Theil Index for Health Inequality

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.