A directed acyclic graph for interactions.

Area of Science:

• Causal inference
• Statistical modeling
• Epidemiology

Background:

• Standard Directed Acyclic Graphs (DAGs) model causal relationships but lack a framework for variable interactions.
• Interactions, where a variable's effect depends on another's value, are crucial but not standardly depicted in DAGs.

Purpose of the Study:

• Propose a novel DAG framework, the interaction DAG (IDAG), to represent and analyze causal interactions.
• Provide tools to understand confounded interactions and different types of causal effects (total, direct, indirect).
• Illustrate threats to generalizability and identify variables for valid population-level inference.

Main Methods:

• Introduced interaction DAGs (IDAGs) as an extension of standard DAGs.
• IDAGs use nodes for causal effects instead of outcomes.
• Developed concepts analogous to standard DAGs for interaction analysis, including confounded interaction and effect decomposition.

Main Results:

• IDAGs offer an intuitive and rigorous method for illustrating causal interactions.
• The framework distinguishes between causal and non-causal sources of effect variation.
• IDAGs guide empirical estimation of interactions and strategies for generalizability.

Conclusions:

• IDAGs provide a powerful tool for visualizing and analyzing complex causal interactions.
• The framework enhances understanding of effect modification and its impact on generalizability.
• IDAGs facilitate robust causal inference by accounting for interactions and ensuring valid population-level estimates.