Mortality in a heterogeneous population

Summary No one is interested in lowering the death rate, except insofar as this implies an extension of life. In a homogeneous population, but not otherwise, a given percentage increase in the expectation of life is equal to the percentage reduction in death rate. If we compare two populations, one with death rate μ and the other with death rate μ(1+ δ), then the expectation of life of the second is greater by nearly—δ/μ, where δ is small and negative. But this is true only if the same probability of dying μ applies to each individual. If, unknown to the analyst, the population contains two sub-populations with different mortality chances, and all the difference in rates between the two is in one of the groups with mortality δ1, then in one simple model the true difference in expectation will be—(μ/μ1)2δ/μ The latter will be smaller than—δ/μ if mortality μ1 for the group in which the improvement falls is greater than the rate μ in the population as a whole.