Compare methods

	Theil Index for Health Inequality	Relative Index of Inequality
Field	Social Epidemiology	Social Epidemiology
Family	Process / pipeline	Regression model
Year of origin	2008	1997
Originator	Henri Theil (entropy index); Sam Harper & John Lynch; Luisa Borrell & Makram Talih (health-disparity applications)	Anton E. Kunst & Johan P. Mackenbach; Jamie Sergeant & David Firth (estimation/inference)
Type	Entropy-based decomposable index of inequality applied to health disparities	Regression-based relative measure of health inequality across ordered SES groups
Seminal source	Harper, S., Lynch, J., Meersman, S. C., Breen, N., Davis, W. W., & Reichman, M. E. (2008). An Overview of Methods for Monitoring Social Disparities in Cancer with an Example Using Trends in Lung Cancer Incidence by Area-Socioeconomic Position and Race-Ethnicity, 1992-2004. American Journal of Epidemiology, 167(8), 889-899.	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.
Aliases	Theil Index, Theil's T, Theil Entropy Index of Health Disparity, Symmetrized Theil Index	RII, Relative Index, Kunst-Mackenbach Relative Index of Inequality, Relative Slope Index of Inequality
Related	4	4
Summary	The Theil index is an entropy-based measure of inequality, adapted from information theory, that quantifies how disproportionately a quantity is distributed across groups - and in social epidemiology it measures how unequally ill health (or its burden) is shared across population subgroups defined by race-ethnicity, area socioeconomic position, or other categories. Its defining advantage over simpler disparity measures is additive decomposability: total inequality splits cleanly into a between-group component and a within-group component, so analysts can ask how much overall health disparity is due to differences among, say, racial groups versus differences among areas inside those groups. Harper, Lynch, and colleagues' 2008 American Journal of Epidemiology overview placed the Theil index among the recommended summary measures for monitoring social disparities in health, illustrating it with trends in U.S. lung-cancer incidence. Borrell and Talih's 2011 Statistics in Medicine paper introduced a symmetrized version that removes the standard index's dependence on which group is treated as the reference and derived its variance for complex survey data. Because it is reference-free, decomposable, and population-weighted, the Theil index is well suited to multi-group, nested disparity analysis where ordered-rank measures like the concentration index do not apply.	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.