We propose a Bayesian latent variable model to characterize covariate-specific dependence structures among multiple modalities of asynchronously collected multivariate data. This setting commonly arises in longitudinal biomedical research, especially in observational and clinical studies of complex diseases, where dynamic and heterogeneous dependence across biomarker modalities can be biologically and clinically informative. However, quantitative analysis is often challenged by asynchronous collection of multimodal profiles due to study design and data collection constraints. For example, the biological diagnosis and staging of Alzheimer's disease require integrated evaluation of multimodal biomarkers, including imaging and biofluid biomarkers, and the Alzheimer's Disease Neuroimaging Initiative (ADNI) study has collected biomarker profiles longitudinally on varying schedules for over two decades. Common analytic strategies that rely solely on complete multimodal profiles or analyze each modality separately can result in information loss and biased estimates. Therefore, we aim to jointly incorporate all available observations to estimate the population-level cross-modal dependence structures (e.g., covariance or correlation matrices) that evolve over time and vary across demographic or clinical groups. The proposed model uses modality-specific low-rank loading matrices with shared latent variables to integrate information across modalities, visits, and subjects, while accounting for repeated measurements. The application to ADNI data reveals clinically meaningful patterns in longitudinal cross-modal biomarker dependence, and the simulation study shows improved recovery under limited modality synchrony.

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