Heterogeneity,dependence among causes of death and Gompertz

Heterogeneity in a population with respect to mortality, or variation in “frailty”; among members of that population, which has been discussed extensively in the literature over the last decade and a half is essential to any realistic model of dependence among causes of death. The main problem then is the development of a mortality model incorporating heterogeneity and cause of death which is both realistic and of manageable proportions.

In a recent paper (J. H. Pollard, 1991), it has been shown that many life table results are remarkably insensitive to the strict shape of the mortality curve, at least for more developed populations, and that accurate approximations can in many cases be obtained knowing only the mortality rates at two representative ages (e.g. 50 and 70). These results and the Gompertz “law”; of mortality can be used to develop manageable approximate formulae for the expectation of life under heterogeneity and correlation among the causes of death. The formulae are confirmed by simulation.

Numerical results indicate, somewhat surprisingly, that the effects of correlation among causes of death, even at quite high levels, on expectation of life and changes on expectation of life when particular causes of death are reduced or eliminated are relatively minor.     

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.     

The Relation Between Actual and Intrinsic Growth Rates

This paper demonstrates that, to a close approximation, the intrinsic growth rate of a population is equal to the mean of age-specific growth rates below age T, the mean length of a generation. This mean is normally close to the growth rate of the entire population block below age T. Therefore, when a disparity exists between the intrinsic growth rate and the actual growth rate of a population (whether or not net migration is included in both rates), it must be attributable to an unusual growth rate of the population block above age T. One implication is that the ‘momentum of population growth’ is entirely confined to the age span above T, approximately age 28 in developing countries to-day.     

Social Capital and Community Heterogeneity

Recent findings indicate that more pronounced community heterogeneity is associated with lower levels of social capital. These studies, however, concentrate on specific aspects in which people differ (such as income inequality or ethnic diversity). In the present paper, we introduce the number of parties in the local party system as a more encompassing measure of community heterogeneity. This builds on the argument that the number of relevant socio-economic cleavages in the population (i.e. heterogeneity) determines the level of party system fragmentation. Using data on 307 Flemish municipalities, we find that municipalities with a more heterogeneous population indeed have lower levels of social capital. Hence, our study endorses—and generalizes—previous results linking community heterogeneity to lower levels of social capital.

Comment on ‘The random variation in rates based on total enumeration of events’ by J. R. Udry,C. Teddlie,C. M. Suchindran

This comment builds on the work of Udry et al., developing a model of random variation of vital rates in small geographical areas. The model is based on the division of the variance of vital rates into three parts; that which would occur in a homogenous population; that due to population heterogeneity; and that due to yearly fluctuations in the underlying basis for the mean value of the probability of the vital event in question. Contrary to Udry et al., this model demonstrates that population heterogeneity must decrease the overall vital rate variance. Using birth rates presented in Udry et al., a test of the new model demonstrates the importance of the third factor, yearly fluctuations, in determining year-to-year variation in birth rates.     

Calculation of the expected lifetime lost due to an extra risk

Methods are given for estimating the average years of life lost when a person is discovered to be at risk from an extra hazard. The methods use the probability per year of the extra risk striking, and the mean and standard deviation of lifetime in the absence of the risk. The formulae are simple enough that only a hand‐held calculator is needed.     

First Exits from the Swedish Labor Market Due to Disability

Nowadays, with an increasingly aging population, an increasing proportion of the population on disability benefits, and an implicitly lower level of economic output and foregone tax revenue, disability has become a major public policy issue in many countries. Estimating both single risk and competing risks models on a Swedish longitudinal database, this study analyzes the risk of exit from the labor market due to disability at a certain age, conditional on having remained in the labor force until that age. The explanatory variables did not have identical coefficients across destination types. For example, the estimated single risk model shows that a higher level of education decreased the hazard of exiting the labor market with a disability pension, while the estimated competing risks model suggests that a higher level of education increased the hazard of exiting with a partial disability pension, but it decreased the hazard of exiting with a full disability pension.

Effects of Lactation on Post-partum Amenorrhoea: Re-estimation Using Data from a Longitudinal Study in Guatemala

In this paper we re-estimate the effects of breastfeeding patterns on the timing of resumption of menses after controlling for maternal nutrition and maternal stressor variables. The analysis shows that simple hazard models, used on data from a longitudinal study in Guatemala, provide estimates of effects on timing of resumption of menstruation that are (a) comparable to others discussed in the recent literature and (b) generally consistent with hypotheses relating patterns of lactation, maternal nutritional status, and maternal stressors to processes that accelerate (decelerate) resumption of anovulatory cycles.     

Multistate life‐tables and regression models

A survey is given of the use of modern statistical techniques in event history analysis, and in particular in the study of multi‐state life‐tables in demography. Emphasis is placed on the interplay between partial likelihood and nonparametric maximum likelihood based methods, a) when analysing semi‐Markov models or models with repeated spells, and b) in frailty models for inobservable heterogeneity.     

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.     

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.     

On a Pandemic Threshold Theorem of the Early Kermack–McKendrick Model with Individual Heterogeneity

A pandemic threshold theorem of the Kermack–McKendrick epidemic system with individual heterogeneity is proved from the definition of R ₀ by Diekmann, Heesterbeek, and Metz. The early Kermack–McKendrick epidemic model is extended to recognize individual heterogeneity, where the state variable indicates an epidemiological state or genetic, physiological, or behavioral characteristics such as risk of infection. With the basic reproduction number R ₀ for the heterogeneous population, the final size equation of the limit epidemic starting from a completely susceptible steady state at t = ?∞ has a unique positive solution if and only if R ₀  > 1. The main result is that the positive solution of the final size equation gives the lower bound of the intensity of any epidemic starting from a host population composed of susceptible and a few infected individuals who spread on a noncompact domain of the trait variable.     

A probability model for census adjustment

The census can be adjusted using capture‐recapture techniques: capture in the census, recapture in a special Post Enumeration Survey (PES) done after the census. The population is estimated using the Dual System Estimator (DSE). Estimates are made separately for demographic groups called post strata; adjustment factors are then applied to these demographic groups within small geographic areas. We offer a probability model for this process, in which several sources of error can be distinguished. In this model, correlation bias arises from behavioral differences between persons counted in the census and persons missed by the census. The first group may on the whole be more likely to respond to the PES: if so, the DSE will be systematically too low, and that is an example of correlation bias. Correlation bias is distinguished from heterogeneity, which occurs if the census has a higher capture rate in some geographic areas than others. Finally, ratio estimator bias and variance are considered. The objective is to clarify the probabilistic foundations of the DSE, and the definitions of certain terms widely used in discussing that estimator.     

Heterogeneity in the intergenerational transmission of educational attainment: evidence from Switzerland on natives and second-generation immigrants

This study applies rich data from the 2000 Swiss census to investigate the patterns of intergenerational education transmission for natives and second-generation immigrants. The level of secondary schooling attained by youth aged 17 is related to their parents’ educational outcomes based on data on the entire Swiss population. Extending economic theories of child educational attainment, we derive hypotheses regarding the patterns of intergenerational education transmission. The data yield substantial heterogeneity in intergenerational transmission across population groups. Only a small share of this heterogeneity is explained by the predictions of economic theory.

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.     

Ageing of a giant: a stochastic population forecast for China, 2006–2060

This paper presents a stochastic population forecast for China with a special emphasis on population ageing. The so-called scaled model for error was used to quantify the uncertainty attached to the population predictions. Data scarcity was a major problem in the specification of the expected error of the population forecast. Therefore, the error structures estimated for European countries were used with some modifications, taking into account the large size and heterogeneity of the Chinese population. The stochastic forecast confirms the expectation of extremely rapid population ageing during the first half of the twenty-first century in China. The old age dependency ratio (OADR) will certainly increase. Simply maintaining the current demographic rates (no international migration) would drive the OADR to 0.42 in 2060, four times the current level. Including expected declines in mortality and net outmigration in the projection would increase the median OADR in 2060 to 0.59, with a 80% prediction interval of [0.47, 0.75]. In particular, the oldest-old population will grow much faster than any other age group. This development has major implications for policy-making in China.

How responsive is U.S. population growth to immigration? A situational sensitivity analysis

There has been public concern about the effect of immigration on population growth in the U.S. But how responsive is population growth to immigration? This paper examines the sensitivity of intrinsic population growth to immigration and situates such sensitivity in fertility and survival changes. The application of second derivatives on a modified Leslie matrix facilitates the analysis of situational sensitivity of U.S. population growth to immigration. The results show that the sensitivity to immigration is not as influential as the sensitivity to fertility, and that the sensitivity to immigration further depends on changes in fertility and survival.     

Paperbark and pinard: A historical account of maternity care in one remote Australian Aboriginal town

Background and aimMaternity care in remote areas of the Australian Northern Territory is restricted to antenatal and postnatal care only, with women routinely evacuated to give birth in hospital. Using one remote Aboriginal community as a case study, our aim with this research was to document and explore the major changes to the provision of remote maternity care over the period spanning pre-European colonisation to 1996.MethodsOur research methods included historical ethnographic fieldwork (2007–2013); interviews with Aboriginal women, Aboriginal health workers, religious and non-religious non-Aboriginal health workers and past residents; and archival review of historical documents.FindingsWe identified four distinct eras of maternity care. Maternity care staffed by nuns who were trained in nursing and midwifery serviced childbirth in the local community. Support for community childbirth was incrementally withdrawn over a period, until the government eventually assumed responsibility for all health care.ConclusionsThe introduction of Western maternity care colonised Aboriginal birth practices and midwifery practice. Historical population statistics suggest that access to local Western maternity care may have contributed to a significant population increase. Despite population growth and higher demand for maternity services, local maternity services declined significantly. The rationale for removing childbirth services from the community was never explicitly addressed in any known written policy directive. Declining maternity services led to the de-skilling of many Aboriginal health workers and the significant community loss of future career pathways for Aboriginal midwives. This has contributed to the current status quo, with very few female Aboriginal health workers actively providing remote maternity care.     

Induced population growth and induced technological progress: Their interaction in the accelerating stage

A simple model of Malthusian population growth combined with population‐induced technological progress generates accelerating growth. The model may be relevant for a first stage of growth in which natural resource limitations can be overcome through technological progress; it is not applicable to a later stage in which resource constraints are more resistant. Parameter values are roughly inferred from historical experience. Exogenously more rapid population growth initially depresses income, perhaps for up to several centuries, then raises it without limit. More rapid population growth is desirable only when the social discount rate is less than the ratio of the parameters for induced technical progress and static diminishing returns. Imposed population fluctuations cause inverse movements in incomes, so that induced progress is very difficult to detect empirically even for population fluctuations up to 500 years.     

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.