Multiple decrement models can be formulated as a special case of multiple state models. As with a multiple state model, we consider a life aged (x) who, at time point (t) (age (x+t)) is in one of (n+1) potential outcomes, (0,1, ldots, n). Specifically, we let (Y(t)) (sometimes denoted as (Y(x+t)) ) be a categorical random variable with potential outcomes (0,1, ldots, n).
In a multiple decrement model, we start in state 0 but all other states are absorbing states, where it is not possible to leave.
Figure 1. Multidecrement Model as a MultiState Representation.
Both the “Alive-Dead” and the “Accidental Death” Models are special cases of multiple decrement models. For some other special cases, consider the following.