Relative Index of Inequality
Also known as: RII, Relative Index, Kunst-Mackenbach Relative Index of Inequality, Relative Slope Index of Inequality
The relative index of inequality (RII) is the relative counterpart of the slope index of inequality: instead of the absolute difference in a health outcome between the bottom and top of the socioeconomic hierarchy, it expresses that difference as a ratio. Like the SII, it is built from a regression of the outcome on each group's position in the cumulative socioeconomic distribution, so it uses the whole population and accounts for group sizes rather than comparing only the extreme categories. Mackenbach and Kunst's 1997 overview recommended the RII alongside the SII as the standard pair of summary measures for socioeconomic health inequality, precisely because relative and absolute inequality can move in opposite directions and both need to be reported. Sergeant and Firth's 2006 Biostatistics paper clarified the various definitions of the RII, compared estimation strategies, and supplied a parametric bootstrap for valid confidence intervals. The RII is dimensionless, which makes it directly comparable across outcomes, time periods, and populations with very different baseline rates. It is a mainstay of comparative health-inequality research and routine surveillance.
Key highlights
- Unitless ratio scale makes it directly comparable across outcomes, populations, and time periods with different baseline rates.
- Uses the whole population and group sizes via the rank regression, avoiding extreme-group instability.
- Naturally fitted as a log-linear or logistic rank model, integrating with standard regression machinery.
- Complements the slope index, revealing relative inequality trends that absolute measures can hide.
Intuition
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How it works
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When to use it
Use the relative index of inequality when you want a unitless, ratio-scale summary of the socioeconomic gradient in a health outcome that is comparable across outcomes, populations, and time despite differing baseline rates. It is the natural partner to the slope index of inequality, and reporting both is best practice because relative and absolute inequality can diverge. The RII is well suited to cross-national comparisons and to long-run trend analysis where overall rates change substantially, since it strips out the baseline level. It is inappropriate when the SES categories are not ordinal, when population shares are unknown, or when the policy question genuinely concerns absolute burden rather than proportional disparity. Be careful to state which definition of the RII you are using, and prefer model-based or bootstrap intervals over crude approximations when samples are small or the gradient is non-linear.
Strengths & limitations
- Unitless ratio scale makes it directly comparable across outcomes, populations, and time periods with different baseline rates.
- Uses the whole population and group sizes via the rank regression, avoiding extreme-group instability.
- Naturally fitted as a log-linear or logistic rank model, integrating with standard regression machinery.
- Complements the slope index, revealing relative inequality trends that absolute measures can hide.
- Captures only relative inequality, which can rise even as absolute gaps shrink, so it must be paired with the SII.
- Multiple competing definitions share the RII name, risking confusion if the chosen version is not stated.
- Requires an ordinal SES variable and accurate population shares to construct the rank axis.
- Simple confidence intervals can be inaccurate, particularly in small samples or with non-linear gradients.
Common pitfalls
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Applications
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Frequently asked
How is the RII related to the slope index of inequality?
Both come from the same regression of the outcome on a 0-to-1 socioeconomic rank axis that uses the whole population. The slope index reads off the absolute difference between the bottom and top of the hierarchy; the relative index expresses that gradient as a ratio - for instance, how many times higher disease is at the bottom than at the top - or as the slope divided by the mean. They are absolute and relative views of the same gradient and are meant to be reported together, since they can move in different directions.
Why can the RII rise while the SII falls?
Because they measure inequality on different scales. Suppose mortality drops sharply for everyone but the disadvantaged remain proportionally worse off. The absolute gap (SII) can shrink simply because all rates are lower, while the ratio of disadvantaged-to-advantaged mortality (RII) stays the same or even grows. This divergence is exactly why analysts report both: an improvement in absolute inequality can coexist with stagnant or worsening relative inequality, and the policy implications differ.
Why do different papers report different RII values for the same data?
Because 'relative index of inequality' names several non-identical quantities. One common version is the bottom-to-top rate ratio from a log-linear model; another is the slope index divided by the mean outcome. These answer slightly different relative questions and need not be equal. Sergeant and Firth catalogued these definitions and recommended clear reporting plus a parametric bootstrap for confidence intervals. Always state which definition and estimation method you used so your RII can be compared with others.
Sources
- 1.Mackenbach, J. P., & Kunst, A. E. (1997). Measuring the magnitude of socio-economic inequalities in health: an overview of available measures illustrated with two examples from Europe. Social Science & Medicine, 44(6), 757-771.
- 2.Sergeant, J. C., & Firth, D. (2006). Relative index of inequality: definition, estimation, and inference. Biostatistics, 7(2), 213-224.
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Cite this page
ScholarGate. (2026, June 23). Relative Index of Inequality. ScholarGate. https://scholargate.app/social-epidemiology/relative-index-of-inequality