Directed acyclic graph
Also known as: Causal graph
A diagram of arrows that encodes which variables cause which.
What it means
A directed acyclic graph represents causal assumptions as nodes (variables) connected by single-headed arrows (direct causes), with no feedback loops. DAGs make a researcher's beliefs about the causal structure explicit and let them read off, by simple path rules, which variables must be adjusted for to estimate an effect without bias and — crucially — which must not. They expose subtle traps: conditioning on a collider or a mediator can create bias rather than remove it. By turning identification into a graphical problem, DAGs have become a standard language for designing and critiquing observational studies.
Reading the graph
A DAG is read through three elementary structures. In a chain, A points to B points to C, association flows from A to C until you condition on B, which blocks it. In a fork, A and C share a common cause B, so they move together for no causal reason, and conditioning on B removes that spurious link. In a collider, A and C both point into B, the path is already blocked, and conditioning on B (or anything downstream of it) opens it, manufacturing a dependence that was never there. A path is open when every node on it transmits association; an effect is unbiased when every non-causal path between exposure and outcome is blocked. This bookkeeping, called d-separation, replaces intuition about which variables to control with a rule you can check.
Choosing what to adjust for
The practical payoff is a recipe for picking covariates. The back-door criterion says: to estimate the effect of an exposure on an outcome, find a set of variables that blocks every back-door path (a path entering the exposure through an incoming arrow) without opening a collider and without sitting on the causal pathway itself. Software such as dagitty enumerates the valid adjustment sets automatically once the graph is drawn. The criterion tells you which variables to leave alone as often as which to include. Adjusting for a mediator attenuates the effect you meant to measure; adjusting for a collider adds bias, and adjusting for an instrument amplifies whatever confounding bias remains. This directly inverts the widespread instinct to control for everything available, which a DAG shows can make an estimate worse rather than better.
How it is used, and how well
Causal diagrams migrated from Pearl's computer-science work into epidemiology after Greenland, Pearl and Robins translated them for health researchers, and they now appear in journals' reporting standards. A 2021 review of applied health studies by Tennant and colleagues found DAGs increasingly common but frequently reported incompletely: many papers omitted the full graph, never stated the resulting adjustment set, or drew arrows without justifying them. The COVID-19 pandemic supplied a vivid case study. Griffith and colleagues showed that analyses drawn from non-representative samples, such as hospital patients or volunteers, could conjure protective effects through collider bias, precisely the trap a DAG is built to expose. Adoption has since spread beyond epidemiology into economics, ecology and psychology, where graphical models are taught as a first-line tool for observational design.
Limits and caveats
A DAG encodes assumptions; it does not test them. Data rarely fix the direction of an arrow, and different graphs can imply the same observed correlations, so two careful analysts can defend incompatible adjustment sets from the same dataset. Nothing on the diagram is quantitative: it shows which paths exist, not how strong they are, so a technically unbiased adjustment can still leave large residual bias from an unmeasured confounder you simply never drew. The acyclicity requirement rules out genuine feedback and simultaneous causation, and time-varying treatments that both affect and are affected by later confounders need extensions such as marginal structural models. A DAG is therefore a discipline for making beliefs explicit and arguing about them, not a machine that extracts the right answer from data alone.
Examples
A DAG showing Smoking → Tar → Cancer tells you that adjusting for tar would block the very pathway you want to estimate.
Before testing whether coffee harms the heart, a team draws smoking as a cause of both coffee drinking and heart disease. The arrows show smoking must be adjusted for.
In a hiring study, job offers are caused by both talent and interview coaching. The graph warns that controlling for offers conditions on a collider and manufactures a link that isn't there.
Estimating whether a training grant raises wages, a team notes the grant works partly by lifting confidence. The DAG marks confidence as a mediator, so adjusting for it would erase part of the effect.
Studying whether a fitness app's reminders increase workouts, analysts restrict to users who stayed subscribed. Because both reminders and workouts affect staying subscribed, the graph warns this selection conditions on a collider.
First described in Judea Pearl (1995, 2000); Greenland, Pearl & Robins (1999).
Key references
- Tennant, P. W. G., Murray, E. J., Arnold, K. F., Berrie, L., Fox, M. P., Gadd, S. C., ... Ellison, G. T. H. (2021). Use of directed acyclic graphs (DAGs) to identify confounders in applied health research: review and recommendations. International Journal of Epidemiology, 50(2), 620-632. doi.org/10.1093/ije/dyaa213
- Griffith, G. J., Morris, T. T., Tudball, M. J., Herbert, A., Mancano, G., Pike, L., ... Hemani, G. (2020). Collider bias undermines our understanding of COVID-19 disease risk and severity. Nature Communications, 11, 5749. doi.org/10.1038/s41467-020-19478-2
- Rohrer, J. M. (2018). Thinking clearly about correlations and causation: Graphical causal models for observational data. Advances in Methods and Practices in Psychological Science, 1(1), 27-42. doi.org/10.1177/2515245917745629
- Textor, J., van der Zander, B., Gilthorpe, M. S., Liskiewicz, M., & Ellison, G. T. (2016). Robust causal inference using directed acyclic graphs: the R package 'dagitty'. International Journal of Epidemiology, 45(6), 1887-1894. doi.org/10.1093/ije/dyw341
- Greenland, S., Pearl, J., & Robins, J. M. (1999). Causal diagrams for epidemiologic research. Epidemiology, 10(1), 37-48. doi.org/10.1097/00001648-199901000-00008
- Pearl, J. (1995). Causal diagrams for empirical research. Biometrika, 82(4), 669-688. doi.org/10.1093/biomet/82.4.669