Causal inference targeting a concentration index for studies of health inequalities
Mohammad Ghasempour, Xavier de Luna, Per E. Gustafsson
TL;DR
This paper defines a counterfactual concentration index $G(e)$ to quantify how an exposure (e.g., education) causally affects income-related health inequality, and shows how to identify this target under standard causal assumptions. It derives efficient influence functions for the estimands and develops EIF-based estimators (one-step and estimating equation) that are regular, asymptotically linear, and locally efficient, with robustness to slower nuisance-function convergence through rate-robustness properties. Finite-sample performance is assessed via simulations, highlighting when EIF-based estimators outperform naive plug-in approaches, especially under model misspecification. The authors apply the method to Swedish cohort data, finding that higher education levels reduce income-related health inequality after adjusting for confounding, while noting potential residual confounding and the value of sensitivity analyses for ignorability assumptions.
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.