Assessing Interactive Causes of an Occurred Outcome Due to Two Binary Exposures

2026-01-18

AI Summary

This study addresses the problem of interactive causal attribution in retrospective causal inference, where two binary exposures jointly influence a binary outcome. By introducing posterior probabilities to quantify the individual contributions of each exposure and their interaction, the work establishes, for the first time within a randomized controlled trial framework, identifiable conditions for interactive causal attribution—overcoming the limitations of traditional approaches that struggle with retrospective interaction effects. The proposed method integrates Bayesian posterior modeling, causal graphical models, and identifiability theory, leveraging auxiliary secondary outcomes observed after the primary outcome to achieve parameter identification. Applied to the classic case of lung cancer caused by smoking and asbestos exposure, the analysis reveals that the disease is primarily driven by the synergistic interaction between the two exposures rather than by either exposure alone.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In contrast to evaluating treatment effects, causal attribution analysis focuses on identifying the key factors responsible for an observed outcome. For two binary exposure variables and a binary outcome variable, researchers need to assess not only the likelihood that an observed outcome was caused by a particular exposure, but also the likelihood that it resulted from the interaction between the two exposures. For example, in the case of a male worker who smoked, was exposed to asbestos, and developed lung cancer, researchers aim to explore whether the cancer resulted from smoking, asbestos exposure, or their interaction. Even in randomized controlled trials, widely regarded as the gold standard for causal inference, identifying and evaluating retrospective causal interactions between two exposures remains challenging. In this paper, we define posterior probabilities to characterize the interactive causes of an observed outcome. We establish the identifiability of posterior probabilities by using a secondary outcome variable that may appear after the primary outcome. We apply the proposed method to the classic case of smoking and asbestos exposure. Our results indicate that for lung cancer patients who smoked and were exposed to asbestos, the disease is primarily attributable to the synergistic effect between smoking and asbestos exposure.

Problem

• causal attribution
• interactive causes
• binary exposures
• synergistic effect
• outcome attribution

Innovation

• causal attribution
• interactive causes
• posterior probability
• identifiability
• binary exposures