Annex 11. Overview of summary measures of health inequality: definition, calculation and interpretation
Table A11.1 provides an overview of selected summary measures of health inequality including pairwise measures and complex measures. For each measure, the table shows the formula and specifies whether the measure is absolute or relative, pairwise or complex, weighted or unweighted and ordered or non-ordered. It indicates whether the measure has a unit, the value of no inequality and the interpretation.
TABLE A11.1 Overview of summary measures of health inequality: definition, calculation and interpretation
| Summary measure | Formula |
Absolute/ relative |
Pairwise/ complex |
Weighted/ unweighted |
Ordered/ non-ordered |
Unit | Value of no inequality | Interpretation |
|---|---|---|---|---|---|---|---|---|
| Pairwise measures | ||||||||
| Difference (D) | \[D = y_A - y_B\] | Absolute | Pairwise | Unweighted |
Ordered/ non-ordered |
Unit of indicator | Zero | Larger absolute values indicate higher levels of inequality. |
| Ratio (R) | \[R = y_A / y_B\] | Relative | Pairwise | Unweighted |
Ordered/ non-ordered |
No unit | One | R takes only positive values. Values further from 1 indicate higher levels of inequality. |
| Complex measures | ||||||||
| Ordered measures | ||||||||
| Regression-based measures | ||||||||
| Slope index of inequality (SII) | \[SII = \hat{v}_1 - \hat{v}_0\] | Absolute | Complex | Weighted | Ordered | Unit of indicator | Zero | Positive values indicate a concentration among advantaged subgroups. Negative values indicate a concentration among disadvantaged subgroups. Larger absolute values indicate higher levels of inequality. |
| Relative index of inequaulity (RII) | \[RII = \hat{v}_1 / \hat{v}_0\] | Relative | Complex | Weighted | Ordered | No unit | One | RII takes only positive values. Values >1 indicate a concentration among advantaged subgroups. Values <1 indicate a concentration among disadvantaged subgroups. Values further from 1 indicate higher levels of inequality. |
| Ordered disproportionality measures | ||||||||
| Absolute concentration index (ACI) | \[ACI = \sum_j p_j(2X_j - 1)y_j\] | Absolute | Complex | Weighted | Ordered | Unit of indicator | Zero | Positive values indicate a concentration of the indicator among advantaged subgroups. Negative values indicate a concentration of the indicator among disadvantaged subgroups. Larger absolute values indicate higher levels of inequality. |
| Relative concentration index (RCI) | \[RCI = \frac{ACI}{\mu} \times 100\] | Relative | Complex | Weighted | Ordered | No unit | Zero | RCI is bounded between −1 and +1 (or −100 and +100 if multiplied by 100). Positive values indicate a concentration of the indicator among advantaged subgroups. Negative values indicate a concentration of the indicator among disadvantaged subgroups. Larger absolute values indicate higher levels of inequality. |
| Non-ordered measures | ||||||||
| Mean difference from best-performing subgroup (unweighted) (MDBU) | \[MDBU = \frac{1}{n} \times \sum_j |y_j - y_{best}|\] | Absolute | Complex | Unweighted | Non-ordered | Unit of indicator | Zero | MDBU takes only positive values. Larger values indicate higher levels of inequality. |
| Mean difference from best-performing subgroup (weighted) (MDBW) | \[MDBW = \sum_j p_j |y_j - y_{best}|\] | Absolute | Complex | Weighted | Non-ordered | Unit of indicator | Zero | MDBW takes only positive values. Larger values indicate higher levels of inequality. |
| Mean difference from reference point (unweighted) (MDRU) | \[MDRU = \frac{1}{n} \times \sum_j |y_j - y_{ref}|\] | Absolute | Complex | Unweighted | Non-ordered | Unit of indicator | Zero | MDRU takes only positive values. Larger values indicate higher levels of inequality. |
| Mean difference from reference point (weighted) (MDRW) | \[MDRW = \sum_j p_j |y_j - y_{ref}|\] | Absolute | Complex | Weighted | Non-ordered | Unit of indicator | Zero | MDRW takes only positive values. Larger values indicate higher levels of inequality. |
| Mean difference from mean (unweighted) (MDMU) | \[MDMU = \frac{1}{n} \times \sum_j |y_j - \mu|\] | Absolute | Complex | Unweighted | Non-ordered | Unit of indicator | Zero | MDMU takes only positive values. Larger values indicate higher levels of inequality. |
| Mean difference from mean (weighted) (MDMW) | \[MDMW = \sum_j p_j |y_j - \mu|\] | Absolute | Complex | Weighted | Non-ordered | Unit of indicator | Zero | MDMW takes only positive values. Larger values indicate higher levels of inequality. |
| Index of disparity (unweighted) (IDISU) | \[IDISU = \frac{MDMU}{\mu} \times 100\] | Relative | Complex | Unweighted | Non-ordered | No unit | Zero | IDISU takes only positive values. Larger values indicate higher levels of inequality. |
| Index of disparity (weighted) (IDISW) | \[IDISW = \frac{MDMW}{\mu} \times 100\] | Relative | Complex | Weighted | Non-ordered | No unit | Zero | IDISW takes only positive values. Larger values indicate higher levels of inequality. |
| Variance measures | ||||||||
| Between-group variance (BGV) | \[BGV = \sum_j p_j(y_j - \mu)^2\] | Absolute | Complex | Weighted | Non-ordered | Squared unit of indicator | Zero | BGV takes only positive values. Larger values indicate higher levels of inequality. |
| Between-group standard deviation (BGSD) | \[BGSD = \sqrt{BGV}\] | Absolute | Complex | Weighted | Non-ordered | Unit of indicator | Zero | BGSD takes only positive values. Larger values indicate higher levels of inequality. |
| Coefficient of variation (COV) | \[COV = \frac{BGSD}{\mu} \times 100\] | Relative | Complex | Weighted | Non-ordered | No unit | Zero | COV takes only positive values. Larger values indicate higher levels of inequality. |
| Non-ordered disproportionality measures | ||||||||
| Theil index (TI) | \[TI = \sum_j p_j \frac{y_j}{\mu} \ln(\frac{y_j}{\mu}) \times 1000\] | Relative | Complex | Weighted | Non-ordered | No unit | Zero | TI takes only positive values. Larger values indicate higher levels of inequality. |
| Mean log deviation (MLD) | \[MLD = \sum_j p_j (-\ln(\frac{y_j}{\mu})) \times 1000\] | Relative | Complex | Weighted | Non-ordered | No unit | Zero | MLD takes only positive values. Larger values indicate higher levels of inequality. |
| Impact measures | ||||||||
| Population attributable risk (PAR) | \[PAR = y_{ref} - \mu\] | Absolute | Complex | Weighted |
Ordered/ non-ordered |
Unit of indicator | Zero | PAR takes only positive values for favourable indicators and only negative values for adverse indicators. Larger absolute values indicate higher levels of inequality. |
| Population attributable fraction (PAF) | \[PAF = \frac{PAR}{\mu} \times 100\] | Relative | Complex | Weighted |
Ordered/ non-ordered |
No unit | Zero | PAF takes only positive values for favourable indicators and only negative values for adverse indicators. Larger absolute values indicate higher levels of inequality. |
\(y_A\) = estimate for subgroup A.
\(y_B\) = estimate for subgroup B.
\(y_j\) = estimate for subgroup j.
\(y_{best}\) = estimate for best-performing subgroup.
\(y_{ref}\) = estimate for reference point.
\(p_j\) = population share for subgroup j.
\(X_j = \sum_{i=1}^j p_i - 0.5(p_j)\) = relative rank of subgroup j.
\(\mu\) = setting average.
\(\hat{v}_0\) = predicted value of the hypothetical person at the bottom of the social group distribution (rank 0).
\(\hat{v}_1\) = predicted value of the hypothetical person at the top of the social group distribution (rank 1).
\(n\) = number of subgroups.