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In many biomedical studies, multiple sourced data with varied features are observed on the same subjects. Examples include longitudinal markers measured along with a time-to-event outcome of interest and multiset data with varied dimensions. To extract the association structure from the multi-sourced data poses great challenges. We present two Bayesian frameworks utilizing latent variables in order to provide solutions for these two specific data scenarios. For modeling longitudinal markers measured along with a time-to-event outcome, we develop a fully Bayesian joint longitudinal-survival model that uses a latent class structure to facilitate discovery of subgroups exhibiting distinct behavior, and our formulation incorporates estimation of the number of subgroups and offers enhanced flexibility with a subgroup-specific piecewise linear log baseline hazard. For modeling multiset data with varied dimensions, we propose a Bayesian framework that uses latent factors to decompose data into four conceptual parts: joint structure induced by the latent factors shared across all the sets, partial association structure induced by the latent factors shared by the associated subsets of the multiset data, individual structure induced by latent factors unique to each set, and noise. Our method enables flexible selection of latent factors and discovery of association structure as well as variable selection in the joint structure (and, if desired, in the partial association structure). For both methods, we show the ability and the performance by simulation, and use real data for demonstration.
