  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 R\'{e}nyi 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 R\'{e}nyi 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.
