Reassessing socioeconomic inequalities in mortality via distributional similarities

Table 1 Common measures of socioeconomic inequalities in mortality

Measure	Formula and description	Properties
Range/Ratio	\(\text {Range} = m_k - m_1\) \(\text {Ratio} = \frac{m_k}{m_1}\) The difference/ratio of the measure of mortality between the most advantaged and the least advantaged group.	It is a simple and readily interpretable measure, and it can be applied to non-ordinal socioeconomic variables. However, it only reflects information of the extreme groups.
Slope index of inequality	\(m_i=\alpha + \beta R_i\) \(\text {SII} = \hat{\beta }\) It is the slope coefficient (\(\hat{\beta }\)) of the regression line between the group-specific mortality measure against their relative rank of socioeconomic status.	It measures the socioeconomic gradient in the mortality measure. It reflects the patterns of all social groups and considers the proportion of population in each group. It is often estimated by weighted least square regression, though other models have been proposed. However, it can only be applied to ordered groups.
Relative index of inequality	\(m_i=\alpha + \beta R_i\) \(\text {RII} = \frac{\hat{\beta }+\hat{\alpha }}{\hat{\alpha }}\) It is the relative counterpart of the SII. It can also be estimated as \(\hat{\beta }/\bar{m}\).

Let \(m_i\) be the mortality measure (life expectancy, lifespan disparity, median age at death, etc.), \(w_i\) the population share and \(R_i = \frac{1}{2}w_i + {\sum }_{j=1}^{i-1}w_j\) the relative rank of group i. Where \(i \in 1,..,k\), and k is the number of groups, and \(\bar{m}\) the mean of the mortality measure of all groups. [11, 26, 29]

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