Limits to Human Life Span Through Extreme Value Theory

Limits to lifespan growth

A long-standing human lifespan debate is revival, and the consensus is yet to come on whether the maximum human lifespan is reaching a limit or not. This study discusses how mathematical constraints inherent in survival curves indicate a limit on maximum lifespans, implying that humans would have inevitable limits to lifespan growth.

On the emergence of the correlation between life expectancy and the variance in the age at death

Recent empirical studies have found various patterns in the correlations between lifespan inequality and life expectancy in modern human populations. However, it is unclear how general these regularities are. Here we establish three theorems that provide theoretical foundations for such regularities. We show that for populations with a finite maximum lifespan ω, and under certain continuity assumptions, the variance in the age at death is bounded by a function of lifespan that has a maximum and tends to zero as life expectancy tends to zero and ω. We show how the change in said variance is determined by a particular interplay between the coefficient of variation and the mean age in the population. These results lead to three hypotheses-a three-phased pattern of change for the correlation between the variance and life expectancy, a particular shape of the associated variance function, and that survival curve Type is one driver of the pattern. We illustrate those hypotheses empirically via a study of the 10 countries in the Human Mortality Database with the oldest available data. Our results elucidate the emergence of the aforementioned correlation patterns and provide demographically meaningful conditions under which those correlations reverse.

Why Gilgamesh failed: the mechanistic basis of the limits to human lifespan

The purpose of this Perspective is to clarify for an interdisciplinary audience the fundamental concepts of human longevity and provide evidence for a limit to human lifespan. This observed limit is placed into a broader framework by showing how it has arisen through the process of evolution and by enumerating the molecular mechanisms that may enforce it. Finally, we look toward potential future developments and the prospects for possibly circumventing the current limit.

The curse of the plateau. Measuring confidence in human mortality estimates at extreme ages

In recent years, the importance of describing mortality at the limits of the life span has led to a number of relevant and controversial studies. Whereas considerable efforts have been devoted to collecting data and estimating models on the oldest-old individuals, the testing of statistical confidence about the conclusions of analyses at extreme ages has been largely neglected. How certain can we be in saying that the risk of dying increases, levels out, or, paradoxically, decreases over age 105? Can we recognize particular mortality age patterns at such high ages? In this paper, it is shown that very little can be confidently asserted about mortality at extreme ages. Instead of analysing actual data, we perform a series of simulation studies mimicking actual scenarios from controlled mechanisms. Our findings are thus robust with respect to factors such as particular observation schemes, heterogeneity, and data quality issues. Given the sample sizes currently available and the levels of mortality experienced in present populations, we show that before age 110, only a Gompertzian increase of mortality may be detected. Afterwards a plateau will be regularly recognized as the most suitable pattern, regardless of the complexity of the true underlying mortality.

Comparison of Japanese Centenarians' and Noncentenarians' Medical Expenditures in the Last Year of Life

IMPORTANCE

Although research has shown that centenarians tend to experience shorter periods of serious illness compared with other age groups, few studies have focused on the medical expenditures of centenarians as a potential indicator of the scale of medical resources used in their last year of life.

OBJECTIVE

To compare Japanese centenarians' and noncentenarians' monthly medical expenditures during the year before death according to age and sex.

DESIGN, SETTING, AND PARTICIPANTS

This retrospective cohort study used linked national health and long-term care insurance data collected from April 2013 to March 2018 in Nara Prefecture, Japan, for residents aged 75 years or older who were insured under the Medical Care System for older adults and died between April 2014 and March 2018. Data were analyzed from April 2013 to March 2018.

EXPOSURES

Age of 100 years or older (centenarians) vs 75 to 99 years (noncentenarians).

MAIN OUTCOMES AND MEASURES

The numbers of unique inpatients and outpatients and medical expenditures related to decedents' hospitalization and outpatient care were extracted and analyzed based on sex and age group. The Jonckheere-Terpstra test was used to identify trends in unadjusted medical expenditures by age group, and generalized estimating equations were used to estimate monthly median expenditures by age group with adjustment for comorbidity burden and functional status.

RESULTS

Of 34 317 patients aged 75 to 109 years (16 202 men [47.2%] and 18 115 women [52.8%]) who died between April 2014 and March 2018, 872 (2.5%) were aged 100 to 104 years (131 men [15.0%] and 741 women [85.0%]) and 78 (0.2%) were aged 105 to 109 years (fewer than 10 were men). The analysis of unadjusted medical expenditures in the last year of life showed a significant trend of lower expenditures for the older age groups; the median adjusted total expenditures during the 30 days before death by age group were $6784 (IQR, $4884-$9703) for ages 75 to 79 years, $5894 (IQR, $4292-$8536) for 80 to 84 years, $5069 (IQR, $3676-$7150) for 85 to 89 years, $4205 (IQR, $3085-$5914) for 90 to 94 years, $3522 (IQR, $2626-$4861) for 95 to 99 years, $2898 (IQR, $2241-$3835) for 100 to 104 years, and $2626 (IQR, $1938-$3527) for 105 to 109 years. The proportion of inpatients among all patients in the year before death also decreased with increasing age: 4311 of all 4551 patients aged 75 to 79 years (94.7%); 43 of all 78 patients aged 105 to 109 years (55.1%); 2831 of 2956 men aged 75 to 79 years (95.8%); 50.0% of men aged 105 to 109 years (the number is not reported owing to the small sample size); 1480 of 1595 women aged 75 to 79 years (92.8%); and 55.7% of women aged 105 to 109 years (the number of women is not reported to prevent back-calculation of the number of men). Specifically, 274 of 872 patients aged 100 to 104 years (31.4%) and 35 of 78 patients aged 105 to 109 years (44.9%) had not been admitted to a hospital in the year before death.

CONCLUSIONS AND RELEVANCE

This cohort study found that medical expenditures in the last year of life tended to be lower for centenarians than for noncentenarians aged 75 years or older in Japan. The proportion of inpatients also decreased with increasing age. These findings may inform future health care services coverage and policies for centenarians.

Human mortality at extreme age

We use a combination of extreme value statistics, survival analysis and computer-intensive methods to analyse the mortality of Italian and French semi-supercentenarians. After accounting for the effects of the sampling frame, extreme-value modelling leads to the conclusion that constant force of mortality beyond 108 years describes the data well and there is no evidence of differences between countries and cohorts. These findings are consistent with use of a Gompertz model and with previous analysis of the International Database on Longevity and suggest that any physical upper bound for the human lifespan is so large that it is unlikely to be approached. Power calculations make it implausible that there is an upper bound below 130 years. There is no evidence of differences in survival between women and men after age 108 in the Italian data and the International Database on Longevity, but survival is lower for men in the French data.