Bounding the Probability of Causation in Mediation Analysis

TL;DR

This paper explores how to better bound the probability of causation in mediation analysis, especially when a mediating variable is observed and certain assumptions like no direct effect are met.

Contribution

It introduces new bounds for the probability of causation in mediation analysis under specific assumptions, extending existing methods.

Findings

Bounds can be improved with additional information.

No direct effect and no confounding simplify the bounds.

Provides a new analysis for observed mediators.

Abstract

Given empirical evidence for the dependence of an outcome variable on an exposure variable, we can typically only provide bounds for the "probability of causation" in the case of an individual who has developed the outcome after being exposed. We show how these bounds can be adapted or improved if further information becomes available. In addition to reviewing existing work on this topic, we provide a new analysis for the case where a mediating variable can be observed. In particular we show how the probability of causation can be bounded when there is no direct effect and no confounding. Keywords: Causal inference, Mediation Analysis, Probability of Causation