Table A1.

Overview of summary measures of health inequality: formulas, characteristics and interpretation.

Summary Measure	Formula	Absolute/Relative	Simple/Complex	Ordered/Non-ordered	Weighted/Unweighted	Unit	Value of No Inequality	Interpretation
Simple measures
Difference (D)	$D=y_1-y_2$	Absolute	Simple	N/A	Unweighted	Unit of indicator	Zero	The larger the absolute value of D, the higher the level of inequality.
Ratio (R)	$R=y_1/y_2$	Relative	Simple	N/A	Unweighted	No unit	One	R assumes only positive values. The further the value of R from 1, the higher the level of inequality.
Complex measures
Ordered measures
Disproportionality measures
Absolute concentration index (ACI)	$ACI={\displaystyle \sum }_j{p}_j\left(2X_j-1\right)y_j$	Absolute	Complex	Ordered	Weighted	Unit of indicator	Zero	Positive (negative) values indicate a concentration of the indicator among the advantaged (disadvantaged). The larger the absolute value of ACI, the higher the level of inequality.
Relative concentration index (RCI)	$RCI=\frac{ACI}{\mu }\ast 100$	Relative	Complex	Ordered	Weighted	No unit	Zero	RCI is bounded between −100 and +100. Positive (negative) values indicate a concentration of the indicator among the advantaged (disadvantaged). The larger the absolute value of RCI, the higher the level of inequality.
Regression-based measures
Slope index of inequality (SII)	$SII=v_1-v_0$	Absolute	Complex	Ordered	Weighted	Unit of indicator	Zero	Positive values indicate a concentration among the advantaged and negative values indicate a concentration among the disadvantaged. The larger the absolute value of SII, the higher the level of inequality.
Relative index of inequality (RII)	$RII=v_1/v_0$	Relative	Complex	Ordered	Weighted	No unit	One	RII assumes only positive values. Values > 1 indicate a concentration among the advantaged and values < 1 values indicate a concentration among the disadvantaged. The further the value of RII from 1, the higher the level of inequality.
Non-ordered measures
Variance measures
Between-group variance (BGV)	$BGV={\displaystyle \sum }_j{p}_j{\left(y_j-\mu \right)}^2$	Absolute	Complex	Non-ordered	Weighted	Squared unit ofindicator	Zero	BGV assumes only positive values with larger values indicating higher levels of inequality.
Between-group standard deviation (BGSD)	$BGSD=\sqrt{{\displaystyle \sum }_j{p}_j{\left(y_j-\mu \right)}^2}$	Absolute	Complex	Non-ordered	Weighted	Unit of indicator	Zero	BGSD assumes only positive values with larger values indicating higher levels of inequality.
Coefficient of variation (COV)	$COV=\frac{BGSD}{\mu }\ast 100$	Relative	Complex	Non-ordered	Weighted	Unit of indicator	Zero	COV assumes only positive values with larger values indicating higher levels of inequality.
Mean difference measures
Mean difference from mean (unweighted) (MDMU)	$MDMU=\frac{1}{n}\ast {\displaystyle \sum }_j\left|y_j-\mu \right|$	Absolute	Complex	Non-ordered	Unweighted	Unit of indicator	Zero	MDMU assumes only positive values with larger values indicating higher levels of inequality.
Mean difference from mean (weighted) (MDMW)	$MDMW={\displaystyle \sum }_j{p}_j\left|y_j-\mu \right|$	Absolute	Complex	Non-ordered	Weighted	Unit of indicator	Zero	MDMW assumes only positive values with larger values indicating higher levels of inequality.
Mean difference from best-performing subgroup (unweighted) (MDBU)	$MDBU=\frac{1}{n}\ast {\displaystyle \sum }_j\left|y_j-y_{ref}\right|$	Absolute	Complex	Non-ordered	Unweighted	Unit of indicator	Zero	MDBU assumes only positive values with larger values indicating higher levels of inequality.
Mean difference from best-performing subgroup (weighted) (MDBW)	$MDBW={\displaystyle \sum }_j{p}_j\left|y_j-y_{ref}\right|$	Absolute	Complex	Non-ordered	Weighted	Unit of indicator	Zero	MDBW assumes only positive values with larger values indicating higher levels of inequality.
Index of disparity (unweighted) (IDIS)	$IDISU=\frac{\frac{1}{n}\ast {\displaystyle \sum }_j\left|y_j-\mu \right|}{\mu }\ast 100$	Relative	Complex	Non-ordered	Unweighted	No unit	Zero	IDISU assumes only positive values with larger values indicating higher levels of inequality.
Index of disparity (weighted) (IDISW)	$IDISW=\frac{{\displaystyle \sum }_j{p}_j\left|y_j-\mu \right|}{\mu }\ast 100$	Relative	Complex	Non-ordered	Weighted	No unit	Zero	IDISW assumes only positive values with larger values indicating higher levels of inequality.
Disproportionality measures
Theil index (TI)	$TI={\displaystyle \sum }_j{p}_j\frac{y_j}{\mu }ln\frac{y_j}{\mu }\ast 1000$	Relative	Complex	Non-ordered	Weighted	No unit	Zero	The larger the absolute value of TI, the greater the level of inequality.
Mean log deviation (MLD)	$\mathrm{MLD}={\displaystyle \sum }_j{p}_j(-\ln \left(\frac{y_j}{\mu }\right))\ast 1000$	Relative	Complex	Non-ordered	Weighted	No unit	Zero	The larger the absolute value of MLD, the higher the level of inequality.
Impact measures
Population attributable risk (PAR)	$PAR=y_{ref}-\mu$	Absolute	Complex	Ordered/ Non-ordered	Weighted	Unit of indicator	Zero	PAR assumes only positive values for favourable indicators and only negative values for adverse indicators. The larger the absolute value, the higher the level of inequality.
Population attributable fraction (PAF)	$PAF=\frac{PAR}{\mu }\ast 100$	Relative	Complex	Ordered/ Non-ordered	Weighted	No unit	Zero	PAF assumes only positive values for favourable indicators and only negative values for adverse indicators. The larger the absolute value of PAF, the larger the level of inequality.

$y_1$ = Estimate for subgroup 1. Usually the most-advantaged subgroup (ordered dimensions) or the best-performing subgroup (non-ordered dimensions). $y_2$ = Estimate for subgroup 2. Usually the most-disadvantaged subgroup (ordered dimensions) or the worst-performing subgroup (non-ordered dimensions). $y_j$ = Estimate for subgroup j. $y_{ref}$ = Estimate for reference subgroup. Usually the most-advantaged subgroup (ordered dimensions) or the best-performing subgroup (non-ordered dimensions). $p_j$ = Population share for subgroup j. $X_j={\displaystyle \sum }_j{p}_j-0.5p_j$ = Relative rank of subgroup j. $\mu$ = Setting average. $v_0$ = Predicted value of the hypothetical person at the bottom of the social-group distribution (rank 0). $v_1$ = Predicted value of the hypothetical person at the top of the social-group distribution (rank 1). $n$ = Number of subgroups.