A Markov model for sequences of ordinal data from a relapsing-remitting disease

Many chronic diseases follow a course with multiple relapses into periods with severe symptoms alternating with periods of remission; experimental allergic encephalomyelitis, the animal model for multiple sclerosis, is an example of such a disease. A finite Markov chain is proposed as a model for analyzing sequences of ordinal data from a relapsing-remitting disease. The proposed model is one in which the state space is expanded to include information about the relapsing-remitting status as well as the ordinal severity score, and a reparameterization is suggested that reduces the number of parameters needed to be estimated. The Markov model allows for a wide range of relapsing-remitting behavior, provides an understanding of the stochastic nature of the disease process, and allows for efficient estimation of important characteristics of the disease course (such as mean first passage times, occupation times, and steady-state probabilities). These methods are applied to data from a study of the effect of a treatment (transforming growth factor-beta 1) on experimental allergic encephalomyelitis.