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.     

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)     

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.     

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.     

中国老年人虚弱指数与死亡风险及队列差异

利用中国老年人健康长寿影响因素调查（ CLHLS ）2002－2011年跟踪调查数据,通过多种健康指标构建中国老年人虚弱指数,运用增长曲线模型和Cox等比例风险函数的研究方法,对中国老年人虚弱指数和死亡风险及其队列差异进行了深入分析。研究发现,女性虚弱指数比男性高,增长速度也比男性快,但是死亡风险比男性低;出生较晚的队列与出生早的队列相比,虚弱指数会更高,他们的增长程度更快;受教育程度高的老年人虚弱指数低,但是其增长速度却比受教育程度低的老年人要高。     

The Biodemography of Variation in Human Frailty

A population is composed of individuals who are heterogeneous in their susceptibility to death and disease. This heterogeneity is reflected in the age-specific incidence or mortality (hazard) function. This variation has typically been hidden--that is, not measured directly--and has generally been modeled in a purely empirical statistical way, because there is no theory in demography for the distribution of frailty. A substantial fraction of variation in frailty, however, has an underlying genetic basis, for which there is a formal theory. This theory, based on evolutionary biology and on the nature of mendelian transmission, provides prior constraints on the distribution of variation in the population as well as providing methods for identifying genes involved in many important diseases. The accumulating effects of environmental exposures with age are another major component of variation in frailty. In some important instances, this variation and its effect on the age-specific hazard function can also be understood in terms of cause-specific biological processes. These biological considerations may enable demographers to model frailty, and thus mortality, in a better way.     

Multidimensionality of Longitudinal Data: Unlocking the Age-Happiness Puzzle

In social economic data analysis, sometimes the explanatory variables that are statistically significant in OLS regressions in cross-section or pooled data become insignificant after controlling for individual fixed effects. This phenomenon was observed in the study of the relationship between age and happiness. The discrepancy in estimates between regressions with and without controlling for individual fixed effects was known as the age-happiness mystery. This paper points out that OLS regressions based on cross-section data reflect the difference in average happiness across birth cohorts. In contrast, regressions controlling for individual fixed effects reflect the change in happiness over life cycle within individuals. For the first time in the literature, the co-existence of a cross-section U shape and a longitudinally declining pattern in the relationship between age and happiness is established. Using data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey, this paper explains the exact meaning of fixed-effects regressions of happiness on age, gives insight into the age-happiness puzzle, and raises the awareness of multidimensionality of longitudinal data.     

Inherited frailty and longevity

The life spans of parents and children appear only weakly related, even though parents affect their children's longevity through both genetic and environmental influences. These influences can be summarized as a correlation between parents' and children's frailty. It is shown that even if children perfectly inherit their frailty from their parents, parents' life spans explain little of the variance in children's life spans, because the variance in life expectancies among people with different frailties is small compared with the variance in life spans among people at the same level of frailty. By interpreting frailty as a relative risk in a proportional-hazard model, longevity as a duration or waiting time, and inheritance as an invariance in relative risk over time, one can extend this result to repeatable events involving fertility, migration, marriage, unemployment, and so forth.     

Discrete Barker Frailty and Warped Mortality Dynamics at Older Ages

We develop a discrete variant of a general model for adult mortality influenced by the delayed impact of early conditions on adult health and mortality. The discrete variant of the model builds on an intuitively appealing interpretation of conditions that induce delayed effects and is an extension of the discrete form of the standard frailty model with distinct implications. We show that introducing delayed effects is equivalent to perturbing adult mortality patterns with a particular class of time-/age-varying frailty. We emphasize two main results. First, populations with delayed effects could experience unchanging or increasing adult mortality even when background mortality has been declining for long periods of time. Although this phenomenon also occurs in a regime with standard frailty, the distortions can be more severe under a regime with Barker frailty. As a consequence, conventional interpretations of the observed rates of adult mortality decline in societies that experience Barker frailty may be inappropriate. Second, the observed rate of senescence (slope of adult mortality rates) in populations with delayed effects could increase, decrease, or remain steady over time and across adult ages even though the rate of senescence of the background age pattern of mortality is time- and age-invariant. This second result implies that standard interpretations of empirical estimates of the slope of adult mortality rates in populations with delayed effects may be misleading because they can reflect mechanisms other than those inducing senescence as conventionally understood in the literature.     

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....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." (SUMMARY IN FRE)     

Prevalence of Low Physical Activity and its Relation to Social Environment in Deprived Areas in the London Borough of Redbridge

Achieving adequate levels of physical activity (PA) is important to maintain health and prevent chronic disease. The costs of inadequate physical activity to the NHS have been estimated at over a billion pounds annually. While socio-demographic characteristics such as age, sex and ethnicity have been reported to be associated with different levels of PA, there is evidence that people??s social environments may also be important in encouraging a physically active lifestyle. The objective of this paper is to describe associations between the social environment and physical activity among the poorer communities in an outer London Borough, when other socio-demographic factors are controlled for. A household survey was carried out in six poorer neighbourhoods in Redbridge in 2008 as part of a wider health needs assessment. The questionnaire included questions allowing estimation of levels of physical activity as well as extent of social environment [social network score (SNS) and social support score (SSS)]. A random sample of households was taken and a total of 799 completed responses from over 16 year old were obtained. The association between physical activity and the social environment controlling for socio-demographic characteristics was estimated using a logistic nested model. Higher SNS was significantly associated with younger age, Black ethnicity, higher education level, higher household income and higher levels of PA in bivariate analyses. Higher SSS was positively associated with Indian ethnicity, higher household income and area of residence. In multivariate analyses higher levels of PA were significantly associated with wider social networks and stronger social support, educational level and marital status. Despite its limitations, our findings confirm that the relationship between low physical activity and weak social networks and low social support, observed in general population studies, also occurs in deprived communities in London. The relationship merits further exploration given the limited evidence on the effectiveness of interventions to promote physical activity.     

老年人与子女同住 对老年健康的影响分析

随着我国老龄化程度的持续加深和疾病谱的转变,当前社会存在大量老年照料需求,尽管国家和社会在积极构建养老服务体系,但短期内与子女同住的家庭养老模式仍将发挥重要作用。与子女同住会对老年健康产生一定的影响,这种影响对于不同健康程度的老年人也存在差异。本文基于南加州大学经济与社会研究中心提供的Harmonized CHARLS 2013-2015年追踪数据,选取我国60岁及以上老年群体为研究对象,以虚弱指数表征健康结果,采用OLS回归和分位数回归的方法探讨与子女同住的居住模式对老年健康的影响及这一影响对不同虚弱程度的老年人是否匀质,通过滞后模型设计和倾向值匹配法控制可能存在的内生性问题。研究发现居住模式与虚弱指数存在显著的正向关系,表明居住模式会影响老年健康水平;与子女同住对老年人健康存在负面效应,而在父母附近分而不离的居住模式相较于与子女同住而言对老年人的健康更为有利;与子女同住对老年健康的这种负向影响对于不同虚弱程度的老年人而言是非线性、非匀质的,大致呈先增后降的倒U形分布,表明不同健康状况的老年人对子女的照料需求是不同的,这种影响在不同性别、城乡和年龄段的老年群体间各有差异。这就为与子女同住的居住模式提供了一些警示,与子女同住不能改变老年健康衰减的趋势,应尽量减少或规避可能增加老年人晚年健康负担的风险性因素,让"家"真正成为老年人安享晚年的港湾。     

BRASS' RELATIONAL MODEL: A STATISTICAL ANALYSIS

Brass' relational model is based on a linear relationship between the logits of the cumulative probability of dying before age x in a standard mortality distribution and those observed in any population. In this study the appropriate way to estimate the linear parameters associated with Brass' model is clarified. Five methods are presented to estimate the coefficients associated with Brass' relational model. Each method is applied to simulated data to examine the efficiencies of each model in mortality estimation.     

Child mortality in rural India

This paper focuses on infant and child mortality in rural areas of India. We construct a flexible duration model, which allows for frailty at multiple levels and interactions between the child’s age and individual, socioeconomic, and environmental characteristics. The model is estimated using the Indian National Family and Health Survey 1998/1999. The estimation results show that socioeconomic and environmental characteristics have significantly different impacts on mortality rates at different ages. These are particularly important immediately after birth. The parameter estimates indicate that child mortality can be reduced substantially, particularly by improving the education of women, providing safe water, and reducing indoor air pollution caused by dirty cooking fuels. Finally, we still found substantial differences in mortality rates between states, which are associated with differences in schooling expenditures, female immunization, and poverty rates.     

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.     

The influence of the farm size on the parity of a farming family in Poland

This paper aims at statistical identification of the relationship between the parity of farming families and the area of the farm and the role this variable plays among variables describing the model of families' parity. To reach this objective results of a questionnaire survey were used, one performed among the group of individual farmers' families keeping agricultural accounting in 1985. The analysis covered 1291 rural farming couples who married in the years 1920-1984. According to the results obtained, the thesis posed by W. Stys with regard to positive relationships between parity in a family and the farm's area only relates to marriages entered into between 1920-1964. In single five-year marriage cohorts, a change of shape of this relationship was observed. It took the shape of a parabolic function or polynomial of the third order. The research results showed that in marriage cohorts with finished fertility, variable area of the farm turned out to be almost insignificant in explaining changes in the number of live born children compared to other demographic factors, especially cultural and demographic ones.     

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.     

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.     

The Association Between Individual Income and Remaining Life Expectancy at the Age of 65 in the Netherlands

This article quantifies the association between individual income and remaining life expectancy at the statutory retirement age (65) in the Netherlands. For this purpose, we estimate a mortality risk model using a large administrative data set that covers the 1996–2007 period. Besides age and marital status, the model includes as covariates individual and spouse’s income as well as a random individual specific effect. It thus allows for dynamic selection based on both observed and unobserved characteristics. We find that conditional on marital status, individual income is about equally strong and negatively associated with mortality risk for men and women and that spouse’s income is only weakly associated with mortality risk for women. For both men and women, we quantify remaining life expectancy at age 65 for low-income individuals as approximately 2.5 years less than that for high-income individuals.