Demographic indicators, models, and testing

The use of simple demographic indicators to describe mortality dynamics can obscure important features of the survival curve, particularly during periods of rapid change, such as those caused by internal or external factors, and especially at the oldest or youngest ages. Therefore, instead of the generally accepted Gompertz method, other methods based on demographic indicators are often used. In human populations, chronic phenoptosis, in contrast to age-independent acute phenoptosis, is characterized by rectangularization of the survival curve and an accompanying increase in average life expectancy at birth, which can be attributed to advances in society and technology. Despite the simple geometric interpretation of the phenomenon of rectangularization of the survival curve, it is difficult to notice one, detecting changes in the optimal coefficients in the Gompertz-Makeham law due to high computational complexity and increased calculation errors. This is avoided by calculating demographic indicators such as the Keyfitz entropy, the Gini coefficient, and the coefficient of variation in lifespan. Our analysis of both theoretical models and real demographic data shows that with the same value of the Gini coefficient in the compared cohorts, a larger value of the Keyfitz entropy indicates a greater proportion of centenarians relative to average life expectancy. On the contrary, at the same value of the Keyfitz entropy, a larger value of the Gini coefficient corresponds to a relatively large mortality at a young age. We hypothesize that decreases in the Keyfitz entropy may be attributable to declines in background mortality, reflected in the Makeham term, or to reductions in mortality at lower ages, corresponding to modifications in another coefficient of the Gompertz law. By incorporating dynamic shifts in age into survival analyses, we can deepen our comprehension of mortality patterns and aging mechanisms, ultimately contributing to the development of more reliable methods for evaluating the efficacy of anti-aging and geroprotective interventions used in gerontology.