The expected time lost due to an extra risk

The difference between the mean remaining lifetime in a baseline and a more risky environment is investigated. Two models for a more severe environment are considered. The additive hazards model describes an additional independent risk, whereas the proportional hazards model does not require the assumption of independence. It is shown that the expected time lost due to an extra risk decreases with time for heterogeneous population. The origin of this interesting effect is in the fact that ‘the weakest populations are dying out first’. Simple examples are considered.