用于死亡率比较的Wasserstein距离：生存的绝对差异与净差异
The Wasserstein Distance for Mortality Comparisons: Absolute versus Net Differences in Survival
浏览论文内容
中文总结 AI 辅助
该研究将Wasserstein距离与出生时预期寿命差距关联，发现多数人群对的生存函数不相交，预期寿命差距可量化死亡率模式的总体差异，为死亡率比较提供新视角。
中文摘要 AI 辅助
众所周知，出生时预期寿命的差距可视为两条生存函数之间的净差异。当改为计算两条生存函数之间的绝对差异时，我们得到一种分布不平等度量，称为Wasserstein距离。该度量通过将一个概率分布转换为另一个的最小成本来量化两个概率分布之间的距离。本文将Wasserstein距离与出生时预期寿命的差距关联起来：只要生存函数不相交，两种度量就相互对应，即在不相交的情况下，净差异等于绝对差异。曲线是否相交由年龄别死亡率的累积差异决定；当特定人群的累积生存优势因后期年龄的死亡率升高超过早期生存优势而逆转时，就会发生相交。这些情况特别值得关注，因为即使两个人群的死亡率模式差异很大，生存的净差异（或预期寿命差距）也可能很小。在实证分析中，我们使用人类死亡率数据库1990至2020年的生命表数据寻找这类情况：在69188个人群对中，59.8%的比较存在生存函数相交，但生存优势逆转的幅度通常很小。因此我们得出结论，在大多数情况下，出生时预期寿命的差距不仅是均值的比较，还量化了两种死亡率模式之间的总体差异。
英文摘要
It is well known that the gap in life expectancy at birth can be seen as the net difference between two survivorship functions. When calculating the absolute difference between the two survivorship functions instead, we derive a distributional inequality measure which is called the Wasserstein distance. The measure quantifies how far apart two probability distributions are by the minimal cost of transporting one into the other. This paper relates the Wasserstein distance to the difference in life expectancy at birth. Both measures correspond to each other, whenever the survivorship functions do not cross, i.e., the net difference equals the absolute difference in the no crossing case. Whether the curves cross is driven by the accumulated difference in age-specific death rates. Crossing occurs in situations where an accumulated survival advantage for given populations is reversed because elevated death rates at later ages outweigh the earlier survival advantage. These cases are particularly interesting because the net difference in survival (or the life expectancy gap) may be small even though the two populations show very different mortality schedules. In our empirical analysis, we search for these cases using life table data from Human Mortality Database life tables for the period 1990 to 2020. Across 69 188 population pairs, survivorship functions cross in 59.8 % of comparisons. Yet, the magnitude of the reversal in survivorship is usually very small. We therefore conclude that in most cases, the gap in life expectancy at birth is not only a comparison of means but quantifies the overall difference between the two mortality regimes
