# Nonparametric causal mediation analysis for stochastic interventional (in)direct effects

arXiv: https://arxiv.org/abs/2009.06203 · HTML: https://mlsanity.com/paper/2009.06203/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2020.

## Built on by (most cited first, 3 of 3)

- [Application of targeted maximum likelihood estimation in public health and epidemiological studies: a systematic review](https://mlsanity.com/paper/2303.07329/) (2023)
- [General targeted machine learning for modern causal mediation analysis](https://mlsanity.com/paper/2408.14620/) (2024)
- [Identifying and Estimating Causal Direct Effects Under Unmeasured Confounding](https://mlsanity.com/paper/2604.01501/) (2026)

## Abstract (arXiv)

Causal mediation analysis has historically been limited in two important ways: (i) a focus has traditionally been placed on binary treatments and static interventions, and (ii) direct and indirect effect decompositions have been pursued that are only identifiable in the absence of intermediate confounders affected by treatment. We present a theoretical study of an (in)direct effect decomposition of the population intervention effect, defined by stochastic interventions jointly applied to the treatment and mediators. In contrast to existing proposals, our causal effects can be evaluated regardless of whether a treatment is categorical or continuous and remain well-defined even in the presence of intermediate confounders affected by treatment. Our (in)direct effects are identifiable without a restrictive assumption on cross-world counterfactual independencies, allowing for substantive conclusions drawn from them to be validated in randomized controlled trials. Beyond the novel effects introduced, we provide a careful study of nonparametric efficiency theory relevant for the construction of flexible, multiply robust estimators of our (in)direct effects, while avoiding undue restrictions induced by assuming parametric models of nuisance parameter functionals. To complement our nonparametric estimation strategy, we introduce inferential techniques for constructing confidence intervals and hypothesis tests, and discuss open source software implementing the proposed methodology.