# Insights into the "cross-world" independence assumption of causal mediation analysis

arXiv: https://arxiv.org/abs/2003.10341 · HTML: https://mlsanity.com/paper/2003.10341/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2020.

## Built on by (most cited first, 7 of 7)

- [The Curse of Multiple Mediators: Hidden Interaction Effects in Activation Patching](https://mlsanity.com/paper/2606.27510/) (2026)
- [Local Causal Discovery for Structural Evidence of Direct Discrimination](https://mlsanity.com/paper/2405.14848/) (2024)
- [Retrospective Counterfactual Prediction by Conditioning on the Factual Outcome: A Cross-World Approach](https://mlsanity.com/paper/2603.27320/) (2026)
- [Causal inference for the expected number of recurrent events in the presence of a terminal event](https://mlsanity.com/paper/2306.16571/) (2023)
- [Assessing Surrogate Heterogeneity in Real World Data Using Meta-Learners](https://mlsanity.com/paper/2504.15386/) (2025)
- [Testing Full Mediation of Treatment Effects and the Identifiability of Causal Mechanisms](https://mlsanity.com/paper/2603.04109/) (2026)
- [Identifying and Estimating Causal Direct Effects Under Unmeasured Confounding](https://mlsanity.com/paper/2604.01501/) (2026)

## Abstract (arXiv)

Causal mediation analysis is a useful tool for epidemiological research, but it has been criticized for relying on a "cross-world" independence assumption that is empirically difficult to verify and problematic to justify based on background knowledge. In the present article we aim to assist the applied researcher in understanding this assumption. Synthesizing what is known about the cross-world independence assumption, we discuss the relationship between assumptions for causal mediation analyses, causal models, and non-parametric identification of natural direct and indirect effects. In particular we give a practical example of an applied setting where the cross-world independence assumption is violated even without any post-treatment confounding. Further, we review possible alternatives to the cross-world independence assumption, including the use of computation of bounds that avoid the assumption altogether. Finally, we carry out a numerical study in which the cross-world independence assumption is violated to assess the ensuing bias in estimating natural direct and indirect effects. We conclude with recommendations for carrying out causal mediation analyses.