Signature
alpha = mu - SII / 2; RII_ratio = (alpha + SII) / alpha
| Inputs | Definition | Unit |
|---|---|---|
mu | Population-weighted mean health across all groups | health units, for example years of QALE |
SII | Slope index of inequality from HE-FM-HINQ-002 | health units, in the same unit as mu |
alpha | Predicted health at rank 0, the intercept of the fitted line. Above zero | health units, for example years of QALE |
|---|---|---|
RII_ratio | Relative index of inequality as the ratio of predicted health at rank 1 to predicted health at rank 0 | 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
Ratio relative index of inequality in one Excel cell
With population-weighted mean health in a cell named MeanHealth and the slope index in a cell named SII, Excel returns the ratio form directly: the numerator is predicted health at rank 1 and the denominator predicted health at rank 0.
=(MeanHealth+SII/2)/(MeanHealth-SII/2)
Assumptions
Same fitted line for the ratio relative index and the slope index
Both predicted values come from the population-weighted line used for the slope index, with ranks at the midpoint of each group's range. A line fitted with other ranks or weights gives a different intercept and a different ratio.
Intercept above zero for the ratio relative index
The ratio is defined only when predicted health at rank 0 is above zero. For an indicator with low values in the disadvantaged groups a steep line can bring the intercept close to zero, and the ratio then becomes very large.
Worked examples
Ratio relative index for five equal deprivation quintiles
In the article's example the intercept is 68 minus half of 12.5, or 61.75 years, and predicted health at rank 1 is 74.25 years. The ratio 74.25 / 61.75 = 1.2024, which the article rounds to 1.20.
mu = 68; SII = 12.5; alpha = 61.75; RII_ratio = 1.2024
Ratio relative index after a gain of 1 year in every quintile
Under Programme A in the article the slope index stays at 12.5 years but mean health rises to 69 years, so the intercept is 62.75 years and the ratio falls to 75.25 / 62.75 = 1.1992.
mu = 69; SII = 12.5; alpha = 62.75; RII_ratio = 1.1992
Common errors
Using cumulative shares instead of midpoints as ranks for the ratio relative index
Placing each quintile at the end of its range, from 0.2 to 1.0, leaves the slope at 12.5 years for equal shares but moves the intercept to 68 minus 0.6 times 12.5, or 60.5 years. The ratio becomes 73.0 / 60.5 = 1.2066 instead of 1.2024.
Sources
WHO handbook definition of the relative index of 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 3.5, tip box on other applications of the slope index of inequality and concentration index (printed page 45), which generates the relative index in the same manner as the slope index but divides the predicted values at rank 1 and rank 0 rather than subtracting them.
Canonical Identity
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