Bayesian Joint Model with Latent Time Shifts for Multivariate Longitudinal Data with Informative Dropout

Abstract Dementia often has an insidious onset with considerable individual differences in disease manifestation. Nonlinear mixed-effects models with latent time shifts have been proposed to investigate the long-term disease progression and individual disease stages. The latent time shift is a horizontal shift in time that aligns patients along a global timeline for disease progression. However, these models ignore informative dropout due to dementia or death, which may result in biased estimates of the longitudinal parameters. To account for informative dropout due to dementia or death, we propose a multivariate nonlinear joint model with latent time shifts. This joint model uses a multivariate nonlinear mixed-effects model with latent time shifts to model the correlated longitudinal markers of cognitive decline, and simultaneously, a proportional hazards model to incorporate dropout due to dementia or death. We investigate two association structures between the longitudinal process and the time to event process: the current value structure and the shared random effect structure. We compare the proposed joint model with separate models that ignore informative dropout across various simulation settings. The proposed joint models with correctly specified association structures show the best performance. Even the models with misspecified association structures outperform the separate models that does not consider informative dropout. We conclude that our proposed joint model with latent time shifts offers more accurate and robust estimates than the latent time disease progression models that neglect informative dropout. Future research will involve incorporating competing risks and other parametrizations of the longitudinal model into this joint model framework.