A Bayesian Approach to Longitudinal Categorical Data in a Continuous Time Markov Chain Model

Continuous time Markov chain (CTMC) models are frequently used in medical research for studies of disease progression, but they are rarely applied to thranstheretical modes (TTM). Existing literatures focus on models with restrictions of one-step transitions or with small number of states. TTM, however, often have four or more states and all one-step transitions are conceptually allowed. Though the well developed R package MSM is capable of dealing models with up to five states, it has been reported that standard errors for some parameters are dramatically underestimated. In this research, a Bayesian approach is proposed to handle general Markov chain models, where the likelihood is numerically evaluated using ordinal differential equation solvers and posterior samples are generated using the Metropolis Hasting algorithm. The proposed method offers accurate point and interval estimates. In addition, this flexible approach incorporates aforementioned models as special cases and can be easily extended to advanced CTMC models.