Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 32 / 2 / d

The mean holding time from a transition intensity matrix is $-1/q_{rr}$. Apply this to the fitted exit rates and use monotonic inversion for each confidence interval:Thus the expected state durations are 86.96 months and 31.45 months, respectively. A confidence interval for a reciprocal rate reverses the endpoint order; the negative diagonal rates must first be converted to positive exit rates.

For the expected absorption time in an illness-death model, the time spent initially in the mild state is followed by an additional severe-state duration only if progression occurs before death. That probability is $0.0072/0.0115$. ThereforeThis is an unconditional mean including both possible paths to death, not a mean conditional on progression.