Signature
AG = h_J - h_1; RG = h_J / h_1
| Inputs | Definition | Unit |
|---|---|---|
h_J | Mean health in group J, the most advantaged of the J ordered groups, for example the least deprived quintile | health units, for example years of QALE |
h_1 | Mean health in group 1, the most disadvantaged group, for example the most deprived quintile. Above zero for the ratio | health units, in the same unit as h_J |
AG | Absolute gap: mean health in the most advantaged group minus mean health in the most disadvantaged group | units of the health variable, for example years of QALE |
|---|---|---|
RG | Relative gap, or rate ratio: mean health in the most advantaged group divided by mean health in the most disadvantaged group | ratio, without unit |
Function
Health inequality measures across ordered population groups
Maps the mean health of population groups, ordered from the most to the least disadvantaged, and the share of the population in each group to summary measures of socioeconomic-related health inequality: the absolute and relative gaps between the extreme groups, the slope index of inequality, the relative index of inequality in two forms and the concentration index. The measures describe how health varies with socioeconomic position and do not say whether that variation is unfair, which is the separate judgement of health inequity. The Atkinson index, which ignores the ranking of groups, has its own records on the Atkinson index page (HE-FN-ATK-001) and is not repeated here.
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Implementations
Excel
Absolute and relative health gaps in two Excel cells
With mean health in the most advantaged group in a cell named HealthTop and in the most disadvantaged group in a cell named HealthBottom, the two formulas return the absolute gap and the rate ratio.
=HealthTop-HealthBottom; =HealthTop/HealthBottom
Assumptions
Health inequality gaps use only the two extreme groups
Only groups 1 and J enter the formulas. The groups in between and the size of each group are ignored, which the WHO handbook gives as the two main limitations of simple measures. The slope index of inequality and the concentration index on this page use every group and weight each by its population share.
Ratio-scale health for the relative health gap
The ratio needs health measured on a ratio scale with h_1 above zero, such as QALE in years. The order of the groups in the ratio is stated with the result, because the reciprocal reads in the opposite direction.
Worked examples
Health gaps across five deprivation quintiles
In the article's illustrative example the least deprived quintile has a QALE of 72 years and the most deprived 62 years. The absolute gap is 10 years and the rate ratio is 72 / 62 = 1.161.
h_J = 72; h_1 = 62; AG = 10; RG = 1.161
Health gaps after a proportional gain of 2% in every quintile
Under Programme B in the article every quintile gains 2%, giving 73.44 years in the least deprived quintile and 63.24 years in the most deprived. The absolute gap widens to 10.2 years while the rate ratio stays at 1.161.
h_J = 73.44; h_1 = 63.24; AG = 10.2; RG = 1.161
Common errors
Judging a change in health inequality on one gap measure alone
The two gaps can move in opposite directions. In the article's example a gain of 1 year in every quintile leaves the absolute gap at 10 years while the rate ratio falls from 1.161 to 1.159, and a gain of 2% in every quintile leaves the ratio at 1.161 while the gap widens to 10.2 years. Both are therefore reported, as the WHO handbook recommends.
Sources
WHO handbook definitions of the difference and ratio for health inequality
World Health Organization. Handbook on health inequality monitoring: with a special focus on low- and middle-income countries. Geneva: World Health Organization; 2013. Section 3.2, which defines the difference and the ratio as the simple measures of absolute and relative inequality between two subgroups; section 3.3 on their two limitations; and the summary, which recommends reporting both absolute and relative measures.
Rate ratio and rate difference giving opposite conclusions on health inequality
Harper S, King NB, Meersman SC, Reichman ME, Breen N, Lynch J. Implicit value judgments in the measurement of health inequalities. Milbank Quarterly. 2010;88(1):4-29. Case study 1, which defines the rate ratio and the rate difference and shows relative inequality rising while absolute inequality falls in the same data.
Canonical Identity
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