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In many longitudinal studies, there may exist informative observation times and a dependent terminal event that stops the follow-up. In this paper, we propose a joint model for analysis of longitudinal data with informative observation times and a dependent terminal event via two latent variables. Estimation procedures are developed for parameter estimation, and asymptotic properties of the proposed estimators are derived. Simulation studies demonstrate that the proposed method performs well for practical settings. An application to a bladder cancer study is illustrated. [ABSTRACT FROM AUTHOR]

Longitudinal data occur in many clinical and observational studies, and in many situations, longitudinal responses are often correlated with observation times. In this article, we propose a new joint model for the analysis of longitudinal data with informative observation times via two random effects. In particular, an additive mixed effect model is used for observation times. Estimating equation approaches are developed for parameter estimation, and asymptotic properties of the resulting estimators are established. In addition, some graphical and numerical procedures are provided for model checking. The finite-sample behavior of the proposed method is evaluated through simulation studies, and an application to a bladder cancer study is illustrated. [ABSTRACT FROM AUTHOR]

Hidden Markov models (HMMs) describe the relationship between two stochastic processes, namely, an observed outcome process and an unobservable finite-state transition process. Given their ability to model dynamic heterogeneity, HMMs are extensively used to analyze heterogeneous longitudinal data. A majority of early developments in HMMs assume that observation times are discrete and regular. This assumption is often unrealistic in substantive research settings where subjects are intermittently seen and the observation times are continuous or not predetermined. However, available works in this direction restricted only to certain special cases with a homogeneous generating matrix for the Markov process. Moreover, early developments have mainly assumed that the number of hidden states of an HMM is fixed and predetermined based on the knowledge of the subjects or a certain criterion. In this article, we consider a general continuous-time HMM with a covariate specific generating matrix and an unknown number of hidden states. The proposed model is highly flexible, thereby enabling it to accommodate different types of longitudinal data that are regularly, irregularly, or continuously collected. We develop a maximum likelihood approach along with an efficient computer algorithm for parameter estimation. We propose a new penalized procedure to select the number of hidden states. The asymptotic properties of the estimators of the parameters and number of hidden states are established. Various satisfactory features, including the finite sample performance of the proposed methodology, are demonstrated through simulation studies. The application of the proposed model to a dataset of bladder tumors is presented. [ABSTRACT FROM AUTHOR]