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

"Many ideas in the analysis of heterogeneous mortality are based on the relationship between individual and observed hazard rates. This connection is established with the help of conditional averaging procedure: The observed risk of death at age x is calculated among those who survive this age. The analogy of this result for bivariate survival model with correlated individual hazards is derived. In the case of correlated frailty model the parametric specification of the mean, variance and correlation coefficient of the bivariate frailty distribution among survivors is obtained. The relationship between local association measure and the characteristics of the bivariate frailty distribution among survivors is established." (SUMMARY IN FRE)     

Frailty selection in bivariate survival models: A cautionary note

One problem that researchers face in analyzing the survival times of groups of related individuals is selecting how the distribution of frailty—an unobserved (or not adequately observed) random factor— should be specified. Several distributions have received attention—for instance, the gamma distribution and a nonparametric N‐point, discrete probability distribution. Researchers have selected these distributions more for mathematical convenience than for their ability to represent biological, social, or economic reality, and the implications of choosing one functional representation of frailty over alternative choices have not been studied extensively. In particular, researchers have paid little attention to the type of association that exists among survival times of individuals in a group or between those of a pair under specific frailty distributions. This research paper explores the association among survival times under gamma, inverse Gaussian, nonparametric N‐point, and Poisson distributions. It shows that the pattern and strength of this association depends on how the distribution of frailty is specified.     

Correlated individual frailty: an advantageous approach to survival analysis of bivariate data

"We develop a new model of bivariate survival based on the notion of correlated individual frailty. We analyze the properties of this model and suggest a new approach to the analysis of bivariate data that does not require a parametric specification--but permits estimation--of the form of the hazard function for individuals. We empirically demonstrate the advantages of the model in the statistical analysis of bivariate data." (SUMMARY IN FRE)     

Age patterns of mortality for older women: An analysis using the age‐specific rate of mortality change with age

The age‐specific rate of mortality change with age, defined by k(x) = d Inμ(x)/dx, where μ(x) is the age‐specific death rate at exact age x, is estimated for middle and old ages in ten selected populations that are considered to have relatively accurate age data. For females in each of the study populations, k(x) follows a bell‐shaped curve that usually peaks around age 75. In some of the populations, the age pattern of k(x) for males is confounded with substantial cohort variations, which seem to reflect long‐term impacts of their World War I experiences.

Among the mathematical models proposed by Gompertz, Makeham, Perks and Beard, only the Perks model is consistent with the bell‐shaped pattern of k(x). It is shown that, if the risk of death for every individual follows the Makeham equation and if the individual frailty is gamma‐distributed, then the age‐specific death rate follows the Perks equation.     

Is the outcome of frailty syndrome gender dependent?

ABSTRACT

We assessed the relationship between the stages of the frailty syndrome and the development of limitations in the activities of daily living, hospitalization, and death among women aged ≥80 as compared to men over the course of 12 months. The Fried criteria and selected tests of comprehensive geriatric assessment were performed in 213 participants (phase 1). After 12 months, detailed feedback on the general health and functioning was collected (phase 2). Statistically significantly higher mortality (p < .05) was found among men as compared to women. The number of deaths in the frail group was higher among frail men than frail women (p < .007).     

Dynamics of Mixed Coalitions Under Social Cohesion Constraints

ABSTRACT

Parameters for the birth and death diffusion life table model subject to downward jumps randomly occurring at a constant rate are estimated. The jump magnitudes have a beta distribution with support [0, l_x ], where l_x is the total number of survivors prior to the jump. The estimation method is maximum likelihood. The Cramer–Rao Lower bound and the asymptotic distribution for the MLE are derived. The model is applied to the U.S. men′s population from 1900 to 1999.     

A dynamic multistate model of robustness and frailty

Dynamic multistate models can show realistic population dynamics over time, model complex cycles, and encompass the life history of a cohort. This paper uses a recently developed approach to obtain the analytic solution of a time‐dependent multidimensional differential equation. The illustrative robust/frail model presented shows that the assumption of fixed individual frailty can be abandoned in a two living state model that allows transitions between health statuses and nonproportional hazards of death.     

A Meta-Analysis of the Relationship Between Spirituality and Quality of Life

The relationship between spirituality and various dimensions of health and quality of life has been extensively examined during the past decade. Though several literature reviews have been conducted in an attempt to synthesize research findings pertaining to the relationship between spirituality and health, a meta-analysis of studies examining spirituality in relation to quality of life has not been identified. The present study was designed to: (a) determine whether there is empirical support for a relationship between spirituality and quality of life, (b) provide an estimate of the strength of this relationship, and (c) examine potential moderating variables affecting this relationship. The research design followed accepted methods for quantitative meta-synthesis. Potential moderating effects of several methodological differences and sample characteristics were examined using meta-analytic approaches with multivariate linear regression and analysis of variance. An extensive multidisciplinary literature search resulted in 3,040 published reports that were manually screened according to pre-established selection criteria. Subsequent to the selection process, 62 primary effect sizes from 51 studies were included in the final analysis. A random effects model of the bivariate correlation between spirituality and quality of life resulted in a moderate effect size (r = 0.34, 95% CI: 0.28–0.40), thereby providing support for the theoretical framework underlying the study wherein spirituality was depicted as a unique concept that stands in relationship to quality of life. Subsequent regression analyses indicated that differences among operational definitions of spirituality and quality of life were associated with the variability in estimates of the magnitude of the relationship (R² = 0.27). Other potential moderators, such as age, gender, ethnicity, religious affiliation and sampling method were examined but the findings pertaining to these variables were inconclusive because of limitations associated with the sample of primary studies. The implications of this study are mostly theoretical in nature and raise questions about the commonly assumed multidimensional conceptualization of quality of life.     

Understanding Mortality Rate Deceleration and Heterogeneity

ABSTRACT

Generic relationships between heterogeneity in population frailty and flattening of aggregate population hazard functions at extreme ages are drawn from classical mathematical results on the limiting behavior of Laplace transforms. In particular, it shows that the population hazard function converges to a constant precisely when the distribution of unobserved heterogeneity in initial mortalities behaves asymptotically as a polynomial near zero.     

Random walk Green kernels in the neutral Moran model conditioned on survivors at a random time to origin

In the theory of finite discrete-time birth and death chains with absorbing endpoint boundaries, the evaluation of both additive and multiplicative path functionals is made possible by their Green and λ–potential kernels. These computations are addressed in the context of such Markov chains. The application to the neutral Moran model of population genetics yields first hitting and return times. A neutral Moran bridge model, forward and backward in time, for a given total number x of survivors of a single common ancestor at some random time T to the origin of times, yields the age of a mutant allele currently observed to have x copies of itself. This forward theory of age, made possible by Green kernels, is comparable to Watterson’s backward theory of age, which makes use of the reversibility of the Moran chain.     

Methods for combining ancillary data in stochastic compartment models of cancer mortality: Generalization of heterogeneity models∗

In analyzing mortality data there may be available information from survey and other sources that describe the marginal distribution of risk factors. We present a mortality model where nationally representative survey data on risk factor distributions are combined with data on cohort mortality rates to increase information, i.e., a fixed marginal risk factor distribution is combined with a cohort model representing unobserved individual risk heterogeneity. The model is applied to lung cancer mortality in nine U.S. white male cohorts aged 30 to 70 in 1950 and followed 38 years. Estimates of the cohort specific proportions of smokers were made from the National Health Interview Survey. Comparisons are made for models with different patterns of changes with age of individual heterogeneity.     

Functional consequences of work-related spinal musculoskeletal symptoms in a cohort of Australian midwives

BackgroundEarly evidence suggests spinal musculoskeletal symptoms are as prevalent in Australian midwives as in samples of nurses. Functional consequences of these symptoms include sick leave and functional incapacity, which are costly at both individual and workplace levels. To date there have been no studies of these consequences in midwives.QuestionWhat risk factors are associated with sick leave and functional incapacity among midwives with spinal musculoskeletal symptoms?MethodsWe undertook a cross-sectional study of qualified Australian midwives who completed the baseline survey of the Nurses and Midwives e-Cohort Study. A comprehensive set of independent variables were examined for bivariate associations with the main outcomes of sick leave and functional incapacity due to work-related musculoskeletal symptoms in the neck, upper or lower back. Associations that achieved a p value < .1 were entered into multiple logistic regression models.Findings729 midwives with a mean age of 46 years were eligible for inclusion. Functional incapacity was more than twice as common as sick leave. Severity of worst pain was the explanatory variable most strongly associated with each main outcome and the only one significant for both. Psychological job demands showed a significant association with sick leave, while several individual factors were associated with both outcomes. Only the association of poorer general health with functional incapacity remained significant in all three spinal regions.ConclusionOur sample reported considerable work-related musculoskeletal pain and functional incapacity. Factors associated with sick leave and functional incapacity in midwives should be confirmed by longitudinal studies with the aim of developing tertiary prevention strategies.     

Social Support for Exercise by Experts in Older Women Post–Hip Fracture

ABSTRACT

Using the data of the Baltimore Hip Study 5 (a home-based exercise intervention), this study examined how social support for exercise by experts (SSE-E) affected the self-efficacy, outcome expectations, and exercise behavior among older women following a hip fracture. The total sample included 164 females aged 65 years (M = 81.0; SD = 6.9) who had surgical repair of a nonpathologic hip fracture. Model testing showed a direct relationship between SSE-E and outcome expectations for exercise. There was, however, no direct or indirect relationship between SSE-E and self-efficacy or exercise behavior. The positive effect of SSE-E on the outcome expectations for exercise in older women recovering from a hip fracture provides an opportunity for health care providers in improving physical activity in this population.     

Population growth with variable family size

The Sharpe‐Lotka continuous time deterministic model of population growth is developed to take account of some possible forms of mother‐daughter fertility association, characterised here by a bivariable measure, A. This leads to a linear double integral equation for which, subject to certain conditions, a finite time solution can be found by Laplace transform methods and thus also model specific results relating the intergenerational fertility effect to the long term population growth rate and magnitude are established. The quantitative implications of the theory are illustrated by a consideration of a general bilinear form of A and in this context numerical results illustrating the finite time growth and also the long term distribution of fertility levels in the stable female population are obtained. In particular, it is shown that different fertility specific subpopulations can coexist indefinitely.     

Estimation of life expectancy — cohort life table

Life tables are traditionally built with linear assumptions for the survival curve. Here, considering that survivors can remain at the end of the observation period, the author shows that non linear modeling is more appropriate. With data on cervix uteri cancer, e0 ≈ 12.5 years with standard error ≈ 2.8 years with infinite time horizon, but e0 ≈ 6.0 years with standard error ≈ 0.1 year in interval with finite time horizon [0, 12 years]. The average hazard function is introduced to estimate the life expectancy, and the actuarial estimate of the hazard function is showed to under‐estimate the true hazard values under the exponential distribution. Finally, a sensitivity analysis of the probabilities of death on the estimation of life expectancy completes the study.     

Food limitation of population density in the orb-wed spider,Nephila clavata

Summary Field studies were conducted to clarify whether variation in food availability among habitats influences population density, and whether population density has a negative effect on foraging success in the orb-web spider,Nephila clavata. Lifetime food consumption per individual (i.e., foraging success) strongly correlated with mean body size of adult females and mean fecundity in populations. Also, there was a positive correlation between foraging success and population density. Since foraging success reflected potential prey availability in the habitat, food resource appeared to be a limiting factor for populations in this spider. Mean fecundity per individual correlated with population density of the following year, suggesting that decreased reproduction is a major component of food limitation on population density. Consistent defferences in mean body size between particular sites were observed over years, while such difference was less obvious in density. Thus, ranking of food abundance among habitats seems to be predictable between years. A field experiment revealed that an artificial increase in population density had no negative effect on the feeding rate of individuals, suggesting that intraspecific competition for food is not important in this species.     

Sarcopenia and Decreased Muscle Strength in the Elderly Woman: Resistance Training as a Safe and Effective Intervention

ABSTRACT

A principle component of age-related weakness and frailty in women is sarcopenia. This decrease in skeletal muscle mass is a progressive syndrome that will affect the quality of life for elderly women by decreasing the ability to perform many activities of daily living. Strength training is known to be an effective means of increasing muscular strength and size in many populations, and can be utilized successfully to significantly improve muscle strength, muscle mass and functional mobility in elderly women up to the age of 96 years. Such exercise can minimize the syndrome of physical frailty due to decreased muscle mass and strength. Any rehabilitation or exercise program for the elderly woman would benefit from the inclusion of such a training regime.     

Enhancing a Randomized Response Model to Estimate Population Means to Sensitive Questions

ABSTRACT

Candidate parametric mortality models are tested graphically. If the model is correct, the transformed data are distributed exponentially. The graphical test is based on scale and space inference. It involves smoothing of the hazard rate and simultaneous confidence intervals. It is applied to a frailty model used to set annuity reserves. Simulation and the comparison with other non-graphical tests shows that the graphical test helps localize discrepancies of empirical data with respect to the tested model.     

Are Cohort Mortality Rates Autocorrelated?

In this paper the author examines the proposition that heterogeneity in individual frailty leads to autocorrelation in cohort mortality rates. A simple model is used to construct analytic expressions for the covariance of cohort mortality rates at different ages under a number of alternative assumptions about the stochastic process generating shocks in mortality. The model then is used to construct a procedure that uses correlations in cohort mortality rates to estimate the extent of heterogeneity in a population without relying on strong assumptions about the distribution of frailty or the shape of the underlying hazard. The procedure then is used to show that cohort mortality data from France are consistent with a generalized random-effects model in which frailty is gamma-distributed.