A symmetrized Theil index measure of health disparities: An example using dental caries in U.S. children and adolescents

While the health status of Americans has generally improved over time, health disparities among groups of the population have been pervasive. Designing a measure that tracks the resulting disparities remains a challenge. In this paper, we propose a new measure of health disparities the Symmetrized Theil Index (STI), and derive its design-based sampling variance in grouped survey data. Because STI is symmetric, it circumvents the drawback of the Theil Index in how groups are weighted: indeed, the latter is mostly influenced by groups with high disease frequencies. Moreover, STI is related to Pearson's chi-square test of independence for binary data, and to the F-test in one-way analysis-of-variance for continuous data. We illustrate our approach using data on dental caries for children and adolescents from the third National Health and Nutrition Examination Surveys (NHANES III; 1988-1994) and NHANES 1999-2004. Tooth decay remains the most common chronic disease in U.S. children and adolescents. Although their oral health has generally improved, we find no change in the prevalence or severity of untreated tooth decay in U.S. children and adolescents between surveys. These findings are consistently observed for both the overall STI and its between-group component across gender, race/ethnicity, country of birth, survey respondent's education, income and poverty-income ratio.