Errors as a primary cause of late-life mortality deceleration and plateaus

An underappreciated peculiarity of late-life human mortality kinetics assessed through the lens of a generalization of the Gompertz-Makeham law

Much attention in biogerontology is paid to the deceleration of mortality rate increase with age by the end of a species-specific lifespan, e.g. after ca. 90 years in humans. Being analyzed based on the Gompertz law µ(t)=µ0e^γt with its inbuilt linearity of the dependency of lnµ on t, this is commonly assumed to reflect the heterogeneity of populations where the frailer subjects die out earlier thus increasing the proportions of those whose dying out is slower and leading to decreases in the demographic rates of aging. Using Human Mortality Database data related to France, Sweden and Japan in five periods 1920, 1950, 1980, 2018 and 2020 and to the cohorts born in 1920, it is shown by LOESS smoothing of the lnµ-vs-t plots and constructing the first derivatives of the results that the late-life deceleration of the life-table aging rate (LAR) is preceded by an acceleration. It starts at about 65 years and makes LAR at about 85 years to become 30% higher than it was before the acceleration. Thereafter, LAR decreases and reaches the pre-acceleration level at ca. 90 years. This peculiarity cannot be explained by the predominant dying out of frailer subjects at earlier ages. Its plausible explanation may be the acceleration of the biological aging in humans at ages above 65-70 years, which conspicuously coincide with retirement. The decelerated biological aging may therefore contribute to the subsequent late-life LAR deceleration. The biological implications of these findings are discussed in terms of a generalized Gompertz-Makeham law µ(t) = C(t)+µ0e^f(t).

Using a penalized likelihood to detect mortality deceleration

We suggest a novel method for detecting mortality deceleration by adding a penalty to the log-likelihood function in a gamma-Gompertz setting. This is an alternative to traditional likelihood inference and hypothesis testing. The main advantage of the proposed method is that it does not involve using a p-value, hypothesis testing, and asymptotic distributions. We evaluate the performance of our approach by comparing it with traditional likelihood inference on both simulated and real mortality data. Results have shown that our method is more accurate in detecting mortality deceleration and provides more reliable estimates of the underlying parameters. The proposed method is a significant contribution to the literature as it offers a powerful tool for analyzing mortality patterns.

Early-life physical performance predicts the aging and death of elite athletes

Athleticism and the mortality rates begin a lifelong trajectory of decline during early adulthood. Because of the substantial follow-up time required, however, observing any longitudinal link between early-life physical declines and late-life mortality and aging remains largely inaccessible. Here, we use longitudinal data on elite athletes to reveal how early-life athletic performance predicts late-life mortality and aging in healthy male populations. Using data on over 10,000 baseball and basketball players, we calculate age at peak athleticism and rates of decline in athletic performance to predict late-life mortality patterns. Predictive capacity of these variables persists for decades after retirement, displays large effect sizes, and is independent of birth month, cohort, body mass index, and height. Furthermore, a nonparametric cohort-matching approach suggests that these mortality rate differences are associated with differential aging rates, not just extrinsic mortality. These results highlight the capacity of athletic data to predict late-life mortality, even across periods of substantial social and medical change.

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.

Projecting Mortality Rates to Extreme Old Age with the CBDX Model

We introduce a simple extension to the CBDX model to project cohort mortality rates to extreme old age. The proposed approach fits a polynomial to a sample of age effects, uses the fitted polynomial to project the age effects to ages beyond the sample age range, then splices the sample and projected age effects, and uses the spliced age effects to obtain mortality rates for the higher ages. The proposed approach can be used to value financial instruments such as life annuities that depend on projections of extreme old age mortality rates.

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.

What have we learned about mortality patterns over the past 25 years?

In this paper, I examine progress in the field of mortality over the past 25 years. I argue that we have been most successful in taking advantage of an increasingly data-rich environment to improve aggregate mortality models and test pre-existing theories. Less progress has been made in relating our estimates of mortality risk at the individual level to broader mortality patterns at the population level while appropriately accounting for contextual differences and compositional change. Overall, I find that the field of mortality continues to be highly visible in demographic journals, including Population Studies. However much of what is published today in field journals could just as easily appear in neighbouring disciplinary journals, as disciplinary boundaries are shrinking.

Medawar and Hamilton on the selective forces in the evolution of ageing

Both Medawar and Hamilton contributed key ideas to the modern evolutionary theory of ageing. In particular, they both suggested that, in populations with overlapping generations, the force with which selection acts on traits declines with the age at which traits are expressed. This decline would eventually cause ageing to evolve. However, the biological literature diverges on the relationship between Medawar's analysis of the force of selection and Hamilton's. Some authors appear to believe that Hamilton perfected Medawar's insightful, yet ultimately erroneous analysis of this force, while others see Hamilton's analysis as a coherent development of, or the obvious complement to Medawar's. Here, the relationship between the two analyses is revisited. Two things are argued for. First, most of Medawar's alleged errors that Hamilton would had rectified seem not to be there. The origin of these perceived errors appears to be in a misinterpretation of Medawar's writings. Second, the mathematics of Medawar and that of Hamilton show a significant overlap. However, different meanings are attached to the same mathematical expression. Medawar put forth an expression for the selective force on age-specific fitness. Hamilton proposed a full spectrum of selective forces each operating on age-specific fitness components, i.e. mortality and fertility. One of Hamilton's expressions, possibly his most important, is of the same form as Medawar's expression. But Hamilton's selective forces on age-specific fitness components do not add up to yield Medawar's selective force on age-specific fitness. It is concluded that Hamilton's analysis should be considered neither as a correction to Medawar's analysis nor as its obvious complement.

Social Inequality and the Future of U.S. Life Expectancy

Despite decades of progress, the future of life expectancy in the United States is uncertain due to widening socioeconomic disparities in mortality, continued disparities in mortality across racial/ethnic groups, and an increase in extrinsic causes of death. These trends prompt us to scrutinize life expectancy in a high-income but enormously unequal society like the United States, where social factors determine who is most able to maximize their biological lifespan. After reviewing evidence for biodemographic perspectives on life expectancy, the uneven diffusion of health-enhancing innovations throughout the population, and the changing nature of threats to population health, we argue that sociology is optimally positioned to lead discourse on the future of life expectancy. Given recent trends, sociologists should emphasize the importance of the social determinants of life expectancy, redirecting research focus away from extending extreme longevity and towards research on social inequality with the goal of improving population health for all.

Are We Approaching a Biological Limit to Human Longevity?

Until recently human longevity records continued to grow in history, with no indication of approaching a hypothetical longevity limit. Also, earlier studies found that age-specific death rates cease to increase at advanced ages (mortality plateau) suggesting the absence of fixed limit to longevity too. In this study, we reexamine both claims with more recent and reliable data on supercentenarians (persons aged 110 years and older). We found that despite a dramatic historical increase in the number of supercentenarians, further growth of human longevity records in subsequent birth cohorts slowed down significantly and almost stopped for those born after 1879. We also found an exponential acceleration of age-specific death rates for persons older than 113 years in more recent data. Slowing down the historical progress in maximum reported age at death and accelerated growth of age-specific death rates after age 113 years in recent birth cohorts may indicate the need for more conservative estimates for future longevity records unless a scientific breakthrough in delaying aging would happen. The hypothesis of approaching a biological limit to human longevity has received some empirical support and it deserves further study and testing.

Cardio-metabolic consequences of dietary carbohydrates: reconciling contradictions using nutritional geometry

Carbohydrates are the major source of dietary energy, but their role in health and disease remains controversial. Recent epidemiological evidence suggests that the increased consumption of carbohydrates is associated with obesity and increased risk of mortality and dietary trials show that carbohydrate restriction leads to weight loss and improved glycaemic status in obese and diabetic subjects. In contrast, the diets of populations with long and healthy lifespans (e.g. traditional Okinawans from Japan) are high in carbohydrate and low in protein, and several clinical and preclinical studies have linked low-carbohydrate-high-protein diets with increased mortality risk. In this paper we attempt to reconcile these contradictory findings by moving beyond traditional single-nutrient analyses to consider the interactions between nutrients on health outcomes. We do so using the Geometric Framework (GF), a nutritional modelling platform that explicitly considers the main and interactive effects of multiple nutrients on phenotypic characteristics. Analysis of human data by GF shows that weight loss and improved cardio-metabolic outcomes under carbohydrate restriction derive at least in part from reduced caloric intake due to the concomitantly increased proportion of protein in the diet. This is because, as in many animals, a specific appetite for protein is a major driver of food intake in humans. Conversely, dilution of protein in the diet leverages excess food intake through compensatory feeding for protein ('protein leverage'). When protein is diluted in the diet by readily digestible carbohydrates and fats, as is the case in modern ultra-processed foods, protein leverage results in excess calorie intake, leading to rising levels of obesity and metabolic disease. However, when protein is diluted in the diet by increased quantities of less readily digestible forms of carbohydrate and fibre, energy balance is maintained and health benefits accrue, especially during middle age and early late-life. We argue that other controversies in carbohydrate research can be resolved using the GF methodology in dietary studies.

The increasing lifespan variation gradient by area-level deprivation: A decomposition analysis of Scotland 1981-2011

Life expectancy inequalities are an established indicator of health inequalities. More recent attention has been given to lifespan variation, which measures the amount of heterogeneity in age at death across all individuals in a population. International studies have documented diverging socioeconomic trends in lifespan variation using individual level measures of income, education and occupation. Despite using different socioeconomic indicators and different indices of lifespan variation, studies reached the same conclusion: the most deprived experience the lowest life expectancy and highest lifespan variation, a double burden of mortality inequality. A finding of even greater concern is that relative differences in lifespan variation between socioeconomic group were growing at a faster rate than life expectancy differences. The magnitude of lifespan variation inequalities by area-level deprivation has received limited attention. Area-level measures of deprivation are actively used by governments for allocating resources to tackle health inequalities. Establishing if the same lifespan variation inequalities emerge for area-level deprivation will help to better inform governments about which dimension of mortality inequality should be targeted. We measure lifespan variation trends (1981-2011) stratified by an area-level measure of socioeconomic deprivation that is applicable to the entire population of Scotland, the country with the highest level of variation and one of the longest, sustained stagnating trends in Western Europe. We measure the gradient in variation using the slope and relative indices of inequality. The deprivation, age and cause specific components driving the increasing gradient are identified by decomposing the change in the slope index between 1981 and 2011. Our results support the finding that the most advantaged are dying within an ever narrower age range while the most deprived are facing greater and increasing uncertainty. The least deprived group show an increasing advantage, over the national average, in terms of deaths from circulatory disease and external causes.

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

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.

A universal transcriptomic signature of age reveals the temporal scaling of Caenorhabditis elegans aging trajectories

We collected 60 age-dependent transcriptomes for C. elegans strains including four exceptionally long-lived mutants (mean adult lifespan extended 2.2- to 9.4-fold) and three examples of lifespan-increasing RNAi treatments. Principal Component Analysis (PCA) reveals aging as a transcriptomic drift along a single direction, consistent across the vastly diverse biological conditions and coinciding with the first principal component, a hallmark of the criticality of the underlying gene regulatory network. We therefore expected that the organism's aging state could be characterized by a single number closely related to vitality deficit or biological age. The "aging trajectory", i.e. the dependence of the biological age on chronological age, is then a universal stochastic function modulated by the network stiffness; a macroscopic parameter reflecting the network topology and associated with the rate of aging. To corroborate this view, we used publicly available datasets to define a transcriptomic biomarker of age and observed that the rescaling of age by lifespan simultaneously brings together aging trajectories of transcription and survival curves. In accordance with the theoretical prediction, the limiting mortality value at the plateau agrees closely with the mortality rate doubling exponent estimated at the cross-over age near the average lifespan. Finally, we used the transcriptomic signature of age to identify possible life-extending drug compounds and successfully tested a handful of the top-ranking molecules in C. elegans survival assays and achieved up to a +30% extension of mean lifespan.

Late-life mortality is underestimated because of data errors

Knowledge of true mortality trajectory at extreme old ages is important for biologists who test their theories of aging with demographic data. Studies using both simulation and direct age validation found that longevity records for ages 105 years and older are often incorrect and may lead to spurious mortality deceleration and mortality plateau. After age 105 years, longevity claims should be considered as extraordinary claims that require extraordinary evidence. Traditional methods of data cleaning and data quality control are just not sufficient. New, more strict methodologies of data quality control need to be developed and tested. Before this happens, all mortality estimates for ages above 105 years should be treated with caution.

This Primer explores recent evidence that demographic data errors can explain away apparent late-life mortality plateaus, proposing that traditional methods of data quality control are insufficient, and that claims of human longevity greater than 105 years should be considered extraordinary and require extraordinary evidence.

Evidence That Jeanne Calment Died in 1934-Not 1997

I present a body of data that, I argue, cumulatively casts serious doubt on the validity of Jeanne Calment's accepted world record of human life span. First, I assess the plausibility of the record based on the life spans of other centenarians in the International Database of Longevity (IDL) and critique some arguments put forward previously in support of that plausibility, including the longevity of Calment's ancestors. Second, I review the literature dedicated to Calment and discuss multiple contradictions in her interviews, biographies, photos, and documents. I argue that the evidence from these sources motivates renewed consideration of the previously rejected hypothesis that Jeanne's daughter Yvonne acquired her mother's identity after her death to avoid financial problems and that Jeanne Calment's death was reported as Yvonne's death in 1934. Finally I discuss the importance of reconsidering the principles of validation, due to the possibility of similar problems regarding other exceptionally long-lived people and the mistaken inferences that researchers may draw from flawed datasets. The phenomenon of Jeanne Calment may prove to be an instructive example of the uncertainty of seemingly well-established facts.

Plane inclinations: A critique of hypothesis and model choice in Barbi et al

This study highlights how the mortality plateau in Barbi and colleagues can be generated by low-frequency, randomly distributed age-misreporting errors. Furthermore, sensitivity of the late-life mortality plateau in Barbi and colleagues to the particular age range selected for regression is illustrated. Collectively, the simulation of age-misreporting errors in late-life human mortality data and a less-specific model choice than that of Barbi and colleagues highlight a clear alternative hypothesis to explanations based on evolution, the cessation of ageing, and population heterogeneity.