Bayesian shared parameter joint models for heterogeneous populations.

Joint models (JMs) for longitudinal and time-to-event data are an important class of biostatistical models in health and medical research. When the study population consists of heterogeneous subgroups, standard JMs may be inadequate, leading to misleading results or loss of information. Joint latent class models (JLCMs) and their variants have been proposed to incorporate latent class structures into JMs. JLCMs are useful for identifying latent subgroups, uncovering deeper insights into relationships between the outcomes, and improving prediction performance. We consider the problem of Bayesian inference for the generic form of JLCMs, which poses significant computational challenges due to the complex nature of the posterior distribution. We propose a new Bayesian inference framework to tackle these challenges. Our approach leverages state-of-the-art Markov chain Monte Carlo techniques and parallel computing for parameter estimation and model selection regarding the number of latent classes. Through a simulation study, we demonstrate the feasibility and superiority of our proposed method over the existing approach. Additionally, we provide practical guidance on model and prior specification, which has received little attention, to facilitate the implementation of such complex models. We illustrate our method using data from the PAQUID prospective cohort study, where the outcomes of interest include a longitudinal measurement of cognitive performance and time to dementia diagnosis. Our analysis provides deeper insights into the latent class characteristics underlying the study population. Supplementary Information: The online version contains supplementary material available at 10.1007/s11222-025-10647-1.