Mediation analysis breaks down the causal effect of a treatment on an outcome into an indirect effect, acting through a third group of variables called mediators, and a direct effect, operating through other mechanisms. Mediation analysis is hard because confounders between treatment, mediators, and outcome blur effect estimates in observational studies. Many estimators have been proposed to adjust on those confounders and provide accurate causal estimates. We consider parametric and non-parametric implementations of classical estimators and provide a thorough evaluation for the estimation of the direct and indirect effects in the context of causal mediation analysis for binary, continuous, and multi-dimensional mediators. We assess several approaches in a comprehensive benchmark on simulated data. Our results show that advanced statistical approaches such as the multiply robust and the double machine learning estimators achieve good performances in most of the simulated settings and on real data. As an example of application, we propose a thorough analysis of factors known to influence cognitive functions to assess if the mechanism involves modifications in brain morphology using the UK Biobank brain imaging cohort. This analysis shows that for several physiological factors, such as hypertension and obesity, a substantial part of the effect is mediated by changes in the brain structure. This work provides guidance to the practitioner from the formulation of a valid causal mediation problem, including the verification of the identification assumptions, to the choice of an adequate estimator.

We provide new insights into the finding that Medicaid increased emergency department (ED) use from the Oregon experiment. Using nonparametric causal machine learning methods, we find economically meaningful treatment effect heterogeneity in the impact of Medicaid coverage on ED use. The effect distribution is widely dispersed, with significant positive effects concentrated among high-use individuals. A small group - about 14% of participants - in the right tail with significant increases in ED use drives the overall effect. The remainder of the individualized treatment effects is either indistinguishable from zero or negative. The average treatment effect is not representative of the individualized treatment effect for most people. We identify four priority groups with large and statistically significant increases in ED use - men, prior SNAP participants, adults less than 50 years old, and those with pre-lottery ED use classified as primary care treatable. Our results point to an essential role of intensive margin effects - Medicaid increases utilization among those already accustomed to ED use and who use the emergency department for all types of care. We leverage the heterogeneous effects to estimate optimal assignment rules to prioritize insurance applications in similar expansions.