Methods for measuring health inequalities (Part III)
Maria Cristina Schneider, Carlos Castillo-Salgado, Jorge Bacallao, Enrique Loyola, Oscar J. Mujica, Manuel Vidaurre, and Anne Roca.

Gini coefficient and Lorenz curve
The Gini coefficient is based on the Lorenz curve, that is a cumulative frequency curve that compares the empirical distribution of a variable with its uniform distribution (based on equality), represented by a diagonal line. The greater the distance, or more properly, the greater the area included between the Lorenz curve and the diagonal, the greater the inequality. The classical example is the distribution of income in a population.

For application in a health context, the abscissa or x-axis represents the cumulative proportion for the population and the ordinate or y-axis, the cumulative proportion for the health variable being studied. The individuals/groups or geographical units that make up the population are ordered by the health variable being studied, from the worst situation to the best situation. The greater the area between the curve and the diagonal, the greater the inequality. The curve can be below or above the diagonal, depending on the variable used. When this is beneficial for the population (for example, access to drinking water), the curve is below the diagonal line, while when it is detrimental (for example, deaths) the curve is above the diagonal line.

One of the ways to measure the degree of inequality is the Gini coefficient, that is a summary measure of the deviation of the Lorenz curve with respect to the diagonal line for equality (figure 3). The Gini coefficient is twice the area between the curve of Lorenz and the diagonal; its value ranges from 0 (perfect equality) to 1 (total inequality).

Concentration curve and concentration index
If the population or geographical units are ordered by socioeconomic status, and not by a health variable, one can include the socioeconomic dimension in the analysis. The concentration curve and concentration index are calculated by the same method as the Lorenz curve and the Gini coefficient, but incorporating the social dimension. The concentration index takes values between –1 and + 1. Values are negative when the curve is above the diagonal line and positive when it is below the diagonal. If the orderings by the socioeconomic variable and the health variable coincide, then the Lorenz and concentration curves also coincide, as do the concentration index and the Gini coefficient. Given that the order of the countries used in the previous examples by the socioeconomic variable is the same as that by the health variable, in the following example the countries are ordered by the current value of GNP per capita, without adjusting for purchasing power parity. Thus one avoids getting results identical to those in the previous example.

If the order does not vary considerably, results for the Gini coefficient and the concentration index tend to be similar, particularly when the number of observations is large. In a study that analyzed a larger number of subnational data for several health indicators it was shown that, for health variables related to socioeconomic factors, differences between the Gini coefficient and the concentration index are small.

Comparison of the best known indicators
According to Wagstaff,4 among the indicators analyzed in their publication (rate ratio, Gini coefficient, modified Gini coefficient, index of dissimilarity, slope index of inequality (SII) and relative index of inequality (RII), and concentration index), only the RII and the concentration index meet the necessary requirements for the measurement of the inequalities cited above:
1) they reflect the socioeconomic dimension of inequalities in the health field;
2) they use information on the entire population, and
3) they are sensitive to redistribution of the population among different social groups.

In the review carried out by Thió,12 this author notes that Kunst and Mackenbach5 are inclined toward use of standard regression models and by regression using percentiles (RII), that according to them are the measures that best satisfy the following criteria:

• Validity: the indicators should measure both the direction and the strength of the association between socioeconomic level and health. Measures based on ratios, the population attributable risk (PAR), and the index of dissimilarity do not measure health inequalities well when there is not a clear gradient from the highest class to the lowest. Measures that do not take into account the socioeconomic group (Gini coefficient, Lorenz curve) obviously do not have this attribute.

• Precision: the indicators should make it possible to calculate confidence intervals for the estimates, especially when working with small samples. In order to increase precision it is important to take into account information on all the socioeconomic groups, something that measures that compare the extremes do not do. It is difficult to calculate confidence intervals for the Gini coefficient and the index of dissimilarity because their distributional properties are complicated.

• Flexibility: the indicator should make it possible to calculate both absolute and relative measures. Furthermore, it is desirable to be able to control for the effect of confounding factors and this is only possible using regression models.


Advantages and disadvantages of the indicators presented
In favor of the rate ratio and the rate difference it can be noted that they are the easiest to calculate and interpret, even by people without academic training. Their great disadvantage is that they overlook inequalities among intermediate groups. Another important limitation is that they do not take into account the sizes of different groups.5

The advantage of the effect index is that it encompasses all socioeconomic groups (and not only the extremes) and that its calculation incorporates other variables.5 Its disadvantage is that it is necessary to have statistical knowledge to select the best model and interpret the results. Furthermore, the assumptions for regression can be restrictive and in many cases make it not applicable.

PAR is easy to calculate and interpret. Its other advantage is that it not only measures the health indicator for groups with high socioeconomic levels (compared with the total population), but also takes into account the size of the population of different groups, because the larger the groups with high values of the indicator, the greater is the potential for reduction of the global indicator.5

The index of dissimilarity is not sensitive to the direction of the association between socioeconomic level and health.12 Furthermore, it is not recommended for analysis of health status because it presupposes redistribution of the burden of disease or death, that is inadmissible from the ethical standpoint.

The RII and the SII have the advantage of taking into account the size of the population and the relative socioeconomic position of groups. These measures are sensitive to the average health situation of the population.12 However, their calculation and interpretation are relatively complex and can yield unreliable results when they are applied to small samples with aggregate data.

The Lorenz curve and the Gini coefficient take full advantage of the information on all subjects or population groups but their disadvantage is that they overlook socioeconomic status.5 Murray and López13 have pointed out, in addition, that the Gini coefficient is not very sensitive to changes in the size of inequality in mortality of age groups above 15 years. Moreover, information on the coefficient is not sufficient for understanding the form of the inequality if it is not accompanied by the corresponding curve.

The concentration index incorporates the socioeconomic dimension, but shares the other disadvantages noted for the Gini coefficient.


Types of results that the indicators provide
The indicators presented provide different measures of inequality in health. Some make it possible to estimate how many more times an event occurs in a particular group, in comparison with another group in an opposed situation; others make it possible to estimate how many cases of a given event could be avoided if the situation improved, or what proportion of a given event occurs in a poorer section of the population.

The rate ratio and the RII provide similar information, although the complexity of the method for obtaining them is different. The former is simpler and only takes extreme groups into account. There is a similar contrast between the rate difference and the SII. Nevertheless, the results are not identical. Each investigator must define the degree of sophistication desired for their study.

The PAR obtained through the simplified formula is the measure that is most indicated when the purpose is to obtain data for rapid decision-making. The PAR calculated using regression models makes it possible to control for confounding factors and, as a result, to obtain more complete information, but it is subject to the limitations of verification of the adjustments made and the assumptions for the regression model.

Both the PAR and the index of dissimilarity provide percentage measures of inequality, but the calculation of the former is based on the group or geographical unit with the best socioeconomic status, while the latter takes into account all groups and reduces them to a common reference value. The choice between these two measures depends on the purposes of the study.5 The index of dissimilarity suggests a less ambitious goal, but this is perhaps more realistic.

The underlying logic of the Gini coefficient and the concentration index is the same but the latter has the advantage of including the socioeconomic dimension, which, in turn, poses the risk of doing this through use of an inappropriate indicator. In a study that compared the results of the Gini coefficient and the concentration index grouping the departments into socioeconomic levels, lower values were found for the concentration index in the 17 variables studied (14 health variables and 3 socioeconomic variables).

Some of the indicators require more complex instruments, such as statistical packages or more complicated methods of calculation. Choice of these indicators depends on the knowledge of the researcher and the objectives of the study. Nevertheless, whatever the indicator, what is important is that it is interpreted adequately and that its scope and its limitations are known.

If the objective of the study is to gain a general view of the issue for practical purposes, for action, rather than for strictly scholarly purposes, it is preferable to use less complex indicators that are easier to calculate and interpret. Thus, measurement of inequalities could have a more immediate application. However, whenever possible, these results should be compared with the results from those from using the most powerful methods, although they are more complex.


Different indicators can lead to different conclusions
The use of different indicators can lead to different conclusions about the existence of inequalities. Wagstaff4 gives the example of a study on the relationship between chronic diseases and social class in Sweden, compared with another one carried out in England and Wales, in which opposite conclusions were reached using the rate ratio and the concentration index. Regardless of the type of indicator, it is very important that there be a descriptive analysis of the differences and that, whenever possible, more than one indicator is used. Thus the likelihood of correct findings increases.

The existence of low levels of inequality in health always depends on the groups being compared and does not imply that good health conditions exist. In order to interpret the results, it is important to provide a context for them and to take into account the variables used and the scenario in which they existed. There are no set threshold values for high or low inequality, so that the decision tends to be difficult unless the indicators have extreme values, and it is always contextual.


Final considerations
The search for equity in health is one of the principal current objectives of PAHO. It is not enough only to speak about inequalities, but it is also necessary to demonstrate objectively their existence. Measurement of inequalities between countries and within a single country is the first step for taking decisions to implement actions and strategies designed to reduce, and ultimately to eliminate, such inequalities. Transforming the results of these studies into policies is a challenge that it is necessary to confront. To do this, it is necessary to find ways to integrate researchers and decision-making bodies and to develop the capacity of the personnel who work with the decision-making bodies to carry out their own studies on possible inequalities in the field of health.

Once the situation is measured and corresponding actions and strategies are implemented, it is also necessary to measure the impact of these actions and strategies.


References (Part III)
4. Wagstaff A, Paci P, Van Doorslaer E. On the measurement of inequalities in health. Soc Sci Med 1991;33:545–557.

5. Kunst AE, Mackenbach JP. Measuring socioeconomic inequalities in health. WHO Regional Office for Europe, 1994 (document EUR/ ICP/RPD 416). Acceso el 12 noviembre 2002. Disponible en: http://www.who.dk/Document/PAE/Measrpd416.pdf.

11. Brown MC. Using Gini-style indices to evaluate the spatial patterns of health practitioners: theoretical considerations and an application based on Alberta data. Soc Sci Med 1994;38:1243–1256.

12. Thió CB. Las desigualdades sociales en la salud. Revisión de la bibliografía. Barcelona: Adjuntament de Barcelona, Instituto Municipal de Salud Pública, Imprenta Municipal; 1996.

13. Murray CJL, López AD. Estimating causes of death: new methods and global and regional applications for 1990. En: Murray CJL López, AD, eds. The global burden of disease: a comprehensive assessment of mortality and disability from diseases, injuries, and risk factors in 1990 and projected to 2020. Cambridge, MA: Harvard University Press; 1996.

The references respect the order of the original article.


Source:
Originally published with the title “Métodos de medición de las desigualdades de salud” in Pan American Journal of Public Health 12(6), 2002.


—from: Epidemiological Bulletin, Vol. 26 No. 2, June 2005

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