Bayesian joint model with latent time shifts for longitudinal data with informative dropout

Dementia often has an insidious onset with considerable individual differences in disease manifestation. Disease progression models incorporating latent time shifts have been proposed to investigate 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 lead to bias in estimating longitudinal trajectories.

To account for informative dropout, we propose a nonlinear joint model with latent time shifts. This joint model uses a multivariate nonlinear disease progression model with latent time shifts to model the correlated longitudinal cognitive measures, and simultaneously, a proportional hazards model to incorporate time to dementia or death. We evaluate and compare different association structures between the longitudinal and dropout processes within the joint models via a simulation study. In addition, we compare the joint models with the disease progression model that ignores informative dropout. We further applied the proposed joint model to a cohort study to analyze longitudinal cognitive measures from neuropsychological tests, together with time to dementia or death.

In the simulation study, the proposed joint model with the correct association structure yields optimal performance in estimating both longitudinal trajectories and latent time shifts. Even the joint model with a misspecified association structure outperforms the disease progression model that neglects informative dropout. In the real data application, we estimated both trajectories and latent time shifts from longitudinal cognitive measures and demonstrated their associations with the hazard of dementia or death, confirming the presence of informative dropout.

Our proposed joint model offers more accurate and robust estimates than the latent time disease progression model that does not consider informative dropout. Our method provides insights into cognitive health in the presence of dementia and death.