Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 207 / 2 / c

Assume the 1000 individuals are initially disease-free. The event being counted is onset during the ten-year period, not occupancy of the pre-clinical state at its end. Using the estimated transition intensity as a constant onset rate and linearity of expectation, the expected number of onsets isThe first-order approximation $1000\times 0.005\times 10=50$ is close, but does not account for depletion of the disease-free group.