Open Access
June 2013 A reference-invariant health disparity index based on Rényi divergence
Makram Talih
Ann. Appl. Stat. 7(2): 1217-1243 (June 2013). DOI: 10.1214/12-AOAS621


One of four overarching goals of Healthy People 2020 (HP2020) is to achieve health equity, eliminate disparities, and improve the health of all groups. In health disparity indices (HDIs) such as the mean log deviation (MLD) and Theil index (TI), disparities are relative to the population average, whereas in the index of disparity (IDisp) the reference is the group with the least adverse health outcome. Although the latter may be preferable, identification of a reference group can be affected by statistical reliability. To address this issue, we propose a new HDI, the Rényi index (RI), which is reference-invariant. When standardized, the RI extends the Atkinson index, where a disparity aversion parameter can incorporate societal values associated with health equity. In addition, both the MLD and TI are limiting cases of the RI. Also, a symmetrized Rényi index (SRI) can be constructed, resulting in a symmetric measure in the two distributions whose relative entropy is being evaluated. We discuss alternative symmetric and reference-invariant HDIs derived from the generalized entropy (GE) class and the Bregman divergence, and argue that the SRI is more robust than its GE-based counterpart to small changes in the distribution of the adverse health outcome. We evaluate the design-based standard errors and bootstrapped sampling distributions for the SRI, and illustrate the proposed methodology using data from the National Health and Nutrition Examination Survey (NHANES) on the 2001–04 prevalence of moderate or severe periodontitis among adults aged 45–74, which track Oral Health objective OH-5 in HP2020. Such data, which use a binary individual-level outcome variable, are typical of HP2020 data.


Download Citation

Makram Talih. "A reference-invariant health disparity index based on Rényi divergence." Ann. Appl. Stat. 7 (2) 1217 - 1243, June 2013.


Published: June 2013
First available in Project Euclid: 27 June 2013

zbMATH: 06279871
MathSciNet: MR3113507
Digital Object Identifier: 10.1214/12-AOAS621

Keywords: alpha–gamma divergence , Epidemiological methods , health inequalities , rescaled bootstrap , survey data , Taylor series linearization

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.7 • No. 2 • June 2013
Back to Top