Concept Architecture
Concept
Theoretically, Slope Index of Inequality (SII) is an absolute measure of socioeconomic inequality that quantifies the difference in a health outcome between the most and least advantaged individuals while incorporating the entire socioeconomic distribution. Rather than comparing only extreme groups, the SII uses regression methods based on ranked socioeconomic position, making it sensitive to the size and ordering of all socioeconomic groups. The concept is founded on regression analysis, epidemiology and health equity measurement and is widely used in population health and health economics.
Mathematically, the SII is estimated by regressing the health outcome on the fractional socioeconomic rank (ridit score). The regression coefficient represents the absolute difference in the expected value of the health outcome between individuals at the bottom and top of the socioeconomic hierarchy. Linear regression is commonly used for continuous outcomes, while generalised linear models may be used for binary or count outcomes with appropriate transformations.
In practice, individuals or population groups are ranked according to socioeconomic status, assigned fractional ranks based on their cumulative population share, and analysed using weighted regression. The estimated regression slope provides the SII, with positive values indicating that the health outcome is concentrated among higher socioeconomic groups and negative values indicating concentration among lower socioeconomic groups. In health economics, the SII is frequently applied to evaluate inequalities in health status, healthcare utilisation, preventive service uptake and health-related quality of life.
Purpose
Used to quantify the absolute socioeconomic gradient in health outcomes or healthcare utilisation across the entire population, supporting equity assessment, policy evaluation and monitoring of health inequalities over time.
Mathematical Formulae
Primary Formula
Y? = ?? + ??R? + �?
SII = ??
where:
- Y? = health outcome
- R? = fractional socioeconomic rank (ridit score)
- ?? = Slope Index of Inequality
Supporting Formulae
Fractional socioeconomic rank:
R? = (i ? 0.5) / n
Predicted inequality:
SII = ?(R = 1) ? ?(R = 0)
Weighted regression objective:
min ? w?(Y? ? ?? ? ??R?)�
where:
- w? = population weight
Related Mathematical Methods
- Relative Index of Inequality
- Ridit Score
- Weighted Linear Regression
- Generalised Linear Models
- Concentration Index
- Concentration Curve
- Health Inequality Measurement
Example
A health economist evaluates influenza vaccination coverage across socioeconomic quintiles. Individuals are ranked by household income and assigned fractional socioeconomic ranks. A weighted linear regression of vaccination coverage on the fractional rank estimates:
?? = 18.4 percentage points
The Slope Index of Inequality is therefore 18.4 percentage points, indicating that predicted vaccination coverage among the highest socioeconomic group exceeds that of the lowest group by 18.4 percentage points after accounting for the entire socioeconomic distribution.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| RANK.AVG | =(RANK.AVG(A2,$A$2:$A$1001,1)-0.5)/COUNT($A$2:$A$1001) | Calculate fractional socioeconomic ranks. |
| LINEST | =LINEST(B2:B1001,C2:C1001,TRUE,TRUE) | Estimate the regression coefficient representing the SII. |
| SUMPRODUCT | =SUMPRODUCT(D2:D1001,E2:E1001) | Apply population weights in preliminary weighted calculations. |
| FORECAST.LINEAR | =FORECAST.LINEAR(1,B2:B1001,C2:C1001)-FORECAST.LINEAR(0,B2:B1001,C2:C1001) | Calculate the predicted difference between the highest and lowest socioeconomic ranks. |
VBA (Optional)
Automate calculation of fractional socioeconomic ranks, weighted regression estimation and production of Slope Index of Inequality reports across multiple health outcomes.
Sources
- Pamuk ER. Social class inequality in mortality from 1921 to 1972 in England and Wales. Population Studies. 1985;39:17?31.
- Mackenbach JP, Kunst AE. Measuring the magnitude of socio-economic inequalities in health: An overview of available measures illustrated with two examples from Europe. Social Science & Medicine. 1997;44(6):757?771.
- Harper S, Lynch J. Methods for Measuring Cancer Disparities: Using Data Relevant to Healthy People 2010 Cancer-Related Objectives.
- O'Donnell O, van Doorslaer E, Wagstaff A, Lindelow M. Analyzing Health Equity Using Household Survey Data. World Bank.
- World Health Organization. Handbook on Health Inequality Monitoring.
Related Concepts (2)
Library
Publications
1
Distributional Cost-Effectiveness Analysis: Quantifying Health Equity Impacts and Trade-Offs — Cookson, Griffin, Norheim & Culyer, 1st Edition ed., 2020 (Oxford University Press)
The definitive practical guide to distributional cost-effectiveness analysis (DCEA), a suite of methods for quantifying who gains and who loses from health programmes and the trade-offs between improving total health and reducing unfair health inequality. Volume 7 in the Handbooks in Health Economic Evaluation series.
BookView source →
Frequently Asked Questions (6)
What is the slope index of inequality?
A summary measure of absolute health inequality across a socioeconomic gradient, estimated using regression across the full distribution rather than two extremes.
Source: Mackenbach & Kunst 1997
What kind of health inequality does the slope index of inequality summarise?
The slope index of inequality summarises absolute health inequality across a full socioeconomic gradient, expressing the gap in a health measure between the top and bottom of that range. Rather than comparing only the richest and poorest, it is estimated by regression across the whole distribution, so every group contributes to the result. This gives an absolute reading of inequality, complementing the relative picture that a concentration index provides. Measuring the absolute health gap along the social scale is what it does. Mackenbach and Kunst (1997) set out the method.
Source: Mackenbach & Kunst 1997
What does the slope index of inequality measure?
The slope index of inequality measures absolute health inequality across a socioeconomic gradient, capturing the difference in health associated with socioeconomic position across the full distribution. So the slope index measures absolute inequality across the gradient, which is why it uses the full distribution, since it summarises how health changes with socioeconomic position across all groups, and measuring the absolute difference in health across the socioeconomic gradient captures inequality more fully than comparing only the top and bottom groups.
Source: Mackenbach & Kunst 1997
How is the slope index of inequality estimated?
The slope index of inequality is estimated using regression across the full socioeconomic distribution, relating health to socioeconomic position across all groups rather than only comparing two extremes. So the slope index is estimated by regression over the full distribution, which is why it differs from extreme comparisons, since using regression across all socioeconomic groups captures the gradient more completely, and estimating it this way gives a measure of absolute health inequality that reflects the whole distribution rather than just the difference between the richest and poorest.
Source: Mackenbach & Kunst 1997
Why is the slope index of inequality used?
The slope index of inequality is used to measure health inequality across the whole socioeconomic gradient in absolute terms, giving a fuller picture than comparing only two extreme groups. So the slope index is used for a full-gradient measure, which is why it uses regression, since it captures inequality across all socioeconomic groups rather than just the extremes, and using the slope index provides a summary of absolute health inequality that reflects the entire socioeconomic distribution, supporting the analysis of how health varies with socioeconomic position.
Source: Mackenbach & Kunst 1997
How does the slope index of inequality relate to the concentration index?
The slope index of inequality relates to the concentration index in that both summarise socioeconomic health inequality, with the slope index measuring absolute inequality across the gradient and the concentration index measuring relative inequality. So the slope index and concentration index are related inequality measures, which is why they are compared, since both quantify socioeconomic health inequality but in different ways, and while the concentration index captures relative inequality from the concentration curve, the slope index captures absolute inequality across the gradient, together providing complementary measures of health inequality.
Source: Mackenbach & Kunst 1997
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 1 Jan 2026
Content version: 1.0.0
Canonical Identity
- Term code
- HS-HP-HE-028
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