Relative index of inequality: Definition, estimation, and inference

Jamie C. Sergeant, David Firth

    Research output: Contribution to journalArticlepeer-review


    The relative index of inequality (RII) is a commonly used measure of the extent to which the occurrence of an outcome such as chronic illness or early death varies with socioeconomic status or some other background variable. The standard RII estimator applies only to linear variation in incidence rates. In this paper a general definition of the RII is introduced, alternative approaches to point estimation are considered, and a parametric bootstrap method is suggested for the construction of approximate confidence intervals. Estimation based on cubic splines fitted by maximum penalized likelihood is developed in some detail, and the proposed approach handles naturally the commonly needed adjustment for a 'standardizing' covariate such as age. Death rates in a large longitudinal study in England and Wales from 1996-2000 are analyzed in order to illustrate the various methods. A small simulation study explores the relative merits of different estimators. The approach based on cubic splines is found to reduce bias substantially, at the expense of some increase in variance, when variation in incidence rates is nonlinear. © The Author 2005. Published by Oxford University Press. All rights reserved.
    Original languageEnglish
    Pages (from-to)213-224
    Number of pages11
    Issue number2
    Publication statusPublished - Apr 2006


    • Bootstrap
    • Cross-validation
    • Health inequality
    • Interval-censored covariate
    • Penalized likelihood
    • Slope index
    • Smoothing spline


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