Directed Acyclic Graph

A directed acyclic graph (DAG) is a diagram of nodes and one-way arrows used to encode an investigator's assumptions about the causal relationships among variables. In epidemiology, DAGs make those assumptions explicit and provide formal rules for deciding which variables to adjust for to estimate a causal effect without introducing bias.

Definition

A directed acyclic graph is a graph in which nodes represent variables and directed edges represent assumed direct causal effects, with no path that returns to its starting node, used to derive which adjustments identify a causal effect.

Scope

This topic covers the structure and reading of causal DAGs, the concepts of confounders, mediators, and colliders, and the graphical rules, notably d-separation and the back-door criterion, that link a drawn graph to a valid adjustment set. It is a methodological reference, not clinical guidance.

Core questions

• How can assumptions about causal structure be represented explicitly?
• Which variables must be adjusted for, and which must not, to estimate a causal effect?
• How do confounders, mediators, and colliders differ in a causal graph?

Key concepts

• Nodes and directed edges
• Confounder, mediator, and collider
• Back-door path and back-door criterion
• d-separation
• Collider bias
• Minimal sufficient adjustment set

Mechanisms

In a DAG, an arrow from one variable to another encodes an assumed direct causal effect, and the absence of an arrow encodes an assumed absence of direct effect. Pearl's back-door criterion (pearl-1995) identifies a set of variables that, when conditioned on, blocks all non-causal (back-door) paths between exposure and outcome while leaving the causal path open, yielding an unbiased adjustment set. Greenland, Pearl, and Robins (greenland-pearl-robins-1999) translated this graphical theory for epidemiologists, showing how confounders should be controlled, mediators generally should not be when estimating total effects, and colliders must not be conditioned on because doing so opens a spurious path (collider bias). Adjusting for the wrong variables can therefore create bias rather than remove it (schisterman-2009), and software such as dagitty operationalises these rules (textor-2016).

Clinical relevance

DAGs guide how confounding control is planned in studies that inform clinical and public-health evidence, helping readers see why a particular adjustment was or was not made. They describe analytic reasoning and are not a basis for individual diagnostic or treatment decisions.

Epidemiology

Causal DAGs are now a standard part of designing and reporting observational studies across epidemiology, used to justify covariate selection and to anticipate selection and collider bias. Tools like dagitty have made formal DAG analysis routine in applied work (textor-2016).

History

Pearl introduced causal diagrams and the back-door criterion to formalise causal inference from non-experimental data (pearl-1995), and Greenland, Pearl, and Robins brought the framework into epidemiology in 1999 (greenland-pearl-robins-1999). Subsequent applied work clarified pitfalls such as overadjustment and collider bias (schisterman-2009) and produced widely used software for analysing DAGs (textor-2016).

Debates

Can adjusting for more covariates do harm?

DAG theory shows that conditioning on mediators or colliders can introduce bias, so adding covariates is not automatically safer; selecting an adjustment set requires explicit causal assumptions rather than statistical convenience.

Key figures

• Judea Pearl
• Sander Greenland
• James Robins
• Enrique Schisterman

Seminal works

• pearl-1995
• greenland-pearl-robins-1999

Frequently asked questions

What does 'acyclic' mean in a directed acyclic graph?

It means no variable can, by following the direction of the arrows, eventually cause itself; effects flow in one direction without feedback loops.

Why can adjusting for a collider create bias?

A collider is a variable caused by two others; conditioning on it opens a spurious association between its causes, so adjusting for it can introduce bias rather than remove confounding.