Statistical inferences of extended concentration indices for directly standardized rates

Abstract

The relative concentration index (RCI) and the absolute concentration index (ACI) have been widely used for monitoring health disparities with ranked health determinants. The RCI has been extended to allow value judgments about inequality aversion by Pereira in 1998 and by Wagstaff in 2002. Previous studies of the extended RCI have focused on survey sample data. This paper adapts the extended RCI for use with directly standardized rates (DSRs) calculated from population-based surveillance data. A Taylor series linearization (TL)–based variance estimator is developed and evaluated using simulations. A simulation-based Monte Carlo (MC) variance estimator is also evaluated as a comparison. Following Wagstaff's approach in 1991, we extend the ACI for use with DSRs. In all simulations, both the TL and MC methods produce valid variance estimates. The TL variance estimator has a simple, closed form that is attractive to users without sophisticated programming skills. The TL and MC estimators have been incorporated into a beta version of the National Cancer Institute's Health Disparities Calculator, a free statistical software tool that enables the estimation of 11 commonly used summary measures of health disparities for DSRs.