Nonparametric efficient causal mediation with intermediate confounders

Summary 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 efficient influence function in the nonparametric statistical model. We use the efficient influence function to develop two asymptotically optimal nonparametric estimators that leverage data-adaptive regression for the estimation of nuisance parameters: a one-step estimator and a targeted minimum loss estimator. We further present results establishing the conditions under which these estimators are consistent, multiply robust, n^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 risky behaviour in adolescent girls.