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.

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.

Genes, demography, and life span: the contribution of demographic data in genetic studies on aging and longevity.

In population studies on aging, the data on genetic markers are often collected for individuals from different age groups. The purpose of such studies is to identify, by comparison of the frequencies of selected genotypes, "longevity" or "frailty" genes in the oldest and in younger groups of individuals. To address questions about more-complicated aspects of genetic influence on longevity, additional information must be used. In this article, we show that the use of demographic information, together with data on genetic markers, allows us to calculate hazard rates, relative risks, and survival functions for respective genes or genotypes. New methods of combining genetic and demographic information are discussed. These methods are tested on simulated data and then are applied to the analysis of data on genetic markers for two haplogroups of human mtDNA. The approaches suggested in this article provide a powerful tool for analyzing the influence of candidate genes on longevity and survival. We also show how factors such as changes in the initial frequencies of candidate genes in subsequent cohorts, or secular trends in cohort mortality, may influence the results of an analysis.

Half of the variation in susceptibility to mortality is genetic: findings from Swedish twin survival data.

Molecular epidemiological studies confirm tremendous variability in genetic and environmental susceptibility to disease and death for humans. This variability as well as the roles of genetic and environmental factors in susceptibility to death can be estimated in the analysis of survival data on related individuals (e.g., twins). In this paper, correlated gamma-frailty models are applied to survival data on Swedish twins to estimate genetic parameters in six models of susceptibility. It is shown that the frailty model with additive genetic and nonshared environmental components fits the data best. The estimate of narrow-sense heritability in gamma frailty is about 50%. The results of genetic analysis confirm our earlier findings from the studies of Danish twins that about 50% of individual susceptibility approximated by gamma-distributed frailty is heritable.

What difference does the dependence between durations make? Insights for population studies of aging.

The interpretation of age-specific changes in hazards, relative risks, genetic parameters and other indicators of aging calculated from data on related individuals should take into account the regularities of bivariate selection. Due to such selection the hazard rate calculated for twins who have survived to a certain age may be lower than for singletons, even if marginal chances of survival for all individuals are the same. In a mixed population of relatives the proportion of pairs with closer family links increases with age, even if all marginal individual chances of survival are the same. The proportion of chronic conditions for MZ twins observed in a cross-sectional study may be different from that of DZ twins. The age-dependence of relative risks calculated in genetic-epidemiological studies of twins does not necessarily reflect changes in genetic influence on individual susceptibility to disease and death during the aging process. The age-related changes in heritability of susceptibility estimated in twin studies may have nothing to do with changes in the genetic determination of diseases with age. These issues are illustrated by empirical graphs together with the results of modeling and statistical analysis.

The genetic component of discrete disability traits: an analysis using liability models with age-dependent thresholds.

The presence of familial and genetic effects in the Activities-of-Daily-Life (ADL) data collected in the first wave of the 1995 Longitudinal Study of Aging of Danish Twins (LSADT) older than 75 is tested using multithreshold liability models of disability with age-dependent thresholds. These models are developed for discrete scores represented by five disability scales of male and female Danish twins. The presence of familial effects is revealed in all five scales of disability data for females and in three scales of data for males. Genetic effects are found to be significant in all four levels of aggregation of the Upper Limb-T (T = tiredness) disability scale for females and in the PADL-H (H = need for help) scale for males. Genetic effects are also pronounced in the Mobility-T scale for females and in the Lower Limb-T scale for males and females. For females, the genetic effects in the T-scale seem to be more pronounced than in the H-scale. For males, genetic effects are more pronounced in the H-scale. The estimates for MZ correlations in liability tend to be higher than the estimates for DZ correlations in almost all cases, which suggests that additional genetic effects may be revealed should the sample size of the ADL data be increased.

Biodemographic trajectories of longevity.

Old-age survival has increased substantially since 1950. Death rates decelerate with age for insects, worms, and yeast, as well as humans. This evidence of extended postreproductive survival is puzzling. Three biodemographic insights--concerning the correlation of death rates across age, individual differences in survival chances, and induced alterations in age patterns of fertility and mortality--offer clues and suggest research on the failure of complicated systems, on new demographic equations for evolutionary theory, and on fertility-longevity interactions. Nongenetic changes account for increases in human life-spans to date. Explication of these causes and the genetic license for extended survival, as well as discovery of genes and other survival attributes affecting longevity, will lead to even longer lives.

How heritable is individual susceptibility to death? The results of an analysis of survival data on Danish, Swedish and Finnish twins.

Molecular epidemiological studies confirm a substantial contribution of individual genes to variability in susceptibility to disease and death for humans. To evaluate the contribution of all genes to susceptibility and to estimate individual survival characteristics, survival data on related individuals (eg twins or other relatives) are needed. Correlated gamma-frailty models of bivariate survival are used in a joint analysis of survival data on more than 31,000 pairs of Danish, Swedish and Finnish male and female twins using the maximum likelihood method. Additive decomposition of frailty into genetic and environmental components is used to estimate heritability in frailty. The estimate of the standard deviation of frailty from the pooled data is about 1.5. The hypothesis that variance in frailty and correlations of frailty for twins are similar in the data from all three countries is accepted. The estimate of narrow-sense heritability in frailty is about 0.5. The age trajectories of individual hazards are evaluated for all three populations of twins and both sexes. The results of our analysis confirm the presence of genetic influences on individual frailty and longevity. They also suggest that the mechanism of these genetic influences may be similar for the three Scandinavian countries. Furthermore, results indicate that the increase in individual hazard with age is more rapid than predicted by traditional demographic life tables.

How frailty models can be used for evaluating longevity limits: taking advantage of an interdisciplinary approach.

In this paper we discuss an approach to the analysis of mortality and longevity limits when survival data on related individuals with and without observed covariates are available. The approach combines the ideas of demography and survival analysis with methods of quantitative genetics and genetic epidemiology. It allows us to analyze the genetic structure of frailty in the Cox-type hazard model with random effects. We demonstrate the implementation of this strategy to survival data on Danish twins. We then evaluate the resulting lower bounds for biological limits of human longevity. Finally, we discuss the limitations of this approach and directions of further research.

Untangling genetic influences on smoking, body mass index and longevity: a multivariate study of 2464 Danish twins followed for 28 years.

A multivariate twin study was conducted in order to evaluate to what extent smoking, BMI and longevity are influenced by common genetic factors. The study was based on a 28-year follow-up of a sample of 2464 Danish twins who were born in the period 1890-1920 and who answered a questionnaire, including requests for information on smoking status, height and weight, in 1966. By 1994, approximately 2/3 of the sample had died. To compensate for the right-censoring, age at death was imputed for twins who were still alive by using survival analysis; all living subjects were more than 73 years old (mean 80 years, SD 5) in 1994. Proportions of covariance resulting from genetic and environmental factors in common and unique to the three traits were estimated from covariance matrices using the structural equation model approach. The study found no evidence for a substantial impact of common genetic factors on smoking, BMI and longevity. This suggests that only a small fraction of the genetic influences on longevity is mediated via a genetic influence on smoking and BMI and, furthermore, that it is unlikely that the associations between smoking and mortality and between BMI and mortality are confounded by common genetic factors.

Survival of related individuals: an extension of some fundamental results of heterogeneity analysis.

"Many ideas in the analysis of heterogeneous mortality are based on the relationship between individual and observed hazard rates. This connection is established with the help of conditional averaging procedure: The observed risk of death at age x is calculated among those who survive this age. The analogy of this result for bivariate survival model with correlated individual hazards is derived. In the case of correlated frailty model the parametric specification of the mean, variance and correlation coefficient of the bivariate frailty distribution among survivors is obtained. The relationship between local association measure and the characteristics of the bivariate frailty distribution among survivors is established." (SUMMARY IN FRE)

Genetic analysis of durations: correlated frailty model applied to survival of Danish twins.

Population studies of changes in human morbidity and mortality require models which take into account the influence of genetic and environmental factors on life-related durations, such as age at onset of the disease or disability, age at death, etc. In this paper we show how a bivariate survival model based on the concept of correlated individual frailty can be used for the genetic analysis of durations. Six genetic models of frailty are considered and applied to Danish twin survival data. The results of statistical analysis allow us to conclude that at least 50% of variability in individual frailty is determined by environmental factors. The approach suggests a method of estimation of the lower bound for the biological limit of human longevity. Directions for further research are discussed.

Correlated individual frailty: an advantageous approach to survival analysis of bivariate data.

"We develop a new model of bivariate survival based on the notion of correlated individual frailty. We analyze the properties of this model and suggest a new approach to the analysis of bivariate data that does not require a parametric specification--but permits estimation--of the form of the hazard function for individuals. We empirically demonstrate the advantages of the model in the statistical analysis of bivariate data." (SUMMARY IN FRE)

A duality in aging: the equivalence of mortality models based on radically different concepts.

Several alternative mortality models fit Swedish old-age mortality data equally well. The models build on two different concepts of the heterogeneity of individuals in a population. The first concept concerns fixed, genetic differences among individuals in their risk of death. The second concept involves acquired susceptibility to death due to physiological changes and environmental influences. We show that alternative mortality models based on either of these two concepts or some mix of them lead to the same parametric form of observed age-specific death rates. We discuss this duality property of mortality processes and show that even when a mortality model fits the data, the concepts used to construct the model may not be correct.