Hidden heterogeneity poses serious challenges to survival analysis because the observed (aggregate) and the unobservable (individual) hazard functions may differ markedly from each other. However, the recent discovery of the so-called “mortality plateau” (i.e., the approximately constant value when mortality levels off, at very old ages) has brought new insights and pushed researchers towards the use of the gamma-Gompertz mortality model. Among the assumptions of this model, two are particularly relevant here: the shape, not the level, of the individual hazard function is a constant and so is the rate of ageing, i.e., the relative increase in mortality risks as people get older. The latter, however, does not pass empirical tests: the rate of ageing seems to vary (albeit only slightly) by age, gender, birth cohort and country. In this paper, we propose a new model (EGG, or extended gamma-Gompertz) which overcomes this limitation by allowing the rate of ageing to increase gradually with age before converging to a constant value, as in Gompertz. While preserving all the fine theoretical and empirical properties of its simpler predecessor, the EGG model adapts better to empirical reality, i.e., in this paper, the mortality profile of the cohorts born between 1820 and 1899 in five countries with high-quality data. The advantages of this more refined mortality model are discussed.

隐藏的异质性对生存分析提出了严峻的挑战，因为观察到的（汇总）和不可观察到的（个体）危险函数可能彼此明显不同。但是，最近发现的所谓“死亡率高原”（即，在很老的年龄死亡率水平下降时的近似恒定值）带来了新的见识，并促使研究人员朝着使用伽马-戈姆珀兹死亡率模型迈进。在该模型的假设中，有两个特别重要：个体危害函数的形状而不是水平是一个常数，老龄化率也是一个常数，即随着年龄的增长，死亡风险相对增加。然而，后者并没有通过经验检验：老龄化率似乎因年龄，性别，出生人群和国家而异（尽管只有很小的差异）。在本文中，我们提出了一种新模型（EGG或扩展的伽马-戈姆佩兹），该模型通过允许老化率随着年龄的增长逐渐增加，然后收敛到恒定值（例如Gompertz），从而克服了这一限制。EGG模型在保留其较简单的前辈的所有优良理论和经验属性的同时，更适合于经验现实，即，在本文中，使用高质量数据的五个国家在1820年至1899年之间出生的队列死亡率。讨论了这种更精确的死亡率模型的优点。EGG模型更适合于经验现实，即，在本文中，具有高质量数据的五个国家在1820年至1899年之间出生的队列死亡率。讨论了这种更精确的死亡率模型的优点。EGG模型更适合于经验现实，即，在本文中，具有高质量数据的五个国家在1820年至1899年之间出生的队列死亡率。讨论了这种更精确的死亡率模型的优点。