One or more rates of ageing? The extended gamma-Gompertz model (EGG)

Abstract

Hidden heterogeneity poses serious challenges to survival analysis because the observed (aggregate) and the unobservable (individual) hazard functions may differ markedly from each other. However, the recent discovery of the so-called “mortality plateau” (i.e., the approximately constant value when mortality levels off, at very old ages) has brought new insights and pushed researchers towards the use of the gamma-Gompertz mortality model. Among the assumptions of this model, two are particularly relevant here: the shape, not the level, of the individual hazard function is a constant and so is the rate of ageing, i.e., the relative increase in mortality risks as people get older. The latter, however, does not pass empirical tests: the rate of ageing seems to vary (albeit only slightly) by age, gender, birth cohort and country. In this paper, we propose a new model (EGG, or extended gamma-Gompertz) which overcomes this limitation by allowing the rate of ageing to increase gradually with age before converging to a constant value, as in Gompertz. While preserving all the fine theoretical and empirical properties of its simpler predecessor, the EGG model adapts better to empirical reality, i.e., in this paper, the mortality profile of the cohorts born between 1820 and 1899 in five countries with high-quality data. The advantages of this more refined mortality model are discussed.