Decomposition of Probabilities of Causation with Two Mediators

TL;DR

This paper develops a method to decompose the probability of necessity and sufficiency into pathway-specific components in causal mediation analysis involving two mediators, with theoretical and empirical validation.

Contribution

It introduces a novel decomposition of path-specific PNS with an identification theorem and practical estimators for causal mediation analysis with two mediators.

Findings

Proposed estimators are effective in finite samples.

The method successfully applied to real-world educational data.

Theoretical properties of the estimators are validated.

Abstract

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.