Three dimensions of the survival curve have been developed: (1) "horizontalization," which corresponds to how long a cohort and how many survivors can live before aging-related deaths significantly decrease the proportion of survivors; (2) "verticalization," which corresponds to how concentrated aging-related ("normal") deaths are around the modal age at death (M); and (3) "longevity extension," which corresponds to how far the highest normal life durations can exceed M. Our study shows that the degree of horizontalization increased relatively less than the degree of verticalization in Hong Kong from 1976 to 2001. After age normalization, the highest normal life durations moved closer to M, implying that the increase in human longevity is meeting some resistance.
This paper examines and demonstrates the importance of the adult modal age at death (M) in longevity research. Unlike life expectancy at birth (e 0) and median age at death, M is determined solely by old-age mortality as far as mortality follows a bathtub curve. It represents the location of old-age death heap in the age distribution of deaths, and captures mortality shifts more accurately than conditional life expectancies such as e 65. Although M may not be directly determined from erratic mortality data, a recently developed method for deriving M from the P-spline-smoothed mortality curve based on penalised Poisson likelihood is highly effective in estimating M. Patterns of trends and differentials in M can be noticeably different from those in other lifespan measures, as indicated in some examples. In addition, major mathematical models of adult mortality such as the Gompertz, logistic and Weibull models can be reformulated using M, which plays a critical role as the mortality level parameter in those models.
Kannisto (2001) has shown that as the frequency distribution of ages at death has shifted to the right, the age distribution of deaths above the modal age has become more compressed. In order to further investigate this old-age mortality compression, we adopt the simple logistic model with two parameters, which is known to fit data on old-age mortality well (Thatcher 1999). Based on the model, we show that three key measures of old-age mortality (the modal age of adult deaths, the life expectancy at the modal age, and the standard deviation of ages at death above the mode) can be estimated fairly accurately from death rates at only two suitably chosen high ages (70 and 90 in this study). The distribution of deaths above the modal age becomes compressed when the logits of death rates fall more at the lower age than at the higher age. Our analysis of mortality time series in six countries, using the logistic model, endorsed Kannisto’s conclusion. Some possible reasons for the compression are discussed.
This paper aims to examine changes in common longevity and variability of the adult life span, and attempts to answer whether or not the compression of mortality continues in Switzerland in the years 1876-2005. The results show that the negative relationships between the large increase in the adult modal age at death, observed at least from the 1920s, and the decrease in the standard deviation of the ages at deaths occurring above it, illustrate a significant compression of adult mortality. Typical adult longevity increased by about 10% during the last fifty years in Switzerland, and adult heterogeneity in the age at death decreased in the same proportion. This analysis has not found any evidence suggesting that we are approaching longevity limits in term of modal or even maximum life spans. It ascertains a slowdown in the reduction of adult heterogeneity in longevity, already observed in Japan and other low mortality countries.
This study shows a strong increase in the modal age at death (M) in Japan over a period of 50 calendar years, accompanied by a clear decrease in the standard deviation of ages at death above M (SD(M+)) until the 1990s for men and the mid-1980s for women. For the most recent periods SD(M+) appears to have stopped decreasing, even though M has continued to increase linearly. This stagnation in SD(M+) has been accompanied by stagnation in q(M). The number of deaths at M (d(M)) and the number of deaths at and above M (d(M+)) have increased, but significantly more slowly since the period 1975-79. Since the 1980s an acceleration in the increase of M+kSD(M+), our indicator of the longest life durations, has been essentially due to the pause in SD(M+). Our data do not suggest that we are approaching an upper limit in human longevity.
BackgroundHong Kong has one of the highest life expectancy rankings in the world. The number of centenarians and near-centenarians has been increasing locally and internationally. The relative growth of this population is a topic of immense importance for population and health policy makers. Living long and living well are two overlapping but distinct research topics. We previously conducted a quantitative study on 153 near-centenarians and centenarians to explore a wide range of biopsychosocial correlates of health and “living long”. This paper reports a follow-up qualitative study examining the potential correlates of “living well” among near-centenarians and centenarians in Hong Kong.MethodsSix cognitively, physically, and psychologically sound community-dwelling elders were purposively recruited from a previous quantitative study. Semi-structured interviews were conducted.ResultsFour major themes related to living long and well emerged from the responses of the participants: (a) Positive relations with others, (b) Positive events and happiness, (c) Hope for the future, and (d) Positive life attitude. Specifically, we found that having good interpersonal relationships, possessing a collection of positive life events, and maintaining salutary attitudes towards life are considered as important to psychological well-being by long-lived adults in Hong Kong. Most participants perceived their working life as most important to their life history and retired at very old ages.ConclusionsThese findings also shed light on the relationships between health, work, and old age.
The number of oldest old grew tremendously over the past few decades. However, recent studies have disclosed that the pace of increase strongly varies among countries. The present study aims to specify the level of mortality selection among the nonagenarians and centenarians living currently in five low mortality countries, Denmark, France, Japan, Switzerland, and Sweden, part of the 5-Country Oldest Old Project (5-COOP). All data come from the Human Mortality Database, except for the number of centenarians living in Japan. We disclosed three levels of mortality selection, a milder level in Japan, a stronger level in Denmark and Sweden and an intermediary level in France and Switzerland. These divergences offer an opportunity to study the existence of a trade-off between the level of mortality selection and the functional health status of the oldest old survivors which will be seized by the 5-COOP project.
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