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.
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.
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.
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.
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 long can people live? Opinions of the researchers diverge and debates continue. Is there any systematic way to address this question? In this paper, we suggest an approach to the estimation of the biological limit of human longevity using survival data for twins from different zygocity groups. The approach is based on the genetic model of individual frailty. It combines ideas used in demography and survival analysis with methods of quantitative genetics and genetic epidemiology. The association between the life-spans of related individuals is described by the correlated frailty model of bivariate survival. A version of this model is used in order to estimate heritability of the individual frailty and to calculate the lower bound of human longevity. The limitations of this approach and directions of further research are discussed.
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 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.