Probability aspects of multi-state models

Abstract

Multi-state models are the most commonly used models for describing the development for longitudinal data. A multi-state model is defined as a model for a stochastic process, which at any time point occupies one of a set of discrete states. In medicine, the states can describe conditions like healthy, diseased, diseased with complications, and dead. A change of state is called a transition. This then corresponds to outbreak of disease, occurrence of complications and death. The state structure specifies the states and which transitions from state to state are possible. It is possible to make a figure of the state structure. Some examples of state structures have already been shown in Figures 1.4–1.7. The full statistical model specifies the state structure and the form of the hazard function for each possible transition. This chapter is a description of how multi-state models can be used to model multivariate and multiple survival data. In principle, all kinds of such data can be formulated as multi-state models and this is often convenient for considering predictions. The approach is particularly well suited to event-related dependence. But the approach does have some shortcomings for recurrent events, because it considers states, rather than events (see below). Furthermore, multi-state models consider all data as longitudinal, which make them less useful for repeated measurements and require the censoring pattern for parallel data to be homogeneous.