Decomposition of disparities in life expectancy with applications to administrative health claims and registry data

Research shows that geographic disparities in life expectancy between leading and lagging states are increasing over time while racial disparities between Black and White Americans have been going down. In the 65+ age strata morbidity is the most common cause of death, making differences in morbidity and associated adverse health-related outcomes between advantaged and disadvantaged groups an important aspect of disparities in life expectancy at age 65 (LE65). In this study, we used Pollard's decomposition to evaluate the disease-related contributions to disparities in LE65 for two types of data with distinctly differing structures: population/registry and administrative claims. To do so, we analyzed Pollard's integral, which is exact by construction, and developed exact analytic solutions for both types of data without the need for numerical integration. The solutions are broadly applicable and easily implemented. Applying these solutions, we found that the largest relative contributions to geographic disparities in LE65 were chronic lower respiratory diseases, circulatory diseases, and lung cancer; and, to racial disparities: arterial hypertension, diabetes mellitus, and cerebrovascular diseases. Overall, the increase in LE65 observed over 1998-2005 and 2010-2017 was primarily due to a reduction in the contributions of acute and chronic ischemic diseases; this was partially offset by increased contributions of diseases of the nervous system including dementia and Alzheimer's disease.

Forecasting prevalence and mortality of Alzheimer's disease using the partitioning models

OBJECTIVES

Health forecasting is an important aspect of ensuring that the health system can effectively respond to the changing epidemiological environment. Common models for forecasting Alzheimer's disease and related dementias (AD/ADRD) are based on simplifying methodological assumptions, applied to limited population subgroups, or do not allow analysis of medical interventions. This study uses 5 %-Medicare data (1991-2017) to identify, partition, and forecast age-adjusted prevalence and incidence-based mortality of AD as well as their causal components.

METHODS

The core underlying methodology is the partitioning analysis that calculates the relative impact each component has on the overall trend as well as intertemporal changes in the strength and direction of these impacts. B-spline functions estimated for all parameters of partitioning models represent the basis for projections of these parameters in future.

RESULTS

Prevalence of AD is predicted to be stable between 2017 and 2028 primarily due to a decline in the prevalence of pre-AD-diagnosis stroke. Mortality, on the other hand, is predicted to increase. In all cases the resulting patterns come from a trade-off of two disadvantageous processes: increased incidence and disimproved survival. Analysis of health interventions demonstrates that the projected burden of AD differs significantly and leads to alternative policy implications.

DISCUSSION

We developed a forecasting model of AD/ADRD risks that involves rigorous mathematical models and incorporation of the dynamics of important determinative risk factors for AD/ADRD risk. The applications of such models for analyses of interventions would allow for predicting future burden of AD/ADRD conditional on a specific treatment regime.

Underlying mechanisms of change in cancer prevalence in older U.S. adults: contributions of incidence, survival, and ascertainment at early stages

PURPOSE

To quantitatively evaluate contributions of trends in incidence, relative survival, and stage at diagnosis to the dynamics in the prevalence of major cancers (lung, prostate, colon, breast, urinary bladder, ovaries, stomach, pancreas, esophagus, kidney, liver, and skin melanoma) among older U.S. adults age 65 +.

METHODS

Trend partitioning was applied to the Surveillance, Epidemiology, and End Results Program data for 1973-2016.

RESULTS

Growth of cancer prevalence in older adults decelerated or even decreased over time for all studied cancers due to decreasing incidence and improving survival for most of cancers, with a smaller contribution of the stage at cancer diagnosis. Changes in the prevalence of cancers of the lung, colon, stomach, and breast were predominantly due to decreasing incidence, increasing survival and more frequent diagnoses at earlier stages. Changes in prevalence of some other cancers demonstrated adverse trends such as decreasing survival in localized and regional stages (urinary bladder and ovarian) and growing impact of late-stage diagnoses (esophageal cancer).

CONCLUSION

While decelerating or decreasing prevalence of many cancers were due to a beneficial combination of decreasing incidence and increasing survival, there are cancers for which decelerating prevalence is due to lack of improvement in their stage-specific survival and/or increasing frequency of diagnosis at advanced stages. Overall, if the observed trends persist, it is likely that the burden associated with cancer prevalence in older U.S. adults will be lower  comparing to projections based on constant increasing prevalence have previously estimated.

A forecasting model of disease prevalence based on the McKendrick-von Foerster equation

A new model for disease prevalence based on the analytical solutions of McKendric-von Foerster's partial differential equations is developed. Derivation of the model and methods to cross check obtained results are explicitly demonstrated. Obtained equations describe the time evolution of the healthy and unhealthy age-structured sub-populations and age patterns of disease prevalence. The projection of disease prevalence into the future requires estimates of time trends of age-specific disease incidence, relative survival functions, and prevalence at the initial age and year available in the data. The computational scheme for parameter estimations using Medicare data, analytical properties of the model, application for diabetes prevalence, and relationship with partitioning models are described and discussed. The model allows natural generalization for the case of several diseases as well as for modeling time trends in cause-specific mortality rates.

Theory of partitioning of disease prevalence and mortality in observational data

In this study, we present a new theory of partitioning of disease prevalence and incidence-based mortality and demonstrate how this theory practically works for analyses of Medicare data. In the theory, the prevalence of a disease and incidence-based mortality are modeled in terms of disease incidence and survival after diagnosis supplemented by information on disease prevalence at the initial age and year available in a dataset. Partitioning of the trends of prevalence and mortality is calculated with minimal assumptions. The resulting expressions for the components of the trends are given by continuous functions of data. The estimator is consistent and stable. The developed methodology is applied for data on type 2 diabetes using individual records from a nationally representative 5% sample of Medicare beneficiaries age 65+. Numerical estimates show excellent concordance between empirical estimates and theoretical predictions. Evaluated partitioning model showed that both prevalence and mortality increase with time. The primary driving factors of the observed prevalence increase are improved survival and increased prevalence at age 65. The increase in diabetes-related mortality is driven by increased prevalence and unobserved trends in time-periods and age-groups outside of the range of the data used in the study. Finally, the properties of the new estimator, possible statistical and systematical uncertainties, and future practical applications of this methodology in epidemiology, demography, public health and health forecasting are discussed.

An extension of the Cameron–Martin result

The well-known Cameron–Martin formula allows us to calculate the mathematical expectation where Ws is a Wiener process. This paper extends this result to the case of piecewise continuous martingales. As a particular case the mathematical expectations of a functional of generalized Ornstein– Uhlenbeck processes and pure jump processes are calculated.

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.

Hormesis against aging and diseases: using properties of biological adaptation for health and survival improvement

The idea of using hormesis for postponing aging and improving human health has been recently discussed in scientific literature. This paper shows that redundancy in renewal capacity, some portion of which become activated and manifested in hormesis effects, may originate as a result of interaction between living organisms and their environment. It is shown that such redundancy may normally exist for organisms in the wild, and not only in domesticated and laboratory animals. Further development of the hormesis idea requires: (i) investigating regularities of response to multiple stimuli; (ii) studying slow-time responses (e.g., physiological adaptation) to repeated stimuli; (iii) studying connection between slow and fast (e.g., developing at the cellular and sub-cellular levels) stress responses; (iv) translating knowledge accumulated in studies of animal model systems to humans; (v) evaluating unrealized potential for improving health and longevity using hormetic mechanisms. The use of mathematical and computer modeling for translating experimental knowledge about hormesis effects to humans, as well as connection between studying hormetic mechanisms and analyses of the age trajectories of physiological and biological indices affecting U-shapes curves of morbidity-mortality risks using longitudinal data on aging, health, and longevity are discussed.

Linear Latent Structure Analysis and Modelling of Multiple Categorical Variables

Linear latent structure analysis is a new approach for investigation of population heterogeneity using high-dimensional categorical data. In this approach, the population is represented by a distribution of latent vectors, which play the role of heterogeneity variables, and individual characteristics are represented by the expectation of this vector conditional on individual response patterns. Results of the computer experiments demonstrating a good quality of reconstruction of model parameters are described. The heterogeneity distribution estimated from 1999 National Long Term Care Survey (NLTCS) is discussed. A predictive power of the heterogeneity scores on mortality is analysed using vital statistics data linked to NLTCS.

Assessing genetic association with human survival at multi-allelic loci

Genetic variation plays an important role in natural selection and population evolution. However, it also presents geneticists interested in aging research with problems in data analysis because of the large number of alleles and their various modes of action. Recently, a new statistical method based on survival analysis (the relative risk model or the RR model) has been introduced to assess gene-longevity associations [Yashin et al. (1999) Am J Hum Genet 65: 1178-1193] which outperforms the traditional gene frequency method. Here we extend the model to deal with polymorphic genes or gene markers. Assuming the Hardy-Weinberg equilibrium at birth, we first introduce an allele-based parameterization on gene frequency which helps to cut down the number of frequency parameters to be estimated. We then propose both the genotype and allele-based parameterizations on risk parameters to estimate genotype and allelic relative risks (the GRR and ARR models). While the GRR model allows us to investigate whether the alleles are recessive, dominant or codominant, the ARR model further minimizes the number of parameters to be estimated. As an example, we apply the methods to empirical data on Renin gene polymorphism and longevity. We show that our models can serve as useful tools in searching for important genetic variations implicated in human aging and longevity.

Effect of neuronol on lifespan and development of spontaneous tumors in SAMP-1 mice with genetically accelerated aging

Treatment of female SAMP-1 mice with Neuronol (drug containing succinic acid) given with drinking water starting from the age of 2 months during the whole life prolonged the lifespan and markedly reduced mortality of animals aged 1.5-2 years. Neuronol inhibited the development of spontaneous tumors, primarily lymphomas, and significantly prolonged lifespan in mice with tumors. Long-term treatment with Neuronol had no pathological side effects. Our experiments demonstrated geroprotective and anticarcinogenic activity of Neuronol and safety of its long-term use.

Systemic mechanisms of individual reproductive life history in female Medflies

This paper is the second one in a series of two papers hypothesizing and testing systemic grounds of reproductive life history in the female fruit fly. In the first paper, we analyzed mechanisms of individual fecundity scheduling and have drawn the following conclusions. Individual fecundity in female flies is endowed as a flat pattern with a steady-state period of a constant rate of egg-laying. An individual female reveals three stages in her adult life history: maturation, maturity, and senescence. The first stage is a transient period of achieving a steady state at maturity, which can be maintained until the senescence stage. Thus, an individual fecundity pattern has no maximum. The maximums observed experimentally are averaging-caused artifacts. Two natural causes of deaths exist in flies, senescence-caused ones and premature deaths, probably due to a reproductive overload. In this paper, to confirm these findings, we use individual daily scores of egg-laying in four populations of Mediterranean fruit flies. Based on fecundity scores, we divide each Medfly population into four classes, namely zero-egg, short-, medium- and long-lived egg-layers. We demonstrate that, indeed, the three above findings definitely exist in Medflies. Our procedure allows the efficient storage of individual fecundity in parametric form, with only five numbers for each fly. Finally, this protocol will allow a more precise analysis of fecundity-energy trade-offs in flies carrying appropriate longevity mutations.

The impact of diet switching on resource allocation to reproduction and longevity in Mediterranean fruitflies

Understanding the factors that determine the allocation and utilization of organism resources may provide an insight into the mechanisms of adaptation, ageing and reproduction. Resource allocation, which is regarded as a method of adaptation, increases fitness and is genetically controlled. Experiments with variable diet feeding of female Mediterranean fruitflies (Ceratitis capitata) demonstrated that the feeding regime dramatically influences lifespan, mortality and the reproduction of flies. An analysis of experimental data and numerical experiments reveals that resource allocation could explain lifespan increase when females are switched from a sugar-only to a protein-containing diet. The heterogeneity of the initial female cohort in terms of the total amount of resources and its allocation to the processes of maintenance and reproduction plays a significant role in this.

[A model of resource reallocation during physiological adaptation in Mediterranean fruit fly females]

Analysis of experimental data on longevity and fertility of females of Mediterranean fruit fly Ceratitis capitata demonstrates that flies lay fewer eggs on the average as the average life-span increases. At the same time, the values of individual life-span and the number of eggs laid are positively correlated. To explain these results, a resource model describing the allocation and reallocation of resources between two basic functions, reproduction and maintenance, was proposed. The reallocation of resources, is triggered by changes in environmental conditions such as diet changes, and the parameters of reallocation depend on the current environmental conditions. Modeling demonstrated that the results of experiments are greatly influenced by population selection and heterogeneity.

Logistic regression models for polymorphic and antagonistic pleiotropic gene action on human aging and longevity

In this paper, we apply logistic regression models to measure genetic association with human survival for highly polymorphic and pleiotropic genes. By modelling genotype frequency as a function of age, we introduce a logistic regression model with polytomous responses to handle the polymorphic situation. Genotype and allele-based parameterization can be used to investigate the modes of gene action and to reduce the number of parameters, so that the power is increased while the amount of multiple testing minimized. A binomial logistic regression model with fractional polynomials is used to capture the age-dependent or antagonistic pleiotropic effects. The models are applied to HFE genotype data to assess the effects on human longevity by different alleles and to detect if an age-dependent effect exists. Application has shown that these methods can serve as useful tools in searching for important gene variations that contribute to human aging and longevity.

How an Individual Fecundity Pattern Looks inDrosophilaand Medflies

Reproduction usually is characterized by a mean-population fecundity pattern. Such a pattern has a maximum at earlier ages and a subsequent gradual decline in egg production. It is shown that individual fecundity trajectories do not follow such a pattern. In particular, the regular individual fecundity pattern has no maximum so that experimentally observed maximums are average-related artifacts. The three-stage description of individual fecundity, which includes maturation, maturity, and reproductive senescence, is more appropriate. Data are presented for Drosophila and Mediterranean fruitfly females that clearly confirm this hypothesis. A systematic error between egg-laying scores and the regular individual pattern allows for evaluation of how close the random scores are to the pattern. The first finding of the analysis of the systematic errors is that they are consistent with the three-stage hypothesis and do not contradict the absence of the maximum in the regular individual pattern. The other finding is the existence of obvious dynamic properties of the systematic error. The slow decrease in egg-laying at the maturity stage might be the result of a cost of mating. It can also be a consequence of "structural" senescence, that is, a slow rate accumulation of oxidative damage in the gonads.

Variability of the SIRT3 gene, human silent information regulator Sir2 homologue, and survivorship in the elderly

The human sirtuin 3 (SIRT3) gene encodes a putative mitochondrial NAD-dependent deacetylase (SIRT3) which belongs to the evolutionary conserved family of sirtuin 2 proteins. Studies in model organisms have demonstrated that SIR2 genes control lifespan, while no data are available regarding a possible role of SIRT3 in human longevity. By analysing the genotype-specific survival function relevant to the G477T marker of SIRT3, we found that in males the TT genotype increases (p=0.0272), while the GT genotype decreases (p=0.0391) survival in the elderly. Since SIRT3 lies in a chromosomal region (11p15.5) where four genes potentially associated with longevity are located (HRAS1, Insulin-like Growth Factor 2, Proinsulin, and Tyrosine Hydroxylase) we tested for linkage-disequilibrium between G477T alleles and alleles of the above genes. The disequilibrium was not significant in any case, thus suggesting that SIRT3 itself, or a gene strictly linked to SIRT3, may have a role in human longevity.

What does a fly's individual fecundity pattern look like? The dynamics of resource allocation in reproduction and ageing

Reproduction is usually characterised by an average fecundity pattern having a maximum at earlier ages and a subsequent gradual decline later on. An individual fecundity trajectory does not follow such a pattern and has no maximum. A three-stage pattern, which includes maturation, maturity and reproductive senescence, is a more appropriate description. An analysis of the power balance of an adult female fly during its life course allows us to predict two critical periods in an individual life history. The first crisis occurs at early ages when the increasing power demand becomes greater than the power supply. It often results in premature death. The surviving flies enjoy maturity and lay eggs at a presumably constant rate. The second critical period at advanced ages ends up in a senescence-caused death. Our approach predicts that there will be a bimodal death time distribution for a population of flies.

How the analysis of genetic mutations can help us to solve basic problems in gerontology? II. Life extending genetic modifications in budding yeast S. cereviseae, fruit fly D. melanogaster and laboratory mice M. musculus

Most studies of aging are conducted in humans and domestic or laboratory animals, i.e. in conditions where artificial environment protection is applied, This yields changes in physiology and behavior, which set up organism's state unobserved in wild life. This state may be less adequate to the evolutionary adjusted genetic construction of an organism, which generates a hypothesis that in natural niches the aging rate can be lower and stress resistance can be higher than in captivity despite the fact that life expectancy in habitat is essentially lower than that in laboratory conditions due to high external mortality. Direct test of this hypothesis is difficult because of problems related to reconstruction of natural environment conditions in the laboratory. Substantial life-extending effect of some mutated genes can serve as indirect test of the hypothesis. We propose that in some cases genetic mutations can distort reaction of an organism on environmental cues and change control parameters of its life cycle. As a result such mutants in laboratory may partly demonstrate life traits similar to those observed in natural environment, e.g. associated with high stress resistance and low rate of aging. These features combined with low external mortality in laboratory conditions may lead to significant extension in the life span of mutants. Recently we considered 56 life-extending gene modifications in nematode C. elegans (Adv. Gerontol., 2003, Vol. 11), scattered in many publications. In this paper we consider pertinent life-extending gene modifications corresponded to the budding yeast S. cerevisease (29 genes), fruit fly D. melanogaster (22 genes) and laboratory mice M. musculus (8 genes).

How the analysis of genetic mutations can help us to solve basic problems in gerontology? I. Life extending genetic modifications in round worm C. elegans

The results of recent molecular biological studies of aging and longevity confirmed substantial genetic contribution to the life span. The analysis of these findings showed substantial role of specific mutations in genes involved in regulatory processes on both the extra- and intracellular levels. We suggest that difference in responses of intact and mutant animals to the same set of environmental signals may be useful to clarify contribution of organism-environment interactions into the rate of aging, mortality and longevity of respective organisms. In our opinion such clarification is important for better understanding the origin of natural senescence and its dependence on external conditions.

Male/female ratio in centenarians: a possible role played by population genetic structure

All the demographic surveys on the centenarians have highlighted that females outnumber males. The centenarians' male/female (M/F) ratio reported by most studies ranges between 1:4 and 1:7. A puzzling 1:2 ratio was observed in Calabria, a Southern Italian region. To our knowledge only in Sardinia a similar phenomenon had been previously observed. We have therefore used the data of the Italian Institute of Statistics to figure out the centenarians' M/F ratio in the Italian regions. We found that this ratio gradually decreases from South to North. Such a result is certainly due to many factors. Thus, we have explored the possibility, it is also influenced by the genetic structure of the Italian population. In fact, the distribution of the centenarians' M/F ratio turned out to be significantly correlated with the genetic structure of the Italian population as outlined by the principal component analysis.

Heritability of death from coronary heart disease: a 36-year follow-up of 20 966 Swedish twins

OBJECTIVE

The aim of the present study was to evaluate and distinguish between environmental and genetic effects for death from coronary heart disease (CHD) as well as to determine whether the importance of genetic influences is changing with age.

DESIGN

A cohort study with a follow-up time of 36 years.

SUBJECTS

The cohort drawn for the present study includes 20 966 twins born in Sweden between 1886 and 1925 where both twins within a pair still lived within the country in 1961.

METHODS

Concordances and correlated gamma-frailty model were used to assess and distinguish between genetic and environmental influences as well as to evaluate age-related changes in genetic influences.

RESULTS

A total number of 4007 CHD-deaths (2208 males, and 1799 females) was observed. The probability of dying from CHD given that one's twin partner already has died from CHD decreased with increasing age, particularly amongst males. The genetic variation in susceptibility to death from CHD was moderately large, and decreased slightly across time, particularly amongst males. The heritability was 0.57 (95% CI, 0.45-0.69) amongst male twins, and 0.38 (0.26-0.50) amongst female twins.

CONCLUSIONS

The genetic contribution to the variation in CHD-mortality was moderate both in females and males. Furthermore, although genetic effects appeared to be greater at younger ages of death, our findings clearly suggest that genetic factors are in operation throughout the entire life span.

Epithalon decelerates aging and suppresses development of breast adenocarcinomas in transgenic her-2/neu mice

Female transgenic FVB/N mice carrying the breast cancer gene HER-2/neu received epithalon (Ala-Glu-Asp-Gly) in a dose of 1 mg subcutaneously 5 times a week to from the 2nd month of life to death. Epithalon prolonged the average and maximum lifetimes of mice by 13.5 (p<0.05) and 13.9%, respectively. The peptide prolonged the average lifetime of animals without neoplasms (by 34.2%, p<0.05). Epithalon decelerated the development of age-related disturbances in reproductive activity and suppressed the formation of neoplasms. The peptide decreased the incidence of breast adenocarcinomas, lungs metastases (by 1.6 times, p<0.05), and multiple tumors (by 2 times). Epithalon 3.7-fold increased the number of mice without breast tumors (p<0.05), while the number of animals with 6 or more breast tumors decreased by 3 times (p<0.05). Epithalon prolonged the lifetime of mice with breast tumors by 1.4 times (p<0.05). These results indicate that Epithalon possesses geroprotective activity and inhibits breast carcinogenesis in transgenic mice, which is probably related to suppression of HER-2/neu expression.

The influences on human longevity by HUMTHO1.STR polymorphism (Tyrosine Hydroxylase gene)

A new method based on the recently developed relative risk approach is introduced, and applied to data from Italian centenarian study (965 subjects aged from 13 to 109 years old) for investigating influences on longevity by Tyrosine Hydroxylase (TH) gene variability. The strategic parameterization enables the model to disentangle the various ways by which HUMTHO1.STR alleles (alleles 6, 7, 8, 9, 10*, 10, as defined according to the number of repeats) may contribute in reducing or increasing the hazard of death with different patterns of influences. Among all the alleles, we have found that allele 10* (10 imperfect repeats) shows a remarkable dominant and beneficial effect that reduces the log hazard of death in an additive manner. The results confirm that HUMTHO1.STR polymorphism is involved in the modulation of human longevity.

Evolutionary optimality applied to Drosophila experiments: hypothesis of constrained reproductive efficiency

The general purpose of the paper is to test evolutionary optimality theories with experimental data on reproduction, energy consumption, and longevity in a particular Drosophila genotype. We describe the resource allocation in Drosophila females in terms of the oxygen consumption rates devoted to reproduction and to maintenance. The maximum ratio of the component spent on reproduction to the total rate of oxygen consumption, which can be realized by the female reproductive machinery, is called metabolic reproductive efficiency (MRE). We regard MRE as an evolutionary constraint. We demonstrate that MRE may be evaluated for a particular Drosophila phenotype given the fecundity pattern, the age-related pattern of oxygen consumption rate, and the longevity. We use a homeostatic model of aging to simulate a life history of a representative female fly, which describes the control strain in the long-term experiments with the Wayne State Drosophila genotype. We evaluate the theoretically optimal trade-offs in this genotype. Then we apply the Van Noordwijk-de Jong resource acquisition and allocation model, Kirkwood's disposable soma theory. and the Partridge-Barton optimality approach to test if the experimentally observed trade-offs may be regarded as close to the theoretically optimal ones. We demonstrate that the two approaches by Partridge-Barton and Kirkwood allow a positive answer to the question, whereas the Van Noordwijk-de Jong approach may be used to illustrate the optimality. We discuss the prospects of applying the proposed technique to various Drosophila experiments, in particular those including manipulations affecting fecundity.

Heating stress patterns in Caenorhabditis elegans longevity and survivorship

Survival data from Caenorhabditis elegans strain TJ1060 (spe-9; fer-15) following brief exposure to 35 degrees C have been investigated. Three experiments with 3-day-old worms were conducted with heat duration ranging between 0 and 12 hours. A statistically significant increase in life expectancy was observed in the groups heated for less than 2 hours, as compared to the unheated control groups. In different experiments P-values for the observed life spans under the hypothesis that heating has no influence on longevity were P < 0.004 after 0.5 hour heat, P < 0.012 after 1 hour heat and P < 0.055 after 2 hours of heating. A biphasic survival model with Gamma distributed frailty has been constructed to describe the survival of worms after heating. The increase in the remaining life expectancy is determined by more effective protection by heat-induced substances in the ages yanger than 27 days. The unheated control group demonstrated acquired heterogeneity of frailty with chronological age while the heat-induced substances defend the worms in a universal way and protect against the development of frailty.

A homeostatic model of oxidative damage explains paradoxes observed in earlier aging experiments: a fusion and extension of older theories of aging

The Rate of Living and the Threshold Theories of Aging are two contradicting approaches used to explain experimental facts about aging in fruit flies. In this paper we suggest an approach that unifies these theories and removes the contradiction. The approach involves quantitative description of the oxidative stress theory of aging, which is presented in the form of a mathematical homeostatic model. The crucial variable in the model is called 'homeostatic capacity', which is analogous to the classical notion of vitality. We model the process of aging as the age-related accumulation of damage produced by oxidative stress, which reduces the homeostatic capacity of the organism. The model is tested with the experimental data obtained in the classical experiments by Maynard Smith in 1958-1963. Our homeostatic model explains the well-known results of these experiments more accurate than any one of the early theories of aging. We form an hypothesis about the mechanisms underlying the results observed in the experiments and analyze a possible interplay of these mechanisms. Our virtual replication of Maynard Smith's classical experiments demonstrates that mathematical modeling can be a powerful tool to reveal and investigate the inherent genetic and physiological processes underlying the data observed in complicated insect experiments.

A logistic regression model for measuring gene-longevity associations

The logistic regression model is a popular model for data analysis in epidemiological research. In this paper, we use this model to analyze genetic data collected from gene-longevity association studies. This new approach models the probability of observing one genotype as a function of the age of investigated individuals. Applying the model to genotype data on the TH and 3'ApoB-VNTR loci collected from an Italian centenarian study, we show how it can be used to model the different ways that genes affect survival, including sex- and age-specific influences. We highlight the advantages of this application over other available models. The application of the model to empirical data indicates that it is an efficient and easily applicable approach for determining the influences of genes on human longevity.

The new trends in survival improvement require a revision of traditional gerontological concepts

In 1960, Strehler and Mildvan (SM) theoretically predicted that the parameters of the Gompertz approximation to a mortality curve are negatively correlated. This means that the changes in the human mortality rate resulting from improvement in living standards, progress in health care or the influence of other factors must follow certain regularities prescribed by dependence between the Gompertz parameters. Such dependence, called SM correlation, was then confirmed in a number of empirical studies using period data on human mortality. Since the SM theory was based on the cohort model of mortality, it was tacitly assumed that period and cohort SM correlation patterns are similar. The remarkable stability of the SM correlation pattern revealed in these studies was often regarded as manifestation of a universal demographic law regulating changes in the age pattern of mortality rates. In this paper, we investigated trends in mortality decline in France, Japan, Sweden and the United States. In contrast with traditional expectations, we found that the SM correlation pattern was relatively stable only in certain periods of a population's survival history. Recently, several new correlation patterns emerged and, despite some differences in the timing of the changes, the new patterns are remarkably similar in all four countries. Contrary to traditional expectations, the patterns are not the same for cohort and period mortality data when SM correlations are calculated for France, Sweden and the United States. We show that some changes in the patterns of SM correlation admit interpretation in terms of a biological mechanism of individual adaptation (survival trade off). Some other patterns, however, contradict basic postulates of the SM theory. This indicates the need for revision of traditional concepts establishing the relationship between physiological and demographic patterns of aging.

Have the oldest old adults ever been frail in the past? A hypothesis that explains modern trends in survival

Three important results concerning the shape and the trends of the human mortality rate were discussed recently in demographic and epidemiological literature. These are the deceleration of the mortality rate at old ages, the tendency to rectangularization of the survival curve, and the decline of the old age mortality observed in the second part of the 20th century. In this paper we show that all these results can be explained by using a model with a new type of heterogeneity associated with individual differences in adaptive capacity. We first illustrate the idea of such a model by considering survival in a mixture of two subpopulations of individuals (called "labile" and "stable"). These subpopulations are characterized by different Gompertz mortality patterns, such that their mortality rates cross over. The survival chances of individuals in these subpopulations have different sensitivities to changes in environmental conditions. Then we develop a more comprehensive model in which the mortality rate is related to the adaptive capacity of an organism. We show that the trends in survival patterns experienced by a mixture of such individuals resemble those obtained in an analysis of empirical data on survival in developed countries. Lastly, we present evidence of the existence of subpopulations of phenotypes in both humans and experimental organisms, which were used as prototypes in our models. The existence of such phenotypes provides the possibility that at least part of today's centenarians originated from an initially frail part of the cohort.

Cardiovascular mortality in twins and the fetal origins hypothesis

The intrauterine growth patterns for twins are characterized by normal development during the first two trimesters and reduced growth during the third trimester. According to the fetal origins hypothesis this growth pattern is associated with risk factors for cardiovascular morbidity and mortality. We studied cause-specific mortality of 19,986 Danish twin individuals from the birth cohorts 1870-1930 followed from 1952 through 1993. Despite the large sample size and follow-up period we were not able to detect any difference between twins and the general population with regard to all-cause mortality or cardiovascular mortality. Hence, the intrauterine growth retardation experienced by twins does not result in any "fetal programming" of cardiovascular diseases. There is still an important role for twins (and other sibs) to play in the testing of the fetal origins hypothesis, namely in studies of intra-pair differences, which can assess the role of genetic confounding in the association between fetal growth and later health outcome.

Recent advances in human gene-longevity association studies

This paper reviews the recent literature on genes and longevity. The influence of genes on human life span has been confirmed in studies of life span correlation between related individuals based on family and twin data. Results from major twin studies indicate that approximately 25% of the variation in life span is genetically determined. Taking advantage of recent developments in molecular biology, researchers are now searching for candidate genes that might have an influence on life span. The data on unrelated individuals emerging from an ever-increasing number of centenarian studies makes this possible. This paper summarizes the rich literature dealing with the various aspects of the influence of genes on individual survival. Common phenomena affecting the development of disease and longevity are discussed. The major methodological difficulty one is confronted with when studying the epidemiology of longevity involves the complexity of the phenomenon, which arises from the polygenic nature of life span and historical mortality change. We discuss this issue and suggest new methodological approaches.

Ageing and survival after different doses of heat shock: the results of analysis of data from stress experiments with the nematode worm Caenorhabditis elegans

Stress experiments performed on a population of sterilised nematode worms (Caenorhabditis elegans) show a clear hormesis effect after short exposure and clear debilitation effects after long exposure to heat shock. An intermediate duration of exposure results in a mixture of these two effects. In this latter case the survival curves for populations in the stress and control groups intersect. In this paper we develop an adaptation model of stress and apply it to the analysis of survival data from three such stress experiments. We show that the model can be used to explain empirical age-patterns of mortality and survival observed in these experiments. We discuss possible biological mechanisms involved in stress response and directions for further research.

How individual age-associated changes may influence human morbidity and mortality patterns

Patterns of human mortality share common traits in different populations. They include higher mortality in early childhood, lower mortality during the reproductive period, an accelerated increase of mortality near the end of the reproductive period, and deceleration in the mortality increase at oldest old ages. The deceleration of mortality rate is one of the most intriguing recent findings in longevity research. The role of differential selection in this phenomenon has been well studied. Possible contribution of individual aging in the shape of mortality curve is also recognized. However, this contribution has not been studied in details. In this paper, we specify most common patterns of age-associated changes in an individual organism and discuss their possible influence on morbidity and mortality in population. We subdivide individual age-associated changes into three components, having different influence on morbidity and mortality: (1) basal, (2) ontogenetic, and (3) time-dependent. Basal changes are connected with the universal decrease in the rate of living during an individual life. As a result, some phenotypic effects of aging may accumulate in an organism at a slower rate with age. Basal changes are likely to contribute to a plateau of morbidity often observed at old ages, and may partially be responsible for mortality deceleration at oldest old ages. Ontogenetic component is connected with change of the stages of ontogenesis (e.g., the growth, the reproductive period and the climacteric) during an individual life. The ontogenesis-related changes contribute to wave-like patterns of morbidity in population and may partially be responsible for mortality increase at middle ages and its deceleration at old ages. Time-dependent changes are connected with long-time exposure of an organism to different harmful factors. They are most likely to contribute to morbidity and mortality acceleration. We discuss how all three components of individual age-associated changes may interact in human organism and influence patterns of morbidity and mortality in population.

Variations of cardiovascular disease associated genes exhibit sex-dependent influence on human longevity

This article investigates the relationship between the polymorphic variations in genes associated with cardiovascular disease and longevity in the Danish population. A new procedure that combines both demographic and the individual genetic information in determining the relative risks of the observed genetic variations is applied. The sex-dependent influences can be found by introducing sex-specific population survival and incorporating the risk of gene-sex interaction. Three genetic polymorphisms, angiotensinogen M/T235, blood coagulation factor VII (FVII) R/Q353 and FVII-323ins10, manifest significant influences on survival in males, with reduced hazards of death for carriers of the angiotensinogen M235 allele, the F VII Q353 allele, and the FVII-323P10 allele. The results show that some of these genotypes associated with lower risk of CVD could also reduce the carrier's death rate and contribute to longevity. However, the presence of sex-dependent effects and the fact that major CVD-associated genes failed to impose detrimental influence on longevity lead us to concur that the aging process is highly complicated.

The heritability of mortality due to heart diseases: a correlated frailty model applied to Danish twins

Data of the Danish Twin Registry on monozygotic and dizygotic twins are used to analyse genetic and environmental influences on susceptibility to heart diseases for males and females, respectively. The sample includes 7955 like-sexed twin pairs born between 1870 and 1930. Follow-up was from 1 January 1943 to 31 December 1993 which results in truncation (twin pairs were included in the study if both individuals were still alive at the beginning of the follow-up) and censoring (nearly 40% of the study population was still alive at the end of the follow-up). We use the correlated gamma-frailty model for the genetic analysis of frailty to account for this censoring and truncation. During the follow-up 9370 deaths occurred, 3393 deaths were due to heart diseases in general, including 2476 deaths due to coronary heart disease (CHD). Proportions of variance of frailty attributable to genetic and environmental factors were analyzed using the structural equation model approach. Different standard biometric models are fitted to the data to evaluate the magnitude and nature of genetic and environmental factors on mortality. Using the best fitting model heritability of frailty (liability to death) was found to be 0.55 (0.07) and 0.53 (0.11) with respect to heart diseases and CHD, respectively, for males and 0.52 (0.10) and 0.58 (0.14) for females in a parametric analysis. A semi-parametric analysis shows very similar results. These analyses may indicate the existence of a strong genetic influence on individual frailty associated with mortality caused by heart diseases and CHD in both, males and females. The nature of genetic influences on frailty with respect to heart diseases and CHD is probably additive. No evidence for dominance and shared environment was found.

Replication studies in longevity: puzzling findings in Danish centenarians at the 3'APOB-VNTR locus

In Danes we replicated the 3'APOB-VNTR gene/longevity association study previously carried out in Italians, by which the Small alleles (less than 35 repeats) had been identified as frailty alleles for longevity. In Danes, neither genotype nor allele frequencies differed between centenarians and 20-64-year-old subjects. However, when Danish and Italian data were compared, a significant difference (p = 0.0004) was found between the frequencies of Small alleles in youths, which disappeared in centenarians (p = 0.290). Furthermore, the demographic-genetic approach revealed in Danes a significant gene-sex interaction relevant to Long alleles (more than 37 repeats). The different findings in Denmark and Italy suggest that gene/longevity associations are population-specific, and heavily affected by the population-specific genetic and environmental history.

Melatonin increases both life span and tumor incidence in female CBA mice

From the age of 6 months until their natural deaths, female CBA mice were given melatonin with their drinking water (20 mg/l) for 5 consecutive days every month. Intact mice served as controls. The results of this study show that the consumption of melatonin did not significantly influence food consumption, but it did increase the body weight of older mice; it did not influence physical strength or the presence of fatigue; it decreased locomotor activity and body temperature; it inhibited free radical processes in serum, brain, and liver; it slowed down the age-related switching-off of estrous function; and it increased life span. However, we also found that treatment with the used dose of melatonin increased spontaneous tumor incidence in mice. For this reason, we concluded that it would be premature to recommend melatonin as a geroprotector for long-term use.

Mitochondrial DNA haplogroups and APOE4 allele are non-independent variables in sporadic Alzheimer's disease

Allele epsilon4 of the nuclear APOE gene is a leading genetic risk factor for sporadic Alzheimer's disease (AD). Moreover, an allele-specific effect of APOE isoforms on neuronal cell oxidative death is known. Because of the role of the mitochondrial genome (mtDNA) in oxidative phosphorylation and oxidative stress, an interaction between APOE polymorphism and mtDNA inherited variability in the genetic susceptibility to sporadic AD can be hypothesized. We have explored this hypothesis by analyzing mtDNA germline variants (mtDNA haplogroups) in a sample of AD patients (213 subjects) genotyped for APOE and classified as APOE epsilon4 carriers and non-carriers. We found that the frequency distribution of mtDNA haplogroups is different between epsilon4 carriers and non-carriers (P=0.018), thus showing non-random association between APOE and mtDNA polymorphisms. The same analysis, carried out in two samples of healthy subjects (179 age-matched and 210 individuals aged more than 100 years), showed independence between epsilon4 allele and mtDNA haplogroups. Therefore, the APOE/mtDNA interaction is restricted to AD and may affect susceptibility to the disease. In particular, some mtDNA haplogroups (K and U) seem to neutralize the harmful effect of the APOE epsilon4 allele, lowering the epsilon4 odds ratio from statistically significant to non-significant values.

Effect of synthetic thymic and pineal peptides on biomarkers of ageing, survival and spontaneous tumour incidence in female CBA mice

Fifty female CBA mice were injected s.c. either with 0.1 ml saline, or with synthetic thymic dipeptide Lys-Glu or with synthetic pineal tetrapeptide Ala-Glu-Asp-Gly both in a single dose of 0.1 microg/animal monthly for five consecutive days from the age of 6 months until natural death. Lys-Glu did not significantly influence the body weight and food consumption, free radical processes and estrus function in mice and did increase their physical activity with the subsequent decrease in spontaneous lung adenomas incidence. The pineal peptide treatment was failed to modify the food consumption and physical strength of mice, and was followed by the increase in the body weight, mean survival (by 5.3%, P<0.05) and maximum (by 10 months), by slow down of the ageing of estrus function, by the decrease in body temperature, physical activity, free radical processes and spontaneous tumor incidence (mainly, lung adenomas) in mice. These data suggest the geroprotector potential of the pineal peptide.

Anticipation of oxidative damage decelerates aging in virgin female medflies: hypothesis tested by statistical modeling

Empirical analysis of survival data obtained from large samples of Mediterranean fruit flies shows that the trajectory of the mortality rate for virgin females departs from that for females maintained in mixed sex cages. It increases, decelerates, reaches its maximum, declines and then increases again within the reproductive interval. Non-virgin females, however, display an early-age plateau instead of this dip. We assume that these deviations are produced by the interplay between changes in oxygen consumption associated with reproductive behavior and the antioxidant defense that acts against anticipated oxidative damage caused by reproduction. Since there are no data on antioxidant mechanisms in medflies available that explain the observed patterns of mortality, we develop a model of physiological aging based on oxidative stress theory, which describes age-related changes in oxygen consumption and in antioxidative capacity during the reproductive period. Using this model, we simulate virtual populations of 25,000 virgin and non-virgin flies, calculate the respective mortality rates and show that they practically coincide with those of experimental populations. We show that the hypothesis about the biological support of reproduction used in our model does not contradict experimental data. The model explains how the early-age dip and plateau might arise in the mortality rates of female medflies and why the male mortality pattern does not exhibit such deviations.

The network and the remodeling theories of aging: historical background and new perspectives

Two general theories, i.e. "the network theory of aging" (1989) and "the remodeling theory of aging" (1995), as well as their implications, new developments, and perspectives are reviewed and discussed. Particular attention has been paid to illustrate: (i) how the network theory of aging fits with recent data on aging and longevity in unicellular organisms (yeast), multicellular organisms (worms), and mammals (mice and humans); (ii) the evolutionary and experimental basis of the remodeling theory of aging (immunological, genetic, and metabolic data in healthy centenarians, and studies on the evolution of the immune response, stress and inflammation) and its recent development (the concepts of "immunological space" and "inflamm-aging"); (iii) the profound relationship between these two theories and the data which suggest that aging and longevity are related, in a complex way, to the capability to cope with a variety of stressors.

Genes and longevity: lessons from studies of centenarians

In population studies of aging, the data on genetic markers are often collected for individuals from different age groups. The idea of such studies is to identify "longevity" or "frailty" genes by comparing the frequencies of genotypes in the oldest and in the younger groups of individuals. In this paper we discuss a new approach to the analysis of such data. This approach, based on the maximum likelihood method, combines data on genetic markers with survival information obtained from standard demographic life tables. This method allows us to evaluate survival characteristics for individuals carrying respective candidate genes. It can also be used in the estimation of the effects of allele-area and allele-allele interaction, either in the presence or absence of hidden heterogeneity. We apply this method to the analysis of Italian data on genetic markers for five autosomal loci and mitochondrial genomes. Then we discuss basic assumptions used in this analysis and directions of further research.

Genetic nature of individual frailty: comparison of two approaches

The traditional frailty models used in genetic analysis of bivariate survival data assume that individual frailty (and longevity) is influenced by thousands of genes, and that the contribution of each separate gene is small. This assumption, however, does not have a solid biological basis. It may just happen that one or a small number of genes makes a major contribution to determining the human life span. To answer the questions about the nature of the genetic influence on life span using survival data, models are needed that specify the influence of major genes on individual frailty and longevity. The goal of this paper is to test the nature of genetic influences on individual frailty and longevity using survival data on Danish twins. We use a new bivariate survival model with one major gene influencing life span to analyse survival data on MZ (monozygotic) and DZ (dizygotic) twins. The analysis shows that two radically different classes of model provide an equally good fit to the data. However, the asymptotic behaviour of some conditional statistics is different in models from different classes. Because of the limited sample size of bivariate survival data we cannot draw reliable conclusions about the nature of genetic effects on life span. Additional information about tails of bivariate distribution or risk factors may help to solve this problem.

Vitality index in survival modeling: how physiological aging influences mortality

We investigated the relation of the age trajectory of physiological indicators of the average metabolic activity of organisms in a population to the age-specific population mortality rate. We show that a metabolic rate indicator (MRI) can be estimated using traditional physiological measures, such as homeostatic serum glucose concentration, vital capacity, and such. Estimates of the MRI were made from data collected in the Multiple Risk Factor Intervention Trial (MRFIT) study. The relation of the empirical mortality rate and MRI was also tested using MRFIT data. The age trajectory of MRI was evaluated using Swedish mortality data. The mortality results reproduce the "Strehler and Mildvan effect." The average rate of decline of MRI with age coincides with estimates predicted by Strehler using other methods. Possible extensions of the method are discussed.

Genetic factors in susceptibility to death: a comparative analysis of bivariate survival models

BACKGROUND

Molecular epidemiological studies of aging and longevity are focused on evaluating the effects of single genes on susceptibility to disease and death. The effects of all genetic factors on susceptibility can be evaluated from the analysis of survival data on related individuals.

METHOD

The analyses of survival data on Danish monozygotic (MZ) and dizygotic (DZ) twins are performed using gamma, inverse Gaussian and three-parameter correlated frailty models. The semiparametric representations of the respective models are used to obtain maximum likelihood estimates of model parameters. The results are compared using the likelihood ratio test.

RESULTS

The survival of Danish MZ and DZ twins can be characterised by the same marginal hazards and identical univariate frailty distributions for any of the three frailty models. In all three cases the genetic influence on frailty is statistically significant.

CONCLUSION

All three models can be used to study genetic effects on susceptibility. The gamma and inverse Gaussian frailty models fit the Danish twin data equally well. Our analyses show that for the Danish twin data these two models are preferable to the three-parameter model.