title: Relative index of inequality and slope index of inequality: a structured regression framework for estimation.
abstract: BACKGROUND
  The relative index of inequality and the slope index of inequality are the two major indices used in epidemiologic studies for the measurement of socioeconomic inequalities in health. Yet the current definitions of these indices are not adapted to their main purpose, which is to provide summary measures of the linear association between socioeconomic status and health in a way that enables valid between-population comparisons. The lack of appropriate definitions has dissuaded the application of suitable regression methods for estimating the slope index of inequality.
  
  
  METHODS
  We suggest formally defining the relative and slope indices of inequality as so-called least false parameters, or more precisely, as the parameters that provide the best approximation of the relation between socioeconomic status and the health outcome by log-linear and linear models, respectively. From this standpoint, we establish a structured regression framework for inference on these indices. Guidelines for implementation of the methods, including R and SAS codes, are provided.
  
  
  RESULTS
  The new definitions yield appropriate summary measures of the linear association across the entire socioeconomic scale, suitable for comparative studies in epidemiology. Our regression-based approach for estimation of the slope index of inequality contributes to an advancement of the current methodology, which mainly consists of a heuristic formula relying on restrictive assumptions. A study of the educational inequalities in all-cause and cause-specific mortality in France is used for illustration.
  
  
  CONCLUSIONS
  The proposed definitions and methods should guide the use and estimation of these indices in future studies.
authors.affiliation: From the aInserm CépiDc, Le Kremlin-Bicêtre, France; bInserm Centre for Research in Epidemiology and Population Health, U1018, Biostatistics, Villejuif, France; cUniv Paris-Sud, UMRS 1018, Villejuif, France; dConservatoire National des Arts et Métiers, Paris, France; eInserm, UMR_S 1136, Pierre Louis Institute of Epidemiology and Public Health, Paris, France; fSorbonne Universités, UPMC Univ Paris 06, UMR_S 1136, Pierre Louis Institute of Epidemiology and Public Health, Paris, France; and gDepartment of Public Health, Academic Medical Centre, University of Amsterdam, Amsterdam, The Netherlands.
authors.forename: Margarita
authors.initials: M
authors.lastname: Moreno-Betancur
authors.forename: Aurélien
authors.initials: A
authors.lastname: Latouche
authors.forename: Gwenn
authors.initials: G
authors.lastname: Menvielle
authors.forename: Anton E
authors.initials: AE
authors.lastname: Kunst
authors.forename: Grégoire
authors.initials: G
authors.lastname: Rey
mesh_terms: D004522:Educational Status; D005260:Female; D005602:France / Q000453:epidemiology; D054624:Health Status Disparities; D006801:Humans; D016014:Linear Models; D008297:Male; D009026:Mortality; D016016:Proportional Hazards Models; D012044:Regression Analysis; D012923:Social Class; D012959:Socioeconomic Factors; D013223:Statistics as Topic