Causal inference targeting a concentration index for studies of health inequalities

TL;DR

This paper develops a formal framework to assess how exposures like education influence income-related health inequalities using a counterfactual concentration index, providing new estimators with strong statistical properties.

Contribution

It introduces a novel counterfactual concentration index and derives estimators with robustness and efficiency properties, filling a gap in causal analysis of health inequality measures.

Findings

Proposed estimators are $\

Proved conditions for identification of counterfactual concentration indices.

Validated estimators through simulation studies and a case study on education's impact on health inequalities.

Abstract

A concentration index, a standardized covariance between a health variable and relative income ranks, is often used to quantify income-related health inequalities. There is a lack of formal approach to study the effect of an exposure, e.g., education, on such measures of inequality. In this paper we contribute by filling this gap and developing the necessary theory and method. Thus, we define a counterfactual concentration index for different levels of an exposure. We give conditions for their identification, and then deduce their efficient influence function. This allows us to propose estimators, which are regular asymptotic linear under certain conditions. In particular, these estimators are $\sqrt n$-consistent and asymptotically normal, as well as locally efficient. The implementation of the estimators is based on the fit of several nuisance functions. The estimators proposed have rate robustness properties allowing for convergence rates slower than $\sqrt{n}$-rate for some of the nuisance function fits. The relevance of the asymptotic results for finite samples is studied with simulation experiments. We also present a case study of the effect of education on income-related health inequalities for a Swedish cohort.