Atechnique for estimating life expectancy with crude vital rates

This paper describes a method of estimating life expectancy at birth on the basis of crude vital rates. The method is derived from stable population theory and it furnishes good estimates insofar as the current crude vital rates of a population are close to its intrinsic rates. This condition is generally met in closed populations which have not experienced sharp movements in fertility. The method is useful for estimating life expectancy in developing nations with good sample registration systems but for which information on age is of poor quality. It is also useful for estimating the movement of life expectancy in certain European nations in the period prior to regular census taking. There are a number of nations and regions in Europe for which long series of birth and death rates are available but for which census age counts are widely spaced.     

An empirical model to predict arsenic pollution affected life expectancy

A robust, globally implementable and simple empirical model to predict the arsenic pollution affected life expectancy using a stepwise regression was developed. Life expectancy calculated using a life table technique requires crude death rates data that are not available for small administrative units, complex calculations and does not consider socioeconomic parameters. Hence, a model was needed to forecast the impact of arsenic pollution and socioeconomic parameters on life expectancy for locations with limited data availability. A linear multiple regression technique was used to develop an empirical model to predict arsenic pollution affected life expectancy at birth. The model was calibrated using nine arsenic polluted administrative blocks of district Murshidabad, West Bengal, India and tested independently for three other arsenic polluted blocks of the same district. The R ² values for the plot of actual versus predicted life expectancy at birth were 0.98 for calibration, testing and independent validation. The model is complementary to the life table technique and offers a means to assist planning by public health engineers and health policy makers to mitigate arsenic pollution on a community priority basis.     

Trends in senescent life expectancy

The distinction between senescent and non-senescent mortality proves to be very valuable for describing and analysing age patterns of death rates. Unfortunately, standard methods for estimating these mortality components are lacking. The first part of this paper discusses alternative methods for estimating background and senescent mortality among adults and proposes a simple approach based on death rates by causes of death. The second part examines trends in senescent life expectancy (i.e., the life expectancy implied by senescent mortality) and compares them with trends in conventional longevity indicators between 1960 and 2000 in a group of 17 developed countries with low mortality. Senescent life expectancy for females rises at an average rate of 1.54 years per decade between 1960 and 2000 in these countries. The shape of the distribution of senescent deaths by age remains relatively invariant while the entire distribution shifts over time to higher ages as longevity rises.     

Recent perspectives on active life expectancy for older women

This article provides a critical review of recent active life expectancy literature, describing trends of special interest to women. We review findings from leading perspectives used to study life expectancy and active life expectancy, including gender, racial and socioeconomic differences, disease-specific effects, and biodemography. We examine three competing theories of population health that frame active life expectancy research-compression of morbidity, expansion of morbidity, and dynamic equilibrium-concluding there is support for both the compression of morbidity and dynamic equilibrium theories. Policy implications for women include a greater understanding of the role of education and racial and ethnic diversity in active life trends, and an increased public policy emphasis on prevention and treatment of chronic disease, together with adoption of more healthy lifestyles.     

Global patterns of healthy life expectancy for older women

This paper focuses on patterns of healthy life expectancy for older women around the globe in the year 2000, and on the determinants of differences in disease and injury for older ages. Our study uses data from the World Health Organization for women and men in 191 countries. These data include a summary measure of population health, healthy life expectancy (HALE), which measures the number of years of life expected to be lived in good health, and a complementary measure of the loss of health (disability-adjusted life years or DALYs) due to a comprehensive set of disease and injury causes. We examine two topics in detail: (1) cross-national patterns of female-male differences in healthy life expectancy at age 60; and (2) identification of the major injury and disability causes of disability in women at older ages. Globally, the male-female gap is lower for HALE than for total life expectancy. The sex gap is highest for Russia (10.0 years) and lowest in North Africa and the Middle East, where males and females have similar levels of healthy life expectancy, and in some cases, females have lower levels of healthy life expectancy. We discuss the implications of the findings for international health policy.     

Diet,mortality and life expectancy A cross national analysis

There are numerous reasons why mortality and life expectancy vary between countries. Epidemiological studies seem to indicate that dictary variations may be among them. A sample of 51 countries studied with data from the International Comparisons Project and other sources, shows that after controlling for nutrient intake, consumption of medical goods and services, income distribution, weather, and literacy, countries with more meat and poultry in their diet have lower life expectancies after age five. The results for infant mortality and child death between one and five indicate that a more animal-intensive diet may be actually be beneficial, especially if fish consumption is increased and meat and poultry consumption reduced.I thank Jere Behrman, David Crawford, Anil Deolalikar, the Managing Editor, two anonymous referees, and especially Samuel Preston for valuable comments, and Alan Heston and Robert Summers for being generous with their time and their data. Financial support was provided by a Compton Foundation Fellowship. All errors remain my responsibility.     

Trends in life expectancy in wellbeing

Objectives: This paper describes anddiscusses trends in life expectancy inwellbeing between 1989 and 1998.Methods: Data on wellbeing by theBradburn Affect Balance Scale is obtained fromthe Netherlands Continuous Health InterviewSurveys for the calendar years from 1989 to1998. Using Sullivan's method, life expectancyin wellbeing is calculated.Results: For males at the age of 16, lifeexpectancy in wellbeing increases significantlyfrom 52.7 years in 1989 (90.1% of the totallife expectancy) to 54.4 years in 1998(90.8%). This increase is almost completelycaused by the increase in total lifeexpectancy. For females at the age of 16, lifeexpectancy in wellbeing raises significant from54.4 years in 1989 (84.1%) to 56.2 years in1998 (86.3%). This increase is almostcompletely caused by a decrease in the numberof years in a state of distress.For both males and females at the age of 65,the significant increase of life expectancy inwellbeing exceeds the increase in total lifeexpectancy and is mainly caused by the decreasein number of years in distress.Conclusion: Contrary to life expectancyin good perceived health and to disability freelife expectancy – which show a decreasing trend– the overall wellbeing of the population isincreasing. It seems that aspects in human lifethat contribute to wellbeing or quality of lifeother than physical health are gaining inimportance. This makes life expectancy inwellbeing a less appropriate instrument tomonitor changes in population health, but auseful instrument to measure population qualityof life.     

A model for estimating adolescent sterility among married women

A model to estimate adolescent sterility among married women is presented using the principle of convex combination of two or more probability density functions.     

On the decomposition of life expectancy and limits to life

Life expectancy is a measure of how long people are expected to live and is widely used as a measure of human development. Variations in the measure reflect not only the process of ageing but also the impacts of such events as epidemics, wars, and economic recessions. Since 1950, the influence of these events in the most developed countries has waned and life expectancy continues to lengthen unabated. As a result, it has become more difficult to forecast long-run trends accurately, or identify possible upper limits. We present new methods for comparing past improvements in life expectancy and also future prospects, using data from five developed, low-mortality countries. We consider life expectancy in 10-year age intervals rather than over the remaining lifetime, and show how natural limits to life expectancy can be used to extrapolate trends. We discuss the implications and compare our approach with other commonly used methods.

Supplementary material for this article is available at: http://dx.doi.org/10.1080/00324728.2014.972433     

[Age-specific mortality and life expectancy].]

The author attempts to assess the degree of influence of infant mortality on average life expectancy and to develop a method to directly revise average life expectancy given a change in mortality.     

Forecasting differences in life expectancy by education

Forecasts of life expectancy (LE) have fuelled debates about the sustainability and dependability of pension and healthcare systems. Of relevance to these debates are inequalities in LE by education. In this paper, we present a method of forecasting LE for different educational groups within a population. As a basic framework we use the Li–Lee model that was developed to forecast mortality coherently for different groups. We adapted this model to distinguish between overall, sex-specific, and education-specific trends in mortality, and extrapolated these time trends in a flexible manner. We illustrate our method for the population aged 65 and over in the Netherlands, using several data sources and spanning different periods. The results suggest that LE is likely to increase for all educational groups, but that differences in LE between educational groups will widen. Sensitivity analyses illustrate the advantages of our proposed method.     

Steep increase in best-practice cohort life expectancy

We analyze trends in best-practice life expectancy among female cohorts born from 1870 to 1950. Cohorts experience declining rather than constant death rates, and cohort life expectancy usually exceeds period life expectancy. Unobserved mortality rates in non-extinct cohorts are estimated using the Lee-Carter model for mortality in 1960–2008. Best-practice cohort and period life expectancies increased nearly linearly. Across cohorts born from 1870 to 1920 the annual increase in cohort length of life was 0.43 years. Across calendar years from 1870 to 2008, the annual increase was 0.28 years. Cohort life expectancy increased from 53.7 years in the 1870 cohort to 83.8 years in the 1950 cohort. The corresponding cohort/period longevity gap increased from 1.2 to 10.3 years. Among younger cohorts, survival to advanced ages is substantially higher than could have been anticipated by period mortality regimes when these cohorts were young or middle-aged. A large proportion of the additional expected years of life are being lived at ages 65 and older. This substantially changes the balance between the stages of the life cycle.     

A simple equation for estimating the expectation of life at old ages

Abstract There is much direct and indirect evidence that in a number of populations the ages of older persons tend to be exaggerated, both when reported in censuses and in records of deaths. This results in overestimated expectations of life at old ages. The bias may be corrected by estimating the expectation of life at age a, e(a), from the mortality rate and growth rate at age a and above, M(a+) and r(a+), using the equation developed in this paper: 1/ê(a) = M(a+) exp (β . r(a+). M(a+)(-α)). For a ?, 65, α = 1.4 and β = 0.0951 have been chosen. The value of the equation rests on the following: since ages of older persons tend to be exaggerated, there may be an age a such that most age transfer occurs above that age, and age transfer across the age is small or cancels, so that reasonably accurate values of M(a+) and r(a +) can be obtained, even though ages are badly reported above a. The analysis of artificial data on Gompertzian stable popultions aged over 50 and actual statistics for some selected populations has suggested that the equation provides quite accurate estimates of e(a). The equation also seems useful in closing life tables, since it provides a value of e(a) for the highest age group.     

A norm-referenced population health status index based on life expectancy and disability

This paper describes a population health status index for health services research and planning purposes. The H-index uses data on average life expectancy at birth and percent of the population free from disability, however defined. It is useful in comparing the health status of health services areas relative to that of the more healthy areas selected to serve as the norm. The statistical procedure used in deriving the H-index is centour analysis, by means of which the Euclidian distances of the service areas in the study sample in two-dimensional space to the centroid of the normative areas are reflected in the H values computed. The farther away from the centroid, the less resemblance the service area has to the norm and the lower its health status. A computational example with seven normative states and 10 states in the study sample is given.     

The relationship between the life table method and the formula for calculating life expectancy]

The author states that average life expectancy can be determined either by life table methods or by mathematical equations. An attempt is made to prove that the life table method is an approximation of first degree to the equation method. Some inherent contradictions in the concept of average life expectancy are considered.     

A regression approach to estimating the average number of persons per household

In the housing unit method, population is calculated as the number of households times the average number of persons per household (PPH), plus the population residing in group quarters facilities. Estimates of households and the group quarters population can be derived directly from concurrent data series, but estimates of PPH have traditionally been based on previous values or estimates for larger areas. In our study, we developed several regression models in which PPH estimates were based on symptomatic indicators of PPH change. We tested these estimates using county-level data in four states and found them to be more precise and less biased than estimates based on more commonly used methods.     

How slowing senescence translates into longer life expectancy

Mortality decline has historically been largely a result of reductions in the level of mortality at all ages. A number of leading researchers on ageing, however, suggest that the next revolution of longevity increase will be the result of slowing down the rate of ageing. In this paper, we show mathematically how varying the pace of senescence influences life expectancy. We provide a formula that holds for any baseline hazard function. Our result is analogous to Keyfitz's 'entropy' relationship for changing the level of mortality. Interestingly, the influence of the shape of the baseline schedule on the effect of senescence changes is the complement of that found for level changes. We also provide a generalized formulation that mixes level and slope effects. We illustrate the applicability of these models using recent mortality decline in Japan and the problem of period to cohort translation.     

Estimating Indigenous life expectancy: pitfalls with consequences

The methods used by the Australian Bureau of Statistics (ABS) to estimate life expectancies of Aboriginal and Torres Strait Islander peoples in 2009 have been controversial and require critical and sensitive analysis. The introduction by ABS of the direct method for estimating Indigenous life expectancies, based on estimated deaths and populations, has been generally welcomed. But the way this method has been applied and, in particular, death estimates used by the ABS, warrant scrutiny. These estimates were based on a first ever linkage between Indigenous deaths and census records following the 2006 census. Census-based identification was used in place of identification in the death registrations, rather than as a supplementary data source. The various national, state and regional life expectancy estimates published may have been biased upwards by this process. Because the impact of the methodology varies across Australia, regional differentials reported appear substantial but are not soundly based. The questionable ABS results are highlighted and discussed. Analysis based on more comprehensive linkage of death records in New South Wales over 5?years suggests that the ABS methods have understated Indigenous deaths and so overstated life expectancy. The effect of an alternative ABS approach is also discussed. ABS estimates published in 2009 are not necessarily definitive and may well overestimate Aboriginal and Torres Strait Islander life expectancy and underestimate the life expectancy gap. Estimates should be based on accurate estimates of deaths and population. Consultation and a thorough review are essential before the next round of estimates following the findings of the 2011 population census. Closing the Gap commitments focus on eliminating the life expectancy gap between Aboriginal and Torres Strait Islander peoples and other Australians. Life expectancy estimates need to be based on methods and data that are well understood and broadly supported. The alternative is unproductive debate about statistics rather than the range of policies and resourcing issues needed to improve Indigenous health.     

A new method for correcting under-estimation of disabled life expectancy and an application to the chinese oldest-old

This article demonstrates that disabled life expectancies that are based on conventional multistate life-table methods are significantly underestimated because of the assumption of no changes in functional status between age x and death. We present a new method to correct the bias and apply it to data from a longitudinal survey of about 9,000 oldest-old Chinese aged 80-105 collected in 1998 and 2000. In our application, the age trajectories of disability (activities of daily living--ADL), status-specific death rates, and the probabilities of transitions between ADL states of the oldest-old were investigated for the first time in a developing country. In this article, we report estimates of bias-corrected disabled and active life expectancies of the Chinese oldest-old and demonstrate patterns of large differences associated with initial status, gender, and advances in ages. Using combined information on ADL disabilities and length of having been bedridden before dying, we analyze gender and age patterns of the extent of morbidity before dying among the oldest-old and their implications for debates on the hypothesis of compression of morbidity.