Modelling transitional and joint marginal distributions in repeated categorical data.

When a repeated measures endpoint classifies people into several categories, marginal and transitional models provide two distinct approaches for data analysis. Marginal models estimate the probabilities of being in different categories over time. Transitional models estimate the probability of changing between any two given states during follow-up visits. This paper develops transitional and marginal models and applies them to a clinical trial of treatments of opiate addiction. The primary outcome was the presence or absence of opiates in a thrice weekly urine test, administered for 17 weeks. Subjects frequently miss visits, however, and in effect respond in one of three ways to a visit: missing, opiates present or opiates absent. Thus we have three possible states. Our transitional model conditions on the current state and models the transition from state k to one of the other (0, ..., K-1) states using a mutinomial logit model. This model generalizes previous work of Muenz and Rubinstein. Significant covariates in this model are predictive of state changes. Our marginal model views the state at each time point, rather than the transitions, as the primary response. Here we model the probability of being in state k with a multinomial logit model. Correlation within individuals over visits can be handled by applying the approach of Zeger and Liang or the bootstrap. Significant covariates in this model can include more 'global' summaries of a person such as extent of previous opiate use. Both marginal and transitional models are needed to provide a complete description of an individual's behaviour over time since global summaries might not affect transitions. Of particular substantive interest is how the opiate treatments affect both the marginal and transition probabilities.