The CIX is related to the Gini coefficient, which is widely used to measure how much income is concentrated in the hands of the richest in a given country. The Gini coefficient can be expressed in the form of a curve that shows the sample ranked by income on the x-axis, and the cumulative distribution of income on the y-axis. If everyone in the population has the same income, the curve lies exactly over the diagonal and the Gini index is equal to zero. The area between the diagonal and the observed curve is used to measure the degree of income concentration. The CIX uses an analogous approach by ranking individuals according to socioeconomic position on the x-axis and plotting, for example, cumulative intervention coverage on the y-axis. Thus, if every wealth quintile had 20% of all the vaccines distributed in a population, for example, the line would be exactly on the diagonal, and there would be no inequality.
Concentration curve for measles vaccination and underweight using data from the Nigeria 2008 DHS
Typically, however, health interventions are more concentrated towards the richer groups, and the CIX assumes a positive value, as the curve is below the diagonal. Figure 1 (left) shows the example of measles vaccination in Nigeria, where coverage levels in the five quintiles were 17%, 28%, 41%, 58%, and 75%, respectively, and the CIX is equal to 26.5. By contrast, in the case of ill health, where poorer groups are affected more than richer groups, the CIX is negative. So in Nigeria, where underweight prevalence for the wealth quintiles Q1 to Q5 was 36%, 29%, 22%, 16%, and 10%, respectively, the CIX is -22.4 (Figure 1, right). The main downside of the CIX is the lack of direct interpretability of its values. Clearly, a value of 20 means more inequality than a value of eight, but these numbers lack a clear meaning, unlike Q5/Q1 ratios, which are easily interpretable.
You can download the concentration index ado-file for Stata using the following command:
net install cixr, from("https://www.equidade.org/files")
You can also download the CIX ado-file clicking here.
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.
For measuring absolute inequalities, the SII is being increasingly used. This index is typically derived through linear regression of the health outcome on the midpoints of the ranks obtained by ordering the sample by the explanatory variable when using grouped data. The ranks are scaled so that the values range from zero to one. When using ranks based on quintiles, each group includes approximately 20% of the sample, and the midpoints of the ranks are close to 0.1, 0.3, 0.5, 0.7, and 0.9 for the five quintiles, respectively. The SII is the slope of the resulting regression line, and represents the absolute difference in the fitted value of the health indicator between the highest (score of 1) and the lowest (score of 0) values of the socioeconomic indicator rank. Using the same data used to calculate CIX above (measles vaccination in the 2008 Nigeria DHS survey), we get a regression line that crosses the y-axis (where socioeconomic position equals zero) at 7.6% coverage, and crosses the right side of the chart (where socioeconomic position equals one) at 80%. The SII equals 72.4, which is the difference between these two coverage levels, and indicates that vaccine coverage at the top of the wealth scale is 72.4 percentage points higher than at the bottom.
You can download the slope index of inequality ado-file for binary outcomes in Stata using the following command:
net install siilogit, from("https://www.equidade.org/files")
You can also install an alternative version that is intended for continuous outcomes:
net install siilin, from("https://www.equidade.org/files")
You can also download the siilogit ado-file clicking here or the siilin ado-file clicking here
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]