Causal Directed Acyclic Graphs

INTRODUCTION

This JAMA Guide to Statistics and Methods discusses the basics of causal directed acyclic graphs, which are useful tools for communicating researchers’ understanding of the potential interplay among variables and are commonly used for mediation analysis.

The design and interpretation of clinical studies requires consideration of variables beyond the exposure or treatment of interest and patient outcomes, including decisions about which variables to capture and, of those, which to control for in statistical analyses to minimize bias in estimating treatment effects. Causal directed acyclic graphs (DAGs) are a useful tool for communicating researchers’ understanding of the potential interplay among variables and are commonly used for mediation analysis.^1,2 Assumptions are presented visually in a causal DAG and, based on this visual representation, researchers can deduce which variables require control to minimize bias and which variables could introduce bias if controlled in the analysis.^3-5

In an article in JAMA Pediatrics, Ramirez et al⁶ studied the association between atopic dermatitis and sleep duration and quality among children. The authors used a causal DAG (Figure 1 in their article) to illustrate potential relationships among demographic and socioeconomic factors, smoking exposure, comorbid asthma, and allergic rhinitis.

WHAT ARE CAUSAL DAGS AND WHY ARE THEY IMPORTANT?

A causal DAG is a graph with arrows that show the direction of hypothesized causal effects (eg, from atopic dermatitis to sleep quality). Because causality implies ordering in time from cause to effect, cycles are not possible (eg, atopic dermatitis at a given time may affect sleep quality, but sleep quality cannot then affect atopic dermatitis at or before that time). Hence, causal DAGs are directed and acyclic. The lack of an arrow between any 2 variables represents an assumption that there is no direct causal relationship between those variables. The presence of an arrow between 2 variables does not guarantee that a relationship will be observed in the data because, for example, the effect it represents may be negligible.

A complete causal DAG includes, for each possible pair of variables along the paths from cause to effect, any variable that has a causal effect on both members of the pair. Often these additional variables cannot be measured. The causal DAG should also include a variable representing selection of patients included in the study. By providing a visual representation of potential causal pathways that may influence the relationship between patient exposures or treatments and clinical outcomes, causal DAGs help identify sources of bias and ways to adjust for them.

HOW DO CAUSAL DAGS WORK?

Figure 1 shows a causal DAG with study exposure or treatment E and study outcome O (for example, atopic dermatitis E and sleep quality O). The arrow from E to O implies that the value of O may be affected by the value of E. A path ...