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The R\'{e}nyi index (RI) is a one-parameter class of indices that summarizehealth disparities among population groups by measuring divergence between thedistributions of disease burden and population shares of these groups. Therank-dependent RI introduced in this paper is a two-parameter class of healthdisparity indices that also accounts for the association between socioeconomicrank and health; it may be derived from a rank-dependent social welfarefunction. Two competing classes are discussed and the rank-dependent RI isshown to be more robust to changes in the distribution of either socioeconomicrank or health. The standard error and sampling distribution of therank-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 theU.S. Surveillance, Epidemiology and End Results Program. Such data underliemany population-based objectives within the U.S. Healthy People 2020initiative. The rank-dependent RI provides a unified mathematical framework foreliciting various societal positions with regards to the policies that are tiedto such wide-reaching public health initiatives. For example, if populationgroups with lower socioeconomic position were ascertained to be more likely toutilize costly public programs, then the parameters of the RI could be selectedto reflect prioritizing those population groups for intervention or treatment.

Examining socioeconomic health disparities using a rank-dependent R\'{e}nyi index