Joint Hidden Markov Model for Longitudinal and Time-to-Event Data with Latent Variables

This study develops a new joint modeling approach to simultaneously analyze longitudinal and time-to-event data with latent variables. The proposed model consists of three components. The first component is a hidden Markov model for investigating a longitudinal observation process and its underlying transition process as well as their potential risk factors and dynamic heterogeneity. The second component is a factor analysis model for characterizing latent risk factors through multiple observed variables. The third component is a proportional hazards model for examining the effects of observed and latent risk factors on the hazards of interest. A shared random effect is introduced to allow the longitudinal and time-to-event outcomes to be correlated. A Bayesian approach coupled with efficient Markov chain Monte Carlo methods is developed to conduct statistical inference. The performance of the proposed method is evaluated through simulation studies. An application of the proposed model to a general health survey study concerning cognitive impairment and mortality for Chinese elders is presented.