Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 37 / 5 / ii / a

The permitted transitions form the following diagram. Each arrow is labelled by its fitted transition intensity in units of inverse years; the absence of an arrow is a structural restriction, not an estimated small effect.

State 1 can move directly to 2, 3 or 5; state 2 can move to 4 or 5; state 3 can move to 4 or 5; and state 4 can move only to 5. There are no recovery transitions, and state 5 is an absorbing state. The rates of leaving the four living states are the sums of their outgoing arrows:The diagonal generator entries are their negatives, so every row of $Q$ sums to zero. These diagonal entries are not arrows or negative event rates. For example the direct $1\to 5$ rate is $0.004$ per year, while death after reaching another state can occur at a much larger rate. The printed fit has no covariates on the intensities, so it estimates one pooled rate system and contains no treatment-effect comparison, despite the trial's treatment randomization. The reported $-2\ell$ describes the fitted likelihood level; by itself it is not a goodness-of-fit test without a reference or competing model.