volume":"100","author":"Lewandowski","year":"2009","journal-title":"Journal of Multivariate Analysis"},{"key":"2026052110403815800_bib20","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1080\/19466315.2013.783503","article-title":"A two-step multiple imputation for analysis of repeated measures with left-censored and missing data","volume":"5","author":"Liu","year":"2013","journal-title":"Statistics in Biopharmaceutical Research"},{"key":"2026052110403815800_bib21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12874-018-0592-9","article-title":"Joint modeling of multivariate longitudinal data and survival data in several observational studies of Huntington\u2019s disease","volume":"18","author":"Long","year":"2018","journal-title":"BMC Medical Research Methodology"},{"key":"2026052110403815800_bib22","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1146\/annurev-statistics-030718-105048","article-title":"An overview of joint modeling of time-to-event and longitudinal outcomes","volume":"6","author":"Papageorgiou","year":"2019","journal-title":"Annual Review of Statistics and Its Application"},{"key":"2026052110403815800_bib23","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1093\/biostatistics\/kxp041","article-title":"Bayesian random-effects threshold regression with application to survival data with nonproportional hazards","volume":"11","author":"Pennell","year":"2010","journal-title":"Biostatistics"},{"key":"2026052110403815800_bib24","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1177\/0962280212445839","article-title":"Joint latent class models for longitudinal and time-to-event data: a review","volume":"23","author":"Proust-Lima","year":"2014","journal-title":"Statistical Methods in Medical Research"},{"key":"2026052110403815800_bib25","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1210\/jc.2010-1746","article-title":"Change in follicle-stimulating hormone and estradiol across the menopausal transition: effect of age at the final menstrual period","volume":"96","author":"Randolph","year":"2011","journal-title":"The Journal of Clinical Endocrinology and Metabolism"},{"key":"2026052110403815800_bib26","doi-asserted-by":"crossref","first-page":"1366","DOI":"10.1002\/sim.4205","article-title":"A Bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time-to-event","volume":"30","author":"Rizopoulos","year":"2011","journal-title":"Statistics in Medicine"},{"key":"2026052110403815800_bib27","first-page":"455","article-title":"Cox analysis of survival data with non-proportional hazard functions","volume":"41","author":"Schemper","year":"1992","journal-title":"Journal of the Royal Statistical Society Series D: The Statistician"},{"key":"2026052110403815800_bib28","doi-asserted-by":"crossref","first-page":"2473","DOI":"10.1002\/sim.3623","article-title":"The estimation of average hazard ratios by weighted Cox regression","volume":"28","author":"Schemper","year":"2009","journal-title":"Statistics in Medicine"},{"key":"2026052110403815800_bib29","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1093\/aje\/kwj039","article-title":"The limitations due to exposure detection limits for regression models","volume":"163","author":"Schisterman","year":"2006","journal-title":"American Journal of Epidemiology"},{"key":"2026052110403815800_bib30","first-page":"175","volume-title":"SWAN: A Multicenter, Multiethnic, Community-based Cohort Study of Women and the Menopausal Transition","author":"Sowers","year":"2000"},{"key":"2026052110403815800_bib31","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1097\/01.GME.0000123642.76105.6E","article-title":"Anti-m\u00fcllerian hormone is a promising predictor for the occurrence of the menopausal transition","volume":"11","author":"van\u00a0Rooij","year":"2004","journal-title":"Menopause"},{"key":"2026052110403815800_bib32","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1093\/biostatistics\/kxad009","article-title":"Modeling biomarker variability in joint analysis of longitudinal and time-to-event data","volume":"25","author":"Wang","year":"2024","journal-title":"Biostatistics"},{"key":"2026052110403815800_bib33","doi-asserted-by":"crossref","first-page":"30266","DOI":"10.1073\/pnas.2001238117","article-title":"Methods for correcting inference based on outcomes predicted by machine learning","volume":"117","author":"Wang","year":"2020","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"2026052110403815800_bib34","first-page":"1","article-title":"Research on the menopause in the 1990s: report of a WHO scientific group","volume":"866","author":"World Health Organization and others","year":"1996","journal-title":"World Health Organization Technical Report Series"},{"key":"2026052110403815800_bib35","doi-asserted-by":"crossref","first-page":"5748","DOI":"10.1002\/sim.10281","article-title":"A Bayesian approach to modeling variance of intensive longitudinal biomarker data as a predictor of health outcomes","volume":"43","author":"Yu","year":"2024","journal-title":"Statistics in Medicine"},{"key":"2026052110403815800_bib36","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1007\/s10654-018-0367-y","article-title":"Body mass index and age at natural menopause: an international pooled analysis of 11 prospective studies","volume":"33","author":"Zhu","year":"2018","journal-title":"European Journal of Epidemiology"}],"container-title":["Biometrics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biometrics\/article-pdf\/82\/2\/ujag080\/68357741\/ujag080.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biometrics\/article-pdf\/82\/2\/ujag080\/68357741\/ujag080.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T14:40:51Z","timestamp":1779374451000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biometrics\/article\/doi\/10.1093\/biomtc\/ujag080\/8689487"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,9]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,4,9]]}},"URL":"https:\/\/doi.org\/10.1093\/biomtc\/ujag080","relation":{},"ISSN":["0006-341X","1541-0420"],"issn-type":[{"value":"0006-341X","type":"print"},{"value":"1541-0420","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,6]]},"published":{"date-parts":[[2026,4,9]]},"article-number":"ujag080"}}