Mortality Implications of Mortality Plateaus

This article aims to describe in a unified framework all plateau-generating random effects models in terms of (i) plausible distributions for the hazard (baseline mortality) and the random effect (unobserved heterogeneity, frailty) as well as (ii) the impact of frailty on the baseline hazard. Mortality plateaus result from multiplicative (proportional) and additive hazards, but not from accelerated failure time models. Frailty can have any distribution with regularly-varying-at-0 density and the distribution of frailty among survivors to each subsequent age converges to a gamma distribution. In a multiplicative setting the baseline cumulative hazard can be represented as the inverse of the negative logarithm of any completely monotone function. If the plateau is reached, the only meaningful solution at the plateau is provided by the gamma-Gompertz model.