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PubMed2005

A class of Bayesian shared gamma frailty models with multivariate failure time data.

For multivariate failure time data, we propose a new class of shared gamma frailty models by imposing the Box-Cox transformation on the hazard function, and the product of the baseline hazard and the frailty. This novel class of models allows for a very broad range of shapes and relationships between the hazard and baseline hazard functions. It includes the well-known Cox gamma frailty model and a new additive gamma frailty model as two special cases. Due to the nonnegative hazard constraint, this shared gamma frailty model is computationally challenging in the Bayesian paradigm. The joint priors are constructed through a conditional-marginal specification, in which the conditional distribution is univariate, and it absorbs the nonlinear parameter constraints. The marginal part of the prior specification is free of constraints. The prior distributions allow us to easily compute the full conditionals needed for Gibbs sampling, while incorporating the constraints. This class of shared gamma frailty models is illustrated with a real dataset.

Adolescent↗

PubMed2005

Chronic cytomegalovirus infection and inflammation are associated with prevalent frailty in community-dwelling older women.

OBJECTIVES: To evaluate the association between asymptomatic chronic cytomegalovirus (CMV) infection and the frailty syndrome and to assess whether inflammation modifies this association. DESIGN: Cross-sectional analysis. SETTING: Women's Health and Aging Study I & II, Baltimore, Maryland. PARTICIPANTS: Seven hundred twenty-four community-dwelling women aged 70 to 79 with baseline measures of CMV, interleukin-6 (IL-6), and frailty status. MEASUREMENTS: CMV serology and IL-6 concentrations were measured using enzyme-linked immunosorbent assay. Frailty status was based on previously validated criteria: unintentional weight loss, weak grip strength, exhaustion, slow walking speed, and low level of activity. Frail women had three or more of the five components, prefrail women had one or two components, and women who were not frail had none of the components. Multinomial logistic regression adjusted for potential confounders. RESULTS: Eighty-seven percent of women were CMV seropositive, an indication of chronic infection. CMV was associated with prevalent frailty, adjusting for age, smoking history, elevated body mass index, diabetes mellitus, and congestive heart failure (CMV frail adjusted odds ratio (AOR)=3.2, P=.03; CMV prefrail AOR=1.5, P=.18). IL-6 interacted with CMV, significantly increasing the magnitude of this association (CMV positive and low IL-6 frail AOR=1.5, P=.53; CMV positive and high IL-6 frail AOR=20.3, P=.007; CMV positive and low IL-6 prefrail AOR=0.9, P=.73; CMV positive and high IL-6 prefrail AOR=5.5, P=.001). CONCLUSION: Chronic CMV infection is associated with prevalent frailty, a state with increased morbidity and mortality in older adults; inflammation enhances this effect. Further prospective studies are needed to establish a causal relationship between CMV, inflammation, and frailty.

Aged↗

PubMed2006

Bayesian semiparametric dynamic frailty models for multiple event time data.

Many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly, such as infection, hospitalization, recurrence of disease, or tumor onset. To analyze such data, it is necessary to account for within-subject dependency in the multiple event times. Motivated by data from studies of palpable tumors, this article proposes a dynamic frailty model and Bayesian semiparametric approach to inference. The widely used shared frailty proportional hazards model is generalized to allow subject-specific frailties to change dynamically with age while also accommodating nonproportional hazards. Parametric assumptions on the frailty distribution are avoided by using Dirichlet process priors for a shared frailty and for multiplicative innovations on this frailty. By centering the semiparametric model on a conditionally conjugate dynamic gamma model, we facilitate posterior computation and lack-of-fit assessments of the parametric model. Our proposed method is demonstrated using data from a cancer chemoprevention study.

Algorithms↗

PubMed2001

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.

Age Distribution↗

PubMedDate not supplied

Frailty: a public health perspective.

Traditionally, frailty has been conceptualized as reflecting an inevitable decline in abilities usually associated with physical aspects of aging. More recent thinking now sees frailty as reflecting an interaction among individual factors and a range of environmental elements. These emerging models, however, continue to consider frailty as a condition that resides within the individual rather than a situation that exists for the individual. We present a new model that defines frailty as occurring when there is diminished ability to carry out the important practical and social activities of daily living. Factors related to the occurrence of frailty are considered, as are the theoretical and practice implications of viewing frailty as a social construction.

Activities of Daily Living↗

PubMed2002

Frailty and activation of the inflammation and coagulation systems with and without clinical comorbidities: results from the Cardiovascular Health Study.

BACKGROUND: The biological basis of frailty has been difficult to establish owing to the lack of a standard definition, its complexity, and its frequent coexistence with illness. OBJECTIVE: To establish the biological correlates of frailty in the presence and absence of concurrent cardiovascular disease and diabetes mellitus. METHODS: Participants were 4735 community-dwelling adults 65 years and older. Frail, intermediate, and nonfrail subjects were identified by a validated screening tool and exclusion criteria. Bivariate relationships between frailty level and physiological measures were evaluated by Pearson chi2 tests for categorical variables and analysis of variance F tests for continuous variables. Multinomial logistic regression was performed to evaluate multivariable relationships between frailty status and physiological measures. RESULTS: Of 4735 Cardiovascular Health Study participants, 299 (6.3%) were identified as frail, 2147 (45.3%) as intermediate, and 2289 (48.3%) as not frail. Frail vs nonfrail participants had increased mean +/- SD levels of C-reactive protein (5.5 +/- 9.8 vs 2.7 +/- 4.0 mg/L), factor VIII (13 790 +/- 4480 vs 11 860 +/- 3460 mg/dL), and, in a smaller subset, D dimer (647 +/- 1033 vs 224 +/- 258 ng/mL) (P< or =.001 for all, chi2 test for trend). These differences persisted when individuals with cardiovascular disease and diabetes were excluded and after adjustment for age, sex, and race. CONCLUSIONS: These findings support the hypothesis that there is a specific physiological basis to the geriatric syndrome of frailty that is characterized in part by increased inflammation and elevated markers of blood clotting and that these physiological differences persist when those with diabetes and cardiovascular disease are excluded.

Aged↗

PubMed2005

Bayesian inference for recurrent events data using time-dependent frailty.

In medical studies, we commonly encounter multiple events data such as recurrent infection or attack times in patients suffering from a given disease. A number of statistical procedures for the analysis of such data use the Cox proportional hazards model, modified to include a random effect term called frailty which summarizes the dependence of recurrent times within a subject. These unobserved random frailty effects capture subject effects that are not explained by the known covariates. They are typically modelled constant over time and are assumed to be independently and identically distributed across subjects. However, in some situations, the subject-specific random frailty may change over time in the same manner as time-dependent covariate effects. This paper presents a time-dependent frailty model for recurrent failure time data in the Bayesian context and estimates it using a Markov chain Monte Carlo method. Our approach is illustrated by a data set relating to patients with chronic granulomatous disease and it is compared to the constant frailty model using the deviance information criterion.

Bayes Theorem↗

PubMed2005

A correlated frailty model for analysing risk factors in bilateral corneal graft rejection for Keratoconus: a Bayesian approach.

There are many unknown causes that increase the rate of corneal graft rejection. In bilateral cases, some of these unknown causes are common, and some are individual factors. In this paper, we use a correlated frailty model to analyse risk factors for bilateral corneal graft in Keratoconus. Applying the piecewise constant baseline hazard model, we have performed a Bayesian analysis of the correlated frailty model using the Markov chain Monte Carlo method. The correlated frailty model and the shared frailty model are compared by deviance information criterion. The results show more accurate and better fit for the correlated frailty model.

Bayes Theorem↗

PubMed2004

Changes with age in the distribution of a frailty index.

Models of human mortality include a factor that summarises intrinsic differences in individual rates of ageing, commonly called frailty. Frailty also describes a clinical syndrome of apparent vulnerability. In a representative, cross-sectional, Canadian survey (n = 66,589) we calculated a frailty index as the mean accumulation of deficits and previously showed it to increase exponentially with age. Here, its density function exhibited a monotonic change in shape, being least skewed at the oldest ages. Although the shape gradually changed, the frailty index was well fitted by a gamma distribution. Of note, the variation coefficient, initially high, decreased from middle age on. Being able to quantify frailty means that health risks can be summarised at both the individual and group levels.

Adult↗

PubMedDate not supplied

Decreasing mental frailty in at-risk elders.

Frailty may be used to describe those older adults who are in precarious balance between their abilities to maintain health and function and their deficits that threaten the balance. Frailty often is described in purely physical terms, omitting the mental and psychologic aspects. When the term is applied to the mental abilities of older adults, frailty is associated with memory vulnerability in the cognitive domain and depression in the psychologic domain. Compromised thinking, anxiety, and decreased confidence in memory are symptoms of mental frailty. This article examines the effects of aging on memory and the intertwining factors of depression and self-efficacy as treatable antecedents of mental frailty in older adults. The article also describes simple assessment techniques, explores memory improvement strategies, and considers nursing implications.

Aged↗

PubMed1997

A Weibull regression model with gamma frailties for multivariate survival data.

Frequently in the analysis of survival data, survival times within the same group are correlated due to unobserved co-variates. One way these co-variates can be included in the model is as frailties. These frailty random block effects generate dependency between the survival times of the individuals which are conditionally independent given the frailty. Using a conditional proportional hazards model, in conjunction with the frailty, a whole new family of models is introduced. By considering a gamma frailty model, often the issue is to find an appropriate model for the baseline hazard function. In this paper a flexible baseline hazard model based on a correlated prior process is proposed and is compared with a standard Weibull model. Several model diagnostics methods are developed and model comparison is made using recently developed Bayesian model selection criteria. The above methodologies are applied to the McGilchrist and Aisbett (1991) kidney infection data and the analysis is performed using Markov Chain Monte Carlo methods.

Bayes Theorem↗

PubMed2004

Onset of frailty in older adults and the protective role of positive affect.

The aim of this study was to examine the longitudinal association between positive affect and onset of frailty for 1,558 initially nonfrail older Mexican Americans from the Hispanic Established Populations for Epidemiological Studies of the Elderly database. The incidence of frailty increased 7.9% during the 7-year follow-up period. High positive affect was found to significantly lower the risk of frailty. Each unit increase in baseline positive affect score was associated with a 3% decreased risk of frailty after adjusting for relevant risk factors. Findings add to a growing positive psychology literature by showing that positive affect is protective against the functional and physical decline associated with frailty.

Activities of Daily Living↗

PubMed2006

Public health significance of the frailty index.

BACKGROUND: A quantifiable indicator of frailty would be very useful in assessing the health state of older populations, as well as enable the effect of interventions to be evaluated over time. METHODS: A total of 2032 people aged 70 years and over recruited by stratified random sampling, and information obtained regarding physical and functional health, and psychological factors. The frailty index (FI) was constructed from 62 variables. Associations between the FI, and changes in ADL score, mental score, and hospitalization days over a 10-year period were evaluated. RESULTS: For the baseline to 3-year changes, a 0.10 increase in baseline FI is accompanied by a 0.499-point faster drop in ADL score, a 0.223-point faster decline in mental score, and 4.57-day faster increase in hospital days. For 3-10-year changes, frailty was a significant predictor only of changes in mental score, with results indicating that, on average, each increase of 0.10 in the baseline frailty index was associated with 0.613-point drop in mental score during this period. Chronological age and frailty had differential associations with those changes. CONCLUSION: The FI is a valid indicator of morbidity and requirement for health and social services for ageing populations.

Activities of Daily Living↗

PubMed2004

Frailty modelling of testicular cancer incidence using Scandinavian data.

The incidence of testicular cancer is highest among young men, and then decreases sharply with age. This points towards a frailty effect, where some men have a much greater risk of testicular cancer than the majority of the male population. Those with the highest risk get cancer, drain the group of individuals at risk, and leave a healthy male population which has approximately zero risk of testicular cancer. This leads to the observed decrease in incidence. We discuss a frailty model, where the frailty is compound-Poisson-distributed. This allows for a non-susceptible group (of zero frailty). The model is successfully applied to incidence data from the Danish and Norwegian registries. It is indicated that there was a decrease in incidence for males born during World War II in both countries. Bootstrap analysis is used to find the degree of variation in the estimates. In the Armitage-Doll multistage model, the estimated number of transitions needed for a cell to become malignant is close to 3 for non-seminomas and 4 for seminomas in both the Danish and Norwegian data. This paper demonstrates that a model including a frailty effect fits the incidence data well and gives interesting results and interpretations, although this is no proof of the effect's truth.

Adolescent↗

PubMed2004

Assessment of individual risk of death using self-report data: an artificial neural network compared with a frailty index.

OBJECTIVES: To evaluate the potential of an artificial neural network (ANN) in predicting survival in elderly Canadians, using self-report data. DESIGN: Cohort study with up to 72 months follow-up. SETTING: Forty self-reported characteristics were obtained from the community sample of the Canadian Study of Health and Aging. An individual frailty index score was calculated as the proportion of deficits experienced. For the ANN, randomly selected participants formed the training sample to derive relationships between the variables and survival and the validation sample to control overfitting. An ANN output was generated for each subject. A separate testing sample was used to evaluate the accuracy of prediction. PARTICIPANTS: A total of 8,547 Canadians aged 65 to 99, of whom 1,865 died during 72 months of follow-up. MEASUREMENTS: The output of an ANN model was compared with an unweighted frailty index in predicting survival patterns using receiver operating characteristic (ROC) curves. RESULTS: The area under the ROC curve was 86% for the ANN and 62% for the frailty index. At the optimal ROC value, the accuracy of the frailty index was 70.0%. The ANN accuracy rate over 10 simulations in predicting the probability of individual survival mean+/-standard deviation was 79.2+/-0.8%. CONCLUSION: An ANN provided more accurate survival classification than an unweighted frailty index. The data suggest that the concept of biological redundancy might be operationalized from health survey data.

Aged↗

PubMed2005

Relative fitness and frailty of elderly men and women in developed countries and their relationship with mortality.

OBJECTIVES: To investigate the relationship between accumulated health-related problems (deficits), which define a frailty index in older adults, and mortality in population-based and clinical/institutional-based samples. DESIGN: Cross-sectional and cohort studies. SETTING: Seven population-based and four clinical/institutional surveys in four developed countries. PARTICIPANTS: Thirty-six thousand four hundred twenty-four people (58.5% women) aged 65 and older. MEASUREMENTS: A frailty index was constructed as a proportion of all potential deficits (symptoms, signs, laboratory abnormalities, disabilities) expressed in a given individual. Relative frailty is defined as a proportion of deficits greater than average for age. Measures of deficits differed across the countries but included common elements. RESULTS: In each country, community-dwelling elderly people accumulated deficits at about 3% per year. By contrast, people from clinical/institutional samples showed no relationship between frailty and age. Relative fitness/frailty in both sexes was highly correlated (correlation coefficient >0.95, P<.001) with mortality, although women, at any given age, were frailer and had lower mortality. On average, each unit increase in deficits increased by 4% the hazard rate for mortality (95% confidence interval=0.02-0.06). CONCLUSION: Relative fitness and frailty can be defined in relation to deficit accumulation. In population studies from developed countries, deficit accumulation is robustly associated with mortality and with age. In samples (e.g., clinical/institutional) in which most people are frail, there is no relationship with age, suggesting that there are maximal values of deficit accumulation beyond which survival is unlikely.

Age Distribution↗

PubMed2005

Bayesian cure rate frailty models with application to a root canal therapy study.

Due to natural or artificial clustering, multivariate survival data often arise in biomedical studies, for example, a dental study involving multiple teeth from each subject. A certain proportion of subjects in the population who are not expected to experience the event of interest are considered to be "cured" or insusceptible. To model correlated or clustered failure time data incorporating a surviving fraction, we propose two forms of cure rate frailty models. One model naturally introduces frailty based on biological considerations while the other is motivated from the Cox proportional hazards frailty model. We formulate the likelihood functions based on piecewise constant hazards and derive the full conditional distributions for Gibbs sampling in the Bayesian paradigm. As opposed to the Cox frailty model, the proposed methods demonstrate great potential in modeling multivariate survival data with a cure fraction. We illustrate the cure rate frailty models with a root canal therapy data set.

Bayes Theorem↗

PubMed2006

Effects of dehydroepiandrosterone and atamestane supplementation on frailty in elderly men.

BACKGROUND: It has been suggested that the age-related decline of androgens in men plays a distinct role in the development of several aspects of frailty. Therefore, hormone replacement might improve the course of frailty by increasing lean body mass and muscle strength, decreasing fat mass, and improving the subjective quality of life. OBJECTIVE: The objective of the study was to assess whether hormone replacement with dehydroepiandrosterone (DHEA) and/or atamestane might improve the course of frailty. DESIGN: This was a double-blind, randomized, controlled trial. SETTING: The study was conducted in the general community. PARTICIPANTS: Participants included 100 nonhospitalized, nondiseased, independently living men, aged 70 yr and over with low scores on strength tests. Seventeen participants did not complete the trial. INTERVENTION: Subjects were randomly assigned to one of four intervention arms: atamestane (100 mg/d) and placebo, DHEA (50 mg/d) and placebo, a combination of atamestane (100 mg/d) and DHEA (50 mg/d), or two placebo tablets for 36 wk. MAIN OUTCOME MEASURES: Physical frailty was measured by means of a specific test battery, including isometric grip strength, leg extensor power, and physical performance. RESULTS: The randomization was successful, and 83 (83%) men completed the intervention. There were no differences between the treatment arms and placebo group in any of the outcome measurements after intervention. CONCLUSIONS: The results of this double-blind, randomized trial do not support the hypothesis that hormone replacement with DHEA and/or atamestane might improve the course of frailty.

Activities of Daily Living↗