A mixed effects Markov model for repeated binary outcomes with non-ignorable dropout.

In many areas of research, repeated binary measures often represent a two-state stochastic process, where individuals can transition among two states. In a behavioural or physical disability setting, individuals can flow from susceptible or subthreshold state, to an infectious or symptomatic state, and back to a subthreshold state. Quite often the transition among the states happens in continuous time but is observed at discrete, irregularly spaced timepoints which may be unique to each individual. Methods for analyses of such data are typically based on the Markov assumption. Cook (Biometrics 1999; 55:915-920) introduced a conditional Markov model that accommodates the subject-to-subject variation in the model parameters with random effects. We extend this model by adding a non-ignorable dropout component to the model. Specification of the distribution of the random effects is made to guarantee a closed form expression of the marginal likelihood. This methodology is illustrated by applications to a data set from a parasitic field infection survey, a data set from a cocaine treatment study, and a data set from an aging study. Simulations suggest that the shared parameter model is robust with respect to at least one alternative non-ignorable model.