A bayesian approach to longitudinal categorical data in a continuous time markov chain model
Continuous time Markov chain (CTMC) models are widely used to study the progression of a chronic disease but rarely applied to the Transtheoretical models (TTM), a widely applied psychosocial model for health-related outcomes. The TTM often has more than three states, and conceptually allows all possible one-step transitions, which complicates the estimation because the exact likelihood function is difficult to obtain. In addition, intervention effects are often the research interest and often adjusted for covariates. Estimation of CTMC models with covariates is even more complicated because of the increase in model parameters. Existing literature focuses on models with restrictions (e.g., some one-step transitions are not allowed) or models with a small number of states (e.g., three-state models), and therefore the models are not suitable for CTMC models based on TTM. The aim of this dissertation is to develop an estimation procedure for the CTMC model with or without covariates. Bayesian methods are developed, in which the likelihood are evaluated using ordinal differential equation solvers and the posterior samples are generated with the Metropolis Hasting algorithm. Our approach does not require the analytical form of the likelihood function, thus can be viewed as a general method or a unified approach in estimating CTMC models. In other words, the proposed method is capable of incorporating the aforementioned models as special cases and being extended to more complex models (e.g., models with more than five states, hidden Markov models, random effect Markov models, and joint Markov models). In both Chapters II and III, empirical studies are conducted, and our results show that the proposed methods offer very accurate point estimates and precise nominal coverage probabilities. For models without covariates as discussed in Chapter II, the simulation results show that our approach performs better compared with an R package of MSM, a well-developed software package under frequentist framework using conventional estimation method (i.e., analytical form, Eigen decomposition or Padè approximation of the likelihood function). A dataset from nutrition intervention program of the Next Step Trial is used to illustrate our methods.
Ma, Junsheng, "A bayesian approach to longitudinal categorical data in a continuous time markov chain model" (2013). Texas Medical Center Dissertations (via ProQuest). AAI3606146.