Mortality deceleration and mortality selection: three unexpected implications of a simple model

State-Level Education Quality and Trajectories of Cognitive Function by Race and Educational Attainment

Policy Points Education-cognition research overlooks the role of education quality in shaping cognitive function at midlife and older ages, even though quality may be more responsive to federal and state investment in public schooling than attainment. For older US adults who attended school during the early to mid-20th century, the quality of US education improved considerably as federal and state investment increased. Ensuring access to high-quality primary and secondary education may protect against poor cognitive function at midlife and older ages, particularly among Black Americans and persons who complete less education. It may also play an important role in reducing health inequities.

CONTEXT

Although educational attainment is consistently associated with better cognitive function among older adults, we know little about how education quality is related to cognitive function. This is a key gap in the literature given that the quality of US education improved considerably during the early to mid-20th century as state and federal investment increased. We posit that growing up in states with higher-quality education systems may protect against poor cognitive function, particularly among Black adults and adults who completed fewer years of school.

METHODS

We used prospective data on cognitive function from the Health and Retirement Study linked to historical data on state investment in public schools, restricting our sample to non-Hispanic White and Black adults born between 1914 and 1959 (19,096 White adults and 4,625 Black adults). Using race-stratified linear mixed models, we considered if state-level education quality was associated with level and decline in cognitive function and if these patterns differed by years of schooling and race.

FINDINGS

Residing in states with higher-resourced education systems during childhood was associated with better cognitive function, particularly among those who completed less than 12 years of schooling, regardless of race. For White adults, higher-resourced state education systems were associated with higher scores of total cognitive function and episodic memory, but there were diminishing returns as resources increased to very high levels. For Black adults, the relationship between state education resources and cognitive function varied by age with positive associations in midlife and generally null or negative associations at the oldest ages.

CONCLUSIONS

Federal and state investment in public schools may provide students with opportunities to develop important cognitive resources during schooling that translate into better cognitive function in later life, especially among marginalized populations.

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).

Black and white differences in subjective survival expectations: An evaluation of competing mechanisms

While black-white inequality in longevity is well documented in the United States, little is known about how individuals from different race/ethnic groups form their own personal survival expectations. Prior research has found that despite having higher mortality, blacks on average report higher survival expectations relative to whites. Using data from the Health and Retirement Study, we examined racial differences in subjective survival expectations across birth cohorts and provide explanatory mechanisms. We find that blacks-men in particular-were overly optimistic about their survival, but this effect had waned with successive birth cohorts. Furthermore, whereas subjective survival expectations and actual survival were correlated among white men, among black men the most optimistic fared worst. Blacks and whites differed not only in their response patterns, but also in how they weighed the different factors (socioeconomic, psychosocial, health, parental longevity) associated with expected survival. Importantly, those who estimated their survival probability with certainty had positive psychosocial characteristics, irrespective of race, but only whites had better health. These findings underscore the importance of group differences in subjective survival expectations as another potential form of inequality. Racial differences in how long individual expect to live may account for differences in social and economic behavior and outcomes, irrespective of actual longevity differentials.

Patterns in age and cause of death contribution to the sex gap in life expectancy: a comparison among ten countries

Women live longer than men and the absolute difference between male and female mortality risk reaches its maximum at old ages. We decomposed the sex gap in life expectancy and investigated the changes over time of the profile of the age–cause specific contributions with indicators of location, magnitude and dispersion in ten countries. Data were retrieved from the Human Cause-of-Death Database. The decomposition analyses revealed that neoplasm, heart diseases and external causes were the main drivers of the gender gap. We also find two main patterns in the development of age-specific contributions. With mortality delay, regarding neoplasm-related mortality and heart disease-related mortality, the shift (i.e., movement of the modal age at contribution towards older ages) and compression (i.e., dispersion concentrated on a shorter age interval) of the survival advantage of women over a narrower age range reveal that men are gradually improving their survival. This might be linked to improvements in survival, diagnosis and access to treatment, at least to those ages no longer affected by the most significant differences.

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.

Unobserved Population Heterogeneity and Dynamics of Health Disparities

BACKGROUND

A growing body of literature has reported widening educational health disparities across birth cohorts or time periods in the United States, but has paid little attention to the implication of mortality selection on the cohort trend in health disparities.

OBJECTIVE

This study investigates how changes in the variance of unobserved frailty over time may complicate the interpretation of cohort trends in health disparities and life expectancy.

METHODS

We use the microsimulation method to test the effect of mortality selection and further propose a counterfactual simulation procedure to estimate its contribution. Data used in the simulations are based on Panel Studies of Income Dynamics 1968-2013, National Health and Nutrition Examination Survey data 1999-2012, and National Health Interview Survey data 1986-2011.

RESULTS

Simulation shows that mortality selection may generate seemingly contradictory trends in health disparities and life expectancy across birth cohorts at the group and individual level. Life expectancy can change even when individual mortality curve is fixed. In the absence of a change in the causal effect of education on mortality at the individual level, an educational life expectancy gap can change across cohorts as a result of the change in frailty variance. Empirical analysis shows that mortality selection accounts for a sizeable amount of contribution to the widening educational life expectancy gap from the 1950s to 1960s birth cohorts in the United States.

CONTRIBUTION

We demonstrate mortality selection can complicate the cohort trend in health disparities and life expectancy and propose a counterfactual simulation method to evaluate its contribution.

Urinary markers of oxidative stress respond to infection and late-life in wild chimpanzees

Oxidative stress (OS) plays a marked role in aging and results from a variety of stressors, making it a powerful measure of health and a way to examine costs associated with life history investments within and across species. However, few urinary OS markers have been examined under field conditions, particularly in primates, and their utility to non-invasively monitor the costs of acute stressors versus the long-term damage associated with aging is poorly understood. In this study, we examined variation in 5 urinary markers of oxidative damage and protection under 5 validation paradigms for 37 wild, chimpanzees living in the Kibale National Park, Uganda. We used 924 urine samples to examine responses to acute immune challenge (respiratory illness or severe wounding), as well as mixed-longitudinal and intra-individual variation with age. DNA damage (8-OHdG) correlated positively with all other markers of damage (F-isoprostanes, MDA-TBARS, and neopterin) but did not correlate with protection (total antioxidant capacity). Within individuals, all markers of damage responded to at least one if not both types of acute infection. While OS is expected to increase with age, this was not generally true in chimpanzees. However, significant changes in oxidative damage were detected within past-prime individuals and those close to death. Our results indicate that OS can be measured using field-collected urine and integrates short- and long-term aspects of health. They further suggest that more data are needed from long-lived, wild animals to illuminate if common age-related increases in inflammation and OS damage are typical or recently aberrant in humans.

Multidimensional Mortality Selection: Why Individual Dimensions of Frailty Don't Act Like Frailty

Theoretical models of mortality selection have great utility in explaining otherwise puzzling phenomena. The most famous example may be the Black-White mortality crossover: at old ages, Blacks outlive Whites, presumably because few frail Blacks survive to old ages while some frail Whites do. Yet theoretical models of unidimensional heterogeneity, or frailty, do not speak to the most common empirical situation for mortality researchers: the case in which some important population heterogeneity is observed and some is not. I show that, when one dimension of heterogeneity is observed and another is unobserved, neither the observed nor the unobserved dimension need behave as classic frailty models predict. For example, in a multidimensional model, mortality selection can increase the proportion of survivors who are disadvantaged, or "frail," and can lead Black survivors to be more frail than Whites, along some dimensions of disadvantage. Transferring theoretical results about unidimensional heterogeneity to settings with both observed and unobserved heterogeneity produces misleading inferences about mortality disparities. The unusually flexible behavior of individual dimensions of multidimensional heterogeneity creates previously unrecognized challenges for empirically testing selection models of disparities, such as models of mortality crossovers.

Detecting the Effects of Early-Life Exposures: Why Fecundity Matters

Prenatal exposures have meaningful effects on health across the lifecourse. Innovations in causal inference have shed new light on these effects. Here, we motivate the importance of innovation in the characterization of fecundity, and prenatal selection in particular. We argue that such innovation is crucial for expanding knowledge of the fetal origins of later life health. Pregnancy loss is common, responsive to environmental factors, and closely related to maternal and fetal health outcomes. As a result, selection into live birth is driven by many of the same exposures that shape the health trajectories of survivors. Lifecourse effects that are inferred without accounting for these dynamics may be significantly distorted by survival bias. We use a set of Monte Carlo simulations with realistic parameters to examine the implications of prenatal survival bias. We find that even in conservatively specified scenarios, true fetal origin effects can be underestimated by 50% or more. In contrast, effects of exposures that reduce the probability of prenatal survival but improve the health of survivors will be overestimated. The absolute magnitude of survival bias can even exceed small effect sizes, resulting in inferences that beneficial exposures are harmful or vice-versa. We also find reason for concern that moderately sized true effects, underestimated due to failure to account for selective survival, are missing from scientific knowledge because they do not clear statistical significance filters. This bias has potential real-world costs; policy decisions about interventions to improve maternal and infant health will be affected by underestimated program impact.

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.

Robust Respondents and Lost Limitations: The Implications of Nonrandom Missingness for the Estimation of Health Trajectories

OBJECTIVE

We offer a strategy for quantifying the impact of mortality and attrition on inferences from later-life health trajectory models.

METHOD

Using latent class growth analysis (LCGA), we identify functional limitation trajectory classes in the Health and Retirement Study. We compare results from complete case and full information maximum likelihood (FIML) analyses, and demonstrate a method for producing upper- and lower-bound estimates of the impact of attrition on results.

RESULTS

LCGA inferences vary substantially depending on the handling of missing data. For older adults who die during the follow-up period, the widely used FIML approach may underestimate functional limitations by up to 20%.

DISCUSSION

The most commonly used approaches to handling missing data likely underestimate the extent of poor health in aging populations. Although there is no single solution for nonrandom missingness, we show that bounding estimates can help analysts to better characterize patterns of health in later life.

A simulation study of the role of cohort forces in mortality patterns

This study uses the micro-simulation method to investigate the role of cohort forces in age-dependent mortality pattern. We test the micro mechanisms for cohort evolution and mortality selection, and how these two biological and demographic forces may interact with epidemiologic transition to shape the cohort age-dependence of mortality pattern in both early- and later-transition countries. We show that cohort evolution is due to the declining rate of mortality acceleration at the individual level, which is associated with lower initial mortality rates but not smaller variance of frailty distribution in later birth cohorts. The steeper slope of mortality acceleration at the population level among later birth cohorts is due to mortality selection mechanism associated with smaller variance of frailty distribution but not lower initial mortality rates. These two forces jointly shape the non-crossover cohort age-dependence of mortality pattern regardless of the differential mechanisms of epidemiologic transition in early- and later-transition countries.

The Methuselah Effect: The Pernicious Impact of Unreported Deaths on Old-Age Mortality Estimates

We examine inferences about old-age mortality that arise when researchers use survey data matched to death records. We show that even small rates of failure to match respondents can lead to substantial bias in the measurement of mortality rates at older ages. This type of measurement error is consequential for three strands in the demographic literature: (1) the deceleration in mortality rates at old ages; (2) the black-white mortality crossover; and (3) the relatively low rate of old-age mortality among Hispanics, often called the "Hispanic paradox." Using the National Longitudinal Survey of Older Men matched to death records in both the U.S. Vital Statistics system and the Social Security Death Index, we demonstrate that even small rates of missing mortality matching plausibly lead to an appearance of mortality deceleration when none exists and can generate a spurious black-white mortality crossover. We confirm these findings using data from the National Health Interview Survey matched to the U.S. Vital Statistics system, a data set known as the "gold standard" (Cowper et al. 2002) for estimating age-specific mortality. Moreover, with these data, we show that the Hispanic paradox is also plausibly explained by a similar undercount.

On the heterogeneity of human populations as reflected by mortality dynamics

The heterogeneity of populations is used to explain the variability of mortality rates across the lifespan and their deviations from an exponential growth at young and very old ages. A mathematical model that combines the heterogeneity with the assumption that the mortality of each constituent subpopulation increases exponentially with age, has been shown to successfully reproduce the entire mortality pattern across the lifespan and its evolution over time. In this work we aim to show that the heterogeneity is not only a convenient consideration for fitting mortality data but is indeed the actual structure of the population as reflected by the mortality dynamics over age and time. In particular, we show that the model of heterogeneous population fits mortality data better than other commonly used mortality models. This was demonstrated using cohort data taken for the entire lifespan as well as for only old ages. Also, we show that the model can reproduce seemingly contradicting observations in late-life mortality dynamics. Finally, we show that the homogenisation of a population, observed by fitting the model to actual data of consecutive periods, can be associated with the evolution of allele frequencies if the heterogeneity is assumed to reflect the genetic variations within the population.

Evolutionary theory of ageing and the problem of correlated Gompertz parameters

The Gompertz mortality model is often used to evaluate evolutionary theories of ageing, such as the Medawar-Williams' hypothesis that high extrinsic mortality leads to faster ageing. However, fits of the Gompertz mortality model to data often find the opposite result that mortality is negatively correlated with the rate of ageing. This negative correlation has been independently discovered in several taxa and is known in actuarial studies of ageing as the Strehler-Mildvan correlation. We examine the role of mortality selection in determining late-life variation in susceptibility to death, which has been suggested to be the cause of this negative correlation. We demonstrate that fixed-frailty models that account for heterogeneity in frailty do not remove the correlation and that the correlation is an inherent statistical property of the Gompertz distribution. Linking actuarial and biological rates of ageing will continue to be a pressing challenge, but the Strehler-Mildvan correlation itself should not be used to diagnose any biological, physiological, or evolutionary process. These findings resolve some key tensions between theory and data that affect evolutionary and biological studies of ageing and mortality. Tests of evolutionary theories of ageing should include direct measures of physiological performance or condition.

Retired flies, hidden plateaus, and the evolution of senescence in Drosophila melanogaster

Late-life plateaus in age-specific mortality have been an evolutionary and biodemographic puzzle for decades. Although classic theory on the evolution of senescence predicts late-life walls of death, observations in experimental organisms document the opposite trend: a slowing in the rate of increase of mortality at advanced ages. Here, I analyze published life-history data on individual Drosophila melanogaster females and argue for a fundamental change in our understanding of mortality in this important model system. Mortality plateaus are not, as widely assumed, exclusive to late life, and are not explained by population heterogeneity-they are intimately connected to individual fecundity. Female flies begin adult life in the working stage, a period of active oviposition and low but accelerating mortality. Later they transition to the retired stage, a terminal period characterized by limited fecundity and relatively constant mortality. Because ages of transition differ between flies, age-synchronized cohorts contain a mix of working and retired flies. Early- and mid-life plateaus are obscured by the presence of working flies, but can be detected when cohorts are stratified by retirement status. Stage-specificity may be an important component of Drosophila life-history evolution.

On the beginning of mortality acceleration

Physiological senescence is characterized by the increasing limitation of capabilities of an organism resulting from the progressive accumulation of molecular damage, which at group (cohort) level translates into, among other things, an increase in mortality risks with age. Physiological senescence is generally thought to begin at birth, if not earlier, but models of demographic aging (i.e., an increase in mortality risks) normally start at considerably later ages. This apparent inconsistency can be solved by assuming the existence of two mortality regimes: "latent" and "manifest" aging. Up to a certain age, there is only latent aging: physiological senescence occurs, but its low level does not trigger any measurable increase in mortality. Past a certain level (and age), molecular damage is such that mortality risks start to increase. We first discuss why this transition from latent to manifest aging should exist at all, and then we turn to the empirical estimation of the corresponding threshold age by applying Bai's approach to the estimation of breakpoints in time series. Our analysis, which covers several cohorts born between 1850 and 1938 in 14 of the countries included in the Human Mortality Database, indicates that an age at the onset of manifest aging can be identified. However, it has not remained constant: it has declined from about 43 and 47 years, respectively, for males and females at the beginning of the period (cohorts born in 1850-1869) to about 31 for both males and females toward its end (cohorts born in 1920-1938). A discussion of why this may have happened ensues.

On the analysis and interpretation of late-life fecundity in Drosophila melanogaster

Late-life plateaus have been described in both cohort and individual trajectories of fecundity in Drosophila melanogaster females. Here I examine life history data recently analyzed by Le Bourg and Moreau (2014) and show that non-linearity in the cohort trajectory of fecundity is largely explained by heterogeneity in the duration of reproductive life spans. A model specifying linear post-peak decline of fecundity in individual flies provides a better fit to the data than one that combines linear decline with late-life fecundity plateaus. Using repeated measures analysis of variance, I show that age-dependent trends in individual fecundity are mostly linear, while among the most longevous individuals up to 20% of the variation in trends is non-linear. Plateaus in individual trajectories might be explained by evolutionary processes or by random environmental variation. The dominant role of environmental variation is supported by several observations, including the high variability of late-life fecundity, the occurrence of occasional individual plateaus in inbred lines, and the observation of plateaus in only a fraction of the population. Plateau and non-plateau flies identified by Le Bourg and Moreau (2014) have, on average, the same total fecundity and the same fecundity trajectories. The available evidence suggests that the environmental variance for late-life fecundity is sufficiently large to produce occasional individual trajectories that resemble plateaus but are not heritable.