Compare methods

	Relative Index of Inequality	Poisson Rate Regression
Field	Social Epidemiology	Social Epidemiology
Family	Regression model	Regression model
Year of origin	1997	1983
Originator	Anton E. Kunst & Johan P. Mackenbach; Jamie Sergeant & David Firth (estimation/inference)	E. L. Frome (rate formulation); A. C. Cameron & P. K. Trivedi (modern count-data treatment)
Type	Regression-based relative measure of health inequality across ordered SES groups	Generalized linear model for event rates and counts with log link and person-time offset
Seminal source	Mackenbach, J. P., & Kunst, A. E. (1997). Measuring the magnitude of socio-economic inequalities in health: an overview of available measures illustrated with two examples from Europe. Social Science & Medicine, 44(6), 757-771.	Frome, E. L. (1983). The Analysis of Rates Using Poisson Regression Models. Biometrics, 39(3), 665-674.
Aliases	RII, Relative Index, Kunst-Mackenbach Relative Index of Inequality, Relative Slope Index of Inequality	Poisson Regression for Rates, Log-Linear Rate Model, Incidence-Rate-Ratio Regression, Poisson Regression with Offset
Related	4	3
Summary	The relative index of inequality (RII) is the relative counterpart of the slope index of inequality: instead of the absolute difference in a health outcome between the bottom and top of the socioeconomic hierarchy, it expresses that difference as a ratio. Like the SII, it is built from a regression of the outcome on each group's position in the cumulative socioeconomic distribution, so it uses the whole population and accounts for group sizes rather than comparing only the extreme categories. Mackenbach and Kunst's 1997 overview recommended the RII alongside the SII as the standard pair of summary measures for socioeconomic health inequality, precisely because relative and absolute inequality can move in opposite directions and both need to be reported. Sergeant and Firth's 2006 Biostatistics paper clarified the various definitions of the RII, compared estimation strategies, and supplied a parametric bootstrap for valid confidence intervals. The RII is dimensionless, which makes it directly comparable across outcomes, time periods, and populations with very different baseline rates. It is a mainstay of comparative health-inequality research and routine surveillance.	Poisson rate regression is the standard generalized linear model for analyzing event rates and counts, such as the number of deaths, hospitalizations, or new cases observed over a span of person-time. It models the logarithm of the expected event rate as a linear function of covariates, using a Poisson likelihood and a log link, and accommodates differing amounts of exposure by including the log of person-time as an offset. Because coefficients enter on the log scale, their exponentials are incidence-rate ratios that quantify multiplicative effects on the rate. The rate formulation was crystallized in Frome's 1983 Biometrics paper, and the model sits within the broader count-data framework developed comprehensively by Cameron and Trivedi, who also detail its central practical concern: overdispersion, where the variance exceeds the Poisson assumption and standard errors must be corrected.