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PubMed1999

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.

Cohort Studies↗

PubMed2026

Unraveling 'F' factor: towards a genetic-clinical framework for the musculoskeletal-heart crosstalk in metabolic aging.

BACKGROUND: The rising co-occurrence of cardiometabolic diseases and musculoskeletal degeneration poses a critical challenge to healthy aging, yet the shared biological mechanisms underlying this multimorbidity remain poorly defined. This study aimed to establish an integrative clinical-genetic framework to elucidate the common frailty factor, the 'F' factor, that captures the systemic vulnerability linking cardiometabolic multimorbidity (CMM) and musculoskeletal aging. METHODS: Utilizing the prospective China Health and Retirement Longitudinal Study (CHARLS) cohort, we developed and validated novel Frailty-Integrated Indices for CMM risk prediction, evaluated with machine learning models interpreted via SHapley Additive exPlanations (SHAP). Independently, we applied genomic structural equation modeling (Genomic-SEM) to integrate genome-wide association data from six traits-coronary artery disease, type 2 diabetes, hypertension, bone mineral density, frailty, and telomere length-to model a shared latent genetic factor ('F' factor). This was followed by multivariate GWAS, fine-mapping, transcriptome-wide association study (TWAS), gene-based analysis, and functional annotation to prioritize causal genes, pathways, and cell types. RESULTS: Clinically, several Frailty-Integrated Indices significantly improved CMM risk prediction, with the optimal model achieving an AUC of 0.727. Genetically, we modeled a significant shared latent genetic factor ('F' factor), pinpointing novel risk loci and implicating key genes such as APOE and SLC22A3. These genes were enriched in pathways including cellular senescence and cholesterol metabolism and showed specific expression patterns in developmental brain stages and across multi-organ endothelial cells. CONCLUSION: Our findings provide converging evidence for Musculoskeletal‑Heart crosstalk of metabolic aging and inferred the 'F' factor as a genetic correlate of a transdiagnostic state, which links genetic predisposition to metabolic dysregulation, and systemic functional decline. This work provides a multi-level biological characterization of multimorbidity liability, informing early-risk detection and preventive strategies for complex aging-related comorbidities.

Humans↗

PubMed2004

Dependency issues in survival analyses of 55,782 primary hip replacements from 47,355 patients.

Artificial hip joints are used in only one hip for about 85 per cent of the patients and in both hips (bilateral) for about 15 per cent of the patients. The occurrence of bilateral prostheses and the influence they have in survival analyses of joint arthroplasties are seldom considered. In this study we therefore focus on issues related to bilateral primary hip prostheses, time to revision surgery, and some commonly used statistical methods. We used information from 47,355 patients with 55,782 primary hip prostheses reported to the Norwegian Arthroplasty Register between 1987 and 2000. Due to the large number of diagnoses, fixation techniques for the prostheses, and combination of prostheses brands, we furthermore considered a 'homogeneous' subset of 8703 prostheses from 7930 patients with primary osteoarthritis, and Charnley prosthesis fixed with antibiotic-containing Palacos cement. Kaplan-Meier curves for all prostheses, ignoring that some patients have bilateral prostheses, were compared with Kaplan-Meier curves using only the first inserted prostheses, and with survival curves modified for patients with bilateral prostheses. Cox regression analyses were used to assess explanatory variables and to adjust for confounding factors. The results from the ordinary Cox regression analyses were compared with results from a marginal model, a shared gamma frailty model, and a model using a time dependent covariate to condition on failures in the opposite hip. We found no practical difference between the three calculated survival curves for the hip replacement data. The ordinary Cox-model and the marginal model gave equivalent results. In the shared gamma frailty model estimates for the risk factors were comparable with the former two approaches. The estimated frailty variance was higher when all data were used, even after adjustment for confounding factors. For the 'homogeneous' data the estimated frailty variance was negligible. Using a time dependent covariate to condition on previous revisions in the opposite hip, we found a higher risk of revision for the remaining primary hip prosthesis if the opposite hip had been revised (RR = 3.49, p < 0.0001). There was no difference in risk for revision between right and left hip prostheses. If the time interval between the two primary operations was more than two years, for the full data, the first hip prosthesis had an increased risk of revision compared to prostheses in patients with only one prosthesis (RR = 1.25, p = 0.01). For the 'homogeneous' data no statistically significant difference was found between unilateral and bilateral prostheses. A revision in one hip, for patients with bilateral prostheses, is a risk factor for revision of the other hip. Thus, in analyses of prostheses survival, dependencies between two hip prostheses from one patient should be considered. However, ignoring possible dependencies does not necessarily have an impact on the results on standard risk factors.

Aged↗

PubMed1995

Some recent developments for regression analysis of multivariate failure time data.

Cox's seminal 1972 paper on regression methods for possibly censored failure time data popularized the use of time to an event as a primary response in prospective studies. But one key assumption of this and other regression methods is that observations are independent of one another. In many problems, failure times are clustered into small groups where outcomes within a group are correlated. Examples include failure times for two eyes from one person or for members of the same family. This paper presents a survey of models for multivariate failure time data. Two distinct classes of models are considered: frailty and marginal models. In a frailty model, the correlation is assumed to derive from latent variables ("frailties") common to observations from the same cluster. Regression models are formulated for the conditional failure time distribution given the frailties. Alternatively, marginal models describe the marginal failure time distribution of each response while separately modelling the association among responses from the same cluster. We focus on recent extensions of the proportional hazards model for multivariate failure time data. Model formulation, parameter interpretation and estimation procedures are considered.

Clinical Trials as Topic↗

PubMed2006

Femoral bone mineral density in patients with heart failure.

INTRODUCTION: Heart failure and osteoporosis are common conditions in older, frail individuals. It is important to investigate interactions of the common problems in the aging population to devise relevant interventions. METHODS: Sixty individuals (43 men, mean age 77+/-9 years, and 17 women, mean age 78+/-12 years) with heart failure (HF) and 23 age- and gender-matched non-HF controls (15 men, eight women; mean age 77+/-9 years) underwent hip and bone mineral density (BMD) assessments; frailty assessment; physical performance assessment including 6-min walk, grip strength, and self-reported physical activity; and biochemical assessment including calcium, parathyroid hormone (PTH), 25-hydroxy vitamin D (25-OHD), estradiol, creatinine (Cr), and blood urea nitrogen levels (BUN). RESULTS: Significant differences between HF and control groups were found for BMD Z-scores of the femoral neck, total femur, and trochanteric region at the femur (p<.05). Further differences between groups included frailty score (p=.02), 6-min walking distance (p<.001), and self-reported physical activity (p=.001). In addition, several differences between groups were present for calcium (p=.054), PTH (p<.001), 25-OHD (p=.01), Cr (p=.04), and BUN (p=.01). In regression analysis, HF (defined as case, by ejection fraction, or by New York Heart Association class), frailty status, and vitamin D were significant predictors of lower bone mass at the femur. CONCLUSIONS: Individuals with HF have lower BMD, in part related to lower vitamin D status and higher frailty rates. Interventions to optimize vitamin D and physical activity should be explored to prevent bone loss in individuals with heart failure.

Aged↗

PubMed2006

A cluster analysis to define human aging phenotypes.

The definition of a precise and consistent aging phenotype that allows to measure the physical and cognitive decline, as well as the increase of mortality hazard late in life, is a major problem for studies aimed at finding the genetic factors modulating rate and quality of human aging. In this frame, it seems promising the concept of frailty which tends to figure out the subjects who are more vulnerable and more prone to negative outcomes, such as death or hospitalization. Cognitive, functional and psychological measures turned out to be the most effective measures to define frailty, as they condense most of the frailty cycle that occurs in the elderly and is probably responsible of the aging related physical decline. We used MMSE, Hand Grip strength, and GDS as variable parameters in a hierarchical Cluster Analysis (CA) in order to recognise aging phenotypes. By using a sample of 65-85 years old subjects we identified three frailty phenotypes that were consistent from both geriatric and genetic perspectives. Therefore, the method we propose may provide unbiased phenotypes suitable for the identification of genetic variants affecting the quality of aging in this age range. The CA method was less effective in ultranonagenarians, probably due to the high prevalence of frail subjects in this age group that makes difficult to distinguish discrete phenotypes.

Aged↗

PubMed2006

Effects of unmeasured heterogeneity in the linear transformation model for censored data.

We investigate the effect of unobserved heterogeneity in the context of the linear transformation model for censored survival data in the clinical trials setting. The unobserved heterogeneity is represented by a frailty term, with unknown distribution, in the linear transformation model. The bias of the estimate under the assumption of no unobserved heterogeneity when it truly is present is obtained. We also derive the asymptotic relative efficiency of the estimate of treatment effect under the incorrect assumption of no unobserved heterogeneity. Additionally we investigate the loss of power for clinical trials that are designed assuming the model without frailty when, in fact, the model with frailty is true. Numerical studies under a proportional odds model show that the loss of efficiency and the loss of power can be substantial when the heterogeneity, as embodied by a frailty, is ignored.

Clinical Trials as Topic↗

PubMed1997

The protective impact of a covariate on competing failures with an example from a bone marrow transplantation study.

Starting from an applied Bone Marrow Transplantation (BMT) study, the problem of "unexpected protectivity" in competing risks models is introduced, which occurs when one covariate shows a protective impact not expected from a medical perspective. Current explanations found in the statistical literature suggest that unexpected protectivity might be due to the lack of independence between the competing failures. Actually, in the presence of dependence, the Kaplan-Meier curves are not interpretable. Conversely, the cumulative incidence curves remain interpretable, and therefore seem to be a candidate for solving the problem. We discuss the particular nature of dependence in a competing risks framework and illustrate how this dependence may be created via a common frailty factor. A Monte Carlo experiment is set up which accounts also for the association between the observable covariates and the frailty factor. The aim of the experiment is to understand whether and how the bias showed by the estimates could be related to the omitted frailty variable. The results show that dependence alone does not cause false protectivity, and that the cumulative incidence curves suffer the same bias as the survival curves and therefore do not seem to be a solution to false protectivity. Conversely, false protectivity may occur according to the magnitude and the sign of the dependence between the frailty factor and the covariate. The paper ends with some suggestions for empirical research.

Analysis of Variance↗

PubMed1999

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.

Cohort Studies↗

PubMed2001

Two recruitment strategies for a clinical trial of physically frail community-living older persons.

OBJECTIVES: To compare the efficiency and cost of two distinct but complementary recruitment strategies for a clinical trial of physically frail, community-living persons, age 75 and older. DESIGN: In the first recruitment strategy, potential participants were identified and screened for physical frailty during office visits to their primary care physicians; in the second, potential participants were identified from the patient rosters of primary care physicians and were screened for physical frailty in their home. Physical frailty was defined on the basis of slow gait speed and inability to stand from a chair with one's arms folded. SETTING: General community in greater Bridgeport, Connecticut. PARTICIPANTS: Community-living persons, age 75 and older, who met criteria for physical frailty. MEASUREMENTS: Measures of efficiency included the number of persons screened for each participant randomized, the number of persons eligible for each participant randomized, and the refusal rate. Costs were calculated per randomized participant. RESULTS: One hundred eighty-eight participants, with a mean age of 83.2 years, were enrolled over 22 months. One hundred and one participants were enrolled via the office-based strategy; 87 were enrolled via the roster-based strategy. Participants in each group had considerable quadriceps weakness and performed poorly on objective measures of gait and upper- and lower-extremity function. For each participant randomized, the number of persons screened, number of persons eligible, and cost were 15.2, 1.2, and $868, respectively, for the office-based strategy and 11.6, 1.1, and $764, respectively, for the roster-based strategy. The corresponding refusal rates for the two strategies were 14.9% and 10.1%, respectively (P < .001). CONCLUSIONS: Although each recruitment strategy successfully identified older persons who were physically frail, the roster-based strategy was less expensive and performed modestly better on each measure of efficiency than the office-based strategy.

Aged↗

PubMed2002

The accumulation of deficits with age and possible invariants of aging.

This paper extends a method of apprising health status to a broad range of ages from adolescence to old age. The "frailty index" is based on the accumulation of deficits (symptoms, signs, disease classifications) as analyzed in the National Population Health Survey, a representative Canadian population sample (n = 81,859). The accumulation of deficits has both an age-independent (background) component and an age-dependent (exponential) component, akin to the well-known Gompertz-Makeham model for the risk of mortality. While women accumulate more deficits than men of the same age, on average, their rate of accumulation is lower, so the difference in the level of deficits between men and women decreases with age. Two possible invariants of the process of accumulation of deficits were found: (1) the age at which the average proportion of deficits coincides for men and women is 94 years, which closely matches the species-specific lifespan in humans (95 +/- 2); (2) the value of the frailty index (proportion of deficits), which corresponds to that age (0.18). The similarity between mortality kinetics and the accumulation of deficits (frailty kinetics), and the coincidence of the time parameters in the frailty and mortality models make it possible to express mortality risk in terms of accumulated deficits. This provides a simple and accessible tool that might have potential in a number of biomedical applications.

Aged↗

PubMed2004

Selecting factors predictive of heterogeneity in multivariate event time data.

In multivariate survival analysis, investigators are often interested in testing for heterogeneity among clusters, both overall and within specific classes. We represent different hypotheses about the heterogeneity structure using a sequence of gamma frailty models, ranging from a null model with no random effects to a full model having random effects for each class. Following a Bayesian approach, we define prior distributions for the frailty variances consisting of mixtures of point masses at zero and inverse-gamma densities. Since frailties with zero variance effectively drop out of the model, this prior allocates probability to each model in the sequence, including the overall null hypothesis of homogeneity. Using a counting process formulation, the conditional posterior distributions of the frailties and proportional hazards regression coefficients have simple forms. Posterior computation proceeds via a data augmentation Gibbs sampling algorithm, a single run of which can be used to obtain model-averaged estimates of the population parameters and posterior model probabilities for testing hypotheses about the heterogeneity structure. The methods are illustrated using data from a lung cancer trial.

Algorithms↗

PubMed2006

Consequences of heterogeneity in survival probability in a population of Florida scrub-jays.

1. Using data on breeding birds from a 35-year study of Florida scrub-jays Aphelocoma coerulescens (Bosc 1795), we show that survival probabilities are structured by age, birth cohort, and maternal family, but not by sex. Using both accelerated failure time (AFT) and Cox proportional hazard models, the data are best described by models incorporating variation among birth cohorts and greater mortality hazard with increasing age. AFT models using Weibull distributions with the shape parameter > 1 were always the best-fitting models. 2. Shared frailty models allowing for family structure greatly reduce model deviance. The best-fitting models included a term for frailty shared by maternal families. 3. To ask how long a data set must be to reach qualitatively the same conclusions, we repeated the analyses for all possible truncated data sets of 2 years in length or greater. Length of the data set affects the parameter estimates, but not the qualitative conclusions. In all but three of 337 truncated data sets the best-fitting models pointed to same conclusions as the full data set. Shared frailty models appear to be quite robust. 4. The data are not adequate for testing hypotheses as to whether variation in frailty is heritable. 5. Substantial structured heterogeneity for survival exists in this population. Such structured heterogeneity has been shown to have substantial effects in reducing demographic stochasticity.

Aging↗

PubMed2006

Variation in the ciliary neurotrophic factor gene and muscle strength in older Caucasian women.

OBJECTIVES: To determine whether genetic variants in the ciliary neurotrophic factor (CNTF) gene are associated with muscle strength in older women. DESIGN: Cross-sectional analysis of baseline data from the Women's Health and Aging Studies I (1992) and II (1994), complementary population-based studies. SETTING: Twelve contiguous ZIP code areas in Baltimore, Maryland. PARTICIPANTS: Three hundred sixty-three Caucasian, community-dwelling women aged 70 to 79. MEASUREMENTS: Participants were genotyped at the CNTF locus for eight single nucleotide polymorphisms (SNPs), including the null allele rs1800169. The dependent variables were grip strength and the frailty syndrome, identified as presence of three or more of five frailty indicators (weakness, slowness, weight loss, low physical activity, exhaustion). In addition to genotypes, independent variables of body mass index (BMI) and osteoarthritis of the hands were included. RESULTS: Using multivariate linear regression, single SNP analysis identified five SNPs significantly associated with grip strength (P<.05), after adjusting for age, BMI, and osteoarthritis. Haplotype analysis was performed, and a single haplotype associated with grip strength was identified (P<.01). The rs1800169 null allele fully explained the association between this haplotype and grip strength under a recessive model, with individuals homozygous for the null allele exhibiting a 3.80-kg lower (95% confidence interval=1.01-6.58) grip strength. No association was seen between the CNTF null allele and frailty. CONCLUSION: Individuals homozygous for the CNTF null allele had significantly lower grip strength but did not exhibit overt frailty. Larger prospective studies are needed to confirm this finding and extend it to additional populations.

Aged↗

PubMed2005

The heritability of CHD mortality in danish twins after controlling for smoking and BMI.

Cause-specific mortality data on Danish monozygotic and dizygotic twins are used to analyze heritability estimates of susceptibility to coronary heart disease (CHD) after controlling for smoking and Body Mass Index (BMI). The sample includes 1209 like-sexed twin pairs born between 1890 and 1920, where both individuals were still alive in 1966. The participants completed a questionnaire in 1966 which included questions on smoking, height and weight. The analysis was conducted with both sexes pooled due to the relatively small number of twin pairs. Follow-up was conducted from January 1, 1966 to December 31, 1993. The correlated gammafrailty model with observed covariates was used for the genetic analysis of frailty to account for censoring and truncation in the lifetime data. During the follow-up, 1437 deaths occurred, including 435 deaths due to 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 without covariates, heritability of frailty to CHD was found to be 0.45 (0.11). This result changes only slightly to 0.55 (0.13) in a DE model after controlling for smoking and BMI. This analysis underlines the existence of a substantial genetic influence on individual frailty associated with mortality caused by CHD.

Body Mass Index↗

PubMed2000

Modeling Medicare costs of PACE (Program of All-Inclusive Care for the Elderly) populations.

Historically, Medicare has paid PACE providers a monthly capitated rate equal to 95 percent of the site's county AAPCC multiplied by a PACE-specific frailty adjuster of 2.39. The Balanced Budget Act of 1997 makes PACE a permanent provider category and mandates that future Medicare payments be based upon the rate structure of the Medicare+Choice payment system, adjusted for the comparative frailty of PACE enrollees and other factors deemed to be appropriate by the Secretary of Health and Human Services. This study revisits the calculation of the PACE frailty adjuster and explores the effect of risk adjustment on that frailty adjuster.

Activities of Daily Living↗

PubMed1992

Semiparametric estimation of random effects using the Cox model based on the EM algorithm.

Consider a survival experiment where individuals within a certain subset of the population share a common, unobservable, random frailty. Such a frailty could be an unobservable genetic or early environmental effect if individuals were in sibling groups or an environmental effect if individuals were grouped by households. Suppose that if the frailty, omega, is known, the Cox proportional hazards model for the observable covariates is valid with the consequence of the random effect being a multiplicative factor on the hazard rate. Assuming tht the random frailties follow a gamma distribution, estimates of the fixed and random effects are obtained by using an EM algorithm based on a profile likelihood construction. The method developed is applied to the Framingham Heart Study to examine the risks of smoking and cholesterol levels, adjusting for potential random effects.

Adult↗

PubMed2026

Development and Validation of Machine Learning Models for Predicting Early Cognitive Decline Using Home Sensor-Derived Behavioral Data: Sensors in-Home for Elder Wellbeing (SINEW) Cohort Study.

BACKGROUND: As the global population continues to age, the prevalence of geriatric conditions, including dementia and frailty, is also increasing. Early identification of individuals at an elevated risk of these conditions, such as those presenting with mild cognitive impairment (MCI) or prefrailty, can provide a critical window for prompt intervention aimed at preventing or reversing disease progression. To promote such early identification, there is a burgeoning interest in the use of digital sensor technology and predictive modeling. OBJECTIVE: This study aimed to use a continuous, home-based monitoring sensor system for older adults to distinguish those exhibiting normal aging from those with MCI, early dementia, prefrailty, or frailty, and to predict their transition from normal aging to one of these conditions. METHODS: This longitudinal cohort study will recruit 200 community-dwelling adults aged ≥65 years with normal cognition or MCI at baseline. A multi-sensor system will be installed in participants' homes, including passive infrared motion sensors, door contact sensors, bed sensors, medication box sensors, wearable activity bands, and Bluetooth proximity beacons. These devices will continuously capture spatiotemporal activity patterns, mobility indicators, sleep behaviors, and medication-taking routines. Annual assessments will include standardized cognitive tests (eg, Montreal Cognitive Assessment, Mini-Mental State Examination, Rey Auditory-Verbal Learning Test, digit span, Color Trails Test, semantic fluency, Stroop), frailty measures (modified Fried phenotype, gait speed, grip strength), mental health scales, sleep quality, and psychosocial indicators. Sensor-derived features-such as gait variability, activity regularity, sleep fragmentation, and medication adherence patterns-will be integrated with clinical data to develop supervised machine learning models. Planned approaches include logistic regression, random forests, gradient boosting, and deep learning. Model performance will be evaluated using cross-validation and independent test sets. Primary metrics will include area under the receiver operating characteristic curve, sensitivity, specificity, precision, recall, and F1-score. Models will be benchmarked against gold-standard clinical diagnoses and validated using temporal subsets of the dataset. RESULTS: Enrollment for this study started in November 2019 and will continue until March 2030. As of June 2025, we have enrolled 138 participants. Full data analysis has yet to begin. CONCLUSIONS: We aim to develop a reliable and effective sensor system for in-home use that will facilitate the early detection of cognitive and physical decline. In so doing, it will add to our current understanding of digital biomarkers. It is common for older adults to seek clinical intervention only when their cognitive impairment has already reached an advanced stage. The implementation of readily deployable sensor systems within community settings presents us with opportunities for prompt intervention, which holds the potential for delaying or reversing disease progression and allowing for a greater number of functional and meaningful years.

Humans↗