# Decomposition of Probabilities of Causation with Two Mediators

arXiv: https://arxiv.org/abs/2505.04983 · HTML: https://mlsanity.com/paper/2505.04983/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 8 of 8)

- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Probabilities of Causation with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09568/) (2022)
- [Probabilities of Causation for Continuous and Vector Variables](https://mlsanity.com/paper/2405.20487/) (2024)
- [On semiparametric estimation of a path-specific effect in the presence of mediator-outcome confounding](https://mlsanity.com/paper/1710.02011/) (2017)
- [Semiparametric Estimation for Causal Mediation Analysis with Multiple Causally Ordered Mediators](https://mlsanity.com/paper/2011.12751/) (2020)
- [Bounding the Probability of Causation in Mediation Analysis](https://mlsanity.com/paper/1411.2636/) (2014)
- [Mediated probabilities of causation](https://mlsanity.com/paper/2404.07397/) (2024)
- [Mediation Analysis for Probabilities of Causation](https://mlsanity.com/paper/2412.14491/) (2024)

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

- [Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables under Monotonicity Assumptions](https://mlsanity.com/paper/2602.18762/) (2026)
- [Formalizing and falsifying causal pathways of rare events](https://mlsanity.com/paper/2605.31254/) (2026)
- [Same Predictions, Different Harms: Causal Auditing of Patient World Models](https://mlsanity.com/paper/2610.05198/) (2026)

## Abstract (arXiv)

Mediation analysis for probabilities of causation (PoC) provides a fundamental framework for evaluating the necessity and sufficiency of treatment in provoking an event through different causal pathways. One of the primary objectives of causal mediation analysis is to decompose the total effect into path-specific components. In this study, we investigate the path-specific probability of necessity and sufficiency (PNS) to decompose the total PNS into path-specific components along distinct causal pathways between treatment and outcome, incorporating two mediators. We define the path-specific PNS for decomposition and provide an identification theorem. Furthermore, we conduct numerical experiments to assess the properties of the proposed estimators from finite samples and demonstrate their practical application using a real-world educational dataset.