Bounding the probability of causality under ordinal outcomes

TL;DR

This paper extends bounds on the probability of causality from binary to ordinal outcomes, enhancing causal inference in legal and explanatory contexts by incorporating mediator variables for more precise bounds.

Contribution

It generalizes the probability of causality bounds to ordinal outcomes and shows that including mediator variables yields tighter bounds.

Findings

Generalized bounds for ordinal outcomes.

Mediator variables improve causal bounds.

Enhanced causal inference methods.

Abstract

The probability of causation (PC) is often used in liability assessments. In a legal context, for example, where a patient suffered the side effect after taking a medication and sued the pharmaceutical company as a result, the value of the PC can help assess the likelihood that the side effect was caused by the medication, in other words, how likely it is that the patient will win the case. Beyond the issue of legal disputes, the PC plays an equally large role when one wants to go about explaining causal relationships between events that have already occurred in other areas. This article begins by reviewing the definitions and bounds of the probability of causality for binary outcomes, then generalizes them to ordinal outcomes. It demonstrates that incorporating additional mediator variable information in a complete mediation analysis provides a more refined bound compared to the simpler scenario where only exposure and outcome variables are considered.