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.
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.
A fundamental question in aging research is whether humans and other species possess an immutable life-span limit. We examined the maximum age at death in Sweden, which rose from about 101 years during the 1860s to about 108 years during the 1990s. The pace of increase was 0.44 years per decade before 1969 but accelerated to 1. 11 years per decade after that date. More than 70 percent of the rise in the maximum age at death from 1861 to 1999 is attributable to reductions in death rates above age 70. The rest are due to increased numbers of survivors to old age (both larger birth cohorts and increased survivorship from infancy to age 70). The more rapid rise in the maximum age since 1969 is due to the faster pace of old-age mortality decline during recent decades.
Using data from the Human Mortality Database for 29 high-income national populations (1751-2004), we review trends in the sex differential in e(0). The widening of this gap during most of the 1900s was due largely to a slower mortality decline for males than females, which previous studies attributed to behavioural factors (e.g., smoking). More recently, the gap began to narrow in most countries, and researchers tried to explain this reversal with the same factors. However, our decomposition analysis reveals that, for the majority of countries, the recent narrowing is due primarily to sex differences in the age pattern of mortality rather than declining sex ratios in mortality: the same rate of mortality decline produces smaller gains in e(0) for women than for men because women's deaths are less dispersed across age (i.e., survivorship is more rectangular).
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.
A demographic measure is often expressed as a deterministic or stochastic function of multiple variables (covariates), and a general problem (the decomposition problem) is to assess contributions of individual covariates to a difference in the demographic measure (dependent variable) between two populations. We propose a method of decomposition analysis based on an assumption that covariates change continuously along an actual or hypothetical dimension. This assumption leads to a general model that logically justifies the additivity of covariate effects and the elimination of interaction terms, even if the dependent variable itself is a nonadditive function. A comparison with earlier methods illustrates other practical advantages of the method: in addition to an absence of residuals or interaction terms, the method can easily handle a large number of covariates and does not require a logically meaningful ordering of covariates. Two empirical examples show that the method can be applied flexibly to a wide variety of decomposition problems. This study also suggests that when data are available at multiple time points over a long interval, it is more accurate to compute an aggregated decomposition based on multiple subintervals than to compute a single decomposition for the entire study period.
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.
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