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

Rapid dynamics of electrophysiological connectome states are heritable

Time-varying changes in whole-brain connectivity patterns, or connectome state dynamics, are a prominent feature of brain activity with broad functional implications. While infra-slow (<0.1Hz) connectome dynamics have been extensively studied with fMRI, rapid dynamics highly relevant for cognition are poorly understood. Here, we asked whether rapid electrophysiological connectome dynamics constitute subject-specific brain traits and to what extent they are under genetic influence. Using source-localized EEG connectomes during resting-state (N=928, 473 females), we quantified heritability of multivariate (multi-state) features describing temporal or spatial characteristics of connectome dynamics. States switched rapidly every ~60-500ms. Temporal features were heritable, particularly, Fractional Occupancy (in theta, alpha, beta, and gamma bands) and Transition Probability (in theta, alpha, and gamma bands), representing the duration spent in each state and the frequency of state switches, respectively. Genetic effects explained a substantial proportion of phenotypic variance of these features: Fractional Occupancy in beta (44.3%) and gamma (39.8%) bands and Transition Probability in theta (38.4%), alpha (63.3%), beta (22.6%), and gamma (40%) bands. However, we found no evidence for heritability of spatial features, specifically states' Modularity and connectivity pattern. We conclude that genetic effects strongly shape individuals' connectome dynamics at rapid timescales, specifically states' overall occurrence and sequencing.

To Be Frail or Not to Be Frail: This Is the Question-A Critical Narrative Review of Frailty

Many factors have contributed to rendering frailty an emerging, relevant, and very popular concept. First, many pandemics that have affected humanity in history, including COVID-19, most recently, have had more severe effects on frail people compared to non-frail ones. Second, the increase in human life expectancy observed in many developed countries, including Italy has led to a rise in the percentage of the older population that is more likely to be frail, which is why frailty is much a more common concern among geriatricians compared to other the various health-care professionals. Third, the stratification of people according to the occurrence and the degree of frailty allows healthcare decision makers to adequately plan for the allocation of available human professional and economic resources. Since frailty is considered to be fully preventable, there are relevant consequences in terms of potential benefits both in terms of the clinical outcome and healthcare costs. Frailty is becoming a popular, pervasive, and almost omnipresent concept in many different contexts, including clinical medicine, physical health, lifestyle behavior, mental health, health policy, and socio-economic planning sciences. The emergence of the new "science of frailty" has been recently acknowledged. However, there is still debate on the exact definition of frailty, the pathogenic mechanisms involved, the most appropriate method to assess frailty, and consequently, who should be considered frail. This narrative review aims to analyze frailty from many different aspects and points of view, with a special focus on the proposed pathogenic mechanisms, the various factors that have been considered in the assessment of frailty, and the emerging role of biomarkers in the early recognition of frailty, particularly on the role of mitochondria. According to the extensive literature on this topic, it is clear that frailty is a very complex syndrome, involving many different domains and affecting multiple physiological systems. Therefore, its management should be directed towards a comprehensive and multifaceted holistic approach and a personalized intervention strategy to slow down its progression or even to completely reverse the course of this condition.

Efficient and accurate frailty model approach for genome-wide survival association analysis in large-scale biobanks

With decades of electronic health records linked to genetic data, large biobanks provide unprecedented opportunities for systematically understanding the genetics of the natural history of complex diseases. Genome-wide survival association analysis can identify genetic variants associated with ages of onset, disease progression and lifespan. We propose an efficient and accurate frailty model approach for genome-wide survival association analysis of censored time-to-event (TTE) phenotypes by accounting for both population structure and relatedness. Our method utilizes state-of-the-art optimization strategies to reduce the computational cost. The saddlepoint approximation is used to allow for analysis of heavily censored phenotypes (>90%) and low frequency variants (down to minor allele count 20). We demonstrate the performance of our method through extensive simulation studies and analysis of five TTE phenotypes, including lifespan, with heavy censoring rates (90.9% to 99.8%) on ~400,000 UK Biobank participants with white British ancestry and ~180,000 individuals in FinnGen. We further analyzed 871 TTE phenotypes in the UK Biobank and presented the genome-wide scale phenome-wide association results with the PheWeb browser.

Dynamic trajectories of connectome state transitions are heritable

The brain’s functional connectome is dynamic, constantly reconfiguring in an individual-specific manner. However, which characteristics of such reconfigurations are subject to genetic effects, and to what extent, is largely unknown. Here, we identified heritable dynamic features, quantified their heritability, and determined their association with cognitive phenotypes. In resting-state fMRI, we obtained multivariate features, each describing a temporal or spatial characteristic of connectome dynamics jointly over a set of connectome states. We found strong evidence for heritability of temporal features, particularly, Fractional Occupancy (FO) and Transition Probability (TP), representing the duration spent in each connectivity configuration and the frequency of shifting between configurations, respectively. These effects were robust against methodological choices of number of states and global signal regression. Genetic effects explained a substantial proportion of phenotypic variance of these features (h² = 0.39, 95% CI = [.24,.54] for FO; h² = 0. 43, 95% CI = [.29,.57] for TP). Moreover, these temporal phenotypes were associated with cognitive performance. Contrarily, we found no robust evidence for heritability of spatial features of the dynamic states (i.e., states’ Modularity and connectivity pattern). Genetic effects may therefore primarily contribute to how the connectome transitions across states, rather than the precise spatial instantiation of the states in individuals. In sum, genetic effects impact the dynamic trajectory of state transitions (captured by FO and TP), and such temporal features may act as endophenotypes for cognitive abilities.

A competing risks model with binary time varying covariates for estimation of breast cancer risks in BRCA1 families

Mammographic screening and prophylactic surgery such as risk-reducing salpingo oophorectomy can potentially reduce breast cancer risks among mutation carriers of BRCA families. The evaluation of these interventions is usually complicated by the fact that their effects on breast cancer may change over time and by the presence of competing risks. We introduce a correlated competing risks model to model breast and ovarian cancer risks within BRCA1 families that accounts for time-varying covariates. Different parametric forms for the effects of time-varying covariates are proposed for more flexibility and a correlated gamma frailty model is specified to account for the correlated competing events.We also introduce a new ascertainment correction approach that accounts for the selection of families through probands affected with either breast or ovarian cancer, or unaffected. Our simulation studies demonstrate the good performances of our proposed approach in terms of bias and precision of the estimators of model parameters and cause-specific penetrances over different levels of familial correlations. We applied our new approach to 498 BRCA1 mutation carrier families recruited through the Breast Cancer Family Registry. Our results demonstrate the importance of the functional form of the time-varying covariate effect when assessing the role of risk-reducing salpingo oophorectomy on breast cancer. In particular, under the best fitting time-varying covariate model, the overall effect of risk-reducing salpingo oophorectomy on breast cancer risk was statistically significant in women with BRCA1 mutation.

17th IHIW component "Immunogenetics of Ageing" - New NGS data

The 'Immunogenetics of Aging' project is a component introduced in the 14th International HLA and Immunogenetics Workshop (IHIW) and developed further within subsequent workshops. The aim was to determine the relevance of immunogenetic markers, focusing on HLA, cytokine genes, and some innate immunity genes, for successful aging and an increased capacity to reach the extreme limits of life-span. Within the 17th IHIW we applied Next Generation Sequencing methods to refine further HLA associations at allele level in longevity, and to extend our knowledge to additional loci such as HLA-DQA1, HLA-DPB1 and HLA-DPA1. Analysis of relatively small number of healthy elderly and young controls from four populations showed that some HLA class I and class II alleles were significantly positively associated with healthy aging. Additionally we observed statistically significant differences in HLA allele distribution when the analysis was performed separately in elderly females and males compared to sex-matched young controls. Haplotypes, probably associated with better control of viral and malignant diseases were increased in the elderly sample. These preliminary NGS data could confirm our hypotheses that survival and longevity might be associated with selection of HLA alleles and haplotypes conferring disease resistance or susceptibility. Therefore HLA alleles and haplotypes could be informative immunogenetic markers for successful ageing.

A latent class model for competing risks

Survival data analysis becomes complex when the proportional hazards assumption is violated at population level or when crude hazard rates are no longer estimators of marginal ones. We develop a Bayesian survival analysis method to deal with these situations, on the basis of assuming that the complexities are induced by latent cohort or disease heterogeneity that is not captured by covariates and that proportional hazards hold at the level of individuals. This leads to a description from which risk-specific marginal hazard rates and survival functions are fully accessible, 'decontaminated' of the effects of informative censoring, and which includes Cox, random effects and latent class models as special cases. Simulated data confirm that our approach can map a cohort's substructure and remove heterogeneity-induced informative censoring effects. Application to data from the Uppsala Longitudinal Study of Adult Men cohort leads to plausible alternative explanations for previous counter-intuitive inferences on prostate cancer. The importance of managing cardiovascular disease as a comorbidity in women diagnosed with breast cancer is suggested on application to data from the Swedish Apolipoprotein Mortality Risk Study. Copyright © 2017 John Wiley & Sons, Ltd.

Power and sample size calculation for paired recurrent events data based on robust nonparametric tests

The purpose of this paper is to develop a formula for calculating the required sample size for paired recurrent events data. The developed formula is based on robust non-parametric tests for comparing the marginal mean function of events between paired samples. This calculation can accommodate the associations among a sequence of paired recurrent event times with a specification of correlated gamma frailty variables for a proportional intensity model. We evaluate the performance of the proposed method with comprehensive simulations including the impacts of paired correlations, homogeneous or nonhomogeneous processes, marginal hazard rates, censoring rate, accrual and follow-up times, as well as the sensitivity analysis for the assumption of the frailty distribution. The use of the formula is also demonstrated using a premature infant study from the neonatal intensive care unit of a tertiary center in southern Taiwan. Copyright © 2017 John Wiley & Sons, Ltd.

Correlated gamma-based hidden Markov model for the smart asthma management based on rescue inhaler usage

Asthma is a very common chronic disease that affects a large portion of population in many nations. Driven by the fast development in sensor and mobile communication technology, a smart asthma management system has become available to continuously monitor the key health indicators of asthma patients. Such data provides opportunities for healthcare practitioners to examine patients not only in the clinic (on-site) but also outside of the clinic (off-site) in their daily life. In this paper, taking advantage from this data availability, we propose a correlated gamma-based hidden Markov model framework, which can reveal and highlight useful information from the rescue inhaler-usage profiles of individual patients for practitioners. The proposed method can provide diagnostic information about the asthma control status of individual patients and can help practitioners to make more informed therapeutic decisions accordingly. The proposed method is validated through both numerical study and case study based on real world data. Copyright © 2017 John Wiley & Sons, Ltd.

Genetic analysis of cause of death in a mixture model of bivariate lifetime data

A mixture model in multivariate survival analysis is presented, whereby heterogeneity among subjects creates divergent paths for the individual’s risk of experiencing an event (i.e., disease), as well as for the associated length of survival. Dependence among competing risks is included and rendered testable. This method is an extension of the bivariate correlated gamma-frailty model. It is applied to a data set on Danish twins, for whom cause-specific mortality is known. The use of multivariate data solves the identifiability problem which is inherent in the competing risk model of univariate lifetimes. We analyse the influence of genetic and environmental factors on frailty. Using a sample of 1470 monozygotic (MZ) and 2730 dizygotic (DZ) female twin pairs, we apply five genetic models to the associated mortality data, focusing particularly on death from coronary heart disease (CHD). Using the best fitting model, the inheritance risk of death from CHD was 0.39 (standard error 0.13). The results from this model are compared with the results from earlier analysis that used the restricted model, where the independence of competing risks was assumed. Comparing both cases, it turns out, that heritability of frailty on mortality due to CHD change substantially. Despite the inclusion of dependence, analysis confirms the significant genetic component to an individual’s risk of mortality from CHD. Whether dependence or independence is assumed, the best model for analysis with regard to CHD mortality risks is a model assuming that additive factors are responsible for heritability in susceptibility to CHD. The paper ends with a discussion of limitations and possible further extensions to the model presented.

Survival Models on Unobserved Heterogeneity and their Applications in Analyzing Large-scale Survey Data

In survival analysis, researchers often encounter multivariate survival time data, in which failure times are correlated even in the presence of model covariates. It is argued that because observations are clustered by unobserved heterogeneity, the application of standard survival models can result in biased parameter estimates and erroneous model-based predictions. In this article, the author describes and compares four methods handling unobserved heterogeneity in survival analysis: the Andersen-Gill approach, the robust sandwich variance estimator, the hazard model with individual frailty, and the retransformation method. An empirical analysis provides strong evidence that in the presence of strong unobserved heterogeneity, the application of a standard survival model can yield equally robust parameter estimates and the likelihood ratio statistic as does a corresponding model adding an additional parameter for random effects. When predicting the survival function, however, a standard model on multivariate survival time data can result in serious prediction bias. The retransformation method is effective to derive an adjustment factor for correctly predicting the survival function.

Joint analysis of bivariate competing risks survival times and genetic markers data

Bivariate survival models with discretely distributed frailty based on the major gene concept and applied to the data on related individuals such as twins and sibs can be used to estimate the underlying hazard, the relative risk and the frequency of the longevity allele. To determine the position of the longevity gene, additional genetic markers data are needed. If the action of the longevity allele does not depend on its position in the genome, these two problems can be solved separately using a two-step procedure. We proposed an extension of this method allowing us to search the position of two longevity genes at a chromosome using the bivariate survival data with correlated competing risks combined with genetic markers data. We have studied the properties of the model with two longevity genes located on the same and on different chromosomes using simulated data sets.

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 infiuences on individual frailty and longevity. They also suggest that the mechanism of these genetic infiuences 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.

Latent Curve Analyses of Longitudinal Twin Data Using a Mixed-Effects Biometric Approach

In a recent article McArdle and Prescott (2005) showed how simultaneous estimation of the bio-metric parameters can be easily programmed using current mixed-effects modeling programs (e.g., SAS PROC MIXED). This article extends these concepts to deal with mixed-effect modeling of longitudinal twin data. The biometric basis of a polynomial growth curve model was used by Vandenberg and Falkner (1965) and this general class of longitudinal models was represented in structural equation form as a latent curve model by McArdle (1986). The new mixed-effects modeling approach presented here makes it easy to analyze longitudinal growth-decline models with biometric components based on standard maximum likelihood estimation and standard indices of goodness-of-fit (i.e., χ2, df, εa). The validity of this approach is first checked by the creation of simulated longitudinal twin data followed by numerical analysis using different computer programs (i.e., Mplus, Mx, MIXED, NLMIXED). The practical utility of this approach is examined through the application of these techniques to real longitudinal data from the Swedish Adoption/Twin Study of Aging (Pedersen et al., 2002). This approach generally allows researchers to explore the genetic and nongenetic basis of the latent status and latent changes in longitudinal scores in the absence of measurement error. These results show the mixed-effects approach easily accounts for complex patterns of incomplete longitudinal or twin pair data. The results also show this approach easily allows a variety of complex latent basis curves, such as the use of age-at-testing instead of wave-of-testing. Natural extensions of this mixed-effects longitudinal approach include more intensive studies of the available data, the analysis of categorical longitudinal data, and mixtures of latent growth-survival/ frailty models.

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.

Risk prediction of complex diseases from family history and known susceptibility loci, with applications for cancer screening

Risk prediction based on genomic profiles has raised a lot of attention recently. However, family history is usually ignored in genetic risk prediction. In this study we proposed a statistical framework for risk prediction given an individual's genotype profile and family history. Genotype information about the relatives can also be incorporated. We allow risk prediction given the current age and follow-up period and consider competing risks of mortality. The framework allows easy extension to any family size and structure. In addition, the predicted risk at any percentile and the risk distribution graphs can be computed analytically. We applied the method to risk prediction for breast and prostate cancers by using known susceptibility loci from genome-wide association studies. For breast cancer, in the population the 10-year risk at age 50 ranged from 1.1% at the 5th percentile to 4.7% at the 95th percentile. If we consider the average 10-year risk at age 50 (2.39%) as the threshold for screening, the screening age ranged from 62 at the 20th percentile to 38 at the 95th percentile (and some never reach the threshold). For women with one affected first-degree relative, the 10-year risks ranged from 2.6% (at the 5th percentile) to 8.1% (at the 95th percentile). For prostate cancer, the corresponding 10-year risks at age 60 varied from 1.8% to 14.9% in the population and from 4.2% to 23.2% in those with an affected first-degree relative. We suggest that for some diseases genetic testing that incorporates family history can stratify people into diverse risk categories and might be useful in targeted prevention and screening.

Evaluating the heritability explained by known susceptibility variants: a survey of ten complex diseases

Recently, an increasing number of susceptibility variants have been identified for complex diseases. At the same time, the concern of "missing heritability" has also emerged. There is however no unified way to assess the heritability explained by individual genetic variants for binary outcomes. A systemic and quantitative assessment of the degree of "missing heritability" for complex diseases is lacking. In this study, we measure the variance in liability explained by individual variants, which can be directly interpreted as the locus-specific heritability. The method is extended to deal with haplotypes, multi-allelic markers, multi-locus genotypes, and markers in linkage disequilibrium. Methods to estimate the standard error and confidence interval are proposed. To assess our current level of understanding of the genetic basis of complex diseases, we conducted a survey of 10 diseases, evaluating the total variance explained by the known variants. The diseases under evaluation included Alzheimer's disease, bipolar disorder, breast cancer, coronary artery disease, Crohn's disease, prostate cancer, schizophrenia, systemic lupus erythematosus (SLE), type 1 diabetes and type 2 diabetes. The median total variance explained across the 10 diseases was 9.81%, while the median variance explained per associated SNP was around 0.25%. Our results suggest that a substantial proportion of heritability remains unexplained for the diseases under study. Programs to implement the methodologies described in this paper are available at http://sites.google.com/site/honcheongso/software/varexp.

Insights from comparative analyses of aging in birds and mammals

Many laboratory models used in aging research are inappropriate for understanding senescence in mammals, including humans, because of fundamental differences in life history, maintenance in artificial environments, and selection for early aging and high reproductive rate. Comparative studies of senescence in birds and mammals reveal a broad range in rates of aging among a variety of taxa with similar physiology and patterns of development. These comparisons suggest that senescence is a shared property of all vertebrates with determinate growth, that the rate of senescence has been modified by evolution in response to the potential life span allowed by extrinsic mortality factors, and that most variation among species in the rate of senescence is independent of commonly ascribed causes of aging, such as oxidative damage. Individuals of potentially long-lived species, particularly birds, appear to maintain high condition to near the end of life. Because most individuals in natural populations of such species die of aging-related causes, these populations likely harbor little genetic variation for mechanisms that could extend life further, or these mechanisms are very costly. This, and the apparent evolutionary conservatism in the rate of increase in mortality with age, suggests that variation in the rate of senescence reflects fundamental changes in organism structure, likely associated with the rate of development, rather than physiological or biochemical processes influenced by a few genes. Understanding these evolved differences between long-lived and short-lived organisms would seem to be an essential foundation for designing therapeutic interventions with respect to human aging and longevity.

Longevity and correlated frailty in multigenerational families

Multigenerational pedigrees provide an opportunity for assessing the effects of unobserved environmental and genetic effects on longevity (i.e., frailty). This article applies Cox proportional hazards models to data from three-generation pedigrees in the Utah Population Database using two different frailty specification schemes that account for common environments (shared frailty) and genetic effects (correlated frailty). In a model that includes measures of familial history of longevity and both frailty effects, we find that the variance component due to genetic factors is comparable to the one attributable to shared environments: Standard deviations of the correlated and the shared frailty distributions are 0.143 and 0.186, respectively. Through simulations, we also show a greater reduction in the bias of parameter estimates for fixed covariates through the use of the correlated frailty model.

A correlated frailty model with long-term survivors for estimating the heritability of breast cancer

The aim of this study is to investigate the role of genetics and environment in susceptibility to breast cancer (frailty). An interdisciplinary approach was adopted, combining a correlated frailty-mixture model with genetic equations, allowing for decomposition of the frailty variance into genetic and environmental components. In addition, the possibility that a fraction of the population under study is 'immune' to the disease is evaluated, and changes in heritability estimates introducing a fraction of non-susceptible individuals are determined. The methodology is applied to breast cancer data from the Swedish Twin Registry, including information about all female monozygotic and dizygotic twin pairs born in Sweden between 1886 and 1967. The inferential problem is solved in a Bayesian framework and the numerical work is carried out using Markov chain Monte Carlo (MCMC) methods.

A flexible model for multivariate interval-censored survival times with complex correlation structure

We focus on the analysis of multivariate survival times with highly structured interdependency and subject to interval censoring. Such data are common in developmental genetics and genetic epidemiology. We propose a flexible mixed probit model that deals naturally with complex but uninformative censoring. The recorded ages of onset are treated as possibly censored ordinal outcomes with the interval censoring mechanism seen as arising from a coarsened measurement of a continuous variable observed as falling between subject-specific thresholds. This bypasses the requirement for the failure times to be observed as falling into non-overlapping intervals. The assumption of a normal age-of-onset distribution of the standard probit model is relaxed by embedding within it a multivariate Box-Cox transformation whose parameters are jointly estimated with the other parameters of the model. Complex decompositions of the underlying multivariate normal covariance matrix of the transformed ages of onset become possible. The new methodology is here applied to a multivariate study of the ages of first use of tobacco and first consumption of alcohol without parental permission in twins. The proposed model allows estimation of the genetic and environmental effects that are shared by both of these risk behaviours as well as those that are specific.

Longitudinal models of growth and survival applied to the early detection of Alzheimer's disease

This article explores new statistical methodologies for using longitudinal data in the early prediction of Alzheimer's disease (AD). Specifically, the authors examine some new techniques that allow the joint or "shared" estimation of longitudinal components based on both duration (survival) and quantitative changes (growth curves). These new shared growth-survival parameter models may be used to characterize the declining functions that anticipate the onset of AD. The authors apply these models to data from the Kungsholmen Project, a longitudinal study of aging in Stockholm, Sweden. They examine age-based survival-frailty models for the onset of AD, latent growth-decline curve models for changes in cognition over age, and 3 alternative forms of models for the shared relationships of survival and early cognitive decline. The accuracy and reliability of this approach is considered for a better understanding of the developmental course of AD in these data, including the potential removal of biases due to subject selection.

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.

Disentangling the genetic determinants of human aging: biological age as an alternative to the use of survival measures

The choice of a phenotype is critical for the study of a complex genetically regulated process, such as aging. To date, most of the twin and family studies have focused on broad survival measures, primarily age at death or exceptional longevity. However, on the basis of recent studies of twins and families, biological age has also been shown to have a strong genetic component, with heritability estimates ranging from 27% to 57%. The aim of this review is twofold: first, to summarize growing consensus on reliable methods of biological age assessment, and second, to demonstrate validity of this phenotype for research in the genetics of aging in humans.

Genetic influences on CHD-death and the impact of known risk factors: comparison of two frailty models

The importance of some recognized risk factors on genetic influences for coronary heart disease (CHD) needs further clarification. The aim of the present study was therefore to study the impact of known risk factors on genetic influences for CHD-death. Both twin (correlated gamma-frailty) and non-twin models (univariate gamma-frailty) were utilized and compared regarding their suitability for genetic analyses. The study population consisted of twins born in Sweden between 1886 and 1925. As expected, our findings indicate that genetic influences are important for CHD-death. Inclusion of risk factors in the twin-model increased heritability estimates, primarily due to a substantial reduction in non-shared environmental variances. The genetic influences for CHD-death are only marginally mediated through the risk factors among males, but more so among females. Although the outcome phenotype used in the present study is not behavioral, the analyses demonstrate the potential of frailty models for quantitative genetic analyses of categorical phenotypes.

Genetic influences on life span and survival among elderly African-Americans, Caribbean Hispanics, and Caucasians

An investigation of the genetic influences on life span and survival was conducted among elderly African-Americans, Caribbean Hispanics, and Caucasians Medicare recipients (ages 65-104 years). Family history information on 13,161 parents and siblings was obtained. Heritability of life span varied by the age and by ethnic group being lowest for African-Americans. We recalculated the heritability coefficients for life span including only probands and their siblings, but the differences across ethnic groups persisted. In contrast the heritability of survival was more similar across ethnic groups but was similar to that for life span. Heritability coefficients for survival in probands and their siblings revealed little difference between ethnic groups and suggested that as much as 35% of the variation in survival may be genetically influenced. These results indicate that life span and survival are genetically influenced. Comparisons across generations and ethnic groups indicate that changes in environmental hygiene, social welfare, and health care systems are significant contributors to life span and survival, but genetic influences are also important. Identifying the genes associated with life span and survival will provide insight into how the genes interact with environment to influence aging in humans.

A Bivariate Frailty Model with a Cure Fraction for Modeling Familial Correlations in Diseases

We suggest a cure-mixture model to analyze bivariate time-to-event data, as motivated by the article of Chatterjee and Shih (2001, Biometrics 57, 779-786), but with a simpler estimation procedure and the correlated gamma-frailty model instead of the shared gamma-frailty model. This approach allows us to deal with left-truncated and right-censored lifetime data, and accounts for heterogeneity, as well as for an insusceptible (cure) fraction in the study population. We perform a simulation study to evaluate the properties of the estimates in the proposed model and apply it to breast cancer incidence data for 5857 Swedish female monozygotic and dizygotic twin pairs from the so-called old cohort of the Swedish Twin Registry. This model is used to estimate the size of the susceptible fraction and the correlation between the frailties of the twin partners. Possible extensions, advantages, and limitations of the proposed method are discussed.

Three-state frailty model for age at onset of dementia and death in Swedish twins

We present a frailty model to estimate the relative importance of genetic and environmental factors on age at onset of dementia in a twin design. We use modern survival methodology to define a model that accounts simultaneously for longitudinal aspects, e.g., left truncation and right censoring in data, and the multivariate nature of twin data. Additionally, we present a novel three-state frailty model, with nondemented, demented, and dead states, describing variation in the onset of disease and mortality simultaneously in one model, while accounting for possible dependence for the two competing events. The frailty structure, i.e., the latent random effects structure, mimics the traditional twin model for continuous variables used in quantitative genetics, and as such describes within-pair dependence. This in turn leads to estimates for intrapair correlations, as well as for additive genetic, and shared and nonshared environmental components of variance. A hierarchical Bayesian model formulation and Gibbs sampling are used to estimate posterior distributions of the parameters. The models are applied to Swedish Twin Registry data on the onset of dementia in elderly twins. Based on the three-state frailty model, we estimate the intrapair correlations for dementia to be 0.87 [90% credible interval: 0.61,0.98] and 0.68[0.18,0.91] for MZ and DZ twins, respectively. Based on our model, we estimate that genetic effects account for about one third, and shared environmental effects for almost a half, of the variation in dementia hazards between individuals. More data, however, are needed to gain precision in these estimates.

The heritability of cause-specific mortality: a correlated gamma-frailty model applied to mortality due to respiratory diseases in Danish twins born 1870-1930

The genetic influence on susceptibility to diseases of the respiratory system and all-cause mortality was studied using data for identical (MZ) and fraternal (DZ) twins. Data from the Danish Twin Register include 1344 MZ and 2411 DZ male twin pairs and 1470 MZ and 2730 DZ female twin pairs born between 1870 and 1930, where both individuals were alive on 1 011943. We used the correlated gamma-frailty model. Proportions of variance in frailty attributable to genetic and environmental factors were assessed using the structural equation model approach. For all-cause mortality the correlation coefficients of frailty for MZ twins tend to be higher than for DZ twins. For mortality with respect to respiratory diseases this effect was only seen in females, whereas males showed the opposite effect. Five 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 biometric model heritability for cause of death was found to be 0.58 (0.07) for all-cause mortality (AE-model) and zero for diseases of the respiratory system for males. Heritability was 0.63 (0.11) for all-cause mortality (DE-model) and 0.18 (0.09) for diseases of the respiratory system (DE-model) for females. The analysis confirms the presence of a strong genetic influence on individual frailty associated with all-cause mortality. For respiratory diseases, no genetic influence was found in males and only weak genetic influence in females. The nature of genetic influences on frailty with respect to all-cause mortality is probably additive in males and dominant in females, whereas for frailty with respect to deaths caused by respiratory diseases in females, there are genetic factors present which are caused by dominance. Environmental influences are non-shared with exception of frailty with respect to respiratory diseases in males, where the shared environment plays an important role.

A multistate model for the genetic analysis of the ageing process

In this paper a multivariate frailty model is suggested that can be used in the genetic analysis of the ageing process as a whole, simplified to consisting of the states 'healthy', 'disabled' and 'deceased'. The model allows us to evaluate simultaneously the relative magnitude of genetic and environmental influences on frailty variables corresponding to the period of good health and to the life span. The frailty variables can be interpreted as susceptibility to illness or death. The model can be applied to data on groups of related individuals (twins, siblings, a litter). One of the major advantages of this model is that it allows one to include groups of individuals where some or all members of the group are already deceased at the time of observation. The current health status of the living individuals and the exact life span of individuals who are already deceased is the only information necessary for the application of the model. Questions concerning the identifiability of the model based on current health status data and estimation strategies are discussed in the context of specifying the model for twins. Finally, the results of a sample analysis of twin data on prostate cancer are presented.

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.

A centenarian-only approach for assessing gene-gene interaction in human longevity

In this study, we introduce a centenarian-only approach to the assessment of gene-gene interaction that contributes to human longevity. This approach corresponds to the non-traditional case-only method in the genetic study of gene and disease associations. We first describe how the method can be implemented to screen for gene-gene interaction in human longevity. Then we apply the method to centenarian data collected from an Italian centenarian study in order to detect the interactions between the REN gene and the mitochondrial haplotypes. A significant interaction between REN gene allele 10 and the mitochondrial H haplotype, which may favour longevity, was found. Important features of the application in human longevity studies are highlighted and discussed. Since centenarians constitute a special population representing successful ageing, the centenarian-only approach will be an important tool in the search for major genes that contribute to human longevity.

Biological implications of the Weibull and Gompertz models of aging

Gompertz and Weibull functions imply contrasting biological causes of demographic aging. The terms describing increasing mortality with age are multiplicative and additive, respectively, which could result from an increase in the vulnerability of individuals to extrinsic causes in the Gompertz model and the predominance of intrinsic causes at older ages in the Weibull model. Experiments that manipulate extrinsic mortality can distinguish these biological models. To facilitate analyses of experimental data, we defined a single index for the rate of aging (omega) for the Weibull and Gompertz functions. Each function described the increase in aging-related mortality in simulated ages at death reasonably well. However, in contrast to the Weibull omega(W), the Gompertz omega(G) was sensitive to variation in the initial mortality rate independently of aging-related mortality. Comparisons between wild and captive populations appear to support the intrinsic-causes model for birds, but give mixed support for both models in mammals.

Genetic survival analysis of age-at-onset of bipolar disorder: evidence for anticipation or cohort effect in families

Age-at-onset (AAO) in a number of extended families ascertained for bipolar disorder was analysed using survival analysis techniques, fitting proportional hazards models to estimate the fixed effects of sex, year of birth, and generation, and a random polygenic genetic effect. Data comprised the AAO (for 171 affecteds) or age when last seen (ALS) for 327 unaffecteds, on 498 individuals in 27 families. ALS was treated as the censored time in the statistical analyses. The majority of individuals classified as affected were diagnosed with bipolar I and II (n = 103) or recurrent major depressive disorder (n = 68). In addition to the significant effects of sex and year of birth, a fitted 'generation' effect was highly significant, which could be interpreted as evidence for an anticipation effect. The risk of developing bipolar or unipolar disorder increased twofold with each generation descended from the oldest founder. However, although information from both affected and unaffected individuals was used to estimate the relative risk of subsequent generations, it is possible that the results are biased because of the 'Penrose effect'. Females had a twofold increased risk in developing depressive disorder relative to males. The risk of developing bipolar or unipolar disorder increased by approximately 4% per year of birth. A polygenic component of variance was estimated, resulting in a 'heritability' of AAO of approximately 0.52. In a family showing strong evidence of linkage to chromosome 4p (family 22), the 'affected haplotype' increased the relative risk of being affected by a factor of 46. In this family, there was strong evidence of a time trend in the AAO. When either year of birth or generation was fitted in the model, these effects were highly significant, but neither was significant in the presence of the other. For this family, there was no increase in trinucleotide repeats measured by the repeat expansion detection method in affected individuals compared with control subjects. Proportional hazard models appear appropriate to analyse AAO data, and the methodology will be extended to map quantitative trait loci (QTL) for AAO.

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.

Modeling hazard functions in families

A genetic frailty model is presented for censored age of onset data in nuclear families where individuals carrying a genetic susceptibility gene have an increased risk of becoming affected. We use maximum likelihood via the EM algorithm to estimate the genetic relative risk and the allele frequency under a dominant susceptibility type and a proportional hazards model. When sampling is from a disease registry, likelihood corrections are necessary for reducing bias in the parameter estimates. In these biased samples, the full conditional likelihood is approximated by a likelihood conditional on the proband's age of onset. For unbiased samples, simulations show the distributions of the estimates are similar under both a semiparametric and the correctly specified parametric likelihoods. For biased samples, simulations under the approximate conditional likelihood show the median estimates of the allele frequency and genetic relative risk tend to under- and overestimate, respectively, the true values; however, the approximation is better for rarer allele frequencies (0.0033 vs. 0.01). In practice, large samples or more complex ascertainment corrections are recommended. Using the approximate conditional likelihood on familial breast cancer onset data collected as part of a case-control study at the Fred Hutchinson Cancer Research Center in Seattle, Washington, we estimate an allele frequency of 0.0009 (approximate 95% CI 0.0006-0.002) and a genetic relative risk of 104 (approximate 95% CI 55-181).

Genetic analysis of the age at menopause by using estimating equations and Bayesian random effects models

Multi-wave self-report data on age at menopause in 2182 female twin pairs (1355 monozygotic and 827 dizygotic pairs), were analysed to estimate the genetic, common and unique environmental contribution to variation in age at menopause. Two complementary approaches for analysing correlated time-to-onset twin data are considered: the generalized estimating equations (GEE) method in which one can estimate zygosity-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modelled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the freeware package BUGS.

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.

The heritability of human longevity: a population-based study of 2872 Danish twin pairs born 1870-1900

The aim of this study was to explore, in a large and non-censored twin cohort, the nature (i.e., additive versus non-additive) and magnitude (i.e., heritability) of genetic influences on inter-individual differences in human longevity. The sample comprised all identified and traced non-emigrant like-sex twin pairs born in Denmark during the period 1870-1900 with a zygosity diagnosis and both members of the pairs surviving the age of 15 years. A total of 2872 pairs were included. Age at death was obtained from the Danish Central Person Register, the Danish Cause-of-Death Register and various other registers. The sample was almost non-censored on the date of the last follow-up (May 1, 1994), all but 0.6% had died, leaving a total of 2872 pairs for analysis. Proportions of variance attributable to genetic and environmental factors were assessed from variance-covariance matrices using the structural equation model approach. The most parsimonious explanation of the data was provided by a model that included genetic dominance (non-additive genetic effects caused by interaction within gene loci) and non-shared environmental factors (environmental factors that are individual-specific and not shared in a family). The heritability of longevity was estimated to be 0.26 for males and 0.23 for females. The small sex-difference was caused by a greater impact of non-shared environmental factors in the females. Heritability was found to be constant over the three 10-year birth cohorts included. Thus, longevity seems to be only moderately heritable. The nature of genetic influences on longevity is probably non-additive and environmental influences non-shared. There is no evidence for an impact of shared (family) environment.