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.

Distribution-free models for latent mixed population responses in a longitudinal setting with missing data

Many biomedical and psychosocial studies involve population mixtures, which consist of multiple latent subpopulations. Because group membership cannot be observed, standard methods do not apply when differential treatment effects need to be studied across subgroups. We consider a two-group mixture in which membership of latent subgroups is determined by structural zeroes of a zero-inflated count variable and propose a new approach to model treatment differences between latent subgroups in a longitudinal setting. It has also been incorporated with the inverse probability weighted method to address data missingness. As the approach builds on the distribution-free functional response models, it requires no parametric distribution model and thereby provides a robust inference. We illustrate the approach with both real and simulated data.

Modeling Disease Progression with Longitudinal Markers

In this paper we propose a Bayesian natural history model for disease progression based on the joint modeling of longitudinal biomarker levels, age at clinical detection of disease and disease status at diagnosis. We establish a link between the longitudinal responses and the natural history of the disease by using an underlying latent disease process which describes the onset of the disease and models the transition to an advanced stage of the disease as dependent on the biomarker levels. We apply our model to the data from the Baltimore Longitudinal Study of Aging on prostate specific antigen (PSA) to investigate the natural history of prostate cancer.