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

How the effects of aging and stresses of life are integrated in mortality rates: insights for genetic studies of human health and longevity

Increasing proportions of elderly individuals in developed countries combined with substantial increases in related medical expenditures make the improvement of the health of the elderly a high priority today. If the process of aging by individuals is a major cause of age related health declines then postponing aging could be an efficient strategy for improving the health of the elderly. Implementing this strategy requires a better understanding of genetic and non-genetic connections among aging, health, and longevity. We review progress and problems in research areas whose development may contribute to analyses of such connections. These include genetic studies of human aging and longevity, the heterogeneity of populations with respect to their susceptibility to disease and death, forces that shape age patterns of human mortality, secular trends in mortality decline, and integrative mortality modeling using longitudinal data. The dynamic involvement of genetic factors in (i) morbidity/mortality risks, (ii) responses to stresses of life, (iii) multi-morbidities of many elderly individuals, (iv) trade-offs for diseases, (v) genetic heterogeneity, and (vi) other relevant aging-related health declines, underscores the need for a comprehensive, integrated approach to analyze the genetic connections for all of the above aspects of aging-related changes. The dynamic relationships among aging, health, and longevity traits would be better understood if one linked several research fields within one conceptual framework that allowed for efficient analyses of available longitudinal data using the wealth of available knowledge about aging, health, and longevity already accumulated in the research field.

The vitality model: a way to understand population survival and demographic heterogeneity

A four-parameter model describing mortality as the first passage of an abstract measure of survival capacity, vitality, is developed and used to explore four classic problems in demography: (1) medfly demographic paradox, (2) effect of diet restriction on longevity, (3) cross-life stage effects on survival curves and (4) mortality plateaus. The model quantifies the sources of mortality in these classical problems into vitality-dependent and independent parts, and characterizes the vitality-dependent part in terms of initial and evolving heterogeneities. Three temporal scales express the balance of these factors: a time scale of death from senescence, a time scale of accidental mortality and a crossover time between evolving vs. initial heterogeneity. The examples demonstrate how the first-passage approach provides a unique and informative perspective into the processes that shape the survival curves of populations.

The Application of a Random Effects Model to Censored Twin Data

The authors propose a random effects model to analyze the latent genetic and environmental effects on determining censored outcomes in twin studies. In this model, six normally distributed random effects are used to describe the correlation within twin pairs. The authors employ a Monte Carlo Expectation-Maximization approach for obtaining maximum likelihood estimates of fixed effects and the variances of random effects. The variances of the random effects are reparameterized to be equivalent to genetic and environmental effects in traditional twin models. The authors illustrate this model using data from the Vietnam Era Twin Registry to explore the magnitude of the genetic influence on twin similarity for the age of onset of alcohol abuse. Our results show genetic factors contribute about one third of twin similarity in the age of onset of alcohol abuse in male twins. The application of this model to twin data is discussed.

The shape of things to come: using models with physiological structure to predict mortality trajectories

If mortality rate is viewed as the outcome of processes of behavior, growth and reproduction, then it should be possible to predict mortality rate as a result of those processes. We provide two examples of how this may be done. In the first, we use the method of linear chains to treat mortality that is the result of multiple physiological processes, some of which may have delays. In the second, we assume that mortality is the result of damage associated with growth and metabolism. Both approaches lead to a rich diversity of predicted mortality trajectories. Although many of these look Gompertzian at young ages, the behavior at older ages depends upon the details of the physiological models.

Assessing heterogeneity and correlation of paired failure times with the bivariate frailty model

We consider bivariate survival times for heterogeneous populations, where heterogeneity induces deviations in an individual's risk of an event as well as associations between survival times. The heterogeneity is characterized by a bivariate frailty model. We measure the heterogeneity effects through deviations associated with hazard functions and an association function defined through the conditional hazard functions: the cross-ratio function proposed by Oakes. We show how the deviation and association measures are determined by the frailty distribution. A Gibbs sampling method is developed for Bayesian inferences on regression coefficients, frailty parameters and the heterogeneity measures. The method is applied to a mental health care data set.

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.

How long can humans live? Lower bound for biological limit of human longevity calculated from Danish twin data using correlated frailty model

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.