Standardized mean age at death (MADstd): Exploring its potentials as a measure of human longevity

Background: Period mean age at death (MAD) is affected by a population’s age structure, and therefore by its mortality, fertility, and migration history. Period life expectancy (e_0) is also a mean age at death, for a standardized population with a stationary age structure. It depends only on current mortality rates. Here, we explore a middle ground: an age-standardized measure of period age at death, called MADstd, that includes both past and present mortality influences, while omitting the effects of past fertility and migration. Objective: We want to highlight the common structure of the three measures by expressing them as weighted averages with different weighting functions. This allows us to examine them from the perspective of compositional change; i.e., how changes in the underlying age structure affect MAD, MADstd, and e_0. Methods: We compare MADstd with e_0 and MAD formally and empirically, using data on six countries from 1990 to 2020. A particular focus is given to the effect of the increased mortality in 2020 on the three longevity measures. Results: The e_0 indicator gives a higher average age at death than MAD and MADstd because the relative number of older individuals is comparatively high in the hypothetical period life table population. While e_0 declines between 2019 and 2020, both MAD and MADstd show increases in 2020. This can be attributed to differences in the dynamics of the age structures underlying the three indicators. Only the life table population shifts to younger ages, whereas for the observed population and standardized population in 2020 the relative numbers of older individuals increased. Conclusions: Trends in MAD and MADstd are less sensitive to recent developments in mortality, making e_0 the most valuable for examining changes in period mortality rates over time. Considering the interaction between changes in age-specific mortality rates and changes in the underlying age structure deepens the understanding of diverging time trends in MAD, MADstd, and e_0. Contribution: We use the formulas developed by Vaupel and Canudas-Romo (2002) to study the change in all three measures over time. Formulas provided by Vaupel and Zhang (2012) are used to study cross-sectional differences in MAD, MADstd, and e_0. These help us to better understand the differences between the longevity measures and their most appropriate applications.