In biomedical research with longitudinal designs, missing values due to intermittent
nonresponse or premature withdrawal are usually 'nonignorable' in the sense that unobserved values are related to the patterns of missingness. When missing values are simply ignored, analyses based on observed-data likelihood may yield biased estimates or invalid inferences. By drawing the framework of a shared-parameter mechanism, the process yielding the repeated count measures and the process yielding missing values can be modelled separately, conditionally on a group of shared parameters. For chronic diseases, Markov transition models can be used to study the transitional features of the pathologic processes. In this paper, Markov chain Monte Carlo (MCMC) algorithms are developed to fit a random-effects Markov transition model (REMTM) for incomplete count repeated measures, within which random effects are shared by the counting process and the missing-data mechanism. Assuming a Poisson distribution for the count measures, the transition probabilities are estimated using a Poisson linear regression model. The missingness mechanism is modeled with a multinomial-logit regression to calculate the transition probabilities of the missingness indicators. The method is demonstrated using both simulated data sets and a practical data set
from a smoking cessation clinical trial.