Analysis of trends in human longevity by new model

TL;DR

This paper introduces a new model based on the Weibull survival function to analyze human longevity trends, revealing potential limits to lifespan despite increases in characteristic life.

Contribution

A novel two-parameter model that better describes survival curves and provides insights into the limits of human longevity compared to traditional models.

Findings

Characteristic life has increased over time.

Rectangularity of survival curves has decreased in recent decades.

Potential limits to human lifespan are suggested by model analysis.

Abstract

Trends in human longevity are puzzling, especially when considering the limits of human longevity. Partially, the conflicting assertions are based upon demographic evidence and the interpretation of survival and mortality curves using the Gompertz model and the Weibull model; these models are sometimes considered to be incomplete in describing the entire curves. In this paper a new model is proposed to take the place of the traditional models. We directly analysed the rectangularity (the parts of the curves being shaped like a rectangle) of survival curves for 17 countries and for 1876-2001 in Switzerland (it being one of the longest-lived countries) with a new model. This model is derived from the Weibull survival function and is simply described by two parameters, in which the shape parameter indicates 'rectangularity' and characteristic life indicates the duration for survival to be 'exp(-1)'. The shape parameter is essentially a function of age and it distinguishes humans from technical devices. We find that although characteristic life has increased up to the present time, the slope of the shape parameter for middle age has been saturated in recent decades and that the rectangularity above characteristic life has been suppressed, suggesting there are ultimate limits to human longevity. The new model and subsequent findings will contribute greatly to the interpretation and comprehension of our knowledge on the human ageing processes.