# Non-parametric efficient causal mediation with intermediate confounders

### Abstract

Interventional effects for mediation analysis were proposed as a solution to the lack of identifiability of natural (in)direct effects in the presence of a mediator-outcome confounder affected by exposure. We present a theoretical and computational study of the properties of the interventional (in)direct effect estimands based on the efficiency bound in the non-parametric statistical model. We derive the efficient influence function, using it to develop two asymptotically optimal, non-parametric estimators that leverage data-adaptive regression for estimation of the nuisance parameters: a one-step estimator and a targeted minimum loss estimator. A free and open source R package implementing our proposed estimators is made readily available on GitHub. We further present results establishing the conditions under which these estimators are consistent, rate multiply robust, $n^{\frac{1}{2}}$-consistent and efficient. We illustrate the finite-sample performance of the estimators and corroborate our theoretical results in a simulation study. We also demonstrate the use of the estimators in our motivating application to elucidate the mechanisms behind the unintended harmful effects that a housing intervention had on adolescent girls’ risk behavior.

Type
Publication
In Biometrika
##### Nima Hejazi
###### PhD Candidate in Biostatistics

My research interests lie at the intersection of causal inference and machine learning, especially as applied to the statistical analysis of complex data from observational studies and experiments in the biomedical and health sciences.