Continuous-time multi-state model

A continuous-time multi-state model represents an individual's evolving status by states and transition intensities, with event times determined by transitions between states.

The transition intensity $q_{rs}(t)$ is the instantaneous rate of moving from state $r$ to state $s$, conditional on occupying state $r$ immediately before time $t$.

A Semi-Markov multi-state model allows transition intensities to depend on the time since entry into the current state, rather than only on the current state and calendar time.

For a finite absorbing continuous-time Markov chain with transient subgenerator $Q_T$, the entry $(-Q_T{)}_{ij}^{-1}$ is the expected time spent in transient state $j$ before absorption when starting from state $i$.