Creating synthetic cohort death distributions by age, sex, and education
We used census-based data assembled and harmonized as part of the Eurothine project [
15]. This comprised sex-specific death counts and exposures by sex, age (aggregated into five-year age intervals), and level of education for 11 European countries (Table
1). The data included both longitudinal census-linked and cross-sectional unlinked studies. Excluded subpopulations were Åland Island from Finland, non-Swiss nationals from Switzerland, and overseas departments, students, the military, and persons born outside of France from the French data.
Table 1
Countries and study type included in the analysis
Sweden2
| 1991-2000 | Longitudinal, census-linked | 48 340 986 | 919 508 | 9.8 |
Norway | 1991-2000 | Longitudinal, census-linked | 22 262 277 | 433 282 | 2.3 |
Finland3
| 1991-2000 | Longitudinal, census-linked | 27 550 171 | 473 873 | 0.0 |
Belgium | 1991-1995 | Longitudinal, census-linked | 27 635 206 | 486 222 | 6.0 |
Switzerland | 1991-2000 | Longitudinal, census-linked | 30 728 441 | 538 619 | 0.6 |
France4
| 1990-1999 | Longitudinal, census-linked | 2 720 978 | 43 024 | 0.0 |
Slovenia | 1991-2000 | Longitudinal, census-linked | 10 325 537 | 165 423 | 1.3 |
Czech Republic | 1999-2003 | Cross-sectional, unlinked | 30 308 765 | 535 264 | 0.0 |
Poland | 2001-2003 | Cross-sectional, unlinked | 65 844 117 | 1 058 745 | 2.0 |
Estonia | 1998-2002 | Cross-sectional, unlinked | 4 141 440 | 60 794 | 2.3 |
Lithuania | 2000-2002 | Cross-sectional, unlinked | 6 189 927 | 115 803 | 0.5 |
Comparable educational levels had been created by regrouping national education schemes into four categories of the International System of Classification of Educations (ISCED): no education to completed primary education (elementary), lower secondary education, higher secondary education, and tertiary education. For three of the countries studied (Norway, Finland, and Switzerland) the two least-educated groups had to be combined by the Eurothine data collection team either because the countries' educational system did not allow for proper differentiation between the two groups or because the proportion of subjects in the lowest educational category was too low to draw meaningful conclusions. The proportion of subjects in each educational category is shown in Table
2.
Table 2
Proportion of subjects in each of the following educational categories by country
Sweden | 0.30 | 0.10 | 0.43 | 0.16 | 0.30 | 0.11 | 0.40 | 0.19 |
Norway | | 0.33 | 0.47 | 0.21 | | 0.41 | 0.44 | 0.15 |
Finland | | 0.51 | 0.28 | 0.21 | | 0.56 | 0.26 | 0.18 |
Belgium | 0.44 | 0.18 | 0.21 | 0.16 | 0.53 | 0.16 | 0.18 | 0.13 |
Switzerland | | 0.22 | 0.55 | 0.23 | | 0.44 | 0.49 | 0.06 |
France | 0.47 | 0.06 | 0.35 | 0.12 | 0.57 | 0.09 | 0.24 | 0.09 |
Slovenia | 0.20 | 0.19 | 0.49 | 0.12 | 0.24 | 0.35 | 0.32 | 0.08 |
Czech Rep. | 0.12 | 0.50 | 0.24 | 0.13 | 0.32 | 0.33 | 0.27 | 0.07 |
Poland | 0.28 | 0.34 | 0.27 | 0.11 | 0.38 | 0.18 | 0.35 | 0.10 |
Estonia | 0.11 | 0.22 | 0.50 | 0.17 | 0.15 | 0.18 | 0.51 | 0.17 |
Lithuania | 0.18 | 0.15 | 0.52 | 0.16 | 0.24 | 0.10 | 0.49 | 0.16 |
The census-linked studies followed individuals for 10 years between the 1990 and 2000 census rounds. Death and exposure counts occurring within this period were aggregated by the participating statistical offices into five-year age groups (ages 30 to 85+ at baseline). Since we were unable to distinguish the year of death, we assumed that all individuals who died over the study died at the midpoint, i.e., deaths to individuals aged 30 at baseline were assumed to have occurred at age 35 (32.5 for Belgium). In the census-unlinked studies, data were aggregated cross-sectionally for a few years around the 2000 census-year round (five-year age groups, ages 30 to 85+). To make the two data formats comparable, we only used ages 35+ in these studies.
To improve the precision of the age at death distribution, the national population death and exposure counts reported by single year of age in the Human Mortality Database (HMD) [
16] were proportioned out to each educational group according to their corresponding shares derived from the Eurothine data for the equivalent time periods. The matching was done by country, sex, and five-year age group. We made the assumption that in the final open-aged category mortality rate ratios between educational groups were the same as those observed in the oldest preceding age category. A previous study showed this to be the case for females but risked overestimating differences for males, who were shown to have decreasing rate ratios between educational groups up to ages 90+ [
17]. Sensitivity analysis revealed few differences in lifespan variation whether assuming constant or decreasing rate ratios over the oldest ages [
5]. Finally, the small number of subjects surviving to the oldest ages led to some random variation in the right tail of the death distributions. To smooth the distribution, we fitted the Kannisto model of old age mortality to ages above 80, extrapolating death counts for both males and females beyond the first age with fewer than 100 male deaths [
18]. More details about the data formats and the data matching procedures can be found in the recent publication by van Raalte et al. [
5].
The result of this matching was sex-specific death rates by single year of age (35 to 110+) and educational level. We then used these death rates to construct male and female life tables for each educational subgroup, thus allowing comparable age distributions of deaths that were not confounded by the age structure of the educational subgroups of the real population.
Measuring and decomposing lifespan disparity
Determining the contribution of educational inequality to total variation in lifespan requires using a measure that is decomposable into its between-group (BG) and within-group (WG) components, such that total variation = BG + WG. The BG inequality component captures the variation in subgroup average lifespans, while the WG component captures the average individual-level variation calculated for each of the subgroups, with both components weighted by the subgroup's population share. The contribution of the stratifying variable (in our case education) to the total variation in lifespans then is simply the BG component divided by the total variation.
Only a few measures of variation are additively decomposable, and of this subset we decided to apply Theil's entropy index (
T). Theil's index was created from information theory to measure the degree of disorder in the distribution [
14]. It is most widely used in studies of economic inequality but has also been applied in recent studies of lifespan variation [
6,
19,
20]. The calculation and decomposition of this measure are presented in Additional file
1. Theil's index takes on greater values with greater dispersion in lifespans although it lacks an intuitive demographic interpretation. A value of 0 would indicate perfect equality (i.e., everyone died at the same age).
Even if measures of lifespan variation are highly correlated [
21,
22], they can arrive at different conclusions depending on their sensitivities to changes at different ends of the age distribution of death [
6]. In particular
T is known to be sensitive to changes in the early part of the distribution and becomes progressively less sensitive to changes at older ages [
23]. We therefore decided to also calculate the variance in age at death (
V), which is more sensitive to changes at older ages of the age at death distribution than
T. Additionally, the variance examines absolute changes in variability (i.e., the measure is insensitive to additive changes to each individual's lifespan), while Theil's index measures relative changes in variability (i.e., the measure is insensitive to proportional changes in each individual's lifespan). The choice of measure is inherently a normative one. From a public health perspective it is clear that reducing lifespan variation by reducing premature mortality is a desirable outcome. It is less obvious whether higher lifespan variation caused by increased survivorship at old ages should be of concern. For this reason we prefer the age at death sensitivity profile of
T. The calculation and decomposition of
V, as well as the full results for this alternative measure are given in Additional file
1.