# Causal mediation analysis for stochastic interventions

## TL;DR

This paper extends causal mediation analysis to stochastic interventions, providing a flexible framework for analyzing direct and indirect effects with weaker assumptions and new estimators, including an efficient one, demonstrated through simulations and a real-world example.

## Contribution

It introduces a decomposition of population intervention effects for stochastic interventions, with identification under weaker assumptions and novel estimators, including an efficient approach.

## Key findings

- Efficient estimator is asymptotically linear under certain conditions.
- Simulation study shows good finite-sample properties of proposed estimators.
- Illustrative example demonstrates practical application to health data.

## Abstract

Mediation analysis in causal inference has traditionally focused on binary exposures and deterministic interventions, and a decomposition of the average treatment effect in terms of direct and indirect effects. In this paper we present an analogous decomposition of the \textit{population intervention effect}, defined through stochastic interventions on the exposure. Population intervention effects provide a generalized framework in which a variety of interesting causal contrasts can be defined, including effects for continuous and categorical exposures. We show that identification of direct and indirect effects for the population intervention effect requires weaker assumptions than its average treatment effect counterpart, under the assumption of no mediator-outcome confounders affected by exposure. In particular, identification of direct effects is guaranteed in experiments that randomize the exposure and the mediator. We discuss various estimators of the direct and indirect effects, including substitution, re-weighted, and efficient estimators based on flexible regression techniques, allowing for multivariate mediators. Our efficient estimator is asymptotically linear under a condition requiring $n^{1/4}$-consistency of certain regression functions. We perform a simulation study in which we assess the finite-sample properties of our proposed estimators. We present the results of an illustrative study where we assess the effect of participation in a sports team on BMI among children, using mediators such as exercise habits, daily consumption of snacks, and overweight status.