The Concentration Index (CIX) is closely related to the Gini coefficient, which is widely used to measure income inequality within a population. The Gini coefficient is based on a curve where individuals are ranked by income on the x-axis and the cumulative share of income is plotted on the y-axis. If income is equally distributed, the curve coincides with the diagonal, and the Gini equals zero. The greater the area between the curve and the diagonal, the higher the level of inequality.
The CIX applies an analogous concept to health variables. Individuals are ranked according to socioeconomic position on the x-axis, while the cumulative distribution of a health variable (e.g., intervention coverage) is plotted on the y-axis. If all socioeconomic groups have equal shares of the health variable—for example, if each wealth quintile accounts for 20% of vaccinations—the curve lies on the diagonal, indicating no inequality.
Concentration curve for measles vaccination and underweight using data from the Nigeria 2008 DHS
In practice, health interventions are often concentrated among wealthier groups, resulting in a curve below the diagonal and a positive CIX. For example, measles vaccination coverage in Nigeria (2008 DHS) increased from 17% in the poorest quintile to 75% in the richest, yielding a CIX of 26.5. Conversely, for adverse health outcomes that disproportionately affect poorer groups, the curve lies above the diagonal and the CIX is negative. In the same dataset, underweight prevalence decreased from 36% to 10% across wealth quintiles, resulting in a CIX of −22.4.
A limitation of the CIX is that its magnitude is not directly intuitive. While higher absolute values indicate greater inequality, the index lacks the straightforward interpretability of simpler measures such as quintile ratios.
Stata implementation
The CIX can be estimated in Stata using the cixr command:
net install cixr, from("https://www.equidade.org/files")The current version of the command:
In partnership with the Countdown to 2030, we also developed a video tutorial to provide instructions on how to calculate and interpret the CIX using Stata.
The Slope Index of Inequality (SII) is a widely used measure of absolute inequality. It is based on a regression model that relates the health outcome to a ranked socioeconomic variable scaled from 0 (lowest position) to 1 (highest position).
When using grouped data (e.g., wealth quintiles), each group represents approximately 20% of the population. The midpoints of the rank distribution are typically around 0.1, 0.3, 0.5, 0.7, and 0.9. The SII corresponds to the slope of the regression line and represents the absolute difference in the predicted value of the health indicator between the top and bottom of the socioeconomic scale.
Using the same Nigeria example, the fitted regression line predicts 7.6% vaccination coverage at the lowest end of the socioeconomic scale and 80% at the highest end. The SII is therefore 72.4 percentage points, indicating a large absolute inequality in coverage.
Stata implementation
The previous commands siilogit and siilin have been replaced by a unified command:
net install sii, from("https://www.equidade.org/files")The new sii command:
In partnership with the Countdown to 2030, we also developed a video tutorial to provide instructions on how to calculate and interpret the SII using Stata.
[For more information on inequality measures, please read Barros and Victora's paper on measuring inequalities]
We also developed the ICEHmeasures package for R, which brings together several key inequality measures in a single toolkit. The package includes:
The package is available on CRAN and can be installed with:
install.packages("ICEHmeasures")This provides an integrated and reproducible workflow for inequality analysis in R.