The slope index of inequality (SII) and the relative index of inequality (RII) are measures of health inequality (Mackenbach, 1997). The SII and RII can be calculated through regression analysis on an indicator of the cumulative relative position of each group with respect to a socioeconomic variable account for both the socioeconomic status (SES) of the groups and the size of the population.
The groups of SES are ordered by decreasing socioeconomic status from higher to lower. Each socioeconomic category is given a score called ridit score, which reflects the average cumulative frequency of the group, a midpoint of the range in the cumulative distribution introduced by Bross (1958). For example, if the highest educated women include 20% of the population, the range of women in this category is from 0.00 to 0.20 and assigned a ridit score of 0.10 (= 0.20/2 = [0 + 0.2]/2), and if the next level of educated women include 50% of the population from .20 to 0.70, the corresponding ridit score is 0.45 (= 0.20 + 0.5/2 = [0.20 + 0.70]/2) and so forth.
SII (rate difference) is the slope of the regression line (b) estimated by the weighted least squares method and represents the change in measured outcome/event when the position of the SES changes by one unit.
RII (rate ratios) can be which can be estimated in two ways: one way is to divide the SII by the mean level of population health or by the frequency of the health problem in the population; the other way is to divide the predicted value of the regression at the highest point (range=1) by the predicted value of the regression at the lowest point (range=0). The second method for the RII is calculated by log-linear—or logistic—regression after the logarithmic—or logit—transformation of the dependent variable. One way to facilitate the interpretation of this measure of the second method may be to express the RII as a percentage by subtracting 1 from it and multiplying the result by 100 (see Table 1 below) (Regidor, 2004).
Other References:
- Software: Health Disparity Measures in HD*Calc - NCI
- NCI (2005). Methods for Measuring Cancer Disparities
- Keppel & CDC (2005). Methodological issues in measuring health disparities
- Cheng (2008). Methods and Software for Estimating Health Disparities: The Case of Children's Oral Health
- Hayes (2002). How to calculate confidence limits for the relative index of inequality?
- Schwarz (2006). The Contributions of Diseases to Increasing Educational Mortality Differential in Austria
- OpenMichigan. Measuring Health Disparities
- BMJ (2017). Say what you mean, mean what you say: inequality and inequity
- Klein (2010): Defining and measuring disparities, inequities, and inequalities in the Healthy People initiative
- Arcaya (2015). Inequalities in health: definitions, concepts, and theories
Calculation of SII and RII using aggregated data (modified from the paper of Regidor, 2004)
SII of the year 1990 = 104.4, the beta coefficient (b) of a linear regression of Ridit90 and Mort90.
RII of the year 1990 can be calculated as SII/(average mortality rate) = 104/134 = 0.7761 (Measures of Health Disparity - NCI (pdf))
ID
|
Men
|
Survey
|
Smoking
|
Ridit
|
Age
|
1
|
1
|
1
|
0
|
0.34
|
53
|
2
|
0
|
1
|
1
|
0.55
|
48
|
3
|
0
|
2
|
0
|
0.34
|
55
|
4
|
1
|
3
|
1
|
0.34
|
40
|
Estimating Relative Index of Inequality (RII) for smoking in men at the first survey:
.glm i.smoking ridit age if survey==1 & men==1, fam(bin) link(log) nolog eform
Estimating Slope Index of Inequality (SII) for smoking in men at the first survey:
.glm i.smoking ridit age if survey==1 & men==1, fam(bin) link(identity)
Estimating trend in RII and SII over time for men:
.glm i.smoking c.ridit##survey age if men==1, fam(bin) link(log) nolog eform
.glm i.smoking c.ridit##survey age if men==1, fam(bin) link(identity)
Estimating gender differences in RII and SII at each survey:
.glm i.smoking c.ridit##men age if survey==1, fam(bin) link(log) nolog
.glm i.smoking c.ridit##men age if survey==1, fam(bin) link(identity)
Estimating if RII and SII changed differently over time in men and women:
.glm i.smoking c.ridit##men##survey age, fam(bin) link (log) nolog
.glm i.smoking c.ridit##men##survey age, fam(bin) link (identity) nolog
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