A random-walk model of human mortality and aging

Consideration is made of the roles of certain types of state space and time scales for a random-walk model of individual physiological status change and death. Because the actual measurement of physiological variables omits many variables relevant to survival, we are forced to view this model as operating in a stochastic state space for a population of individuals where only the frequency distributions are deterministic. In this stochastic state space, under the assumption that the “history” of prior movement contains no additional information, the forward partial differential equation is obtained for the distribution of a population whose movement in the selected space is determined by the randomwalk equations. If the initial distribution of the population in the state space is normal, then certain assumptions about movement and mortality will operate to preserve normality thereafter. Under the assumption of normality, simultaneous ordinary differential equations can be derived from the forward partial differential equation defining the distribution function. Examination of the ordinary simultaneous differential equations shows how parameters for certain models of aging and mortality can be obtained.     

The effects of health histories on stochastic process models of aging and mortality

A model of human health history and aging, based on a multivariate stochastic process with both continuous diffusion and discrete jump components, is presented. Discrete changes generate non-Gaussian diffusion with time varying continuous state distributions. An approach to calculating transition rates in dynamically heterogeneous populations, which generalizes the conditional averaging of hazard rates done in fixed frailty population models, is presented to describe health processes with multiple jumps. Conditional semi-invariants are used to approximate the conditional p.d.f. of the unobserved health history components. This is useful in analyzing the age dependence of mortality and health changes at advanced age (e.g., 95 +) where homeostatic controls weaken, and physiological dynamics and survival manifest nonlinear behavior.     

Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study

A stochastic discrete-time susceptible-exposed-infectious-recovered (SEIR) model for infectious diseases is developed with the aim of estimating parameters from daily incidence and mortality time series for an outbreak of Ebola in the Democratic Republic of Congo in 1995. The incidence time series exhibit many low integers as well as zero counts requiring an intrinsically stochastic modeling approach. In order to capture the stochastic nature of the transitions between the compartmental populations in such a model we specify appropriate conditional binomial distributions. In addition, a relatively simple temporally varying transmission rate function is introduced that allows for the effect of control interventions. We develop Markov chain Monte Carlo methods for inference that are used to explore the posterior distribution of the parameters. The algorithm is further extended to integrate numerically over state variables of the model, which are unobserved. This provides a realistic stochastic model that can be used by epidemiologists to study the dynamics of the disease and the effect of control interventions.     

Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods

Hodgkin–Huxley (HH) models of neuronal membrane dynamics consist of a set of nonlinear differential equations that describe the time-varying conductance of various ion channels. Using observations of voltage alone we show how to estimate the unknown parameters and unobserved state variables of an HH model in the expected circumstance that the measurements are noisy, the model has errors, and the state of the neuron is not known when observations commence. The joint probability distribution of the observed membrane voltage and the unobserved state variables and parameters of these models is a path integral through the model state space. The solution to this integral allows estimation of the parameters and thus a characterization of many biological properties of interest, including channel complement and density, that give rise to a neuron’s electrophysiological behavior. This paper describes a method for directly evaluating the path integral using a Monte Carlo numerical approach. This provides estimates not only of the expected values of model parameters but also of their posterior uncertainty. Using test data simulated from neuronal models comprising several common channels, we show that short (<50 ms) intracellular recordings from neurons stimulated with a complex time-varying current yield accurate and precise estimates of the model parameters as well as accurate predictions of the future behavior of the neuron. We also show that this method is robust to errors in model specification, supporting model development for biological preparations in which the channel expression and other biophysical properties of the neurons are not fully known.     

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.     

Model of hidden heterogeneity in longitudinal data

Variables measured in longitudinal studies of aging and longevity do not exhaust the list of all factors affecting health and mortality transitions. Unobserved factors generate hidden variability in susceptibility to diseases and death in populations and in age trajectories of longitudinally measured indices. Effects of such heterogeneity can be manifested not only in observed hazard rates but also in average trajectories of measured indices. Although effects of hidden heterogeneity on observed mortality rates are widely discussed, their role in forming age patterns of other aging-related characteristics (average trajectories of physiological state, stress resistance, etc.) is less clear. We propose a model of hidden heterogeneity to analyze its effects in longitudinal data. The approach takes the presence of hidden heterogeneity into account and incorporates several major concepts currently developing in aging research (allostatic load, aging-associated decline in adaptive capacity and stress-resistance, age-dependent physiological norms). Simulation experiments confirm identifiability of model's parameters.     

Hierarchical models for combining ecological and case-control data

The ecological study design suffers from a broad range of biases that result from the loss of information regarding the joint distribution of individual-level outcomes, exposures, and confounders. The consequent nonidentifiability of individual-level models cannot be overcome without additional information; we combine ecological data with a sample of individual-level case-control data. The focus of this article is hierarchical models to account for between-group heterogeneity. Estimation and inference pose serious computational challenges. We present a Bayesian implementation based on a data augmentation scheme where the unobserved data are treated as auxiliary variables. The methods are illustrated with a dataset of county-specific infant mortality data from the state of North Carolina.     

The propagation of uncertainty in human mortality processes operating in stochastic environments

This paper presents a model describing how the uncertainty due to influential exogenous processes combines with stochasticity intrinsic to physiological aging processes and propagates through time to generate uncertainty about the future physiological state of the population. Variance expressions are derived for (a) the future values of the physiological variables under the assumption that external factors evolve under a linear stochastic diffusion process, and (b) the cohort survival functions and cohort life expectancies which reflect the uncertainty in the future values of the physiological variables. The model implies that a major component of uncertainty in forecasts of the physiological characteristics of a closed cohort is due to differential rates of survival associated with different realizations of the external process. This suggests that the limits to forecasting may be different in physiological systems subject to systematic mortality than in physical systems such as weather where the concepts of closed cohorts and of mortality selection have no simple analog.     

The age-related dynamics of mortality and the Gompertz-Makeham law

Using the statistics of mortality of Caucasian population of 48 states of the USA (1969-1971) it was demonstrated that the real age dynamics of human mortality may differ significantly both from the Gompertz law and from the Gompertz-Makeham law. Using of the Gompertz-Makeham formula leads to appearance of negative A value in 77 cases out of 96. This makes it difficult to interpret this parameter as a "background" component of mortality. Using of the Gompertz formula in different age groups leads uncoordinated changes in alpha and R0 values in every state. Hence, it is impossible to plot geographically stable characters for Gompertz parameters alpha for subsequent epidemiological analysis. The "aging rate", estimated by parameter is not stable throughout the life span of 30-92 years, but changes with certain pattern.     

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.     

Mate choice and uncertainty in the decision process

The behavior of females in search of a mate determines the likelihood that a high quality male is encountered in the search process and alternative search strategies provide different fitness returns to searchers. Models of search behavior are typically formulated on an assumption that the quality of prospective mates is revealed to searchers without error, either directly or by inspection of a perfectly informative phenotypic character. But recent theoretical developments suggest that the relative performance of a search strategy may be sensitive to any uncertainty associated with the to-be-realized fitness benefit of mate choice decisions. Indeed, uncertainty in the decision process is inevitable whenever unobserved male attributes influence the fitness of searchers. In this paper, we derive solutions to the sequential search strategy and the fixed sample search strategy for the general situation in which observed and unobserved male attributes affect the fitness consequences of female mate choice decisions and we determine how the magnitude of various parameters that are influential in the standard models alter these more general solutions. The distribution of unobserved attributes amongst prospective mates determines the uncertainty of mate choice decisions-the reliability of an observed male character as a predictor of male quality-and the realized functional relationship between an observed male character and the fitness return to searchers. The uncertainty of mate choice decisions induced by unobserved male attributes has no influence on the generalized model solutions. Thus, the results of earlier studies of these search models that rely on the use of a perfectly informative male character apply even if an observed male trait does not reveal the quality of prospective mates with certainty. But the solutions are sensitive to any changes of the distribution of unobserved male attributes that alter the realized functional relationship between an observed character and the fitness return to searchers. For example, the standard sequential search model exhibits a reservation property--the acceptability of prospective mates is delimited by a unique threshold criterion--and the existence of this model property under generalized conditions depends critically on the association between the observed and unobserved male characters. In our formulations of the models we assumed that females use a single male character to evaluate the quality of prospective mates, but the model properties generalize to situations in which male quality is evaluated by a direct inspection of multiple male characters.     

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.     

Aspects of parameter estimation in ascertainment sampling schemes.

It has recently been suggested that ascertainment sampling estimation procedures commonly used are not fully efficient in that the number of unobserved families is an unknown parameter that should be estimated (contrary to common practice) along with the genetic parameters for fully efficient estimation. It has also been suggested that the frequency distribution of family size contains unknown parameters that should similarly be estimated with the genetic parameters. These two suggestions are considered in this paper. It is shown by means of an equivalence theorem that in both cases the estimates and their variances obtained by adopting the suggested procedure are identical with those found by ignoring the unobserved families and by ignoring the family-size distribution. This demonstration leads to a formal justification of further procedures, in particular: (1) use of "method-of-moments" estimators, (2) ignoring the ascertainment scheme in some cases when estimating parameters, and (3) forming estimates of parameters when various parts of the data are obtained by different ascertainment schemes.     

Modeling longitudinal data with nonignorable dropouts using a latent dropout class model

In longitudinal studies with dropout, pattern-mixture models form an attractive modeling framework to account for nonignorable missing data. However, pattern-mixture models assume that the components of the mixture distribution are entirely determined by the dropout times. That is, two subjects with the same dropout time have the same distribution for their response with probability one. As that is unlikely to be the case, this assumption made lead to classification error. In addition, if there are certain dropout patterns with very few subjects, which often occurs when the number of observation times is relatively large, pattern-specific parameters may be weakly identified or require identifying restrictions. We propose an alternative approach, which is a latent-class model. The dropout time is assumed to be related to the unobserved (latent) class membership, where the number of classes is less than the number of observed patterns; a regression model for the response is specified conditional on the latent variable. This is a type of shared-parameter model, where the shared "parameter" is discrete. Parameter estimates are obtained using the method of maximum likelihood. Averaging the estimates of the conditional parameters over the distribution of the latent variable yields estimates of the marginal regression parameters. The methodology is illustrated using longitudinal data on depression from a study of HIV in women.     

Changes in blood chemistry and hematology variables during aging in captive rhesus macaques (Macaca mulatta)

Identifying changes with age in physiological variables of captive nonhuman primates will aid in the proper treatment and clinical diagnosis of these animals, as well as enhance our understanding of nonhuman primate models for human aging. Information for 33 physiological variables was obtained from the Primate Aging Database, a multi-centered database being developed for clinical and research use. Using multiple regression analyses, we investigated the relationship of age to hematological variables, blood chemistry and body weight in 345 captive rhesus monkeys (age range 7-30 years) from three different primate research facilities. The analyses revealed that 15 of these variables show a significant relationship with chronological age and are altered in older as compared with adult animals. Here we present the first phase of a project that will: a) identify changes with age in physiological variables among adult captive rhesus macaques; and b) characterize normative values for the aging rhesus population.     

Aging affects different human muscles in various ways. An image analysis of the histomorphometric characteristics of fiber types in human masseter and vastus lateralis muscles from young adults and the very old

This study is an attempt to objectively evaluate age-related changes in human muscles by use of histomorphometric methods. Aging in humans induces dramatic transformations in the skeletal muscles but little is known as to whether or not the aging processes per se may affect all muscles equally. In this study aging of two human muscles with different functions, origin and nerve supply is compared. Sections were cut from masseter and vastus lateralis muscles obtained from young adults aged 18-24 years and from the very old aged 90-102 years. Muscle fiber types were classified with the traditional myofibrillar ATPase staining. Various histomorphometric parameters of the different fiber types in human masseter and vastus lateralis muscle sections were obtained by image analyses to evaluate the age-related changes in the muscle fibers. The following variables were calculated: the number of each fiber type per photographed area; the area of each fiber and two indicators for the shape of the muscle fibers. In the aging muscles there was no relative preferential loss of a fiber type. High numbers of intermediate ATPase-stained fibers (IM fibers) were found in some old vastus muscles but were only sporadic in young vastus muscles. However, there was no change in the percentage distribution of intermediate ATPase-stained fibers when young and very old human masseter muscles were compared. Incubation of the sections with antimyosin antibodies showed that the IM fibers in old masseter and old vastus contained different myosin heavy chains. Thus ATPase activity and anti-myosin staining displayed a somewhat different pattern of fiber type distribution. The main changes in the shape and area indicated that type I fibers in the masseter became more circular while in the vastus they decreased significantly in size. The type II fibers in the vastus became very small and deviated significantly from circularity whereas the type II fibers in the masseter only exhibited a decrease in the size of the fibers. Histomorphometric measurements show that aging affects different human muscles in various ways.     

Successful aging and sustained good health in the naked mole rat: a long-lived mammalian model for biogerontology and biomedical research

Naked mole rats (NMRs; Heterocephalus glaber) are the longest-living rodents known, with a maximum lifespan of 30 years--5 times longer than expected on the basis of body size. These highly social mouse-sized rodents, naturally found in subterranean burrows in the arid and semiarid regions of the horn of Africa, are commonly used in behavioral, neurological, and ecophysiological research. Very old NMRs (>28 years), like humans, show signs of age-associated pathologies (e.g., muscle loss) as well as the accumulation of lipofuscin pigments, but no signs of tumorigenesis. Indeed, for at least 80% of their lives NMRs maintain normal activity, body composition, and reproductive and physiological functions with no obvious age-related increases in morbidity or mortality rate. Their long lifespan is attributed to sustained good health and pronounced cancer resistance. Clearly physiological and biochemical processes in this species have evolved to dramatically extend both their good health- and lifespan. We and others have tested various current theories using this species as an exceptionally long-lived animal model of successful abrogated aging. Surprisingly, NMRs have high levels of oxidative stress and relatively short telomeres, yet they are extremely resilient when subjected to cellular stressors and appear capable of sustaining both their genomic and protein integrity under hostile conditions. The challenge is to understand how these animals are able to do this. Elucidating these mechanisms will provide useful information for enhancing human life- and healthspan, making the naked mole rat a true "supermodel" for aging research and resistance to chronic age-associated diseases.     

Joint analysis of time-to-event and multiple binary indicators of latent classes

Multiple categorical variables are commonly used in medical and epidemiological research to measure specific aspects of human health and functioning. To analyze such data, models have been developed considering these categorical variables as imperfect indicators of an individual's "true" status of health or functioning. In this article, the latent class regression model is used to model the relationship between covariates, a latent class variable (the unobserved status of health or functioning), and the observed indicators (e.g., variables from a questionnaire). The Cox model is extended to encompass a latent class variable as predictor of time-to-event, while using information about latent class membership available from multiple categorical indicators. The expectation-maximization (EM) algorithm is employed to obtain maximum likelihood estimates, and standard errors are calculated based on the profile likelihood, treating the nonparametric baseline hazard as a nuisance parameter. A sampling-based method for model checking is proposed. It allows for graphical investigation of the assumption of proportional hazards across latent classes. It may also be used for checking other model assumptions, such as no additional effect of the observed indicators given latent class. The usefulness of the model framework and the proposed techniques are illustrated in an analysis of data from the Women's Health and Aging Study concerning the effect of severe mobility disability on time-to-death for elderly women.