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.

中文翻译：

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标准化平均死亡年龄 (MADstd)：探索其作为人类寿命衡量标准的潜力（作者：Markus Sauerberg、Marc Luy）

背景：期间平均死亡年龄（MAD）受到人口年龄结构的影响，因此也受到死亡率、生育率和移民历史的影响。对于具有固定年龄结构的标准化人口来说，时期预期寿命 (e_0) 也是平均死亡年龄。这仅取决于当前的死亡率。在这里，我们探索了一个中间立场：一种死亡时年龄的年龄标准化衡量标准，称为 MADstd，其中包括过去和现在的死亡率影响，同时忽略了过去生育和移民的影响。目标：我们希望通过将三种度量表示为具有不同加权函数的加权平均值来强调它们的共同结构。这使我们能够从成分变化的角度来审视它们；即，底层年龄结构的变化如何影响 MAD、MADstd 和 e_0。方法：我们使用 1990 年至 2020 年六个国家的数据，将 MADstd 与 e_0 和 MAD 进行正式和实证比较。特别关注 2020 年死亡率增加对三个长寿指标的影响。结果：e_0 指标给出的平均死亡年龄高于 MAD 和 MADstd，因为假设时期生命表人口中老年人的相对数量相对较高。虽然 e_0 在 2019 年至 2020 年期间有所下降，但 MAD 和 MADstd 在 2020 年均呈现增长。这可以归因于这三个指标背后的年龄结构动态的差异。仅生命表人口向低龄化转变，而2020年观测人口和标准化人口中，老年个体的相对数量有所增加。结论：MAD 和 MADstd 的趋势对近期死亡率的发展不太敏感，这使得 e_0 对于检查期间死亡率随时间的变化最有价值。考虑特定年龄死亡率变化与潜在年龄结构变化之间的相互作用，加深了对 MAD、MADstd 和 e_0 不同时间趋势的理解。贡献：我们使用 Vaupel 和 Canudas-Romo (2002) 开发的公式来研究所有三个指标随时间的变化。 Vaupel 和Zhang (2012) 提供的公式用于研究MAD、MADstd 和e_0 的横截面差异。这些有助于我们更好地理解寿命衡量标准及其最合适的应用之间的差异。