Compare methods

	Theil Index for Health Inequality	Health Inequality Gini Decomposition
Field	Social Epidemiology	Social Epidemiology
Family	Process / pipeline	Process / pipeline
Year of origin	2008	1985
Originator	Henri Theil (entropy index); Sam Harper & John Lynch; Luisa Borrell & Makram Talih (health-disparity applications)	Robert Lerman & Shlomo Yitzhaki; Adam Wagstaff & Eddy van Doorslaer
Type	Entropy-based decomposable index of inequality applied to health disparities	Inequality-measurement and decomposition pipeline
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.	Lerman, R. I., & Yitzhaki, S. (1985). Income inequality effects by income source: A new approach and applications to the United States. The Review of Economics and Statistics, 67(1), 151-156.
Aliases	Theil Index, Theil's T, Theil Entropy Index of Health Disparity, Symmetrized Theil Index	Health Gini Decomposition, Gini Decomposition by Source, Inter-Individual Health Inequality, Total Health Inequality Gini
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 Gini coefficient is the most familiar single-number summary of inequality, and applied to a health variable it captures total, inter-individual health inequality — how unequally health is distributed across all people, regardless of their socioeconomic position. Its real analytic power comes from decomposition. Robert Lerman and Shlomo Yitzhaki's 1985 covariance formulation rewrites the Gini as twice the covariance between health and its rank divided by the mean, which makes it decomposable into the contributions of separate sources or components, each weighted by its share, its own Gini, and its Gini correlation with the overall distribution. The same machinery supports a between-versus-within-group split. As Wagstaff and van Doorslaer's review of health-inequality measurement explains, this 'pure' inequality view complements socioeconomic measures like the concentration index: the Gini asks how unequal health is, while the concentration index asks how that inequality is patterned by income or rank.