In this paper, we consider a full likelihood method to analyze continuous longitudinal responses with non-ignorable non-monotone missing data. We consider a transition probability model for the missingness mechanism. A first-order Markov dependence structure is assumed for both the missingness mechanism and observed data. This process fits the natural data structure in the longitudinal framework. Our main interest is in estimating the parameters of the marginal model and evaluating the missing-at-random assumption in the Effects of Public Information Study, a cancer-related study recently conducted at the University of Pennsylvania. We also present a simulation study to assess the performance of the model. Copyright © 2012 John Wiley & Sons, Ltd.