Abstract

Patterns of diversity in age at death are examined using e, a dispersion measure that equals the average expected lifetime lost at death. We apply two methods for decomposing differences in e. The first method estimates the contributions of average levels of mortality and mortality age structures. The second (and newly developed) method returns components produced by differences between age- and cause-specific mortality rates. The United States is close to England and Wales in mean life expectancy but has higher life expectancy losses and lacks mortality compression. The difference is determined by mortality age structures, whereas the role of mortality levels is minor. This is related to excess mortality at ages under 65 from various causes in the United States. Regression on 17 country-series suggests that e correlates with income inequality across countries but not across time. This result can be attributed to dissimilarity between the age- and cause-of-death structures of temporal mortality reduction and intercountry mortality variation. It also suggests that factors affecting overall mortality decrease differ from those responsible for excess lifetime losses in the United States compared with other countries. The latter can be related to weaknesses of health system and other factors resulting in premature death from heart diseases, amenable causes, accidents and violence.

Introduction

There has been a long-standing tendency for mortality decreases to be steeper at younger than at older ages. This tendency, also called “rectangularization” of the survival curve (Wilmoth and Horiuchi 1999), facilitates an increase in the average length of life. It also leads to a strong negative correlation between life expectancy and the amount of diversity in the life-table ages at death both across time and across countries. In most cases, temporal increases in life expectancy correspond to decreases in this diversity; and life expectancy is, in most cases, higher in countries where the diversity is lower. Studies showed that since the 1970s, however, in some countries, one can observe increases in average life expectancy coinciding with stable or even increasing disparity in age at death (Shkolnikov et al. 2003; Wilmoth and Horiuchi 1999; Zhang and Vaupel 2008). These authors suggested that the new trend can be explained by an “expansion” of death to advanced ages and also to difficulties in further reduction of mortality at young and middle adult ages.

Shkolnikov et al. (2003) also pointed out considerable intercountry differences with respect to the relationship between life expectancy and the amount of diversity in age at death. In particular, the U.S. population is characterized by unexpectedly high diversity in age at death compared with the average life span because of relatively high proportions of deaths at ages that are much younger and much older than the average life span. It was also found that during a period of emergence of certain public health problems between the mid-1980s and the mid-1990s (Elo and Drevenstadt 2004; Kochanek et al. 1994), the relative interindividual difference in age at death for ages 15 and older increased (Shkolnikov et al. 2003).

Edwards and Tuljapurkar (2005) carried out an extensive study of potential reasons for temporal changes in the standard deviation of age at death for ages 10 and older (S10), with special focus on its high value in the United States. After analyzing relations between S10 and external-cause mortality, race, and educational and income inequalities, the authors concluded that “... sources of differential background inequality in life spans between countries remain unclear and await further research” and that their measure of aggregate mortality inequality had not “simply followed trends in either educational or income inequality....” (Edwards and Tuljapurkar 2005:17, 23).

The present article extends prior work by contributing to methodology for the analysis of diversity in ages at death and also contributes substantive results to the discussion of reasons for slow progress in life expectancy in the United States that was initiated at the 2007 annual meeting of the Population Association of America (Blau et al. 2007).

Apart from S10, interindividual diversity in age at death has been measured by the interquartile range (IQR; Wilmoth and Horiuchi 1999), the Gini coefficient and likely measures of relative inequality (Anand et al. 2001; Gakidou et al. 2003; Shkolnikov et al. 2003; Smits and Monden 2009), the Theil index of inequality (Smits and Monden 2009), and average interindividual difference and the related measures of absolute inequality (Moser et al. 2005; Shkolnikov et al. 2003). These measures differ from each other in some formal properties and also in the degree of their aversion to inequality (Anand 1983; Anand et al. 2001; Shkolnikov et al. 2003). In this article, we use e, a measure highlighted by Vaupel and Canudas Romo (2003). Unlike S10, it covers the entire range of ages and has an important public health interpretation. The value of e quantifies the average life expectancy losses attributable to death. It generally follows Keyfitz’s idea that “everybody dies prematurely” because every death “deprives the person involved of the reminder of his expectation of life” (Keyfitz 1977:61–68).

We will demonstrate that e is also a measure of diversity in age at death equal to a weighted average of interindividual differences in age at death. We will introduce procedures for the decomposition of differences between two e values according to direct and compositional components and according to age- and cause-specific components. The latter allows one to quantify the impact of mortality at different ages and from different causes upon life expectancy losses. Reduction of mortality at the ages, and from the causes, that produce greater impacts on life expectancy losses is the most direct way to accelerate the increase in a population’s longevity. Analysis of age- and cause-of-death components of the decrease in life expectancy losses in the United States and England and Wales and of the equivalent components of the difference in life expectancy losses between the two countries reveals a difference between the two structures. This meaningful difference helps to explain our finding that regression analysis of 17 country-series shows that life expectancy losses correlate with income inequality across countries but not across time. Decomposition analysis also provides information for a discussion of the reasons for particularly high lifetime losses in the United States.

Methods

e as a Measure of Lifetime Losses and of Diversity in Age at Death

The quantity e can be traced back to Mitra (1978). It was further developed by Vaupel (1986) and recently by Zhang and Vaupel (2008).
formula
(1)
where l(y), μ(y), and e(y) are survivorship, the force of mortality, and life expectancy, respectively, expressed as functions of age. The definition makes it clear that ex is the average life expectancy losses caused by death at age [x, x + 1) and older ages. For empirical calculations, the following discrete formulae can be used:
formula
(2a)
formula
(2b)
Equation 2b is slightly more precise because it includes 1−ay, the share of the elementary age interval [y, y + 1) lost by those dying in this interval. If x = 0 and l0 = 1, Eq. 2b yields
formula
(3)
where ay is the share of the elementary age interval [y, y + 1) lived by those dying in this interval.

In the latter expression, the first term is the average amount of expected lifetime lost after ages y (y = 0, 1, . . . , ω−1)attributable to deaths in elementary age intervals [y, y + 1); the second term is the average amount of lifetime lost within elementary age intervals [y, y + 1). The second term usually takes values close to 0.5 years.

Life expectancy at age x + 1 can be also expressed as
formula
where and are mean ages at death within elementary intervals [y, y + 1) and [x, x + 1), respectively.1 Substituting life expectancy by the latter expression in the first term of Eq. 3 yields
formula
(4)
Equation 4 suggests that the core part of e is equal to a weighted interindividual difference in age at death. Thus, there is a clear similarity between e and the numerator of the Gini coefficient, also called the average interindividual difference (AID) in length of life (Moser et al. 2005; Shkolnikov et al. 2003).
formula
(5)
The presence of weights (1 / lx+1) in Eq. 4 suggests that e is somewhat more sensitive than AID to mortality at advanced ages.

The Pearson correlation coefficient between e and AID across all country-year life tables of the Human Mortality Database (n = 1,972) is close to .99 both for males and females. The corresponding correlation coefficients between e and S10 are lower: .71 and .81 for males and females, respectively. Different inequality measures sometimes suggest different judgments about relative levels of inequality (Anand et al. 2001; Shkolnikov et al. 2003; van Raalte 2008). Comparisons within all possible pairs of countries of the Human Mortality Database for the last available year (666 comparisons) reveal about a 4% difference between e-based and AID-based country rankings both for males and females. The corresponding percentages of disagreement between the e-based and S10-based rankings are 8% and 10% for males and females, respectively.

Direct and Compositional Components of Differences and Changes

Keyfitz (1977) and Vaupel (1986) performed the first analyses of the relationship between increases in life expectancy on one side and magnitudes of mortality reduction and shapes of mortality distributions by age on the other. Vaupel and Canudas Romo (2003) considered two factors driving longevity progress: the average rate of mortality reduction and the age pattern of this reduction. Longevity progress depends on each factor and on their interaction.

This idea can be applied to life expectancy losses as well. Any difference between two values of life expectancy losses can be presented as the result of a general mortality reduction undifferentiated by age and of a change in the age pattern of mortality. Consider a population with mortality determined by vectors of age-specific death rates equal to M0 and M1. Then the total difference between the life expectancy losses is a sum of two components produced by the amount of mortality change (direct component) and the age structure of this change (compositional component):
formula
(6a)
formula
(6b)
where the mean rate of mortality change is with mx,1 and mx,0 denoting elements of the vectors M1 and M2, respectively, for age [x, x + 1). Equations 6a and 6b represent a simplified calculation procedure corresponding to that expressed in the continuous form for mean life expectancy by Vaupel and Canudas Romo (2003). The decomposition is based on calculation of the life expectancy losses resulting from application of the same rate of change to each of the initial age-specific death rates. Note that the second (compositional) component (6b) is a residual that combines a “pure” effect of the change in the age distribution of mortality with the effect of interaction between this “pure” effect and the change in the average level of mortality.

Age- and Cause-Specific Components of Differences and Changes

Each term in Eqs. 2a and 2b is a complicated quantity. Indeed, dx = lxqx and therefore depends on mortality at age [x, x + 1) and also ages younger than x. depends on mortality at age [x, x + 1) and older ages. The purpose of age decomposition is to estimate the net contribution of mortality change at a specific age to the total change or difference in an aggregate demographic measure (Andreev et al. 2002). The age-specific contribution must be free from side influences of other ages. Such decompositions of time changes or intercountry differences provide valuable information about the relative importance of mortality dynamics at different ages. Further decomposition by causes of death indicates the relative importance of various diseases and health conditions within the age groups.

In earlier work, we proposed a general algorithm for decomposition of differences between aggregate demographic measures (Andreev et al. 2002). If an aggregate measure (say, life expectancy at birth) is calculated from a vector of age-specific death rates M, the age-specific component of the total difference between two values e0(M′) − e0(M) related to age [x, x + 1) is
formula
(7a)
In this formula, M[x] stands for a vector of age-specific death rates containing elements at ages y from 0 to [x, x + 1) and elements my at ages y from [x + 1, x + 2) to ω. This implies that Eq. 7a defines a decomposition method based on a stepwise replacement of the elements of the vector M by elements of the vector M′. Results of the procedure Eq. 7a are not exactly the same, depending on whether one replaces M by M′ or, vice versa, M′ by M. Hence, it is useful to calculate the second set of components by making the opposite-direction stepwise replacement of the elements by the elements my:
formula
(7b)
Equations 7a and 7b can be used directly for a numerical decomposition but can also be transformed into formulae for the components. It has been shown that these procedures result in well-known formulae for the decomposition of differences between two life expectancy values (Andreev 1982; Andreev et al. 2002; Arriaga 1984):
formula
(8a)
formula
(8b)
The final age-specific components are calculated by averaging .
The same procedure can be applied to e:
formula
(9a)
As in the case of life expectancy, the replacement Eq. 9a can be used not only for a numerical decomposition but also for developing a formula for the age-specific component ηx (Appendix A):
formula
(10a)
The opposite-direction replacement corresponds to the components
formula
(9b)
Then the formula similar to Eq. 10a is
formula
(10b)
The final components are: . As we know, the life expectancy components can be further split by causes of death (Andreev 1982):
formula
(11)
where mx,i denotes death rate at age [x, x + 1) from cause i.
Age- and cause-of-death components can be calculated in the same manner (Appendix B):
formula
(12)

Equations 11 and 12 suggest that for a given elementary age interval [x, x + 1) relative cause-specific shares of the corresponding age-specific component are the same for life expectancy losses and for life expectancy. This is certainly not the case for broader ranges of ages that include several elementary age intervals.

Regression of Life Expectancy Losses on Economic Inequality Across Countries and Time

To identify relationship between life expectancy losses and economic inequality, we use a matrix of observations of values of e and the Gini index of income inequality by country and year. The cross-sectional time series regression is performed on a set of 17 countries for which it was possible to acquire consistent series of Gini indexes based on household incomes since 1975. These countries and regions are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Italy, Japan, New Zealand, Norway, Spain, Sweden, Taiwan, the Netherlands, the United Kingdom, and the United States. Data for the calculations were extracted from the World Income Inequality Database and two additional sources (WIID2 2008; OECD 2008; the World Bank 2008). We did not include country series with numerous gaps or implausible ruptures nor the series for Eastern European countries. For the latter, income data are distorted by periods of political instability and also are likely to contain incomparable segments related to periods before and after the fall of communism. Before running the statistical analysis, we filled in the missing values of the Gini coefficient by interpolation and also by using some additional data sources wherever possible.

Exploratory analysis showed that time lags of 1, 2, and 3 years did not improve the results and that the logarithmic transformation did not change them. In the regression analysis, only quinquennial data were used, including years 1975, 1980, 1985, 1990, 1995, 2000, and 2004–2005. Such data are less likely to be serially correlated than the annual data.

Fixed- and random-effects regressions are performed with the help of the panel regression commands in Stata10 (Stata Corporation 2007). In the regressions, e is taken as the dependent variable and the Gini index of income inequality, and time dummy variables serve as independent variables.

Results

Trends in Life Expectancy and in Life Expectancy Losses

It is generally known that measures of diversity in age at death are strongly and negatively correlated with average length of life (Wilmoth and Horiuchi 1999), and e can be expected to have the same property. In spite of this correlation, the balance between life expectancy and life expectancy losses can differ from one country to another. Figure 1 shows country trajectories for the United States, England and Wales, Japan, and Sweden in the e vs. e space. The figure covers the years after World War II from the moment when life expectancy in each of these countries reached 60 years for males and 65 years for females. Accordingly, the Japanese series covers the period after 1951, while the other three country series start from 1946.

Figure 1 demonstrates a close negative correlation between life expectancy and life expectancy losses and also a relatively high level of life expectancy losses in the United States for most of the period. Although at certain moments in the past, the U.S. e values had been quite close to e values in Japan, England and Wales, and Sweden, the gap between the United States and other countries later widened because of a flatter e trajectory in the United States compared with the other countries. The trajectories for Japan, England and Wales, and Sweden converge remarkably (especially for females) and constitute a clear difference from the United States. Over a long period of time, the U.S. and the English life expectancies have been close to each other. Since the mid-1990s, life expectancy values in England and Wales were higher than those in the United States by about one year for males and by about one-half year for females. In spite of the closeness in average longevities, life expectancy losses are substantially greater in the United States than in England and Wales.

Figure 2 reflects a cross-sectional correspondence in 2002 between life expectancy losses and life expectancy for the 29 developed countries represented in the Human Mortality Database. Once again, one can see a tight negative association between e0 and e (r = −.95 and r = −.82 for males and females, respectively). There are also some differences in e between countries with the same level of life expectancy. The U.S. e values lie considerably higher than the expected values on the trend line. For example, in 2002, an average male death in the United States caused a loss of 12.5 years of lifetime, whereas the corresponding expected value on the trend line is 11.4 years (left panel of Fig. 2). This means that in 2002, an average male death in the United States caused an excess loss of 1.1 years of lifetime compared with what can be expected from experience of other countries. For U.S. females, the observed and the expected values of e in 2002 were 11.1 and 10.0 years, respectively, suggesting the same excess loss of 1.1 years of lifetime.

According to Eq. 2a, the high life expectancy losses in the United States must be produced by peculiar shapes of the distributions. Figure 3 provides a comparison of these distributions between the United States and England and Wales in 1950 and 2002. During this period, in both countries, a gross shift of the whole death distribution toward older ages occurred. At both time points, there is almost no difference between the modes of the two distributions; however, the U.S. distributions in both 1950 and 2002 are more dispersed than those of England and Wales. The U.S. distributions have heavier left tails corresponding to young-middle ages. For males, the intercountry difference reaches maxima at ages around 20 and at ages between 40 and 60. For females, the maximum differences are observed at ages between 40 and 65.

It is remarkable that for males at ages between 25 and 45, the values in the United States in 2002 are almost the same as the ones observed in England and Wales in 1950.

In 1950, age-specific death rates in the United States were, on average, higher than those in England and Wales by about 7% for males and 9% for females. By 2002, these differences increased to 29% and 25%, respectively. Table 1 shows the results of decomposition of differences in life expectancy losses between England and Wales and the United States for the two years. The e differences in favor of England and Wales increased from 1.6 to 1.7 years for males and from 1.0 to 1.2 years for females. Calculations according to Eqs. 6a and 6b make it clear that both in 1950 and 2002, more than 90% of the intercountry difference in e was produced by the compositional component determined by differences between the mortality age structures. The part of the direct component determined by differences between average levels of mortality is minor.

Oeppen (2008) introduced the concept of efficiency of the age pattern of mortality change, which is based on an intuitively clear relationship between progress in average longevity and the amount of life expectancy losses. An “efficient” age pattern of mortality reduction (in terms of the overall longevity gain) is the one that produces greater mortality reductions at ages where the fractions are greater. In this regard, age patterns of mortality change in the United States are far from being optimal because the excess in lifetime losses in the United States relative to other countries has not been decreasing with time.

Age- and Cause-of-Death Components of Change in Life Expectancy Losses Between 1980 and 2002

Equations 7a, 7b, 9a, and 9b allow one to decompose by age the increase in e0 and decrease in e, respectively. Figure 4, which presents age-specific components of changes between 1980 and 20022 in the United States and England and Wales, shows a difference between reactions of the two measures to the same change in age-specific mortality. The life expectancy increases in both countries are largely determined by decreases in death rates at ages from 50–85 (upper panels of Fig. 4). Smaller contributions are produced by reductions of infant deaths and of younger adult mortality at ages 15–50. The younger adult mortality contribution is more important for males than females. In England and Wales, components produced by infant and older adult ages are greater than the equivalent components in the United States. At the same time, the younger adult-age components are greater in the United States than those in England and Wales.

For the life expectancy losses (lower panels of Fig. 4), age patterns of change are quite different. Depending on age, the mortality reduction produces negative or positive contributions to the total e change. At ages younger than a threshold age (denoted by a by Zhang and Vaupel [2008]), mortality reduction contributes to e negatively, whereas mortality reduction at ages older than a contribute to e positively. These two balancing forces producing negative and positive effects on life expectancy losses were defined by Zhang and Vaupel (2008) as mortality compression and mortality expansion, respectively. Lack of mortality compression (e.g., elevated sum of components at ages under age a) is seen as unfavorable from the public health point of view. For the mortality change between 1980 and 2002 in both countries, sums of the negative components of change (mortality compression) were two to three times greater than sums of the positive components (mortality expansion). Finally, the lower panels of Fig. 4 demonstrate that England and Wales experienced greater compression and expansion components of the total e change than the United States.

The threshold age has tended to increase over the last decades, always being somewhat lower than the average life expectancy (Zhang and Vaupel 2008). Between 1980 and 2002, the male a increased from 67.5 to 72.5 years in the United States and from 68.5 years to 74.5 years in England and Wales. During the same period, the female a increased from 76.5 to 78.5 years in the United States and from 75.5 to 79.5 years in England and Wales.

From a public health perspective, the degree of mortality compression is especially important. It shows the extent to which a society is able to protect people from premature death. The fact that the threshold age increases with time means that the ages at death that are considered to be premature are rising. Using cause of death data to examine mortality expansion is more problematic because of the difficulties of determining a single cause of death for the very elderly and because of the use of open age intervals.

Figure 5 shows cause-of-death components of mortality compression in the two countries. As the threshold ages are located within age groups 65–75 and 75–80 for males and females, respectively, the male and female decompositions are being made for ages under 70 and ages under 75, respectively. The cause-specific components of the e decrease between 1980 and 2002 are computed from Eqs. 11 and 12. Both in the United States and in England and Wales, the greatest contributions are produced by coronary and other circulatory diseases. In both countries, major causes of infant death, such as perinatal conditions and congenital abnormalities, are the second greatest contributor to decreasing life expectancy losses under the threshold age. In both countries, considerable contributions are also produced by lowering mortality from lung cancer (males), breast and other cancers (females), traffic accidents (males), and violent causes of death (only for males in the United States).

Comparison between the two countries shows that during 1980–2002, England and Wales experienced greater reduction in e because of chronic conditions, such as circulatory diseases, male lung cancer, and female breast cancer. The United States experienced greater effects related to the reduction of male mortality from accidents and violence.

The Intercountry Differences in Life Expectancy Losses in 2002

Figure 6 exhibits age-specific components of differences between England and Wales and the United States in life expectancy and in life expectancy losses in the year 2002 and reveals marked differences from the age patterns of temporal change in Fig. 4. First, the lower U.S. death rates at ages over 75 produce negative contributions to the e0 difference between the two countries and partly counterbalance positive components produced by the higher U.S. death rates at ages under 75. At the same time, the components of intercountry difference in e are now negative at all ages. Second, the role of older adult age and infant age components is relatively less important in the intercountry differences than the role of the equivalent components in the temporal change. At the same time, the contributions of younger adult ages in the intercountry differences are more important than the equivalent contributions to the temporal change.

The cause-of-death pattern of the intercountry difference in mortality compression (Fig. 7) also differs substantially from the equivalent pattern of temporal change (Fig. 5). Indeed, the role of heart diseases is relatively less prominent in the intercountry difference than in the temporal change, and causes of death characteristic of younger adult ages (such as transport and other accidents, violence, and HIV/AIDS) are more important in the intercountry difference than in the temporal change.

Table 2 shows that if the mortality difference between the United States and England and Wales at ages under the threshold age was instantly eliminated, U.S. average longevity would exceed the values for England and Wales. U.S. life expectancy losses would become much lower, but they would still exceed corresponding values in England and Wales.

Associations Between Life Expectancy Losses and Economic Inequality

Is it only a coincidence that the United States is characterized by one of the developed world’s highest levels of disparity in ages at death and by one of the developed world’s highest levels of economic inequality? To answer this question, we examine whether variation in economic inequality across countries and time is statistically associated with life expectancy losses. Edwards and Tuljapurkar (2005) evaluated the link between time changes in the standard deviation of ages at death above age 10 (S10) and the Gini index of income inequality by visual inspection of the trajectories of the United States and four other countries in the S10-Gini space. We approach it somewhat differently by means of regression analysis of cross-sectional time series connecting life expectancy losses with the Gini index for a greater number of countries and years.

As a preliminary step, the Pearson correlation coefficients are computed across the whole set of country-year points. Correlations between life expectancy and the Gini index appear to be negative (as expected) but small and statistically insignificant: −.20 and −.25 for males and females, respectively. Coefficients of correlation between e and the Gini index are much higher and statistically significant (p < .05): .70 for males and .73 for females.

Table 3 shows the outcomes of three regression models. The first “between” regression is based on the cross-sectional setup. It connects the time-averaged values of e to the corresponding values of the Gini index. For both males and females, e is positively and statistically significantly associated with the Gini index. The second “within” model is a pure longitudinal model with fixed country-effects. The model examines whether, on average, the e trends are associated with the Gini index trends. The Chow test suggests that significant fixed country-effects do exist. There is only a very weak positive association for males (p < .10) and no significant association for females. Even if the association between e and the Gini index exists for males, the regression coefficient of 0.013 indicates that the Gini index would have to be increased by a factor of 10 to produce a moderate increase in e equal to 0.13 year. Although the random effects model (that combines the cross-sectional and the longitudinal approaches) indicates significant and positive relationships (p < .05), the Hausman test suggests priority for the fixed-effects model.

All in all, there is a cross-sectional association between life expectancy losses and income inequality, but temporal changes in life expectancy losses are independent or almost independent of changes in income inequality.

To understand whether a high diversity in age at death in the United States can be attributed to socioeconomic inequalities in health, Edwards and Tuljapurkar (2005) compared distributions of ages at death between broad educational groups and between broad income groups on the basis of data from the National Longitudinal Mortality Survey (NLMS 2007; Rogot et al. 1992). They found that groups of higher income and higher education experienced lower values of the standard deviation of ages at death for ages 10 and older, S10; but even in these groups, S10 values were high when compared with the international standard. Using the same NLMS data, we calculated life expectancy at age 30 and life expectancy losses at ages 30 and older for a larger number of more finely defined educational, income, and racial groups, and also for their two-dimensional combinations (Table 4). During 1979–1985, the differences in life expectancy losses between the most advantaged and the most disadvantaged groups were nearly 5 years. Values of e are about 15 years for African American males and females in the lowest income group compared with e values of 10.5–11 years for white males and females in the highest income group. However, our conclusion remains the same as the one by Edwards and Tuljapurkar (2005): even the most advantaged groups experienced values of e that were still slightly higher than the contemporary values for the entire population of England and Wales, which were below 10 years during 1979–1985.

Summary of Results

This study further develops a toolkit for the analysis of interindividual inequality in the face of death. We focus on e, a quantity measuring diversity in ages at death that is also equal to the amount of expected lifetime lost. We introduce procedures for calculation of this measure from empirical data and two ways to decompose a difference between two e values. The first type of decomposition reflects two fundamental aspects of the mortality pattern and permits estimation of a component produced by the difference between average levels of mortality and a component produced by differences between mortality age structures. The second (and more traditional) type of decomposition is public health–oriented. It allows one to compute components produced by differences between age- and cause-specific mortality rates. Its usage allows one to evaluate the relative importance of contributions of different ages and causes of death to the overall difference between life expectancy losses.

Greater focus on the public health aspect of age-at-death disparity constitutes the main difference between this study and the prior work by Edwards and Tuljapurkar (2005). We use an alternative measure of disparity in age at death that covers the entire range of ages and is more public health–oriented than S10. In addition to temporal change, we pay serious attention to cross-sectional differences among countries that (unlike temporal change) appear to be associated with economic inequality. Using decomposition, we show that excess life expectancy losses in the United States are attributable to certain public health problems related to particular age groups and death causes.

Two empirical analyses of life expectancy losses are completed. First, we consider trends and made intercountry comparisons. The analysis reveals persistently high values of e in the United States that are caused by relatively low mortality compression and relatively high mortality expansion in this country. In 2002, lifetime losses among U.S. males and females were greater by 1.1 year than the values expected on the basis of the experience of other developed countries. Compared with England and Wales, the United States had slightly lower average longevity and much greater life expectancy losses. The first type of decomposition demonstrates that both in the past and now, the e gap between the two countries is mostly determined by the difference between the mortality age structures.

Second, we apply the decomposition by ages and causes of death to decreases in life expectancy losses between 1980 and 2002 in the two countries and to the differences in life expectancy losses between the two countries in 2002. We find the following:

  • Falling infant mortality is a considerable component of the decrease in life expectancy losses in both countries and is much less important as a component of the difference in life expectancy losses between the two countries.

  • Decreasing mortality from cardiovascular diseases and some other chronic conditions (male lung cancer and female breast cancer) at middle and older adult ages constitute a major component of the decrease in life expectancy losses. From 1980 to 2002, this component of mortality compression was greater in England and Wales than in the United States.

  • Decreasing mortality at younger adult ages 15–50 from accidents (especially traffic accidents), violence, heart attacks, HIV/AIDS, and diabetes is less important than the decreasing older-age mortality from major chronic diseases as a component of the decrease in life expectancy losses, but it is more important as a component of the gap in life expectancy losses between the United States and England and Wales.

Seeking interpretations of the observed patterns of life expectancy losses, we carry out additional analyses. We perform regressions connecting e with the Gini index of income inequality on time series for 17 industrialized countries since 1975. We find statistically significant associations across countries but not across time.

Using the NLMS data, we calculate e values for categories of education, income, and race and all their pairwise combinations for the United States. Although life expectancy losses vary significantly across groups, even the lowest e values in the most advantaged groups are still slightly higher than values observed in the total population of England and Wales. In this regard, our substantive conclusion confirms that of Edwards and Tuljapurkar (2005) even though we use much more detailed socioeconomic groupings.

Discussion

The substantive results of this study allow us to discuss two issues. First, they provide insights into determinants of variation in life expectancy losses across time and countries. Second, they prompt more specific explanations for the particularly high level of life expectancy losses in the United States.

When thinking about reasons for variation in life expectancy losses across time and countries, it is useful to combine the regression results with results of decompositions by age and cause for the United States and England and Wales. In this way, one can see that the complete or nearly complete absence of the longitudinal association between life expectancy losses and income inequality corresponds to the important role of decreasing circulatory disease and major cancers at old ages in the temporal decline in life expectancy losses. At the same time, the significance of the cross-sectional association between life expectancy losses and income inequality corresponds to a greater role of mortality at younger adult ages and to more acute and avoidable causes of death in cross-sectional differences in life expectancy losses.

The dissimilarity between the longitudinal and cross-sectional health-income inequality associations is consistent with the conclusions of John Lynch and colleagues (2004), whose extensive review of 98 epidemiological studies pointed out the specificity of the strength of association between income inequality and health in regard to type of health outcome. Empirical studies (especially those involving longitudinal evidence and control for compositional effects) provide little evidence for a general relationship between income inequality and total mortality (Deaton and Lubotsky 2003; Lynch et al. 2001; Lynch et al. 2004b; Mellor and Milyo 2001; Osler et al. 2002; Shibuya et al. 2002). In particular, there is little research support for the relationship between income inequality and mortality or morbidity from major cardiovascular and other chronic diseases of old age (Lynch et al. 2004a:74–76, 81–82). At the same time, certain health outcomes are significantly associated with income inequality. Such associations were detected for the mortality of children and adults of working age and for mortality from certain causes such as homicide, stroke and heart attacks (Daly et al. 2001; Franzini and Spears 2003; Kennedy et al. 1998; Kennedy et al. 1996; Lobmayer and Wilkinson 2000; Lynch et al. 2004a; Osler et al. 2003; Shi et al. 2003; Sohler et al. 2003; Szwarcwald et al. 1999; Wilkinson et al. 1998). The work by Backlund et al. (2007) is especially instructive. The authors applied advanced multilevel techniques to NLMS data and showed that state-level income inequality in 1990 in the United States was associated with differences in state level mortality at ages 25–64 after controlling for the compositional effects of individual characteristics, such as income, education, unemployment, and race. The association was much stronger for men than for women. No such relationship was found for mortality at ages above 65.

This result makes it clear why income inequality can not be a major determinant of general mortality decrease. Indeed, in the United States and other advanced countries, general mortality decrease is determined primarily by cardiovascular and other chronic diseases at older ages that are unrelated to income inequality (Salomon and Murray 2002; Vallin and Meslé 2004).

Thus, our results based on age-cause decompositions and regression analysis of 17 country series agree with the detailed epidemiological evidence. Both suggest that factors for a temporal decrease in life expectancy losses differ from factors for intercountry differences. The decrease in these losses is mostly driven by reduction of major chronic diseases at old ages that can be related to advancement in medical technologies for treatment and diagnostics as well as favorable behavioral changes, such as reduction in smoking (Pampel 2003). The intercountry differences are, to a greater extent, related to health and mortality at younger adult ages that are associated with socioeconomic inequality and relative deprivation, leading in turn to elevation of psychosocial stress (Marmot and Wilkinson 2001; Siegrist 2000; Wilkinson et al. 1998).

In rare cases, large changes in working-age mortality cause substantial changes in total mortality, mean length of life, and life expectancy losses. Such changes were observed in Russia and other ex-USSR countries in the 1990s. Both some of the historical health crises, such as the one in nineteenth century Sweden (Sundin and Willner 2004; Willner 2001), and the recent crisis in the former USSR were largely based on excess mortality of men from causes associated with alcohol and were attributed to psychosocial stress (Marmot and Bobak 2000; Leon and Shkolnikov 1998; Shapiro 1995).

In the modern developed world, such outbreaks of working-age mortality are exceptions from mainstream health progress. In the United States (as in other advanced countries), changes in life expectancy losses are mainly driven by decreasing chronic disease among older people and are unrelated to income inequality. However, the excess in life expectancy losses in the United States relative to other countries is determined by the higher U.S. mortality at younger ages and from causes of death that can be linked to income inequality.

A high level of premature death is a long-standing health problem in the United States. Progress in this area is not rapid enough, and separation between the United States and other countries tends to be sustained. High life expectancy losses in the United States can be seen as a result of persistent adverse conditions, such as cigarette smoking among some groups, and also weaknesses of a health system that is unable to assure accelerated reduction of premature death. Our regression analysis signals that it is likely that at least part of these conditions and weaknesses is related to high income inequality in the United States. It is noteworthy that the United States is the country where income inequality is most consistently linked to population health by research evidence, which is not the case in most other developed countries (Lynch et al. 2004a).

Socioeconomic disparities in health between population groups comprise a part of the total amount of interindividual disparity in respect to age at death (and in life expectancy losses). In the second half of the twentieth century, mortality reversals have been observed twice in the African American population (Elo and Drevenstadt 2004; Geronimus et al. 2001; Kochanek et al. 1994; Preston and Elo 1995). The last episode, lasting from 1984 to 1991, coincided with an increase in age at death disparity among U.S. males aged 15 and older (Shkolnikov et al. 2003). Our analysis of NLMS data demonstrated large differences between higher losses in disadvantaged groups and lower losses in advantaged groups. It is possible that some other important types of inequalities play a role. In the United States, huge geographical differences in mortality are related not only to the variable socioeconomic status of individuals in various places but also to highly variable regional contexts (Ezzati et al. 2008; Murray et al. 2006).

However, the socioeconomic health contrasts are unlikely to be responsible for the total amount of excess life expectancy losses in the United States. Indeed, on the basis of NLMS data, we find that even the lowest losses in advantaged groups are still slightly higher than losses in the total population of England and Wales. Therefore, one can guess that the whole range of variation of losses within the United States is shifted toward higher values compared with the equivalent range in England and Wales. This suggests that there are some adverse factors that affect all or many of the U.S. population groups.

The American health system is one of the candidate factors. An important disadvantage of the United States is the incomplete population coverage and variable performance characteristic of the health system. A detailed investigation by Schoen and How (2006) revealed a range of concrete problems in medical care that are especially significant for working people paying their own medical bills. It was reported that about one-third of Americans at ages under 65 do not have any health insurance, and the same share of people have difficulties paying their medical bills. For people of working age, availability and quality of medical care not only depends on their wealth but also significantly varies across health care plans, states, and hospitals. Only one-half of adults receive the recommended preventive health care, including screening for cancer. Health insurance premiums rose far faster than wages, rising as a share of median incomes. Readmissions to hospitals within 30 days remained high and were variable across the country.

It is likely that the disadvantage of the U.S. health system relative to other advanced countries is tending to increase. Two studies by Nolte and McKee (2003, 2008) estimated mortality from medically amenable causes such as bacterial infections, treatable cancers, cerebrovascular disease, part of ischemic heart disease, and complications of common surgical procedures at ages under 75 in 19 OECD countries. During 1997–1998, the United States occupied the 15th place, with amenable mortality exceeding that in 14 other OECD countries. By 2002–2003, the decline in amenable mortality comprised 17% for all OECD countries and only 4% for the United States. As a result, the United States fell to 19th place.

As we demonstrated, excess mortality from lung cancer and heart diseases at ages under 70 for males and under 75 for females contributes to the lack of mortality compression in the United States. This can be largely related to smoking. In the mid-1960s, the United States was among the nations of the world with the highest rates of smoking, with a smoking prevalence of about 50% and 30% for males and females aged 18 and older, respectively (Garfinkel and Silverberg 1991). By 2005, smoking was dramatically reduced to 26% among males and 22% among females. The steeper decrease in smoking of men from the mid-1960s to 2005 is considered to be the central reason for the recent narrowing of the female-male longevity gap (Pampel 2002; Preston and Wang 2006). Smoking-related mortality in the United States has been estimated directly from survey data (Rogers et al. 2005) and also by indirect methods (Peto et al. 2006; Preston et al. 2010). All these estimates are consistent with each other. According to Peto et al. (2006), 29% of male deaths and 27% of female deaths at ages 35–69 in the United States in 2000 were attributable to smoking. Preston et al. (2010) reported similar figures and demonstrated that among 20 developed countries in 2003, the share of smoking-attributable death in the United States was the highest for females and the sixth highest for males.

Death rates among young and middle-aged adults, especially men, are also related to risks caused by alcohol and substance use. France is a classic example of high alcohol-related mortality that contributes to the high level of disparity in age at death in this country (Edwards and Tuljapurkar 2005; Nizard and Muños-Perez 1993). The United States is also not free of such problems. Between 1992 and 2002, U.S. mortality from unintentional injuries increased by 11% (Paulozzi et al. 2006). In the age group 40–64 years, death rates increased for falls, poisonings, and motor vehicle accidents. The increase was particularly pronounced for poisonings at ages 15–24 and 40–59. The increase in unintentional injuries is likely to be related to rises of drug abuse, alcohol consumption, and binge drinking, and also to the use of prescribed psychoactive substances (CDC 2004a, b; Compton and Volkow 2006; Fingerhut and Cox 1998; Serdula et al. 2004).

Some risk factors are especially characteristic of the United States and also contribute to life expectancy losses at working ages. These are traditionally easy access to firearms, resulting in higher risk of homicide (Kaplan and Geling 1998), and especially active use of automobiles, which increases the risk of fatal traffic accidents (Heuveline 2002).

Finally, it is worth mentioning the rapid spread of obesity that is considered to be a serious public health concern in the United States (Breslow 1952; Kim and Popkin 2006; Olshansky et al. 2005; Sturm 2003; WHO 1998). This process has accelerated: between 1988–1994 and 1999–2000, age-adjusted prevalence of overweight (BMI ≥ 25) increased from 56% to 65%, prevalence of obesity (BMI ≥ 30) increased from 23% to 31%, and prevalence of clinically severe obesity (BMI ≥ 40) increased from 3% to 5% (Flegal et al. 2002; Sturm 2003). In the early 2000s, the U.S. prevalences of overweight (25%) and obesity (7%) among children aged 10–16 years were the second highest among 34 countries (Janssen et al. 2005). Obesity increases the risk of a number of circulatory diseases, Type 2 diabetes, certain cancers, gallbladder disease, and osteoarthritis (Kim and Popkin 2006). The minimal number of annual deaths in the United States attributable to obesity is estimated at 112,000 (Flegal et al. 2005; Mark 2005). Although mortality among the obese tends to decrease with time, the spread of obesity contributes to premature death in the United States, contributes to the gap between the United States and countries with lower levels of obesity, and has the potential to slow down the general mortality decline.

All in all, during the last decades, health progress in the United States was slower than in other advanced nations. It was attenuated by high life expectancy losses. Further monitoring and analysis of these losses, their components, and determinants is a research priority.

Acknowledgements

This study is a part of project “Methods of measurement and decomposition in mortality studies” at the Max Planck Institute for Demographic Research. We would like to express our sincere gratitude to Demography’s invited editor Ken Hill for his constructive and insightful comments on previous versions of the article. We are also grateful to two anonymous reviewers for their helpful comments and rigorous check of the text, formulae, and tables. Finally, we extend our gratitude to Edelgard Katke from MPIDR for formatting of the manuscript.

Notes

1

2

The last year for which the cause-of-death data are currently available for the two countries in the WHO Mortality Database.

Appendix A. Derivation of Formulae for the Age-Decomposition of a Difference Between Two e Values

The general decomposition Eq. 9a yields
formula
By definition of M[x], the quantity dy(M[x]) is equal to for ages y ≤ x and is equal to for ages y > x.
formula

Three lines of the latter expression are parts of the age-specific component related to ages younger than age x, to the age group [x, x + 1), and to ages x + 1 and older, respectively.

Formulae for age-specific components of differences between life expectancies are given in Eq. 8a:
formula
and
formula
Using these formulae, one can obtain the final expression for the component ηx contributed by age interval [x, x + 1) to the total difference e†′e:
formula

Appendix B. Derivation of Formulae for the Age- and Cause-of-Death Decomposition of a Difference Between Two e Values

The continuous definition of e in Eq. 1 together with the general decomposition Eq. 9a allow one to express the component of the total difference produced by a small age interval [x,x + Δx):
formula
(B1)

Three integrals in Eq. B1 are parts of the age-specific component related to ages younger than x, to the age group [x,x + Δx), and to ages x + Δx and older, respectively.

From definitions of the survivorship and the life expectancy functions, it is easy to derive the following relations that hold true for a small Δx (see also Shkolnikov et al. 2003:328):
formula
(B2)
formula
(B3)
Using Eqs. B2 and B3, the second integral in Eq. B1 can be simplified:
formula
(B4)
Taking into account that , and also Eq. B2, the third integral can be transformed:
formula
(B5)
Using (B3), it is possible to show that
formula
This relation helps to transform the first integral in Eq. B1:
formula
(B6)
Replacement of the three original integrals in Eq. B1 by their equivalents from Eqs. B4, B5, and B6 yields
formula
(B7)
This formula is the final expression for the component of the difference between two e values produced by a mortality change within a small age interval [x,x + Δx). Most important, it includes the multiplier. Following our earlier study, one can integrate the left- and right-hand sides of Eq. B7 over the age interval [x, x + 1) (Shkolnikov et al. 2003:328–29) and obtain
formula
Consequently,
formula
where mx,i is the death rate by cause i at age x.

References

Anand, S. (
1983
).
Inequality and poverty in Malaysia: Measurement and decomposition
.
New York
:
Oxford University Press
.
Anand, S., Diderichsen, F., Evans, T., Shkolnikov, V., & Wirth, M. (
2001
).
Measuring disparities in health: Methods and indicators
. In Evans, T., Whitehead, M., Diderichsen, F., & Bhuiya, A. (Eds.),
Challenging inequities in health: From ethics to action
(pp.
49
67
).
New York
:
Oxford University Press
.
Andreev, E. M. (
1982
).
Metod komponent v analize prodoljitelnosty zjizni [The method of components in the analysis of length of life]
.
Vestnik Statistiki
,
9
,
42
7
.
Andreev, E. M., Shkolnikov, V. M., & Begun, A. Z. (2002). Algorithm for decomposition of differences between aggregate demographic measures and its application to life expectancies, healthy life expectancies, parity-progression ratios and total fertility rates. Demographic Research, 7, article 14, 499–522. doi:10.4054/DemRes.2002.7.14.
Arriaga, E. (
1984
).
Measuring and explaining the change in life expectancies
.
Demography
,
21
,
83
96
. 10.2307/2061029
Backlund, E., Rowe, G., Lynch, J., Wolfson, M. C., Kaplan, G. A., & Sorlie, P. D. (
2007
).
Income inequality and mortality: A multilevel prospective study of 521, 248 Individuals in 50 US states
.
International Journal of Epidemiology
,
36
,
590
6
. 10.1093/ije/dym012
Blau, D. (Chair), Berkman, L., Cutler, D., Paxson, C., Smith, J. P., & Vaupel, J. W. (2007, March). Panel discussion on Why is health in the U.S. so much worse than health in other developed countries? Session 113 at the annual meeting of the Population Association of America, New York.
Breslow, L. (
1952/2006
).
Public health aspects of weight control
.
International Journal of Epidemiology
,
35
,
10
2
. 10.1093/ije/dyi249
Centers for Disease Control and Prevention (CDC)
(
2004
).
Trends in motorcycle fatalities associated with alcohol-impaired driving—United States, 1983–2003
.
Morbidity and Mortality Weekly Report
,
53
,
1103
6
.
Centers for Disease Control and Prevention (CDC)
(
2004
).
Unintentional and undetermined poisoning deaths—11 States, 1990–2001
.
Morbidity and Mortality Weekly Report
,
53
,
233
8
.
Compton, W. M., & Volkow, N. D. (
2006
).
Major increases in opioid analgesic abuse in the United States: Concerns and strategies
.
Drug and Alcohol Dependence
,
81
,
103
7
. 10.1016/j.drugalcdep.2005.05.009
Daly, M., Wilson, M., & Vasdev, S. (
2001
).
Income inequality and homicide rates in Canada and the United States
.
Canadian Journal of Criminology–Revue canadienne de criminologie
,
43
,
219
36
.
Deaton, A., & Lubotsky, D. (
2003
).
Mortality, inequality and race in American cities and states
.
Social Science & Medicine
,
56
,
1139
53
. 10.1016/S0277-9536(02)00115-6
Edwards, R. D., & Tuljapurkar, S. (
2005
).
Inequality in life spans and a new perspective on mortality convergence across industrialized countries
.
Population and Development Review
,
31
,
645
74
. 10.1111/j.1728-4457.2005.00092.x
Elo, I. T., & Drevenstadt, G. L. (2004). Cause-specific contributions to black-white differences in male mortality from 1960 to 1995. Demographic Research, Special Collection 2, article 10, 255–276. doi:10.4054/DemRes.2004.S2.10.
Ezzati, M., Friedman, A. B., Kulkarni, S. C., & Murray, C. J. L. (
2008
).
The reversal of fortunes: Trends in county mortality and cross-county mortality disparities in the United States.
.
Public Library of Science Medicine
,
5
,
557
68
.
Fingerhut, L. A., & Cox, C. S. (
1998
).
Poisoning mortality, 1985–1995
.
Public Health Reports
,
113
,
218
33
.
Flegal, K. M., Caroll, M. D., Ogden, C. L., & Johnson, C. L. (
2002
).
Prevalence and trends in obesity among US adults, 1999–2000
.
Journal of the American Medical Association
,
288
,
1723
7
. 10.1001/jama.288.14.1723
Flegal, K. M., Graubard, B. I., Williamson, D. F., & Gail, M. H. (
2005
).
Excess deaths associated with underweight, overweight, and obesity
.
Journal of the American Medical Association
,
293
,
1861
7
. 10.1001/jama.293.15.1861
Franzini, L., & Spears, W. (
2003
).
Contributions of social context to inequalities in years of life lost to heart disease in Texas, USA
.
Social Science & Medicine
,
57
,
1847
61
. 10.1016/S0277-9536(03)00018-2
Gakidou, E. E., Murray, C. J. L., & Frenk, J. (
2003
).
A framework for measuring health inequality
. In Murray, C. J. L., & Evans, D. B. (Eds.),
Health systems performance assessment. Debates, methods and empirism
(pp.
471
484
).
Geneva
:
World Health Organization
.
Garfinkel, L., & Silverberg, E. (
1991
).
Lung cancer and smoking trends in the United States over the past 25 years
.
A Cancer Journal for Clinicians
,
41
,
137
46
. 10.3322/canjclin.41.3.137
Geronimus, A. T., Bound, J., Waidmann, T. A., Colen, C. G., & Steffic, D. (
2001
).
Inequality in life expectancy, functional status, and active life expectancy across selected black and white populations in the United States
.
Demography
,
38
,
227
51
. 10.1353/dem.2001.0015
Heuveline, P. (
2002
).
An international comparison of adolescent and young adult mortality
.
The Annals of the American Academy of Political and Social Science
,
580
,
172
200
. 10.1177/0002716202580001008
Human Mortality Database. (2007). University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). [Database]. Available online at http://www.mortality.org and http://www.humanmortality.de
Janssen, I., Katzmarzyk, P. T., Boyce, W. F., Vereecken, C., Mulvihill, C., Roberts, C., Currie, C., & Pickett, W. (
2005
).
Comparison of overweight and obesity prevalence in school-aged youth from 34 countries and their relationships with physical activity and dietary patterns
.
Obesity Reviews
,
6
,
123
32
. 10.1111/j.1467-789X.2005.00176.x
Kaplan, M. S., & Geling, O. (
1998
).
Firearm suicides and homicides in the United States: Regional variations and patterns of gun ownership
.
Social Science & Medicine
,
46
,
1227
33
. 10.1016/S0277-9536(97)10051-X
Kennedy, B. P., Kawachi, I., & Prothrow-Stith, D. (
1996
).
Income distribution and mortality: Cross sectional ecological study of the Robin Hood index in the United States
.
British Medical Journal
,
312
,
1004
7
.
Kennedy, B. P., Kawachi, I., Glass, R., & Prothrow-Stith, D. (
1998
).
Income distribution, socioeconomic status, and self rated health in the United States: Multilevel analysis
.
British Medical Journal
,
317
,
917
21
.
Keyfitz, N. (
1977
).
Applied mathematical demography
.
New York
:
Wiley
.
Kim, S., & Popkin, B. M. (
2006
).
Commentary: Understanding the epidemiology of overweight and obesity–A real public health concern
.
International Journal of Epidemiology
,
35
,
60
7
. 10.1093/ije/dyi255
Kochanek, K. D., Mauer, J. D., & Rosenberg, H. M. (
1994
).
Why did black life expectancy decline from 1984 through 1989 in the United States?
.
American Journal of Public Health
,
84
,
938
44
. 10.2105/AJPH.84.6.938
Leon, D. A., & Shkolnikov, V. M. (
1998
).
Social stress and the Russian mortality crisis
.
Journal of the American Medical Association
,
279
,
790
1
. 10.1001/jama.279.10.790
Lobmayer, P., & Wilkinson, R. (
2000
).
Income, inequality and mortality in 14 developed countries
.
Sociology of Health & Illness
,
22
,
401
14
. 10.1111/1467-9566.00211
Lynch, J., Davey Smith, G., Harper, S., Hillemeier, M., Ross, N., Kaplan, G., & Wolfson, M. (
2004
).
Is income inequality a determinant of population health? Part 1. A systematic review
.
The Milbank Quarterly
,
82
,
5
99
. 10.1111/j.0887-378X.2004.00302.x
Lynch, J., Davey Smith, G., Hillemeier, M., Shaw, M., Raghunthan, T., & Kaplan, G. (
2001
).
Income inequality, the psychosocial environment, and health: Comparisons of wealthy nations
.
Lancet
,
358
,
194
200
. 10.1016/S0140-6736(01)05407-1
Lynch, J., Harper, S., Davey Smith, G., Ross, N., Wolfson, M., & Dunn, J. (2004b). US Regional and national cause-specific mortality and trends in income inequality: Descriptive findings. Demographic Research, Special Collection 2, article 8, 183–228. doi:10.4054/DemRes.2004.S2.8.
Mark, D. (
2005
).
Deaths attributable to obesity
.
Journal of the American Medical Association
,
293
,
1918
9
. 10.1001/jama.293.15.1918
Marmot, M., & Bobak, M. (
2000
).
International comparators and poverty and health in Europe
.
British Medical Journal
,
321
,
1124
8
. 10.1136/bmj.321.7269.1124
Marmot, M., & Wilkinson, R. G. (
2001
).
Psychosocial and material pathways in the relation between income and health: A response to Lynch et al
.
British Medical Journal
,
322
,
1233
6
. 10.1136/bmj.322.7296.1233
Mellor, J. M., & Milyo, J. (
2001
).
Re-examining the evidence of an ecological association between income inequality and health
.
Journal of Health Politics, Policy and Law
,
26
,
487
522
. 10.1215/03616878-26-3-487
Mitra, S. (
1978
).
A short note on the Taeuber paradox
.
Demography
,
15
,
621
3
. 10.2307/2061211
Moser, K., Shkolnikov, V., & Leon, D. A. (
2005
).
World Mortality 1950–2000: Divergence replaces convergence from the late 1980s
.
Bulletin of the World Health Organization
,
83
,
202
9
.
Murray, C. J. L., Kulkarni, S. C., Michaud, C., Tomijima, N., Bulzacchelli, M. T., Iandiorio, T. J., & Ezzati, M. (
2006
).
Eight Americas: Investigating mortality disparities across race-counties in the United States
.
Public Library of Science Medicine
,
3
,
1513
24
.
Nizard, A., & Muños-Perez, F. (
1993
).
Alcohol, tobacco, and mortality in France since 1950: An estimate of the annual numbers of deaths due to alcohol and tobacco use in 1986
.
Population
,
48
,
571
607
. 10.2307/1534096
NLMS. (2007). National Longitudinal Mortality Survey [Survey site]. Available online at http://www.census.gov/nlms
Nolte, E., & McKee, M. (
2003
).
Measuring the health of nations: Analysis of mortality amenable to health care
.
British Medical Journal
,
327
,
1129
33
. 10.1136/bmj.327.7424.1129
Nolte, E., & McKee, M. (
2008
).
Measuring the health of nations: Updating an earlier analysis
.
Health Affairs
,
1
,
58
71
. 10.1377/hlthaff.27.1.58
Oeppen, J. (2008, April). Comparing the efficiency of mortality changes between countries: An evaluation of past and forecast levels in advanced economies. Paper presented at the annual meeting of the Population Association of America, New Orleans.
Olshansky, S. J., Passaro, D. J., Hershow, R. C., Layden, J., Carnes, B. A., Brody, J., Hayflick, L., Butler, R. N., Allison, D. B., & Ludwig, D. S. (
2005
).
A potential decline in life expectancy in the United States in the 21st century
.
The New England Journal of Medicine
,
352
,
1138
45
. 10.1056/NEJMsr043743
Osler, M., Christensen, U., Due, P., Lund, R., Andersen, I., Diderichsen, F., & Prescott, E. (
2003
).
Income inequality and ischaemic heart disease in Danish men and women
.
International Journal of Epidemiology
,
32
,
375
80
. 10.1093/ije/dyg074
Osler, M., Prescott, E., Gronbak, M., Christensen, U., Due, P., & Engholm, G. (
2002
).
Income inequality, individual income, and mortality in Danish adults: Analysis of pooled data from two cohort studies
.
British Medical Journal
,
324
,
13
. 10.1136/bmj.324.7328.13
Pampel, F. C. (
2002
).
Cigarette use and the narrowing sex differential in mortality
.
Population and Development Review
,
28
,
77
104
. 10.1111/j.1728-4457.2002.00077.x
Pampel, F. C. (
2003
).
Declining sex differences in mortality from lung cancer in high-income nations
.
Demography
,
40
,
45
65
. 10.1353/dem.2003.0007
Paulozzi, L. J., Ballesteros, M. F., & Stevens, J. A. (
2006
).
Recent trends in mortality from unintentional injury in the United States
.
Journal of Safety Research
,
37
,
277
83
. 10.1016/j.jsr.2006.02.004
Peto, R., Lopez, A. D., Boreham, J., & Thun, M. (2006). Mortality from smoking in developed countries 1950–2000 (2nd ed.). Available online at http://www.ctsu.ox.ac.uk/~tobacco
Preston, S. H., & Elo, I. T. (
1995
).
Are educational differentials in adult mortality increasing in the United States?
.
Journal of Aging and Health
,
7
,
476
96
. 10.1177/089826439500700402
Preston, S. H., & Wang, H. (
2006
).
Sex mortality differences in the United States: The role of cohort smoking patterns
.
Demography
,
43
,
631
46
. 10.1353/dem.2006.0037
Preston, S. H., Glei, D., & Wilmoth, J. R. (
2010
).
A new method for estimating smoking-attributable mortality in high-income countries
.
International Journal of Epidemiology
,
39
,
430
8
. 10.1093/ije/dyp360
Rogers, R. G., Hummer, R. A., Krueger, P. M., & Pampel, F. C. (
2005
).
Mortality attributable to cigarette smoking in the United States
.
Population and Development Review
,
31
,
259
92
. 10.1111/j.1728-4457.2005.00065.x
Rogot, E., Sorlie, P. D., Johnson, N. J., & Schmitt, C. A. (1992). Mortality study of 1.3 million persons by demographic, social and economic factors: 1979–1985 follow-up. Second data book. (NIH Publication No. 92–3297). Bethesda, MD: National Institutes of Health, PHS, DHHS.
Salomon, J., & Murray, C. J. L. (
2002
).
The epidemiologic transition revisited: Compositional models for causes of death by age and sex
.
Population and Development Review
,
28
,
205
28
. 10.1111/j.1728-4457.2002.00205.x
Schoen, C., & How, S. K. (
2006
).
National scorecard on U.S. health system performance: Technical report
.
New York
:
Commonwealth Fund
.
Serdula, M. K., Brewer, R. D., Gillespie, C., Denny, C. H., & Mokdad, A. (
2004
).
Trends in alcohol use and binge drinking, 1985–1999: Results of a multi-state survey
.
American Journal of Preventive Medicine
,
26
,
294
8
. 10.1016/j.amepre.2003.12.017
Shapiro, J. (
1995
).
The Russian mortality crisis and its causes
. In Åslund, A. (Ed.),
Russian economic reform at risk
(pp.
149
178
).
London
:
Pinter
.
Shi, L. Y., Macinko, J., Starfield, B., Xu, J. H., & Politzer, R. (
2003
).
Primary care, income inequality, and stroke mortality in the United States–A longitudinal analysis, 1985–1995
.
Stroke
,
34
,
1958
64
. 10.1161/01.STR.0000082380.80444.A9
Shibuya, K., Hashimoto, H., & Yano, E. (
2002
).
Individual income, income distribution, and self-rated health in Japan: Cross sectional analysis of nationally representative sample
.
British Medical Journal
,
324
,
16
9
. 10.1136/bmj.324.7328.16
Shkolnikov, V. M., Andreev, E. M., & Begun, A. Z. (2003). Gini coefficient as a life table function. Computation from discrete data, decomposition of differences and empirical examples. Demographic Research, 8, article 11:305–58. doi:10.4054/DemRes.2003.8.11.
Siegrist, J. (
2000
).
Place, social exchange and health: Proposed sociological framework
.
Social Science & Medicine
,
51
,
1283
93
. 10.1016/S0277-9536(00)00092-7
Smits, J., & Monden, C. (
2009
).
Length of life inequality around the globe
.
Social Science & Medicine
,
68
,
1114
1123
. 10.1016/j.socscimed.2008.12.034
Sohler, N., Arno, P., Chang, C. J., Fang, J., & Schecter, C. (
2003
).
Income inequality and infant mortality in New York City
.
Journal of Urban Health
,
80
,
650
657
.
Stata Corporation. (2007). Stata longitudinal/panel-data reference manual. Release 10. College Station, TX: StataCorp.
Sturm, M. (
2003
).
Increases in clinically severe obesity in the United States, 1986–2000
.
Archives of Internal Medicine
,
163
,
2146
8
. 10.1001/archinte.163.18.2146
Sundin, J., & Willner, S. (
2004
).
Health and vulnerable men. Sweden: From traditional farming to industrialisation
.
Hygiea Internationalis
,
4
,
175
203
. 10.3384/hygiea.1403-8668.0441175
Szwarcwald, C. L., Bastos, F. I., Viacava, F., & de Andrade, C. L. (
1999
).
Income inequality and homicide rates in Rio De Janeiro, Brazil
.
American Journal of Public Health
,
89
,
845
80
. 10.2105/AJPH.89.6.845
Vallin, J., & Meslé, F. (2004). Convergences and divergences in mortality. A new approach to health transition. Demographic Research, Special Collection 2, article 2, 1–44. doi: 10.4054/DemRes.2004.S2.2.
van Raalte, A. (2008, June). Inter-individual inequality in life spans: An examination of four methods and five countries. Presented at the annual meeting of the Canadian Population Society, University of British Columbia, Vancouver, Canada.
Vaupel, J. W. (
1986
).
How change in age-specific mortality affects life expectancy
.
Population Studies
,
40
,
147
57
. 10.1080/0032472031000141896
Vaupel, J. W., & Canudas Romo, V. (
2003
).
Decomposing change in life expectancy: A bouquet of formulas in honor of Nathan Keyfitz’s 90th birthday
.
Demography
,
40
,
201
16
. 10.1353/dem.2003.0018
Wilkinson, R. G., Kawachi, I., & Kennedy, B. (
1998
).
Mortality, the social environment, crime and violence
.
Social Health and Illness
,
20
,
578
97
. 10.1111/1467-9566.00120
Willner, S. (
2001
).
The impact of alcohol consumption on excess male mortality in nineteenth- and early twentieth-century Sweden
.
Hygiea Internationalis
,
2
,
45
70
. 10.3384/hygiea.1403-8668.012145
Wilmoth, J. R., & Horiuchi, S. (
1999
).
Rectangularization revisited: Variability of age at death within human populations
.
Demography
,
36
,
475
96
. 10.2307/2648085
World Health Organization (WHO). (1998). Obesity: Preventing and managing the global epidemic (WHO Technical Report Series No. 894). Geneva: WHO.
World Health Organization (WHO). (2007). The WHO Mortality Database. Detailed data files available online at http://www.who.int/whosis/mort/download/en/index.html
World Income Inequality Database (WIID). (2008). World Income Inequality Database, Wave 2.0b May 2007. Available online at http://www.wider.unu.edu/research/Database/en_GB/database/
Zhang, Z., & Vaupel, J. W. (2008, April). The threshold between compression and expansion of mortality. Presented at the annual meeting of the Population Association of America, New Orleans.