Biomedical research is plagued with problems of missing data, especially in clinical trials of medical and behavioral therapies adopting longitudinal design. After a comprehensive literature review on modeling incomplete longitudinal data based on the full-likelihood functions, this dissertation proposes a Bayesian framework with MCMC strategies for implementing two kind of advanced models: selection models and shared parameter models, for handling intermittent missing values and dropouts that are potentially nonignorable according to various criteria. We combine the advantages of mixed effect models and Markov Transition Models. Simulation study and application to practical data were performed and comparisons with likelihood methods were also made, to show the efficacy and consistency of our methods.