## Measuring Health Inequalities: Gini Coefficient and Concentration Index

Equity in health is one of the basic values that guide the Pan American Health Organization’s technical cooperation with the countries of the American Region. The fundamental difference between inequities and inequalities resides in the fact that inequities represent inequalities that are considered and qualified as unjust and avoidable. As a result, measuring health inequalities represents the first step towards the identification of inequities in health. In the Region of the Americas, the availability of health information aggregated by geographical units generally permits the analysis of inequalities, which should serve as a basis for decision-making. Indeed, 21 countries of the Region already dispose of data at the subnational level within the Core Data Initiative. Carrying out these analyses is essential to reducing the inequities that are characteristic of the health profile of the Region.

There exists a wide variety of summary measures for the magnitude of inequalities in health. One specific indicator is the Gini Coefficient, which, along with the Concentration Index, has been taken from the field of economics and applied to the study of health inequalities.

Gini Coefficient and Lorenz Curve
The Gini coefficient is based on the Lorenz curve, a cumulative frequency curve that compares the distribution of a specific variable with the uniform distribution that represents equality (Figure 1). This equality distribution is represented by a diagonal line, and the greater the deviation of the Lorenz curve from this line, the greater the inequality.

 Figure 1: Areas for calculation of the Gini Coefficient When applying this index to health variables, the cumulative proportion of the population is generally shown on the X axis, and the cumulative proportion of the health variable on the Y axis. The greater the distance from the diagonal line, the greater the inequality. The curve can be below or above the diagonal depending on the variable used. When the variable is beneficial to the population, as for example in the case of access to water, the curve is found below the diagonal line. In contrast, when the variable is prejudicial, as in the case of deaths, it is found above the line.

The Gini Coefficient ranges from 0 to 1, 0 representing perfect equality and 1 total inequality. It corresponds to twice the area between the Lorenz curve and the diagonal (Figure 1). There are different methods to calculate the Gini, but a simple formula, shown below, was provided by Brown (1994).

The first step for calculating the Gini coefficient using geopolitically aggregated data is to sort the geographic units by the health variable (e.g., infant mortality rate) from the worst to the best situation (highest to lowest rate). The rates are then transformed into continuous variables and thecumulative proportion is calculated for both variables. The graph showing the cumulative proportion for the health variable (Y axis) and the cumulative proportion of the population is then prepared, and the Gini coefficient can be calculated as the absolute value of the result of the Brown formula.

Although the level of inequalities is reflected in the value of the Gini coefficient itself (for example, a value very close to 0 will represent a low level of inequality), the interpretation of the coefficient is usually done in comparative terms, by contrasting the calculated value to that of other geographic units, population groups etc. Again, a coefficient of 0.2 will represent a lower level of inequality than a coefficient of 0.4. The cumulative proportions of borth variables can also be read directly from the graphical representation of the Lorenz curve (see following example).

Concentration Index and Concentration Curve
The socioeconomic dimension can be included in the analysis through the calculation of the Concentration Index if the population or the geographic units are ordered by socioeconomic status and not following a health variable. The Concentration Index is calculated in the same way as the Gini Coefficient, but it varies between –1 and +1. The values are negative when the curve is above the diagonal and positive when they are under the curve. If the order resulting from sorting by the socioeconomic and health variables are the same, the concentration index will have the same absolute value as the Gini coefficient.

Following is an example of calculation of Gini Coefficient using infant mortality rates from 5 countries of the Andean area in 1997 (PAHO, Basic indicators brochure 1998). The data for this example are presented in table 1a and table 1b below. The Lorenz Curve is shown in figure 2.

The steps for the calculation of the Gini coefficient and graphing of the Lorenz curve are the following:

• Sort the geographic units by the health variable (infant mortality rate) from the worst situation (highest rate) to the best situation (lowest rate).
• Calculate the number of infant deaths for each geographic unit.
• Calculate what proportion of the total of all infant deaths and what proportion of the total of all live births is observed in each geographical unit.
• Calculate the cumulative proportion of each of the two variables.
• Calculate the Gini coefficient using the formula
• Graph the curve using the X axis for the proportion of the cumulative population (live births) and the Y axis for the proportion of cumulative health variable observations (infant deaths).
• Interpretation:
Gini Coefficient
: In our example, the result was 0.20, which is not a high value and is closer to zero (total equality) than 1 (total inequality). However, to be able to have a complete picture of the situation, it would be necessary to compare this value with the values obtained from the other geographic areas.
Lorenz Curve: For example, we read on the graph that 30% of infant deaths occur among 20% of the population of live births.

Table 1a: Country, GNP per capita, Infant Mortality Rate (IMR), live births, infant deaths, proportion of the live births population, and proportion of deaths

 Country GNP per capita 1996 IMR (per 1,000 LB) 1997 Live births (1,000) 1997 Infant deaths Proportion live births (X1) Proportion Infant deaths Bolivia 2,860 59 250 14,750 0.09 0.17 Peru 4,410 43 621 26,703 0.24 0.31 Ecuador 4,730 39 308 12,012 0.12 0.14 Colombia 6,720 24 889 21,336 0.34 0.24 Venezuela 8,130 22 568 12,496 0.22 0.14 Total 33 2,636 87,297 1 1

Table 1b: cumulative proportion of live births, cumulative proportion of infant deaths and steps for the calculation of the Gini coefficient

 Country Cumulative proportion. live births Cumulative proportion infant deaths Yi+1 + Yi (A) Xi+1 -Xi (B) A * B Bolivia 0.09 0.17 0.17 0.09 0.09 Peru 0.33 0.48 0.65 0.24 0.15 Ecuador 0.45 0.62 1.10 0.12 0.13 Colombia 0.78 0.86 1.48 0.33 0.50 Venezuela 1 1 1.86 0.22 0.40 Total 1.20

 Gini Coefficient: 0.2

 Figure 2: Lorenz Curve Cumulative proportion of infant deaths Cumulative proportion of live births

References:
(1) Whitehead M. The Concepts and Principles of Equity and Health. WHO Regional Office for Europe (EURO). Copenhagen, Denmark. 1991
(2) Brown M. Using Gini-style indices to evaluate the spatial patterns of health practitioners: theoretical considerations and an application based on Alberta data. Soc. Sci. Med. Vol. 38, No. 9. pp. 1243-1256. 1994
(3) Wagstaff A, Paci P, Van Doorslaer E. On the Measurement of Inequalities in health. Soc. Sci. Med. Vol. 33, No. 5. pp. 545-577. 1991

Source: Prepared by Drs. Carlos Castillo-Salgado, Cristina Schneider, Enrique Loyola, Oscar Mujica, Ms. Anne Roca and Mr. Tom Yerg of PAHO's Special Program for Health Analysis (SHA).