  The R\'{e}nyi index (RI) is a one-parameter class of indices that summarize
health disparities among population groups by measuring divergence between the
distributions of disease burden and population shares of these groups. The
rank-dependent RI introduced in this paper is a two-parameter class of health
disparity indices that also accounts for the association between socioeconomic
rank and health; it may be derived from a rank-dependent social welfare
function. Two competing classes are discussed and the rank-dependent RI is
shown to be more robust to changes in the distribution of either socioeconomic
rank or health. The standard error and sampling distribution of the
rank-dependent RI are evaluated using linearization and resampling techniques,
and the methodology is illustrated using health survey data from the U.S.
National Health and Nutrition Examination Survey and registry data from the
U.S. Surveillance, Epidemiology and End Results Program. Such data underlie
many population-based objectives within the U.S. Healthy People 2020
initiative. The rank-dependent RI provides a unified mathematical framework for
eliciting various societal positions with regards to the policies that are tied
to such wide-reaching public health initiatives. For example, if population
groups with lower socioeconomic position were ascertained to be more likely to
utilize costly public programs, then the parameters of the RI could be selected
to reflect prioritizing those population groups for intervention or treatment.
