Journal Article

Mortality implications of mortality plateaus

SIAM Review, 57:1, 61–70 (2015)

Abstract

The article aims at describing 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) 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. 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.

Keywords: mathematical demography, mathematical models, mathematics, probability
The Max Planck Institute for Demographic Research (MPIDR) in Rostock is one of the leading demographic research centers in the world. It's part of the Max Planck Society, the internationally renowned German research society.