Heterogeneity in the Strehler-Mildvan general theory of mortality and aging

Why Does Child Mortality Decrease With Age? Modeling the Age-Associated Decrease in Mortality Rate Using WHO Metadata From 25 Countries

Background: Our previous study analyzed the age trajectory of mortality (ATM) in 14 European countries, while this study aimed at investigating ATM in other continents and in countries with a higher level of mortality. Data from 11 Non-European countries were used. Methods: The number of deaths was extracted from the WHO mortality database. The Halley method was used to calculate the mortality rates in all possible calendar years and all countries combined. This method enables us to combine more countries and more calendar years in one hypothetical population. Results: The age trajectory of total mortality (ATTM) and also ATM due to specific groups of diseases were very similar in the 11 non-European countries and in the 14 European countries. The level of mortality did not affect the main results found in European countries. The inverse proportion was valid for ATTM in non-European countries with two exceptions. Slower or no mortality decrease with age was detected in the first year of life, while the inverse proportion model was valid for the age range (1, 10) years in most of the main chapters of ICD10. Conclusions: The decrease in child mortality with age may be explained as the result of the depletion of individuals with congenital impairment. The majority of deaths up to the age of 10 years were related to congenital impairments, and the decrease in child mortality rate with age was a demonstration of population heterogeneity. The congenital impairments were latent and may cause death even if no congenital impairment was detected.

Why Does Child Mortality Decrease With Age? Modeling the Age-Associated Decrease in Mortality Rate Using WHO Metadata From 14 European Countries

Background: Mortality rate rapidly decreases with age after birth, and, simultaneously, the spectrum of death causes show remarkable changes with age. This study analyzed age-associated decreases in mortality rate from diseases of all main chapters of the 10th revision of the International Classification of Diseases. Methods: The number of deaths was extracted from the mortality database of the World Health Organization. As zero cases could be ascertained for a specific age category, the Halley method was used to calculate the mortality rates in all possible calendar years and in all countries combined. Results: All causes mortality from the 1st day of life to the age of 10 years can be represented by an inverse proportion model with a single parameter. High coefficients of determination were observed for total mortality in all populations (arithmetic mean = 0.9942 and standard deviation = 0.0039). Slower or no mortality decrease with age was detected in the 1st year of life, while the inverse proportion method was valid for the age range [1, 10) years in most of all main chapters with three exceptions. The decrease was faster for the chapter "Certain conditions originating in the perinatal period" (XVI).The inverse proportion was valid already from the 1st day for the chapter "Congenital malformations, deformations and chromosomal abnormalities" (XVII).The shape of the mortality decrease was very different for the chapter "Neoplasms" (II) and the rates of mortality from neoplasms were age-independent in the age range [1, 10) years in all populations. Conclusion: The theory of congenital individual risks of death is presented and can explain the results. If it is valid, latent congenital impairments may be present among all cases of death that are not related to congenital impairments. All results are based on published data, and the data are presented as a supplement.

A 2D analysis of correlations between the parameters of the Gompertz-Makeham model (or law?) of relationships between aging, mortality, and longevity

When mortality (μ), aging rate (γ) and age (t) are treated according to the Gompertz model μ(t) = μ₀e^γt (GM), any mean age corresponds to a manifold of paired reciprocally changing μ₀ and γ. Therefore, any noisiness of data used to derive GM parameters makes them negatively correlated. Besides this artifactual factor of the Strehler-Mildvan correlation (SMC), other factors emerge when the age-independent mortality C modifies survival according to the Gompertz-Makeham model μ(t) = C+μ₀e^γt (GMM), or body resources are partitioned between survival and protection from aging [the compensation effect of mortality (CEM)]. Theoretical curves in (γ, logμ₀) coordinates show how μ₀ decreases when γ increases upon a constant mean age. Within a species-specific range of γ, such "isoage" curves look as nearly parallel straight lines. The slopes of lines constructed by applying GM to survival curves modeled according to GMM upon changes in C are greater than the isoage slopes. When CEM is modeled, the slopes are still greater. Based on these observations, CEM is shown to contribute to SMC associated with sex differences in lifespan, with the effects of several life-extending drugs, and with recent trends in survival/mortality patterns in high-life-expectancy countries; whereas changes in C underlie differences between even high-life-expectancy countries, not only between high- and low-life-expectancy countries. Such interpretations make sense only if GM is not merely a statistical model, but rather reflects biological realities. Therefore, GM is discussed as derivable by applying certain constraints to a natural law termed the generalized Gompertz-Makeham law.

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.

A Tale of Two Concepts: Harmonizing the Free Radical and Antagonistic Pleiotropy Theories of Aging

SIGNIFICANCE

The two foremost concepts of aging are the mechanistic free radical theory (FRT) of how we age and the evolutionary antagonistic pleiotropy theory (APT) of why we age. Both date from the late 1950s. The FRT holds that reactive oxygen species (ROS) are the principal contributors to the lifelong cumulative damage suffered by cells, whereas the APT is generally understood as positing that genes that are good for young organisms can take over a population even if they are bad for the old organisms. Recent Advances: Here, we provide a common ground for the two theories by showing how aging can result from the inherent chemical reactivity of many biomolecules, not just ROS, which imposes a fundamental constraint on biological evolution. Chemically reactive metabolites spontaneously modify slowly renewable macromolecules in a continuous way over time; the resulting buildup of damage wrought by the genes coding for enzymes that generate such small molecules eventually masquerades as late-acting pleiotropic effects. In aerobic organisms, ROS are major agents of this damage but they are far from alone.

CRITICAL ISSUES

Being related to two sides of the same phenomenon, these theories should be compatible. However, the interface between them is obscured by the FRT mistaking a subset of damaging processes for the whole, and the APT mistaking a cumulative quantitative process for a qualitative switch.

FUTURE DIRECTIONS

The manifestations of ROS-mediated cumulative chemical damage at the population level may include the often-observed negative correlation between fitness and the rate of its decline with increasing age, further linking FRT and APT. Antioxid. Redox Signal. 29, 1003-1017.

Modeling the Age-Associated Decrease in Mortality Rate for Congenital Anomalies of the Central Nervous System Using WHO Metadata From Nine European Countries

Background: In humans, the mortality rate dramatically decreases with age after birth, and the causes of death change significantly during childhood. In the present study, we attempted to explain age-associated decreases in mortality for congenital anomalies of the central nervous system (CACNS), as well as decreases in total mortality with age. We further investigated the age trajectory of mortality in the biologically related category "diseases of the nervous system" (DNS). Methods: The numbers of deaths were extracted from the mortality database of the World Health Organization (WHO) for the following nine countries: Denmark, Finland, Norway, Sweden, Austria, the Czech Republic, Hungary, Poland, and Slovakia. Because zero cases could be ascertained over the age of 30 years in a specific age category, the Halley method was used to calculate the mortality rates in all possible calendar years and in all countries combined. Results: Total mortality from the first day of life up to the age of 10 years and mortality due to CACNS within the age interval of [0, 90) years can be represented by an inverse proportion with a single parameter. High coefficients of determination were observed for both total mortality (R2 = 0.996) and CACNS mortality (R2 = 0.990). Our findings indicated that mortality rates for DNS slowly decrease with age during the first 2 years of life, following which they decrease in accordance with an inverse proportion up to the age of 10 years. The theory of congenital individual risk (TCIR) may explain these observations based on the extinction of individuals with more severe impairments, as well as the bent curve of DNS, which exhibited an adjusted coefficient of determination of R ¯ 2 = 0.966. Conclusion: The coincidence between the age trajectories of all-cause and CACNS-related mortality may indicate that the overall decrease in mortality after birth is due to the extinction of individuals with more severe impairments. More deaths unrelated to congenital anomalies may be caused by the manifestation of latent congenital impairments during childhood.

Applying parametric models to survival data: tradeoffs between statistical significance, biological plausibility, and common sense

Parametric models for survival data help to differentiate aging from other lifespan determinants. However, such inferences suffer from small sizes of experimental animal samples and variable animals handling by different labs. We analyzed control data from a single laboratory where interventions in murine lifespan were studied over decades. The minimal Gompertz model (GM) was found to perform best with most murine strains. However, when several control datasets related to a particular strain are fitted to GM, strikingly rigid interdependencies between GM parameters emerge, consistent with the Strehler-Mildvan correlation (SMC). SMC emerges even when survival patterns do not conform to GM, as with cancer-prone HER2/neu mice, which die at a log-normally distributed age. Numerical experiments show that SMC includes an artifact whose magnitude depends on dataset deviation from conformance to GM irrespectively of the noisiness of small datasets, another contributor to SMC. Still another contributor to SMC is the compensation effect of mortality (CEM): a real tradeoff between the physiological factors responsible for initial vitality and the rate of its decline. To avoid misinterpretations, we advise checking experimental results against a SMC based on historical controls or on subgroups obtained by randomization of control animals. An apparent acceleration of aging associated with a decrease in the initial mortality is invalid if it is not greater than SMC suggests. This approach applied to published data suggests that the effects of calorie restriction and of drugs believed to mimic it are different. SMC and CEM relevance to human survival patterns is discussed.

Vitality heterogeneity in the Strehler-Mildvan theory of mortality

In this paper the Strehler-Mildvan theory of mortality and aging is generalised to cover heterogeneity effects in the population. The theory is based on the concept of environmental shocks that cause death of an individual when exceeding its vitality. Heterogeneity is introduced via the value of the vitality of an individual at birth. The main result of the paper is an expression for the observed mortality rate of the heterogeneous population. This mortality rate grows according to Gompertz's Law at midlife-ages, then its growth declines, levelling off at high ages. This behaviour is qualitatively consistent with real mortality rates, which is illustrated for period data of Japanese females in the years 1947, 1967, 1987 and 2007. Finally, the duality between a continuous SM-version and the ρ - γ - Gompertz model is discussed.

How We Fall Apart: Similarities of Human Aging in 10 European Countries

We analyze human aging—understood as health deficit accumulation—for a panel of European individuals, using four waves of the Survey of Health, Aging and Retirement in Europe (SHARE data set) and constructing a health deficit index. Results from log-linear regressions suggest that, on average, elderly European men and women develop approximately 2.5 % more health deficits from one birthday to the next. In nonlinear regressions (akin to the Gompertz-Makeham model), however, we find much greater rates of aging and large differences between men and women as well as between countries. Interestingly, these differences follow a particular regularity (akin to the compensation effect of mortality) and suggest an age at which average health deficits converge for men and women and across countries. This age, which may be associated with human life span, is estimated as 102 ± 2.6 years.

Food availability affects adult survival trajectories depending on early developmental conditions

Food availability modulates survival in interaction with (for example) competition, disease and predators, but to what extent food availability in natural populations affects survival independent of these factors is not well known. We tested the effect of food availability on lifespan and actuarial senescence in a large population of captive zebra finches by increasing the effort required to obtain food, reflecting natural contrasts in food availability. Food availability may not affect all individuals equally and we therefore created heterogeneity in phenotypic quality by raising birds with different numbers of siblings. Low food availability had no effect on lifespan for individuals from benign developmental conditions (raised in small broods), but shortened lifespan for individuals from harsh developmental conditions. The lifespan difference arose through higher baseline mortality rate of individuals from harsh developmental conditions, despite a decrease in the rate of actuarial senescence. We found no evidence for sex-specific environmental sensitivity, but females lived shorter than males due to increased actuarial senescence. Thus, low food availability by itself shortens lifespan, but only in individuals from harsh developmental conditions. Our food availability manipulation resembles dietary restriction as applied to invertebrates, where it extends lifespan in model organisms and we discuss possible reasons for the contrasting results.

Modeling Human Mortality from All Diseases in the Five Most Populated Countries of the European Union

Age affects mortality from diseases differently than it affects mortality from external causes, such as accidents. Exclusion of the latter leads to the "all-diseases" category. The age trajectories of mortality from all diseases are studied in the five most populated countries of the EU, and the shape of these 156 age trajectories is investigated in detail. The arithmetic mean of ages where mortality reaches a minimal value is 8.47 years with a 95% confidence interval of [8.08, 8.85] years. Two simple deterministic models fit the age trajectories on the two sides of the mortality minimum. The inverse relationship is valid in all cases prior to this mortality minimum and death rates exactly decreased to three thousandths of its original size during the first 3000 days. After the mortality minimum, the standard Gompertz model fits the data in 63 cases, and the Gompertz model extended by a small quadratic element fits the remaining 93 cases. This analysis indicates that the exponential increase begins before the age of 15 years and that it is overshadowed by non-biological causes. Therefore, the existence of a mechanism switching that would explain the exponential increase in mortality after the age of 35 years is unlikely.

Onset of mortality increase with age and age trajectories of mortality from all diseases in the four Nordic countries

BACKGROUND

The answer to the question "At what age does aging begin?" is tightly related to the question "Where is the onset of mortality increase with age?" Age affects mortality rates from all diseases differently than it affects mortality rates from nonbiological causes. Mortality increase with age in adult populations has been modeled by many authors, and little attention has been given to mortality decrease with age after birth.

MATERIALS AND METHODS

Nonbiological causes are excluded, and the category "all diseases" is studied. It is analyzed in Denmark, Finland, Norway, and Sweden during the period 1994-2011, and all possible models are screened. Age trajectories of mortality are analyzed separately: before the age category where mortality reaches its minimal value and after the age category.

RESULTS

Resulting age trajectories from all diseases showed a strong minimum, which was hidden in total mortality. The inverse proportion between mortality and age fitted in 54 of 58 cases before mortality minimum. The Gompertz model with two parameters fitted as mortality increased with age in 17 of 58 cases after mortality minimum, and the Gompertz model with a small positive quadratic term fitted data in the remaining 41 cases. The mean age where mortality reached minimal value was 8 (95% confidence interval 7.05-8.95) years. The figures depict an age where the human population has a minimal risk of death from biological causes.

CONCLUSION

Inverse proportion and the Gompertz model fitted data on both sides of the mortality minimum, and three parameters determined the shape of the age-mortality trajectory. Life expectancy should be determined by the two standard Gompertz parameters and also by the single parameter in the model c/x. All-disease mortality represents an alternative tool to study the impact of age. All results are based on published data.

Multiple Metazoan Life-span Interventions Exhibit a Sex-specific Strehler-Mildvan Inverse Relationship Between Initial Mortality Rate and Age-dependent Mortality Rate Acceleration

The Gompertz equation describes survival in terms of initial mortality rate (parameter a), indicative of health, and age-dependent acceleration in mortality rate (parameter b), indicative of aging. Gompertz parameters were analyzed for several published studies. In Drosophila females, mating increases egg production and decreases median life span, consistent with a trade-off between reproduction and longevity. Mating increased parameter a, causing decreased median life span, whereas time parameter b was decreased. The inverse correlation between parameters indicates the Strehler-Mildvan (S-M) relationship, where loss of low-vitality individuals yields a cohort with slower age-dependent mortality acceleration. The steroid hormone antagonist mifepristone/RU486 reversed these effects. Mating and mifepristone showed robust S-M relationships across genotypes, and dietary restriction showed robust S-M relationship across diets. Because nutrient optima differed between females and males, the same manipulation caused opposite effects on mortality rates in females versus males across a range of nutrient concentrations. Similarly, p53 mutation in Drosophila and mTOR mutation in mice caused increased median life span associated with opposite direction changes in mortality rate parameters in females versus males. The data demonstrate that dietary and genetic interventions have sex-specific and sometimes sexually opposite effects on mortality rates consistent with sexual antagonistic pleiotropy.

Compression of Morbidity and Mortality: New Perspectives

Compression of morbidity is a reduction over time in the total lifetime days of chronic disability, reflecting a balance between (1) morbidity incidence rates and (2) case-continuance rates-generated by case-fatality and case-recovery rates. Chronic disability includes limitations in activities of daily living and cognitive impairment, which can be covered by long-term care insurance. Morbidity improvement can lead to a compression of morbidity if the reductions in age-specific prevalence rates are sufficiently large to overcome the increases in lifetime disability due to concurrent mortality improvements and progressively higher disability prevalence rates with increasing age. Compression of mortality is a reduction over time in the variance of age at death. Such reductions are generally accompanied by increases in the mean age at death; otherwise, for the variances to decrease, the death rates above the mean age at death would need to increase, and this has rarely been the case. Mortality improvement is a reduction over time in the age-specific death rates and a corresponding increase in the cumulative survival probabilities and age-specific residual life expectancies. Mortality improvement does not necessarily imply concurrent compression of mortality. This paper reviews these concepts, describes how they are related, shows how they apply to changes in mortality over the past century and to changes in morbidity over the past 30 years, and discusses their implications for future changes in the United States. The major findings of the empirical analyses are the substantial slowdowns in the degree of mortality compression over the past half century and the unexpectedly large degree of morbidity compression that occurred over the morbidity/disability study period 1984-2004; evidence from other published sources suggests that morbidity compression may be continuing.

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.

Single parameter of inverse proportion between mortality and age could determine all mortality indicators in the first year of life

Mortality increase with age in adult population has been studied and modeled by many authors, but relatively little attention has been given to mortality decrease with age after birth. Data split in more detailed age categories can newly test mortality decrease with age. Age trajectories of mortality are studied in 20 age categories in the specific age interval 1-365 days. Four basic models mentioned in literature are tested here. The linear model and the linear model with the specific slope -1 in the log-log scale represent the most successful formalism. Mortality indicators describing the first year could be determined by a single parameter of the model with slope -1 in the log-log scale. All conclusions are based on published data which are presented as a supplement.

Age-Specific Variation in Adult Mortality Rates in Developed Countries

This paper investigates historical changes in both single-year-of-age adult mortality rates and variation of the single-year mortality rates around expected values within age intervals over the past two centuries in 15 developed countries. We apply an integrated Hierarchical Age-Period-Cohort-Variance Function Regression Model to data from the Human Mortality Database. We find increasing variation of the single-year rates within broader age intervals over the life course for all countries, but the increasing variation slows down at age 90 and then increases again after age 100 for some countries; the variation significantly declined across cohorts born after the early 20th century; and the variation continuously declined over much of the last two centuries but has substantially increased since 1980. Our further analysis finds the recent increases in mortality variation are not due to increasing proportions of older adults in the population, trends in mortality rates, or disproportionate delays in deaths from degenerative and man-made diseases, but rather due to increasing variations in young and middle-age adults.

How the effects of aging and stresses of life are integrated in mortality rates: insights for genetic studies of human health and longevity

Increasing proportions of elderly individuals in developed countries combined with substantial increases in related medical expenditures make the improvement of the health of the elderly a high priority today. If the process of aging by individuals is a major cause of age related health declines then postponing aging could be an efficient strategy for improving the health of the elderly. Implementing this strategy requires a better understanding of genetic and non-genetic connections among aging, health, and longevity. We review progress and problems in research areas whose development may contribute to analyses of such connections. These include genetic studies of human aging and longevity, the heterogeneity of populations with respect to their susceptibility to disease and death, forces that shape age patterns of human mortality, secular trends in mortality decline, and integrative mortality modeling using longitudinal data. The dynamic involvement of genetic factors in (i) morbidity/mortality risks, (ii) responses to stresses of life, (iii) multi-morbidities of many elderly individuals, (iv) trade-offs for diseases, (v) genetic heterogeneity, and (vi) other relevant aging-related health declines, underscores the need for a comprehensive, integrated approach to analyze the genetic connections for all of the above aspects of aging-related changes. The dynamic relationships among aging, health, and longevity traits would be better understood if one linked several research fields within one conceptual framework that allowed for efficient analyses of available longitudinal data using the wealth of available knowledge about aging, health, and longevity already accumulated in the research field.

Early cohort mortality predicts the rate of aging in the cohort: a historical analysis

Early environmental influences on later-life health and mortality are well recognized in the doubling of life expectancy since 1800. To further define these relationships, we analyzed the associations between early-life mortality and both the estimated mortality level at age 40 and the exponential acceleration in mortality rates with age characterized by the Gompertz model. Using mortality data from 630 cohorts born throughout the 19th and early 20th century in nine European countries, we developed a multilevel model that accounts for cohort and period effects in later-life mortality. We show that early-life mortality, which is linked to exposure to infection and poor nutrition, predicts both the estimated cohort mortality level at age 40 and the subsequent Gompertz rate of mortality acceleration during aging. After controlling for effects of country and period, the model accounts for the majority of variance in the Gompertz parameters (about 90% of variation in the estimated level of mortality at age 40 and about 78% of variation in the Gompertz slope). The gains in cohort survival to older ages are entirely due to large declines in adult mortality level, because the rates of mortality acceleration at older ages became faster. These findings apply to cohorts born in both the 19th century and the early 20th century. This analysis defines new links in the developmental origins of adult health and disease in which effects of early-life circumstances, such as exposure to infections or poor nutrition, persist into mid-adulthood and remain evident in the cohort mortality rates from ages 40 to 90.

The Strehler-Mildvan correlation from the perspective of a two-process vitality model

The Strehler and Mildvan (SM) general theory of ageing and mortality provides a mechanism-based explanation of Gompertz's law and predicts a log-linear relationship between the two Gompertz coefficients, known as the SM correlation. While the SM correlation is supported by data from developed countries before the second half of the twentieth century, the recent breakdown of the correlation pattern in these countries has prompted demographers to conclude that SM theory needs to be reassessed. In this paper we use a newly developed two-process vitality model to explain the SM correlation and its breakdown in terms of asynchronous trends in acute (extrinsic) and chronic (intrinsic) mortality factors. We propose that the mortality change in the first half of the twentieth century is largely determined by the elimination of immediate hazards to death, whereas the mortality change in the second half is primarily driven by the slowdown of the deterioration rate of intrinsic survival capacity.

Age trajectories of mortality from all diseases in five countries of central Europe during the last decades

Age trajectories of total mortality represent an irreplaceable source of information about the relationship between mortality and age. Total mortality includes death from external causes. Age affects mortality from all diseases differently than it affects mortality from external causes. This study examines mortality with external causes excluded. The resulting category of all-diseases is examined as a helpful tool to better understand the relationship between mortality and age. Age trajectories of all-diseases mortality are studied in Austria, the Czech Republic, Hungary, Poland, and Slovakia. Resulting age trajectories of all-diseases mortality show a strong minimum that is hidden in all-causes mortality. Two deterministic models fit the resulting age trajectories of mortality on either side of the strong mortality minimum. The inverse proportion between mortality and age is used from birth to the age when all-diseases mortality reaches the minimum value. The Gompertz relationship fits age trajectories of all-diseases mortality in 93 out of 183 cases. When extended with a small quadratic element, the Gompertz model is used to fit the remaining 90 cases.

Age trajectories of mortality from all diseases in the six most populated countries of the South America during the last decades

Age trajectories of total mortality represent an irreplaceable source of information about aging. In principle, age affects mortality from all diseases differently than it affects mortality from external causes. External causes (accidents) are excluded here from all causes, and the resultant category "all-diseases" is tested as a helpful tool to better understand the relationship between mortality and age. Age trajectories of all-diseases mortality are studied in the six most populated countries of the South America during 1996-2010. The numbers of deaths for specific causes of death are extracted from the database of WHO, where the ICD-10 revision is used. The all-diseases mortality shows a strong minimum, which is hidden in total mortality. Two simple deterministic models fit the age trajectories of all-diseases mortality. The inverse proportion between mortality and age fits the mortality decreases up to minimum value in all six countries. All previous models describing mortality decline after birth are discussed. Theoretical relationships are derived between the parameter in the first model and standard mortality indicators: Infant mortality, Neonatal mortality, and Postneonatal mortality. The Gompertz model extended with a small positive quadratic element fit the age trajectories of all-diseases mortality after the age of 10 years.

Aging in the context of cohort evolution and mortality selection

This study examines historical patterns of aging through the perspectives of cohort evolution and mortality selection, where the former emphasizes the correlation across cohorts in the age dependence of mortality rates, and the latter emphasizes cohort change in the acceleration of mortality over the life course. In the analysis of historical cohort mortality data, I find support for both perspectives. The rate of demographic aging, or the rate at which mortality accelerates past age 70, is not fixed across cohorts; rather, it is affected by the extent of mortality selection at young and late ages. This causes later cohorts to have higher rates of demographic aging than earlier cohorts. The rate of biological aging, approximating the rate of the senescence process, significantly declined between the mid- and late-nineteenth century birth cohorts and stabilized afterward. Unlike the rate of demographic aging, the rate of biological aging is not affected by mortality selection earlier in the life course but rather by cross-cohort changes in young-age mortality, which cause lower rates of biological aging in old age among later cohorts. These findings enrich theories of cohort evolution and have implications for the study of limits on the human lifespan and evolution of aging.

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

Unobserved heterogeneity in mortality risk is pervasive and consequential. Mortality deceleration-the slowing of mortality's rise with age-has been considered an important window into heterogeneity that otherwise might be impossible to explore. In this article, I argue that deceleration patterns may reveal surprisingly little about the heterogeneity that putatively produces them. I show that even in a very simple model-one that is composed of just two subpopulations with Gompertz mortality-(1) aggregate mortality can decelerate even while a majority of the cohort is frail; (2) multiple decelerations are possible; and (3) mortality selection can produce acceleration as well as deceleration. Simulations show that these patterns are plausible in model cohorts that in the aggregate resemble cohorts in the Human Mortality Database. I argue that these results challenge some conventional heuristics for understanding the relationship between selection and deceleration; undermine certain inferences from deceleration timing to patterns of social inequality; and imply that standard parametric models, assumed to plateau at most once, may sometimes badly misestimate deceleration timing-even by decades.

Lifespan and aggregate size variables in specifications of mortality or survivorship

A specification of mortality or survivorship provides respective explicit details about mortality's or survivorship's relationships with one or more other variables (e.g., age, sex, etc.). Previous studies have discovered and analyzed diverse specifications of mortality or survivorship; these discoveries and analyses suggest that additional specifications of mortality or survivorship have yet to be discovered and analyzed. In consistency with previous research, multivariable limited powered polynomials regression analyses of mortality and survivorship of selected humans (Swedes, 1760-2008) and selected insects (caged medflies) show age-specific, historical-time-specific, environmental-context-specific, and sex-specific mortality and survivorship. These analyses also present discoveries of hitherto unknown lifespan-specific, contemporary-aggregate-size-specific, and lifespan-aggregate-size-specific mortality and survivorship. The results of this investigation and results of previous research help identify variables for inclusion in regression models of mortality or survivorship. Moreover, these results and results of previous research strengthen the suggestion that additional specifications of mortality or survivorship have yet to be discovered and analyzed, and they also suggest that specifications of mortality and survivorship indicate corresponding specifications of frailty and vitality. Furthermore, the present analyses reveal the usefulness of a multivariable limited powered polynomials regression model-building approach. This article shows that much has yet to be learned about specifications of mortality or survivorship of diverse kinds of individuals in diverse times and places.

The quadratic hazard model for analyzing longitudinal data on aging, health, and the life span

A better understanding of processes and mechanisms linking human aging with changes in health status and survival requires methods capable of analyzing new data that take into account knowledge about these processes accumulated in the field. In this paper, we describe an approach to analyses of longitudinal data based on the use of stochastic process models of human aging, health, and longevity which allows for incorporating state of the art advances in aging research into the model structure. In particular, the model incorporates the notions of resistance to stresses, adaptive capacity, and "optimal" (normal) physiological states. To capture the effects of exposure to persistent external disturbances, the notions of allostatic adaptation and allostatic load are introduced. These notions facilitate the description and explanation of deviations of individuals' physiological indices from their normal states, which increase the chances of disease development and death. The model provides a convenient conceptual framework for comprehensive systemic analyses of aging-related changes in humans using longitudinal data and linking these changes with genotyping profiles, morbidity, and mortality risks. The model is used for developing new statistical methods for analyzing longitudinal data on aging, health, and longevity.

How genes influence life span: the biodemography of human survival

BACKGROUND

In genome-wide association studies (GWAS) of human life span, none of the genetic variants has reached the level of genome-wide statistical significance. The roles of such variants in life span regulation remain unclear.

DATA AND METHOD

A biodemographic analyses was done of genetic regulation of life span using data on low-significance longevity alleles selected in the earlier GWAS of the original Framingham cohort.

RESULTS

Age-specific survival curves considered as functions of the number of longevity alleles exhibit regularities known in demography as "rectangularization" of survival curves. The presence of such pattern confirms observations from experimental studies that regulation of life span involves genes responsible for stress resistance.

CONCLUSION

Biodemographic analyses could provide important information about the properties of genes affecting phenotypic traits.

Human actuarial aging increases faster when background death rates are lower: a consequence of differential heterogeneity?

Many analyses of human populations have found that age-specific mortality rates increase faster across most of adulthood when overall mortality levels decline. This contradicts the relationship often expected from Williams' classic hypothesis about the effects of natural selection on the evolution of senescence. More likely, much of the within-species difference in actuarial aging is not due to variation in senescence, but to the strength of filters on the heterogeneity of frailty in older survivors. A challenge to this differential frailty hypothesis was recently posed by an analysis of life tables from historical European populations and traditional societies that reported variation in actuarial aging consistent with Williams' hypothesis after all. To investigate the challenge, we reconsidered those cases and aging measures. Here we show that the discrepancy depends on Ricklefs' aging rate measure, ω, which decreases as mortality levels drop because it is an index of mortality level itself, not the rate of increase in mortality with age. We also show unappreciated correspondence among the parameters of Gompertz-Makeham and Weibull survival models. Finally, we compare the relationships among mortality parameters of the traditional societies and the historical series, providing further suggestive evidence that differential heterogeneity has strong effects on actuarial aging.