Abstract:

Mean age at death in a period life table is a major indicator of population health, as is the table’s variance in age at death. Taylor’s Law is a widely observed empirical pattern that relates variances to means in sets of non-negative measurements via an approximate power function. It has found application to human mortality. We add to this research by showing that Taylor’s Law leads to a model that reasonably describes the relationship between mean age at death in a life table (which is the same as life expectancy at birth) and the life table’s variance in age at death. We built a demonstration model, tested its accuracy, and found that it provides reasonably accurate estimates of variance in age at death in a life table. Employing independent data, the model was used to provide estimates of variance at age in death for six countries, three of which have high levels of life expectancy at birth and three of which have lower levels. The two parameters in Taylor’s Law, a and b, can be interpreted, respectively, as: (1) a ≈ the product of life expectancy at birth and the sum of mean years lived and mean years remaining; and (2) b ≈ the square of life expectancy at birth. This provides Taylor’s Law with a theoretical foundation when it is used to estimate variance in age at death in life tables constructed for human and other species. A significant strength of our application is that where mean age at death itself is estimated, it provides an estimate of variance in age at death that may not otherwise be available. This is useful because major agencies have produced estimates of life expectancy at birth for small areas. We illustrate this important application of the TL Method using empirical data and conclude that there is a need for a model that can produce accurate estimates of variance in age at death in a life table.

摘要：

周期寿命表中的平均死亡年龄是人口健康的主要指标，该表的死亡年龄差异也是如此。泰勒定律是一种广泛观察到的经验模式，它通过近似幂函数将方差与非负测量集合中的均值联系起来。它已发现适用于人类死亡率。我们通过证明泰勒定律导致了一个模型来补充这项研究，该模型合理地描述了生命表中的平均死亡年龄（与出生时的预期寿命相同）与生命表中死亡年龄的方差之间的关系。我们建立了一个演示模型，测试了它的准确性，并发现它可以相当准确地估计生命表中死亡年龄的方差。该模型采用独立数据，用于提供六个国家的死亡年龄方差估计值，其中三个具有较高的出生时预期寿命，而三个较低的水平。泰勒定律中的两个参数 a 和 b 可以分别解释为： (1) a ≈ 出生时预期寿命与平均寿命和平均剩余寿命之和的乘积；(2) b ≈ 出生时预期寿命的平方。这为泰勒定律在用于估计为人类和其他物种构建的生命表中的死亡年龄差异时提供了理论基础。我们的应用程序的一个显着优势是，在估计死亡时的平均年龄本身时，它提供了死亡时年龄的方差估计值，否则可能无法获得。这很有用，因为主要机构已经对小区域的出生时预期寿命进行了估计。