A Functional Joint Model for Survival and Multivariate Sparse Functional Data in Multi-Cohort Alzheimer's Disease Study.

We develop an integrative joint model for multivariate sparse functional and survival data to analyze Alzheimer's disease (AD) across multiple studies. To address missing-by-design outcomes in multi-cohort 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-to-event data through a parsimonious survival model. This framework balances flexibility and interpretability by modeling shared progression trajectories while accommodating cohort-specific 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-cohort variability. Simulation studies confirm its robustness and accuracy, highlighting its value in advancing the understanding of AD progression and supporting clinical decision-making in multi-cohort settings.