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To address missing\u2010by\u2010design outcomes in multi\u2010cohort studies, our approach extends the multivariate functional mixed model (MFMM), which integrates longitudinal outcomes to extract shared disease progression trajectories and links these outcomes to time\u2010to\u2010event data through a parsimonious survival model. This framework balances flexibility and interpretability by modeling shared progression trajectories while accommodating cohort\u2010specific mean functions and survival parameters. For efficient estimation, we incorporate penalized splines into an EM algorithm. Application to three AD cohorts demonstrates the model's ability to capture disease trajectories and account for inter\u2010cohort variability. Simulation studies confirm its robustness and accuracy, highlighting its value in advancing the understanding of AD progression and supporting clinical decision\u2010making in multi\u2010cohort settings.<\/jats:p>","DOI":"10.1002\/sim.70442","type":"journal-article","created":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T08:42:22Z","timestamp":1770972142000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Functional Joint Model for Survival and Multivariate Sparse Functional Data in Multi\u2010Cohort Alzheimer's Disease Study"],"prefix":"10.1002","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-1154-636X","authenticated-orcid":false,"given":"Wenyi","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Statistics North Carolina State University  Raleigh North Carolina 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