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New Trend in Old-Age Mortality: Gompertzialization of Mortality Trajectory

human longevity gompertz

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#1 Engadin

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Posted 23 May 2019 - 02:19 PM


Abstract

 

There is great interest among gerontologists, demographers, and actuaries in the question concerning the limits to human longevity. Attempts at getting answers to this important question have stimulated many studies on late-life mortality trajectories, often with opposing conclusions. One group of researchers believes that mortality stops growing with age at extreme old ages, and that hence there is no fixed limit to the human life span. Other studies found that mortality continues to grow with age up to extreme old ages. Our study suggests a possible solution to this controversy. We found that mortality deceleration is best observed when older, less accurate life span data are analyzed, while in the case of more recent and reliable data there is a persistent mortality growth with age. We compared the performance (goodness of fit) of two competing mortality models – the Gompertz model and the Kannisto (“mortality deceleration”) model – at ages of 80–105 years using data for 1880–1899 single-year birth cohorts of US men and women. The mortality modeling approach suggests a transition from mortality deceleration to the Gompertzian mortality pattern over time for both men and women. These results are consistent with the hypothesis about disappearing mortality deceleration over time due to improvement in the accuracy of age reporting. In the case of more recent data, mortality continues to grow with age even at very old ages. This observation may lead to more conservative estimates of future human longevity records.

 

 

Introduction

 

There is great interest among gerontologists, demographers, and actuaries in the question concerning the limits to human longevity, and whether any fixed limits exist at all. Attempts at getting answers to these important questions have stimulated many studies on late-life mortality trajectories, often with opposing conclusions. One group of researchers claims that mortality stops growing with age at extreme old ages, and that hence there is no fixed limit to the human life span [1]. Other studies found that mortality continues to grow with age even in late life [2]. Recent debates in Gerontology about limits to the human life span have highlighted the need to know better the shape of mortality trajectories at extreme old ages [34].

 

It has long been believed that the exponential growth of the force of mortality with age (the Gompertz law) is followed by a period of deceleration in which mortality growths more slowly than predicted by the Gompertz law [5-8]. Thatcher [7] and Thatcher et al. [8] tested several models of mortality using data from 13 countries with a presumably good quality of mortality statistics and found downward deviation of mortality from the Gompertz law after the age of 80 years. Horiuchi and Wilmoth [6] analyzed age trajectories of life table aging rates in Sweden and Japan and found that the life table aging rate has a tendency to decline after 75–80 years of age, suggesting mortality deceleration. This mortality deceleration eventually produces “late-life mortality leveling-off” and “late-life mortality plateaus” at extreme old ages [5910]. Actuaries (including Gompertz himself) first noted this phenomenon, and they proposed a logistic formula for mortality growth with age in order to account for mortality deceleration at advanced ages. The same phenomenon of “almost non-aging” survival dynamics at extreme old ages was observed in other biological species. In some species (medflies and house flies) the mortality plateau can occupy a sizable part of their life [11]. The existence of mortality plateaus is now well documented for a number of lower organisms [see review in 11]. However, later studies have reported no mortality deceleration at older ages for primates [1213], rodents, and humans [214]. In another study, Gompertz-like mortality was found for Australia, Canada, and the USA and mortality deceleration for a number of European countries [15].

 

Estimation of the force of mortality at very old ages causes difficulties, because of the very small number of survivors to these ages and because of age misreporting by older persons. Age misreporting may be a problem affecting estimates of mortality at older ages [16-19]. Even a small percentage of inaccurate data can greatly distort mortality trajectories at advanced ages [2021]. In most cases, age misreporting at older ages leads to mortality underestimation [22], and even rare errors in age reporting can accumulate at extreme old ages, leading to spurious mortality deceleration [21]. Taking into account that the accuracy of age reporting is positively correlated with education [23], we can hypothesize that improvement of education over time would lead to more accurate age reporting and hence less prevalent mortality deceleration. Also, it is known that birth registration in the USA was introduced gradually, with only 6 states having official birth registration between 1841 and 1890 [24]. Introduction of birth registration improves the quality of age reporting among subsequent birth cohorts. Preliminary data suggest that mortality at advanced ages in earlier US birth cohorts shows stronger deceleration than mortality in later birth cohorts [14].

 

Here we analyze the historical evolution of mortality trajectories at advanced ages using age-specific death rates for 20 cohorts born in 1880–1899 in the USA. We study two competing models describing mortality trajectories (the Gompertz model and the Kannisto model) with the Akaike goodness-of-fit criterion. We hypothesize that mortality deceleration should fade away in more recent birth cohorts due to improvement in age reporting over time.

 

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S O U R C E :   Karger







Also tagged with one or more of these keywords: human longevity, gompertz

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