Modeling human mortality using mixtures of bathtub shaped failure distributions
Modeling human mortality using mixtures of bathtub shaped failure distributions
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DOI：
10.1016/j.jtbi.2006.11.011
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发表时间：
2007-04-07
影响因子：
2
通讯作者：
Zitikis, Ricardas
中科院分区：
文献类型：
--
作者：
Bebbington, Mark;Lai, Chin-Diew;Zitikis, Ricardas
衰老和死亡率通常由Gompertz-Makeham分布来建模，其中成年人的死亡率随着年龄的增长而加速。由此产生的参数被解释为脆弱和活力随着年龄的增长而下降。这很符合“西方化”社会的生活数据，那里的数据准确，分辨率高，并显示出高质量的产后护理的效果。然而，我们表明，当数据分辨率较低，并且在婴儿死亡率中包含相当大的结构时，拟合可能很差。此外，Gompertz-Makeham分布既不符合自然选择的力量，也不符合最近发现的“晚年死亡率减速”。虽然像Heligman-Pollard分布这样的精算模型在理论上可以达到更好的拟合，但缺乏生存函数的封闭形式使得拟合非常困难，并且可能缺乏生物学解释。我们表明，将死亡率分配给外源性或内源性原因的混合，使用减少的加性和灵活的威布尔分布，可以很好地模拟整个生命周期的人类死亡率。混合物的成分与老化的可靠性和生物学理论渐近一致。混合分布的相对简单性使得一种技术变得可行，这种技术使用相应的生存率和危险率函数的曲率函数来确定不同生命阶段的开始和结束，例如婴儿死亡率、自然选择力量的结束和晚年死亡率的减速。我们通过对加拿大和印度尼西亚死亡率数据的比较分析来说明我们的结果。(c) 2006 Elsevier Ltd.版权所有。
Aging and mortality is usually modeled by the Gompertz-Makeham distribution, where the mortality rate accelerates with age in adult humans. The resulting parameters are interpreted as the frailty and decrease in vitality with age. This fits well to life data from 'westernized' societies, where the data are accurate, of high resolution, and show the effects of high quality post-natal care. We show, however, that when the data are of lower resolution, and contain considerable structure in the infant mortality, the fit can be poor. Moreover, the Gompertz-Makeham distribution is consistent with neither the force of natural selection, nor the recently identified 'late life mortality deceleration'. Although actuarial models such as the Heligman-Pollard distribution can, in theory, achieve an improved fit, the lack of a closed form for the survival function makes fitting extremely arduous, and the biological interpretation can be lacking. We show, that a mixture, assigning mortality to exogenous or endogenous causes, using the reduced additive and flexible Weibull distributions, models well human mortality over the entire life span. The components of the mixture are asymptotically consistent with the reliability and biological theories of aging. The relative simplicity of the mixture distribution makes feasible a technique where the curvature functions of the corresponding survival and hazard rate functions are used to identify the beginning and the end of various life phases, such as infant mortality, the end of the force of natural selection, and late life mortality deceleration. We illustrate our results with a comparative analysis of Canadian and Indonesian mortality data. (c) 2006 Elsevier Ltd. All rights reserved.