Why Draw a Causal Diagram?
An observational regression can show how an outcome varies with an exposure after accounting for selected variables. But the regression formula alone does not explain why those variables were selected, which causal pathways they represent, or what assumptions make a causal interpretation plausible. A causal diagram makes those assumptions visible before an analysis is chosen.
The aim is not to draw every detail of a real situation. It is to represent, clearly and consistently, the variables relevant to a particular causal question and the proposed directions of influence among them. The diagram is a compact account of scientific reasoning, not a picture discovered automatically from a data set.
For a question about an exposure and an outcome, use \(A\) for the exposure and \(Y\) for the outcome. Other nodes may represent common causes, variables on a causal pathway, or selection into the data being analyzed. A node is not an arrow: including a variable in a diagram says that it matters to the causal story, while the arrows specify how it is proposed to matter.
From a Substantive Question to Nodes and Arrows
Begin with a well-defined causal question: what exposure contrast is being considered, what outcome is measured, and for which target population and time period? These choices determine what the nodes mean. The earlier material on defining exposure contrasts and specifying a target population and time zero is especially relevant: an arrow cannot be interpreted clearly if the exposure, outcome, or their timing is vague.
Next, list plausible causes of the exposure, causes of the outcome, and events that may occur between exposure and outcome. Make the time ordering explicit. A variable measured before exposure may plausibly influence exposure assignment; a variable that occurs after exposure may instead be a consequence of exposure. Timing does not settle causation, but it rules out some proposed arrow directions.
Then draw arrows for the causal relationships you are willing to propose. If \(C\) is a common cause of exposure \(A\) and outcome \(Y\), the basic pattern is \(C \to A\) and \(C \to Y\). If \(M\) is a mediator, it lies on a causal pathway from exposure to outcome: \(A \to M \to Y\). If \(S\) records whether a person or unit is included in the analyzed data, draw arrows into \(S\) from variables that may influence inclusion.
A path is a sequence of connected nodes, whether or not every arrow points in the same direction along the sequence. Tracing paths helps reveal which causal stories a DAG contains. For example, \(A \to M \to Y\) is a directed causal path from exposure to outcome through a mediator. In contrast, \(A \leftarrow C \to Y\) connects exposure and outcome through their common cause; it is not a causal effect of \(A\) on \(Y\).
Worked Examples
Worked Example: Tutoring and Examination Scores
Suppose an observational question asks whether receiving additional tutoring improves a later examination score among students in a specified school term. Let \(A\) indicate tutoring, \(Y\) be the examination score, \(C\) be prior achievement measured before the term, and \(M\) be attendance at lessons during the term. Assume, for this proposed diagram, that prior achievement can affect both tutoring participation and later scores, that tutoring can affect attendance, and that attendance can affect scores.
The nodes are therefore \(C, A, M,\) and \(Y\). The proposed arrows are:
Now trace the paths. The sequence \(A \to M \to Y\) is a directed pathway: tutoring may affect attendance, which may in turn affect the examination score. The sequence \(A \leftarrow C \to Y\) is another path between tutoring and score. It represents the possibility that prior achievement affects both who receives tutoring and later performance.
The graph does not say that every tutored student attends more often, nor does it quantify any effect. It records a proposed causal structure. In particular, it distinguishes a possible route by which tutoring affects the score from a route that could create an exposure–outcome association because prior achievement influences both. The arrows are assumptions to assess using subject knowledge and study design, not conclusions established by drawing the diagram.
Worked Example: A Medication Study and Follow-Up Selection
Imagine an observational study of whether a medication \(A\) affects a later symptom score \(Y\). Patients with greater baseline symptom severity \(C\) may be more likely to receive the medication and may also have higher later symptom scores. Some patients miss the follow-up visit. Let \(S=1\) mean that a patient has an observed follow-up score. For this hypothetical diagram, suppose medication status and early symptom response can both affect follow-up attendance; let \(E\) denote early symptom response, which occurs after treatment and before the scheduled follow-up.
The proposed arrows are:
The directed sequence \(A \to E \to Y\) represents a possible mediated route from medication to the later score. The path \(A \leftarrow C \to Y\) represents the common-cause route associated with baseline severity. Finally, \(A \to S \leftarrow E \to Y\) shows how selection is connected to treatment and outcome-related response: both \(A\) and \(E\) are proposed causes of being observed at follow-up, and \(E\) is also related to \(Y\).
This last path matters because the analysis includes only patients with \(S=1\). The diagram warns that the observed sample is defined by a variable with causes connected to the exposure and outcome process. It does not, by itself, tell us whether a particular statistical adjustment will remove or create bias; that requires additional criteria. Its immediate use is to make the selection mechanism explicit instead of treating missing follow-up as an irrelevant data-handling detail.
Worked Example: Night Work, Sleep, and Blood Pressure
Suppose the question is whether working night shifts \(A\) affects a later blood pressure measurement \(Y\). Consider age \(C\) and job demands \(D\), both measured before the shift schedule begins. For this hypothetical causal account, suppose age and job demands may influence both shift assignment and blood pressure. Let sleep duration \(M\), measured after the schedule begins, be one way night work could affect blood pressure.
The proposed arrows are:
There are two common-cause paths: \(A \leftarrow C \to Y\) and \(A \leftarrow D \to Y\). There is also the directed pathway \(A \to M \to Y\). Thus the diagram encodes both possible differences in who works nights and a possible way that night work changes the outcome.
Notice how the proposed timing shapes the graph. Sleep duration is placed after the schedule begins because this example treats it as a potential consequence of night work. If the recorded sleep variable were instead a measure taken before the schedule change, the proposed arrows might need to differ. A variable name alone does not determine its role; its definition and measurement time matter.
Checking a Proposed Diagram
Before using a DAG to guide an analysis, check that it matches the question and that its arrows are defensible. A useful review asks whether the diagram has accidentally mixed measurements from different times, omitted an important cause, or treated an outcome consequence as if it preceded exposure. Also verify that no directed cycle has been created. If the proposed arrows include \(A \to M\) and \(M \to A\), for example, the diagram is cyclic and cannot be a DAG; the timing or causal story must be reconsidered.
Name the exposure contrast, outcome, target population, and relevant time period precisely.
Include the exposure, outcome, plausible causes, possible intermediate variables, and variables governing inclusion in the analyzed sample.
Use the study timeline to assess which arrow directions are plausible, while recognizing that timing alone does not prove causation.
Draw each proposed direct influence, then follow connected paths to see how the exposure and outcome may be causally or noncausally connected.
Check for unclear node definitions, unsupported arrows, important omitted causes, and any directed cycle.
What a DAG Can—and Cannot—Tell You
A DAG helps organize causal reasoning. It can show which variables are proposed as common causes, which are on possible pathways from exposure to outcome, and how selection into the observed data may occur. It can also expose disagreement: two analysts may agree on the measured variables but draw different arrows because they have different assumptions about how the study population or treatment process works.
A diagram is not a test of its own assumptions. The observed data may be compatible with more than one causal structure, and drawing an arrow does not estimate the size of an effect. Conversely, a small or absent observed association does not automatically justify deleting a plausible causal arrow. The diagram should be based on substantive knowledge, study timing, and measurement definitions, with uncertainty about its structure acknowledged.
A frequent mistake is to put every measured variable into the diagram and assume that more arrows or more adjustment variables must improve an analysis. That reasoning confuses measurement with causation. A variable belongs in a causal diagram because of its proposed role in the causal process, not merely because it appears in the data set. A second mistake is to label a variable a mediator simply because it is measured after exposure; the proposed causal sequence must support the label.
The purpose here is to draw and interpret the graph, not yet to decide which variables should be adjusted for in a regression. Path tracing gives the structure needed for that next question, but choosing adjustment sets requires additional rules. Keeping these tasks separate prevents an intuitive diagram from being mistaken for a complete identification argument.
Check Your Understanding
For each question, explain your reasoning in terms of nodes, arrows, and paths.
- A study examines whether a job-training program affects later earnings. Prior education may affect both program participation and earnings, while skills acquired during the program may affect earnings. Name the common cause and a possible mediator, and write the corresponding arrows.
- In a DAG, what does the path \(A \leftarrow C \to Y\) represent? Why is it different from the path \(A \to M \to Y\)?
- A study records outcome data only for participants who return a follow-up questionnaire. What does a selection node represent, and what information would you need before drawing arrows into it?
- A proposed diagram contains \(A \to M\) and \(M \to A\). What property of a DAG does this violate, and what should be reconsidered?
- Why does a DAG not establish that its arrows are true or determine the size of an exposure effect?