Many chronic diseases are measured by repeated binary data where the scientific interest is on the transition process between two states of disease activity. Examples include: depression; schizophrenia; multiple sclerosis, and respiratory illness. The course for many of these diseases is inherently heterogeneous, making it difficult to make inference on the transition process. This paper presents a model that incorporates heterogeneity by allowing the transition probabilities to vary randomly across subjects. In the proposed quasi-likelihood formulation for a two-state Markov chain, only the first two moments of the bivariate distribution on the transition probabilities are specified, and we develop a generalized estimating equations (GEE) approach for estimating the mean and variance of this distribution. In addition to estimating the model parameters, we discuss the estimation of derived quantities of the transition matrix such as estimating the expected first passage times and we discuss how we can introduce covariate dependence into the model. We use this methodology to summarize the transitioning pattern of respiratory illness in a group of children with intra-uteral growth retardation, and we conduct a simulation to investigate the finite sample properties of our procedure and to demonstrate marked bias if heterogeneity is ignored.