Stochastic model for analysis of longitudinal data on aging and mortality

Aging-related changes in a human organism follow dynamic regularities, which contribute to the observed age patterns of incidence and mortality curves. An organism's 'optimal' (normal) physiological state changes with age, affecting the values of risks of disease and death. The resistance to stresses, as well as adaptive capacity, declines with age. An exposure to improper environment results in persisting deviation of individuals' physiological (and biological) indices from their normal state (due to allostatic adaptation), which, in turn, increases chances of disease and death. Despite numerous studies investigating these effects, there is no conceptual framework, which would allow for putting all these findings together, and analyze longitudinal data taking all these dynamic connections into account. In this paper we suggest such a framework, using a new version of stochastic process model of aging and mortality. Using this model, we elaborated a statistical method for analyses of longitudinal data on aging, health and longevity and tested it using different simulated data sets. The results show that the model may characterize complicated interplay among different components of aging-related changes in humans and that the model parameters are identifiable from the data.     

Biomarker signatures of aging

Because people age differently, age is not a sufficient marker of susceptibility to disabilities, morbidities, and mortality. We measured nineteen blood biomarkers that include constituents of standard hematological measures, lipid biomarkers, and markers of inflammation and frailty in 4704 participants of the Long Life Family Study (LLFS), age range 30–110 years, and used an agglomerative algorithm to group LLFS participants into clusters thus yielding 26 different biomarker signatures. To test whether these signatures were associated with differences in biological aging, we correlated them with longitudinal changes in physiological functions and incident risk of cancer, cardiovascular disease, type 2 diabetes, and mortality using longitudinal data collected in the LLFS. Signature 2 was associated with significantly lower mortality, morbidity, and better physical function relative to the most common biomarker signature in LLFS, while nine other signatures were associated with less successful aging, characterized by higher risks for frailty, morbidity, and mortality. The predictive values of seven signatures were replicated in an independent data set from the Framingham Heart Study with comparable significant effects, and an additional three signatures showed consistent effects. This analysis shows that various biomarker signatures exist, and their significant associations with physical function, morbidity, and mortality suggest that these patterns represent differences in biological aging. The signatures show that dysregulation of a single biomarker can change with patterns of other biomarkers, and age‐related changes of individual biomarkers alone do not necessarily indicate disease or functional decline.     

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.     

Explainable machine learning framework to predict personalized physiological aging

Attaining personalized healthy aging requires accurate monitoring of physiological changes and identifying subclinical markers that predict accelerated or delayed aging. Classic biostatistical methods most rely on supervised variables to estimate physiological aging and do not capture the full complexity of inter-parameter interactions. Machine learning (ML) is promising, but its black box nature eludes direct understanding, substantially limiting physician confidence and clinical usage. Using a broad population dataset from the National Health and Nutrition Examination Survey (NHANES) study including routine biological variables and after selection of XGBoost as the most appropriate algorithm, we created an innovative explainable ML framework to determine a Personalized physiological age (PPA). PPA predicted both chronic disease and mortality independently of chronological age. Twenty-six variables were sufficient to predict PPA. Using SHapley Additive exPlanations (SHAP), we implemented a precise quantitative associated metric for each variable explaining physiological (i.e., accelerated or delayed) deviations from age-specific normative data. Among the variables, glycated hemoglobin (HbA1c) displays a major relative weight in the estimation of PPA. Finally, clustering profiles of identical contextualized explanations reveal different aging trajectories opening opportunities to specific clinical follow-up. These data show that PPA is a robust, quantitative and explainable ML-based metric that monitors personalized health status. Our approach also provides a complete framework applicable to different datasets or variables, allowing precision physiological age estimation.     

Heart Rate Dynamics after Combined Strength and Endurance Training in Middle-Aged Women: Heterogeneity of Responses

The loss of complexity in physiological systems may be a dynamical biomarker of aging and disease. In this study the effects of combined strength and endurance training compared with those of endurance training or strength training alone on heart rate (HR) complexity and traditional HR variability indices were examined in middle-aged women. 90 previously untrained female volunteers between the age of 40 and 65 years completed a 21 week progressive training period of either strength training, endurance training or their combination, or served as controls. Continuous HR time series were obtained during supine rest and submaximal steady state exercise. The complexity of HR dynamics was assessed using multiscale entropy analysis. In addition, standard time and frequency domain measures were also computed. Endurance training led to increases in HR complexity and selected time and frequency domain measures of HR variability (P<0.01) when measured during exercise. Combined strength and endurance training or strength training alone did not produce significant changes in HR dynamics. Inter-subject heterogeneity of responses was particularly noticeable in the combined training group. At supine rest, no training-induced changes in HR parameters were observed in any of the groups. The present findings emphasize the potential utility of endurance training in increasing the complex variability of HR in middle-aged women. Further studies are needed to explore the combined endurance and strength training adaptations and possible gender and age related factors, as well as other mechanisms, that may mediate the effects of different training regimens on HR dynamics.     

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.     

Mortality and aging in a heterogeneous population: a stochastic process model with observed and unobserved variables

Various multivariate stochastic process models have been developed to represent human physiological aging and mortality. These efforts are extended by considering the effects of observed and unobserved state variables on the age trajectory of physiological parameters. This is done by deriving the Kolmogorov-Fokker-Planck equations describing the distribution of the unobserved state variables conditional on the history of the observed state variables. Given some assumptions, it is proved that the distribution is Gaussian. Strategies for estimating the parameters of the distribution are suggested based on an extension of the theory of Kalman filters to include systematic mortality selection. Various empirical applications of the model to studies of human aging and mortality as well as to other types of "failure" processes in heterogeneous populations are discussed.     

Lifetime sedentary living accelerates some aspects of secondary aging

Lifetime physical inactivity interacts with secondary aging (i.e., aging caused by diseases and environmental factors) in three patterns of response. First, lifetime physical inactivity confers no apparent effects on a given set of physiological functions. Second, lifetime physical inactivity accelerates secondary aging (e.g., speeding the reduction in bone mineral density, maximal oxygen consumption, and skeletal muscle strength and power), but does not alter the primary aging of these systems. Third, a lifetime of physical activity to the age of ～60-70 yr old totally prevents decrements in some age-associated risk factors for major chronic diseases, such as endothelial dysfunction and insulin resistance. The present review provides ample and compelling evidence that physical inactivity has a large impact in shortening average life expectancy. In summary, physical inactivity plays a major role in the secondary aging of many essential physiological functions, and this aging can be prevented through a lifetime of physical activity.     

Bayesian-Estimated Hierarchical HMMs Enable Robust Analysis of Single-Molecule Kinetic Heterogeneity

Single-molecule kinetic experiments allow the reaction trajectories of individual biomolecules to be directly observed, eliminating the effects of population averaging and providing a powerful approach for elucidating the kinetic mechanisms of biomolecular processes. A major challenge to the analysis and interpretation of these experiments, however, is the kinetic heterogeneity that almost universally complicates the recorded single-molecule signal versus time trajectories (i.e., signal trajectories). Such heterogeneity manifests as changes and/or differences in the transition rates that are observed within individual signal trajectories or across a population of signal trajectories. Because characterizing kinetic heterogeneity can provide critical mechanistic information, we have developed a computational method that effectively and comprehensively enables such analysis. To this end, we have developed a computational algorithm and software program, hFRET, that uses the variational approximation for Bayesian inference to estimate the parameters of a hierarchical hidden Markov model, thereby enabling robust identification and characterization of kinetic heterogeneity. Using simulated signal trajectories, we demonstrate the ability of hFRET to accurately and precisely characterize kinetic heterogeneity. In addition, we use hFRET to analyze experimentally recorded signal trajectories reporting on the conformational dynamics of ribosomal pre-translocation (PRE) complexes. The results of our analyses demonstrate that PRE complexes exhibit kinetic heterogeneity, reveal the physical origins of this heterogeneity, and allow us to expand the current model of PRE complex dynamics. The methods described here can be applied to signal trajectories generated using any type of signal and can be easily extended to the analysis of signal trajectories exhibiting more complex kinetic behaviors. Moreover, variations of our approach can be easily developed to integrate kinetic data obtained from different experimental constructs and/or from molecular dynamics simulations of a biomolecule of interest.     

Conservation of physiological dysregulation signatures of aging across primates

Two major goals in the current biology of aging are to identify general mechanisms underlying the aging process and to explain species differences in aging. Recent research in humans suggests that one important driver of aging is dysregulation, the progressive loss of homeostasis in complex biological networks. Yet, there is a lack of comparative data for this hypothesis, and we do not know whether dysregulation is widely associated with aging or how well signals of homeostasis are conserved. To address this knowledge gap, we use unusually detailed longitudinal biomarker data from 10 species of nonhuman primates housed in research centers and data from two human populations to test the hypotheses that (a) greater dysregulation is associated with aging across primates and (b) physiological states characterizing homeostasis are conserved across primates to degrees associated with phylogenetic proximity. To evaluate dysregulation, we employed a multivariate distance measure, calculated from sets of biomarkers, that is associated with aging and mortality in human populations. Dysregulation scores positively correlated with age and risk of mortality in most nonhuman primates studied, and signals of homeostatic state were significantly conserved across species, declining with phylogenetic distance. Our study provides the first broad demonstration of physiological dysregulation associated with aging and mortality risk in multiple nonhuman primates. Our results also imply that emergent signals of homeostasis are evolutionarily conserved, although with notable variation among species, and suggest promising directions for future comparative studies on dysregulation and the aging process.     

Genetic model for longitudinal studies of aging, health, and longevity and its potential application to incomplete data

Many longitudinal studies of aging collect genetic information only for a sub-sample of participants of the study. These data also do not include recent findings, new ideas and methodological concepts developed by distinct groups of researchers. The formal statistical analyses of genetic data ignore this additional information and therefore cannot utilize the entire research potential of the data. In this paper, we present a stochastic model for studying such longitudinal data in joint analyses of genetic and non-genetic sub-samples. The model incorporates several major concepts of aging known to date and usually studied independently. These include age-specific physiological norms, allostasis and allostatic load, stochasticity, and decline in stress resistance and adaptive capacity with age. The approach allows for studying all these concepts in their mutual connection, even if respective mechanisms are not directly measured in data (which is typical for longitudinal data available to date). The model takes into account dependence of longitudinal indices and hazard rates on genetic markers and permits evaluation of all these characteristics for carriers of different alleles (genotypes) to address questions concerning genetic influence on aging-related characteristics. The method is based on extracting genetic information from the entire sample of longitudinal data consisting of genetic and non-genetic sub-samples. Thus it results in a substantial increase in the accuracy of statistical estimates of genetic parameters compared to methods that use only information from a genetic sub-sample. Such an increase is achieved without collecting additional genetic data. Simulation studies illustrate the increase in the accuracy in different scenarios for datasets structurally similar to the Framingham Heart Study. Possible applications of the model and its further generalizations are discussed.     

Shared signatures of social stress and aging in peripheral blood mononuclear cell gene expression profiles

Chronic social stress is a predictor of both aging‐related disease and mortality risk. Hence, chronic stress has been hypothesized to directly exacerbate the process of physiological aging. Here, we evaluated this hypothesis at the level of gene regulation. We compared two data sets of genome‐wide gene expression levels in peripheral blood mononuclear cells (PBMCs): one that captured aging effects and another that focused on chronic social stress. Overall, we found that the direction, although not necessarily the magnitude, of significant gene expression changes tends to be shared between the two data sets. This overlap was observable at three levels: (i) individual genes; (ii) general functional categories of genes; and (iii) molecular pathways implicated in aging. However, we also found evidence that heterogeneity in PBMC composition limits the power to detect more extensive similarities, suggesting that our findings reflect an underestimate of the degree to which age and social stress influence gene regulation in parallel. Cell type‐specific data on gene regulation will be important to overcome this limitation in the future studies.     

Interpretable machine learning for high-dimensional trajectories of aging health

We have built a computational model for individual aging trajectories of health and survival, which contains physical, functional, and biological variables, and is conditioned on demographic, lifestyle, and medical background information. We combine techniques of modern machine learning with an interpretable interaction network, where health variables are coupled by explicit pair-wise interactions within a stochastic dynamical system. Our dynamic joint interpretable network (DJIN) model is scalable to large longitudinal data sets, is predictive of individual high-dimensional health trajectories and survival from baseline health states, and infers an interpretable network of directed interactions between the health variables. The network identifies plausible physiological connections between health variables as well as clusters of strongly connected health variables. We use English Longitudinal Study of Aging (ELSA) data to train our model and show that it performs better than multiple dedicated linear models for health outcomes and survival. We compare our model with flexible lower-dimensional latent-space models to explore the dimensionality required to accurately model aging health outcomes. Our DJIN model can be used to generate synthetic individuals that age realistically, to impute missing data, and to simulate future aging outcomes given arbitrary initial health states.     

Detection of a Novel,Integrative Aging Process Suggests Complex Physiological Integration

Many studies of aging examine biomarkers one at a time, but complex systems theory and network theory suggest that interpretations of individual markers may be context-dependent. Here, we attempted to detect underlying processes governing the levels of many biomarkers simultaneously by applying principal components analysis to 43 common clinical biomarkers measured longitudinally in 3694 humans from three longitudinal cohort studies on two continents (Women’s Health and Aging I & II, InCHIANTI, and the Baltimore Longitudinal Study on Aging). The first axis was associated with anemia, inflammation, and low levels of calcium and albumin. The axis structure was precisely reproduced in all three populations and in all demographic sub-populations (by sex, race, etc.); we call the process represented by the axis “integrated albunemia.” Integrated albunemia increases and accelerates with age in all populations, and predicts mortality and frailty – but not chronic disease – even after controlling for age. This suggests a role in the aging process, though causality is not yet clear. Integrated albunemia behaves more stably across populations than its component biomarkers, and thus appears to represent a higher-order physiological process emerging from the structure of underlying regulatory networks. If this is correct, detection of this process has substantial implications for physiological organization more generally.     

Drivers of age-specific survival in a long-lived seabird: contributions of observed and hidden sources of heterogeneity

1.?We assessed the relative influence of variability in recruitment age, dynamic reproductive investment (time-specific reproductive states) and frailty (unobserved differences in survival abilities across individuals) on survival in the black-legged kittiwake. Furthermore, we examined whether observed variability in survival trajectories was best explained by immediate reproductive investment, cumulative investment, or both. 2.?Individuals that delayed recruitment (≥ age 7) suffered a higher mortality risk than early recruits (age 3), especially later in life, suggesting that recruitment age may be an indicator of individual quality. Although recruitment age helped explain variation in survival, time-varying reproductive investment had a more substantial influence. 3.?The dichotomy of attempting to breed or not explained variability in survival across life better than other parameterizations of reproductive states such as clutch size, brood size or breeding success. In the kittiwake, the sinequanon condition to initiate reproduction is to hold a nest site, which is considered a very competitive activity. This might explain why attempting to breed is the key level of investment that affects survival, independent of the outcome (failure or success). 4.?Interestingly, the more individuals cumulate reproductive attempts over life, the lower their mortality risk, indicating that breeding experience may be a good indicator of parental quality as well. In contrast, attempting to breed at time t increased the risk of mortality between t and t + 1. We thus detected an immediate trade-off between attempting to breed and survival in this population; however, the earlier individuals recruited, and the more breeding experience they accumulated, the smaller the cost. 5.?Lastly, unobserved heterogeneity across individuals improved model fit more (1·3 times) than fixed and dynamic sources of observed heterogeneity in reproductive investment, demonstrating that it is critical to account for both sources of individual heterogeneity when studying survival trajectories. Only after simultaneously accounting for both sources of heterogeneity were we able to detect the 'cost' of immediate reproductive investment on survival and the 'benefit' of cumulative breeding attempts (experience), a proxy to individual quality.     

Prepubertal castration eliminates sex differences in lifespan and growth trajectories in genetically heterogeneous mice

Sex differences in aging and longevity have been widely observed, with females consistently outliving males across human populations. However, the mechanisms driving these disparities remain poorly understood. In this study, we explored the influence of post-pubertal testicular effects on sex differences in aging by prepubertally castrating genetically heterogeneous (UM-HET3) mice, a unique mouse model that emulates human sex differences in age-related mortality. Prepubertal castration eliminated the longevity disparity between sexes by reducing the elevated early- to mid-life mortality rate observed in males and extending their median lifespan to match that of females. Additionally, castration extended the duration of body weight growth and attenuated the inverse correlation between early-age body weight and lifespan in males, aligning their growth trajectories with those of females. Our findings suggest that post-pubertal testicular actions in genetically diverse mice are primarily responsible for sex differences in longevity as well as growth trajectories. These findings offer a foundation for further investigation into the fundamental mechanisms driving sex-specific aging patterns and the development of potential pro-longevity interventions.     

Evolution of aging: Theoretical and practical implications from rattlesnakes

Many reptiles live relatively long lives wherein senescence is postponed to an advanced age. Altering nutrition, reproduction, temperature, and other physiological parameters may favorably contribute to increased life spans. But life spans are also evolved characteristics of populations, and the distinctive longevities also result from selective regimes arising within particular environments. Aging is not favored directly by evolution as a way to clear a population of senescent individuals. Instead, aging is probably an indirect byproduct of selection for early physical vitality. Senescence may result from delayed appearance of deleterious genes later in life (mutation accumulation) or from multiple effects of single genes with overriding favorable effects early but coupled deleterious effects later in life (antagonistic pleiotropy). Both physiological and evolutionary causes contribute to species or even population-specific aging characteristics. Separating environmentally imposed mortality from that attributable to senescence has been aided by compiling maximum life spans of captive reptiles. Further understanding the underlying aging biology of reptiles would be aided by following mortalities of age cohorts, identifying differences in aging between populations, documenting the effects, favorable or not, of husbandry practices, and by characterizing senescence not just by mortality, but also by changes in age-related performance. Theoretical issues, inspired by experimental results in rattlesnakes, suggest conditions under which the chance mortalities of young rattlesnakes together with continued growth of adults might favor late appearance of beneficial genes and thereby account for postponed senescence in some reptiles. © 1996 Wiley-Liss, Inc.     

AnthropoAge,a novel approach to integrate body composition into the estimation of biological age

Aging is believed to occur across multiple domains, one of which is body composition; however, attempts to integrate it into biological age (BA) have been limited. Here, we consider the sex-dependent role of anthropometry for the prediction of 10-year all-cause mortality using data from 18,794 NHANES participants to generate and validate a new BA metric. Our data-driven approach pointed to sex-specific contributors for BA estimation: WHtR, arm and thigh circumferences for men; weight, WHtR, thigh circumference, subscapular and triceps skinfolds for women. We used these measurements to generate AnthropoAge, which predicted all-cause mortality (AUROC 0.876, 95%CI 0.864–0.887) and cause-specific mortality independently of ethnicity, sex, and comorbidities; AnthropoAge was a better predictor than PhenoAge for cerebrovascular, Alzheimer, and COPD mortality. A metric of age acceleration was also derived and used to assess sexual dimorphisms linked to accelerated aging, where women had an increase in overall body mass plus an important subcutaneous to visceral fat redistribution, and men displayed a marked decrease in fat and muscle mass. Finally, we showed that consideration of multiple BA metrics may identify unique aging trajectories with increased mortality (HR for multidomain acceleration 2.43, 95%CI 2.25–2.62) and comorbidity profiles. A simplified version of AnthropoAge (S-AnthropoAge) was generated using only BMI and WHtR, all results were preserved using this metric. In conclusion, AnthropoAge is a useful proxy of BA that captures cause-specific mortality and sex dimorphisms in body composition, and it could be used for future multidomain assessments of aging to better characterize the heterogeneity of this phenomenon.     

Alpine ibex males grow large horns at no survival cost for most of their lifetime

Large horns or antlers require a high energy allocation to produce and carry both physiological and social reproductive costs. Following the principle of energy allocation that implies trade-offs among fitness components, growing large weapons early in life should thus reduce future growth and survival. Evidence for such costs is ambiguous, however, partly because individual heterogeneity can counterbalance trade-offs. Individuals with larger horns or antlers may be of better quality and thus have a greater capacity to survive. We investigated trade-offs between male early horn growth and future horn growth, baseline mortality, onset of actuarial senescence, and rate of ageing in an Alpine ibex (Capra ibex ibex) population. Horn growth of males in early life was positively correlated to their horn length throughout their entire life. Cohort variation and individual heterogeneity both accounted for among-individual variation in horn length, suggesting both long-lasting effects of early life conditions and individual-specific horn growth trajectories. Early horn growth did not influence annual survival until 12 years of age, indicating that males do not invest in horn growth at survival costs over most of their lifetime. However, males with fast-growing horns early in life tended to have lower survival at very old ages. Individual heterogeneity, along with the particular life-history tactic of male ibex (weak participation to the rut until an old age after which they burn out in high mating investment), are likely to explain why the expected trade-off between horn growth and survival does not show up, at least until very old ages.     

Molecular and physiological manifestations and measurement of aging in humans

Biological aging is associated with a reduction in the reparative and regenerative potential in tissues and organs. This reduction manifests as a decreased physiological reserve in response to stress (termed homeostenosis) and a time‐dependent failure of complex molecular mechanisms that cumulatively create disorder. Aging inevitably occurs with time in all organisms and emerges on a molecular, cellular, organ, and organismal level with genetic, epigenetic, and environmental modulators. Individuals with the same chronological age exhibit differential trajectories of age‐related decline, and it follows that we should assess biological age distinctly from chronological age. In this review, we outline mechanisms of aging with attention to well‐described molecular and cellular hallmarks and discuss physiological changes of aging at the organ‐system level. We suggest methods to measure aging with attention to both molecular biology (e.g., telomere length and epigenetic marks) and physiological function (e.g., lung function and echocardiographic measurements). Finally, we propose a framework to integrate these molecular and physiological data into a composite score that measures biological aging in humans. Understanding the molecular and physiological phenomena that drive the complex and multifactorial processes underlying the variable pace of biological aging in humans will inform how researchers assess and investigate health and disease over the life course. This composite biological age score could be of use to researchers seeking to characterize normal, accelerated, and exceptionally successful aging as well as to assess the effect of interventions aimed at modulating human aging.