Piantanelli L
Arch Gerontol Geriatr. 1986 Jul;5(2):107-18. doi: 10.1016/0167-4943(86)90014-2.
A mathematical model of mortality and survival kinetics is proposed based upon the two main aspects of survival data, namely, the rate of vitality reduction with age and its statistical distribution. Certain mathematical assumptions are made on the time-course of both vitality and its distribution. Then, these two aspects are integrated in a single model which can be used to describe survivorship, cumulative mortality or dying. The model is capable of fitting empirical curves even at very advanced ages, where the widely used Gompertz law fails. Examples are provided, derived from populations having rather different lifespans such as rotifers, flies, rats and horses. The model maintains one of the most interesting characteristics of Gompertz law, namely, the possibility to estimate the 'design constant for longevity' relating maximum lifespan to one of the parameters of the model. It also has the potential characteristics enabling it to be used to judge the statistical significance of the difference between two empirical survival curves.
基于生存数据的两个主要方面，即活力随年龄降低的速率及其统计分布，提出了一个死亡率和生存动力学的数学模型。对活力及其分布的时间进程做了某些数学假设。然后，将这两个方面整合到一个单一模型中，该模型可用于描述生存情况、累积死亡率或死亡情况。即使在非常高的年龄阶段，该模型也能够拟合经验曲线，而在这些年龄段广泛使用的冈珀茨定律则不适用。文中给出了一些例子，这些例子来自寿命差异相当大的种群，如轮虫、果蝇、大鼠和马。该模型保留了冈珀茨定律最有趣的一个特征，即能够估计将最大寿命与模型参数之一相关联的“寿命设计常数”。它还具有一些潜在特征，使其能够用于判断两条经验生存曲线之间差异的统计显著性。
