ABSTRACT
FIGURE 7.1 Graphical representation of a survival process as a two-state process; α01(t) is the transition intensity between state 0 and state 1, corresponding here to the hazard function.
We are often interested in events that are not death but, for example, the
occurrence of disease. In the case of chronic illness among the elderly, the risk of dying is also important. It is therefore useful to model the two possible important events: occurrence of disease and death. This can be represented by two counting processes (or a bivariate process). In terms of states, two events define three states: “healthy,” “ill,” “dead.” We can encode these states by values 0, 1, 2 and represent the evolution of the state by a process {X(t), t ≥ 0} where X(t) can take the values 0, 1, 2. Such a process is called a multistate process. This three-state model is the most widely used in epidemiology and is called the illness-death model. We see that there is a duality between event representation and representation by states: an event leads to a different state while a transition from one state to another is an event. In this chapter, we will focus on the multistate point of view which is often more attractive, but the event point of view is more general and will also be discussed.
