中国高龄死亡模式及其与瑞典、日本的比较分析

本文发现只有二个参数的莰尼斯托 (Kannisto)模型 (即简化的罗吉斯特模型 )对中国高龄老人死亡率的拟合效果好于其他五个模型。中国与瑞典、日本 96岁以上的年龄别死亡率比较相近 ,而中国 96岁以下的年龄别死亡率显著高于瑞典、日本。我们认为这一有趣的趋同现象可能主要是由中国高龄老人“劣淘优存”的选择性更强而形成的。我们还发现与发达国家模式类似 ,中国的死亡率随着年龄增加而升高的趋势在 96岁以后的特高年龄段减缓。     

Divergence in Age Patterns of Mortality Change Drives International Divergence in Lifespan Inequality

In the past six decades, lifespan inequality has varied greatly within and among countries even while life expectancy has continued to increase. How and why does mortality change generate this diversity? We derive a precise link between changes in age-specific mortality and lifespan inequality, measured as the variance of age at death. Key to this relationship is a young–old threshold age, below and above which mortality decline respectively decreases and increases lifespan inequality. First, we show for Sweden that shifts in the threshold’s location have modified the correlation between changes in life expectancy and lifespan inequality over the last two centuries. Second, we analyze the post–World War II (WWII) trajectories of lifespan inequality in a set of developed countries—Japan, Canada, and the United States—where thresholds centered on retirement age. Our method reveals how divergence in the age pattern of mortality change drives international divergence in lifespan inequality. Most strikingly, early in the 1980s, mortality increases in young U.S. males led to a continuation of high lifespan inequality in the United States; in Canada, however, the decline of inequality continued. In general, our wider international comparisons show that mortality change varied most at young working ages after WWII, particularly for males. We conclude that if mortality continues to stagnate at young ages yet declines steadily at old ages, increases in lifespan inequality will become a common feature of future demographic change.     

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.     

Separating the Signal From the Noise: Evidence for Deceleration in Old-Age Death Rates

Widespread population aging has made it critical to understand death rates at old ages. However, studying mortality at old ages is challenging because the data are sparse: numbers of survivors and deaths get smaller and smaller with age. I show how to address this challenge by using principled model selection techniques to empirically evaluate theoretical mortality models. I test nine models of old-age death rates by fitting them to 360 high-quality data sets on cohort mortality after age 80. Models that allow for the possibility of decelerating death rates tend to fit better than models that assume exponentially increasing death rates. No single model is capable of universally explaining observed old-age mortality patterns, but the log-quadratic model most consistently predicts well. Patterns of model fit differ by country and sex. I discuss possible mechanisms, including sample size, period effects, and regional or cultural factors that may be important keys to understanding patterns of old-age mortality. I introduce mortfit, a freely available R package that enables researchers to extend the analysis to other models, age ranges, and data sources.     

The Methuselah Effect: The Pernicious Impact of Unreported Deaths on Old-Age Mortality Estimates

We examine inferences about old-age mortality that arise when researchers use survey data matched to death records. We show that even small rates of failure to match respondents can lead to substantial bias in the measurement of mortality rates at older ages. This type of measurement error is consequential for three strands in the demographic literature: (1) the deceleration in mortality rates at old ages; (2) the black-white mortality crossover; and (3) the relatively low rate of old-age mortality among Hispanics, often called the “Hispanic paradox.” Using the National Longitudinal Survey of Older Men matched to death records in both the U.S. Vital Statistics system and the Social Security Death Index, we demonstrate that even small rates of missing mortality matching plausibly lead to an appearance of mortality deceleration when none exists and can generate a spurious black-white mortality crossover. We confirm these findings using data from the National Health Interview Survey matched to the U.S. Vital Statistics system, a data set known as the “gold standard” (Cowper et al. 2002) for estimating age-specific mortality. Moreover, with these data, we show that the Hispanic paradox is also plausibly explained by a similar undercount.     

Deceleration in the age pattern of mortality at olderages

The rate of mortality increase with age tends to slow down at very old ages. One explanation proposed for this deceleration is the selective survival of healthier individuals to older ages. Data on mortality in Sweden and Japan are generally compatible with three predictions of this hypothesis: (1) decelerations for most major causes of death; (2) decelerations starting at younger ages for more “selective” causes; and (3) a shift of the deceleration to older ages with declining levels of mortality. A parametric model employed to illustrate the third prediction relies on the distinction between senescent and background mortality. This dichotomy, though simplistic, helps to explain the observed timing of the deceleration.     

Continued Reductions in Mortality at Advanced Ages

Mortality data for 30 mostly developed countries available in the Kannisto–Thatcher Database on Old‐Age Mortality (KTDB) are drawn on to assess the pace of decline in death rates at ages 80 years and above. As of 2004 this database recorded 37 million persons at these ages, including 130,000 centenarians (more than double the number in 1990). For men, the probability of surviving from age 80 to age 90 has risen from 12 percent in 1950 to 26 percent in 2002; for women, the increase has been from 16 percent to 38 percent. In the lowest‐mortality country, Japan, life expectancy at age 80 in 2006 is estimated to be 6.5 years for men and 11.3 years for women. For selected countries, average annual percent declines in age‐specific death rates over the preceding ten years are calculated for single‐year age groups 80 to 99 and the years 1970 to 2004. The results are presented in Lexis maps showing the patterns of change in old‐age mortality by cohort and period, and separately for men and women. The trends are not favorable in all countries: for example, old‐age mortality in the United States has stagnated since 1980. But countries with exceptionally low mortality, like Japan and France, do not show a deceleration in death rate declines. It is argued that life expectancy at advanced ages may continue to increase at the same pace as in the past.     

Effects of targets and aggregation on the propagation of error in mortality forecasts

Official forecasts of mortality depend on assumptions about target values for the future rates of decline in mortality rates. Smooth functions connect the jump‐off (base‐year) mortality to the level implied by the targets. Three alternative sets of targets are assumed, leading to high, middle, and low forecasts. We show that this process can be closely modeled using simple linear statistical models. These explicit models allow us to analyze the error structure of the forecasts. We show that the current assumption of perfect correlation between errors in different ages, at different forecast years, and for different causes of death, is erroneous. An alternative correlation structure is suggested, and we show how its parameters can be estimated from the past data.

The effect of the level of aggregation on the accuracy of mortality forecasts is considered. It is not clear whether or not age‐ and cause‐specific analyses have been more accurate in the past than analyses based on age‐specific mortality alone would have been. The major contribution of forecasting mortality by cause appears to have been in allowing for easier incorporation of expert opinion rather than in making the. data analysis more accurate or the statistical models less biased.     

Extending the Lee-Carter Method to Model the Rotation of Age Patterns of Mortality Decline for Long-Term Projections

In developed countries, mortality decline is decelerating at younger ages and accelerating at old ages, a phenomenon we call “rotation.” We expect that this rotation will also occur in developing countries as they attain high life expectancies. But the rotation is subtle and has proved difficult to handle in mortality models that include all age groups. Without taking it into account, however, long-term mortality projections will produce questionable results. We simplify the problem by focusing on the relative magnitude of death rates at two ages (0 and 15–19) while making assumptions about changes in rates of decline at other ages. We extend the Lee-Carter method to incorporate this subtle rotation in projection. We suggest that the extended Lee-Carter method could provide plausible projections of the age pattern of mortality for populations, including those that currently have very high life expectancies. Detailed examples are given using data from Japan and the United States.     

Unobserved Heterogeneity Can Confound the Effect of Education on Mortality

Two opposing hypotheses were proposed to explain the life course pattern in the effect of education on mortality: “cumulative advantage,” where the education effect becomes stronger with age, and “age-as-leveler,” where the effect becomes weaker in old age. Most empirical studies bring evidence for the latter hypothesis, but the observed convergence of mortality patterns could be an artifact of selective mortality due to unobserved heterogeneity. A simulation shows that unobserved heterogeneity can bias the estimated effect of education downward so that the cohort-average effect of education decreases in old age regardless of the shape of the underlying subject-specific trajectory.     

A description of the extreme aged population based on improved medicare enrollment data

The mortality and size of the extreme aged population can be studied most accurately with Medicare enrollment data from the Social Security Administration's Master Beneficiary Record after certain types of questionable records are eliminated. With the improved data base we find that mortality rates at the very old ages are higher than published rates, we are more confident of the reality of the race crossover, and we can estimate the number of centenarians more accurately. Furthermore, a large matched-records study shows close agreement on age at death between the Master Beneficiary Record and the death certificate.     

Rectangularization revisited: Variability of age at death within human populations*

Rectangularization of human survival curves is associated with decreasing variability in the distribution of ages at death. This variability, as measured by the interquartile range of life table ages at death, has decreased from about 65 years to 15 years since 1751 in Sweden. Most of this decline occurred between the 1870s and the 1950s. Since then, variability in age at death has been nearly constant in Sweden, Japan, and the United States, defying predictions of a continuing rectangularization. The United States is characterized by a relatively high degree of variability, compared with both Sweden and Japan. We suggest that the historical compression of mortality may have had significant psychological and behavioral impacts.     

A method for deriving mortality estimates from incomplete vital Statistics

Summary Although they are available in many developing countries vital registration records are very little used for mortality estimation which is still mainly based on census returns. However, defective death records may yield accurate estimations of mortality. This procedure requires few data only; a sex-age distribution of the population (preferably at the middle of a period) and a sexage distribution of deaths, either derived from vital records or from census returns to questions relating to deaths during the preceding twelve months. This method is based on the observation that for a fixed age structure of the population, there is a one-one relation between the age structure of deaths (measured by the proportion of deaths at older ages) and the level of mortality (measured by the death rate above a certain minimum age). It is assumed that at ages above this minimum the rate of underregistration of deaths does not vary significantly with age. Therefore, the age distribution of registered deaths makes it possible to estimate the true proportion of deaths at older ages. This in its turn will permit the estimation of the true level of mortality, because of the relation which exists between age structure of deaths and level of mortality. The true level is then compared with the observed, to estimate the rate of underregistration, and observed age-specific death rates can be adjusted in the light of this knowledge.     

Children’s educational attainment,occupation, and income and their parents’ mortality

Using data from Finland, this paper contributes to a small but growing body of research regarding adult children's education, occupation, and income and their parents' mortality at ages 50+ in 1970–2007. Higher levels of children's education are associated with 30–36 per cent lower parental mortality at ages 50–75, controlling for parents' education, occupation, and income. This association is fully mediated by children's occupation and income, except for cancer mortality. Having at least one child educated in healthcare is associated with 11–16 per cent lower all-cause mortality at ages 50–75, an association that is largely driven by mortality from cardiovascular diseases. Children's higher white-collar occupation and higher income is associated with 39–46 per cent lower mortality in the fully adjusted models. At ages 75+, these associations are much smaller overall and children's schooling remains more strongly associated with mortality than children's occupation or income.     

Diverging Trends in Female Old‐Age Mortality: The United States and the Netherlands versus France and Japan

In the most advanced countries, child mortality and adult mortality under age 65 years have fallen so low that further improvement in life expectancy relies almost completely on the decline of mortality at older ages. This phenomenon is particularly pronounced among women, who are far ahead of men in survival rates. Thus, to project the future of life expectancy, this study focuses on trends in female life expectancy at ages 65 and older. Four countries are selected for this analysis: the United States, Netherlands, France, and Japan. It is particularly interesting to understand why American and Dutch trends in female old‐age mortality have been diverging from those in France and Japan for two decades. It is shown here that most of the divergence derives from the fact that decline in cardiovascular mortality is more and more offset by increases in other causes of death in the United States and the Netherlands, while the other two countries are more successful in reducing mortality from all causes at increasingly older ages. This latter phenomenon could represent a new stage of the health transition.     

Mortality in England and Wales from 1848 to 1947

This is a survey of the changing causes of death in England and Wales during the past 100 years. Based on the published mortality statistics of the General Register Office the framework of the survey is a series of specially prepared tables of death rates by sex, age and cause of death for the periods 1848–72, 1901–10, 1921, 1931, 1939 and 1947. Adjustments were made wherever necessary to compensate for changes in medical nomenclature and in the statistical classification of disease.

After allowance has been made for the changing age structure of the population, the male death rate at all ages in 1947 was 42% of the rate in 1846–50, and the female rate 35 %. Maximum improvement was among girls aged 5–9 years, whose death rate in 1947 was 9% of the rate 100 years before.

In 1848–72 the group to which were allocated the largest proportion of the deaths at all ages were the infectious diseases with one-third of the total; and these were followed by the respiratory, nervous and digestive diseases. In 1947, on the other hand, diseases of the circulatory system came first with rather more than one-third of the total at all ages, and these were followed by cancer.

Changes in proportionate mortality rates from various causes have been examined at successive ages from infancy to old age. There was a decline in proportionate mortality from the infectious diseases other than tuberculosis, but increased mortality from tuberculosis in the younger age groups and from violence, circulatory diseases and cancer.

The trends of absolute mortality from the various causes were also studied. The reduction in total mortality was such that whereas there were half a million deaths of civilians registered in England and Wales in 1947, the total would have been over a million had the death rates of 1848–72 still prevailed.

The article concludes with a brief review of the factors responsible for the changes that have taken place.     

Revised regional model life tables at very low levels of mortality

This paper presents and discusses new model life tables at very low mortality, which make use of age-specific death rates from the 1960s, 1970s, and 1980s. These life tables fit recorded death rates in very low mortality populations better than do the existing ones at expectations of life of 77.5 and 80 years. The old tables incorporate too-high mortality at the higher ages and in infancy and they incorporate regional differences that no longer exist. The new tables "close out" the mortality schedules above age 80 more realistically. The convergence of age patterns of mortality at very high life expectancies in populations that used to conform to different families is in itself of demographic interest. Some convergence may perhaps be expected. Sullivan (1973) found that, in Taiwan, the comparison of mortality at ages 1-5 to mortality at 5-35 in the late 1950s showed higher mortality at the younger ages relative to the ensuing 30-year age interval than was found in any of the models, including the South model, which has the highest relative mortality from ages 1-5 among the 4 regional patterns. Then, in the late 1960s, the relation of mortality at 1-5 to mortality at 5-35 in Taiwan fell to a position intermediate between the West and South tables. Sullivan found in data on mortality by cause of death a large reduction in mortality from diarrhea and enteritis, no doubt as a result of environmental sanitation. Mortality from these causes is concentrated among young children, and reduction in deaths from these causes would naturally diminish the excess mortality in this age interval. The East pattern, characterized by very high mortality in infancy (but not from 1-5), may be the result of the prevalence of early weaning or avoidance of breast feeding altogether in the populations characterized by this pattern. As health conditions have improved, evidenced by the overall design of mortality, these special factors are diminished or erased. Model life tables at these very low mortality levels have different uses from most applications of model life tables at higher mortality. The use of model tables to estimate accurate schedules of mortality when the basic data are incomplete or inaccurate is less relevant in this range of mortality levels.     

Far eastern patterns of Mortality

Summary In this paper a mortality pattern is identified which has not previously been described by model mortality schedules and seems to have occurred only in populations in the Far East. Mortality schedules in Taiwan, Hong Kong, Singapore, and Korea during the past several decades have been characterized by excessively high death rates of men at the older ages. This excess mortality has progressively diminished and most recent death rates for men show only slight deviations from West model life tables. An examination of statistics on causes of death suggests that tuberculosis is at least partly responsible for the excess mortality of men.     

Economic Stress, Quality of Life, and Mortality for the Oldest-Old in China

China??s oldest old population is estimated to quadruple by 2050. Yet, poverty rate for the oldest old has been the highest among all age groups in China. This paper investigates the relationship between economic stress, quality of life, and mortality among the oldest-old in China. Both objective economic hardships and perceived economic strain are examined. We base our investigation on data drawn from the Chinese Longitudinal Healthy Longevity Survey conducted between 2000 and 2005. Our sample includes 10,972 men and women between the ages of 80 and 105 in 2000. The data show that about 16% of these oldest-old lived under economic stress in 2000. The risk factors that make one vulnerable to economic stress include age, being male, being widowed or never married, being a minority member, having no education, having no living children, and not having children as main source of income, and having no pension. Economic stress is negatively associated with indicators of quality of life, such as the quality of medical care and mental well-being. The poor quality of life contributes to the higher mortality rate for the oldest old who are under economic stress. Results also show that perceived economic strain increases the risk of mortality by 42% in rural areas, even after controlling for basic demographic characteristics, life style factors, and major health events.?For the rural oldest-old, having children as a main source of income and having access to pension alleviates the negative impact of economic hardship on mortality hazard by 23 and 66% respectively. However, in urban areas, economic stress has no direct impact on the hazard of mortality.