Table 1 Summary of health resource allocation equity measures

Concentration curve, concentration index

Calculate and compare cumulative percentage of population (ranked by socioeconomic factors) and health resource. CI $\mathrm{CI}=\frac{2\times \mathrm{COV}\left(\mathrm{X},\mathrm{H}\right)}{\mathit{M}}$_, COV(X,H) = E(XH)-E(X)E(H)

Complex but aided by statistical software

Systematic assessment, and can be a rough estimation on equity of differences between different regions.

Income of individual, health resource of individual

-not only represent overall inequity, also reflect accurately which social classes allocated with more resource and which less via positive or negative CI value

-incapable of considering the other variables, especially the resource delivery itself.

-socioeconomic factors are taken into consideration when measure the inequity. And which is very sensitive to different social classes

-simple to calculate

-simple to interpret when combine with corresponding curve

-the concentration index must be interpreted with the curve

-does not allow for within or between income group comparisons

Lorenz curve, Gini index

Calculate and compare cumulative percentage of population (ranked by how much resources obtained) and health resource. $\mathit{G}={\displaystyle \sum _{\mathit{i}=1}^{\mathit{k}}{\mathit{P}}_{\mathit{i}}}{\mathit{S}}_{\mathit{i}+1}-{\displaystyle \sum _{\mathit{i}=1}^{\mathit{k}}{\mathit{P}}_{\mathit{i}+1}}{\mathit{S}}_{\mathit{i}}$

Complex but can aided by statistical software

Systematic assessment, and can be a rough estimation on equity of differences between different regions.

Health resource of individual, total health resource, population of area

-a graphical representation of allocation inequality that can be compared over time and between geographic areas

-incapable of showing different kinds of inequality represented by various shapes of Lorenz curves [34]

-simple to calculate

-data readily available

-can be calculated for individual and household level data

-easily interpreted when combine with Gini coefficients

-does not emphasize inequalities in the top or bottom of the spectrum (polarization)

-shows the direction of allocation redistribution but does not indicate where the redistributions are occurring

-does not allow for within or between income group comparisons

-overlook socioeconomic factors

Theil index

Calculate the equity of health resource by population (area) in each region. $\mathit{T}={\displaystyle \sum _{\mathit{i}=1}^{\mathit{n}}{\mathit{P}}_{\mathit{i}}}log\frac{{\mathit{P}}_{\mathit{i}}}{{\mathit{Y}}_{\mathit{i}}}$

complex

Measure equity of the allocation of health resources between different regions or the units.

Population of units or regions, total population , health resources in units or regions, total resource

-shows the contributions to inequality by within group and between group components

-complex to calculate and interpret.

-varies greatly when the distribution varies regardless of the change in distribution occurs at the top, middle or bottom

-high sensitivity to the efficiency of health resource allocation

-resource redistributions will impact the calculation irrespective of whether the redistribution takes place between top and bottom or top and middle

-cannot directly compare populations with different sizes as calculation is dependent on number of individuals in the population or group

Atkinson index

Calculate the health resources of ith region and the proportion of population in which people get the resources. ${\mathit{I}}_{\mathit{R}}=1-{\left[{\displaystyle \sum _{\mathit{i}=1}^{\mathit{n}}{\left(\frac{{\mathit{Y}}_{\mathit{i}}}{\overline{\mathit{Y}}}\right)}^{1-\mathit{\epsilon }}{\mathit{f}}_{\mathit{i}}}\right]}^{\frac{1}{1-\mathit{\epsilon }}}$,if ε ≠ 1_,${\mathit{I}}_{\mathit{R}}=1-exp\left[{\displaystyle \sum _{\mathit{i}=1}^{\mathit{n}}{\mathit{f}}_{\mathit{i}}{log}_{\mathit{e}}\frac{{\mathit{Y}}_{\mathit{i}}}{\overline{\mathit{Y}}}}\right]$,if ε = 1

complex

Assess the inequity of allocation, address needs of inequity assessment in health benefits analysis

Health resource of ith region, the proportion of population in ith region who get the resource, inequality aversion ε

-incorporates a sensitivity parameter directly into the equation.

-sensitivity parameter means that a subjective judgment has been made about inequality

-not intuitive

Chi-square Value Method

Calculate the actual and theoretical frequency of health resources. ${\mathit{X}}^2={\displaystyle \sum _{\mathit{i}=1}^{\mathit{k}}\frac{{\left({\mathit{f}}_{\mathit{i}}-\overline{{\mathit{f}}_{\mathit{i}}}\right)}^2}{\overline{{\mathit{f}}_{\mathit{i}}}}}$

Easy when analyze aided with statistical software

Assess the difference between actual allocation of health resource with the expected allocation

Actual resources in ith region, the total resource, expected frequency of health resource allocation

-sensitive to reflect the inequity of allocation

-always need to standardize the data, otherwise may influence the results

-reveal the trend of equity over time

-the judgment is subjective when based on a certain significance level α

index of dissimilarity

Calculate the health resources and population in each socioeconomic level (region). $\mathit{ID}=\frac{1}{2}{\displaystyle \sum _{\mathit{j}=1}^{\mathit{k}}\left|{\mathit{S}}_{\mathit{jh}}-{\mathit{S}}_{\mathit{jp}}\right|}$

easy

assess the differences of resource allocation in different economic level(region), and calculate the degree of variance

Resource in jth region(or in a certain socioeconomic level), the population in jth region

-can know the differences between the situation of health resource allocation in each region (level) and the proportion of the population in relative region (level)

-can’t reflect the socioeconomic status influence on health resource allocation.

-not intuitive