A practical guide to distinguishing confounders, mediators and colliders, recognising selection bias, and transparently reporting assumptions when estimating the effects of managerial interventions from observational and administrative data
| Summary Points • A DAG is not a data tool but an assumption tool: it makes assumptions about the causal structure among variables graphical and open to scrutiny. • Adjust for a confounder; adjusting for a mediator blocks the total effect; adjusting for (or conditioning on) a collider creates an association that is not there. • The intuition to “control for every available variable” is wrong; only the minimal sufficient adjustment set determines what to adjust for. • In health management, common sources of selection bias (voluntary programme participation, survey response, hospital admission) are usually collider structures. • Reporting the DAG, its assumptions, the adjustment set, and sensitivity to unmeasured confounding communicates a study’s strengths and limitations to the reader. |
1. Introduction: Why DAGs in Health Management?
Most health management research draws causal claims from non-experimental data — administrative records, performance indicators, patient-experience surveys: whether a particular staffing model reduces adverse events, whether accreditation improves quality, whether a leadership approach lowers burnout. In such questions, validity hinges on the assumptions made about which variables should be adjusted for as confounders. In practice, however, covariate selection is often left ungrounded; a common habit is to “put every available variable into the model.” Far from helping, this habit can introduce bias (Krishna, 2025; Merchant, 2002).
The directed acyclic graph (DAG) is a simple yet powerful tool that fills this gap. A DAG represents the researcher’s assumptions about the causal structure between an exposure and an outcome in graphical form and provides an explicit rationale for selecting the confounders to adjust for; its roots lie in probabilistic graphical modelling (Rodrigues, 2022). DAGs are widely used in health and social research to make assumptions explicit, to describe the possible explanations for observed associations — from causal relationships to confounding and selection bias — and thereby to identify the variables that can reduce them (Feeney, 2025). Even so, the tool remains under-used in applied health research, and causal assumptions are frequently left implicit (Krishna, 2025; Rodrigues, 2022). Its use is nonetheless growing in health services research; for example, the relationship between in-hospital surgical waiting time and functional outcomes in older patients has been examined with a DAG-based, pre-specified analysis (Cai, 2023).
This guide approaches DAGs from the health management researcher’s perspective around three verbs: building, interpreting and reporting a DAG. Throughout, a single running example is used: the effect of nurse staffing levels on adverse events. This example is well suited to illustrating the value of DAGs because it sits squarely on the patient-safety and quality agenda and is typically studied with administrative data. The numbers and structures in the example are illustrative and hypothetical.
2. The Basics: Nodes, Arrows and Three Structures
A DAG consists of nodes (variables) and directed arrows (a direct causal effect from one variable to another); being “acyclic” means that following the arrows can never return you to a starting node. For causal inference, the entire language of a DAG reduces to three elementary structures (Figure 1). A confounder is a common cause of both exposure and outcome; it opens a spurious “back-door” path between exposure and outcome and must be adjusted for to close that path. A mediator lies on the causal path from exposure to outcome; adjusting for it blocks part of the very total effect we wish to measure. A collider is a common effect of two variables; conditioning on it (or adjusting for it) creates an association that does not exist (Krishna, 2025).
Figure 1. The three elementary structures of causal inference, with health management examples (N = nurse staffing level; AE = adverse events). (a) A confounder (CM = case mix) must be adjusted for. (b) Adjusting for a mediator (PA = process adherence) blocks the total effect. (c) Conditioning on a collider (survey response) creates a spurious association.
The practical importance of these three structures is considerable: whether a variable should be “controlled for” depends not on whether it is available in the data set, but on its role in the causal structure. The same variable may be a confounder in one study and a mediator or collider in another. The DAG is the tool that makes this role explicit (Merchant, 2002).
3. How to Build a DAG
A good DAG grows not from data but from domain knowledge and theory. Building it can be thought of in five steps. (1) Clarify the research question as one exposure and one outcome, and state the target estimand explicitly (for example, the total effect of staffing level on adverse events). (2) List the exposure, the outcome and every variable that might affect them, drawing on domain experts and the literature. (3) Draw the arrows between variables on the basis of theory and evidence; each arrow is a claim of a direct causal effect. (4) From the resulting DAG, read off the smallest set of variables that must be adjusted for to estimate the exposure–outcome relationship without bias (the minimal sufficient adjustment set). (5) Adjust for that set only, and document your assumptions (Rodrigues, 2022). Ideally a DAG is built before data are collected, at the design and protocol stage; indeed, some studies have built their analytical model and study protocol directly around a DAG (Taylor, 2024). The same approach can be applied in multicentre observational studies (Chen, 2021).
In our running example these steps unfold as follows. The question is the total effect of nurse staffing levels (exposure) on adverse events (outcome). Domain knowledge indicates that several variables affect both staffing levels and adverse events: patients’ case mix / disease severity, hospital size, teaching-hospital status, and bed turnover. These are confounders. Part of the path from staffing to adverse events runs through adherence to care processes; process adherence is a mediator. This structure is shown in Figure 2. The minimal sufficient adjustment set comprises the four confounders; because process adherence is a mediator, it is not adjusted for when the total effect is of interest.
Figure 2. The DAG for the running example: the effect of nurse staffing level (N) on adverse events (AE). Green nodes are confounders and constitute the minimal sufficient adjustment set (CM = case mix, HS = hospital size, TH = teaching hospital, BT = bed turnover); these are adjusted for. The amber node (PA = process adherence) is a mediator and is not adjusted for when estimating the total effect.
| Box 1 — Drawing a DAG with DAGitty DAGitty (dagitty.net) is a widely used, free, browser-based tool for drawing and analysing DAGs. It lets you label variables as exposure, outcome, adjusted, or unobserved; draw the arrows; and have the program return the minimal sufficient adjustment set automatically. The same functionality is available as an R package. In this way, which variables must be adjusted for in a complex DAG is determined algorithmically rather than by hand. |
| Box 2 — Two complementary building approaches • Expert-driven building: the DAG is constructed from the knowledge of subject-matter experts; a structured guide exists for health services research (Rodrigues, 2022). In a managerial context, involving clinicians, nurse managers and quality specialists surfaces implicit assumptions. • Evidence-synthesis-based building (ESC-DAGs): DAG construction is embedded within the stages of a systematic review, combining evidence synthesis with principles of causal inference (Ferguson, 2020). This approach is especially suited to grounding the causal structure in evidence in studies of inequality or intervention (Hesari, 2025; Sultana, 2025). |
4. How to Interpret a DAG
4.1. Reading the minimal sufficient adjustment set
Once a DAG is built, the central task is to identify the smallest set of variables that closes all back-door (confounding) paths between exposure and outcome while opening no new spurious paths. In practice this means observing two rules together: adjust for confounders, but do not adjust for mediators or colliders. This “back-door” logic rests on the DAG’s ability to draw the causal paths explicitly, distinguish confounder, mediator and collider, and determine the minimal number of variables that must be adjusted for (Krishna, 2025).
4.2. Over-adjustment and the mediator trap
One of the most frequent mistakes is to treat a mediator as a confounder and adjust for it. In the running example, entering process adherence (a mediator) into the model blocks the part of staffing’s effect on adverse events that runs through process adherence, understating the total effect. Likewise, the DAG’s distinction between confounders and genuine causal factors makes clear why the tendency to “control for everything” in observational studies is misleading (Pérez-López, 2024). Indeed, identifying confounders with a DAG and adjusting for those only has been shown to yield more defensible estimates than a logistic regression that blindly enters all variables (Li, 2023).
4.3. Measurement error and missing data
A further strength of the DAG is its ability to represent other mechanisms that distort effect estimation. Imperfect measurement of variables or missing data can be modelled by adding nodes (the measured value, a missingness indicator), making visible how these mechanisms induce bias and what must be adjusted for. For instance, the measurement and selection biases arising from a survey’s mode of data collection (face-to-face vs. online) can be explained through DAGs (Tomova, 2026) — a direct contribution for health management research, where self-reported data are common. DAG-based data simulations can also be used to demonstrate, pedagogically, how these biases arise (Duan, 2021). Similarly, the knowledge–attitude–behaviour pathways that determine radiation-protection compliance in a hospital have been explained with DAGs, providing an example of the causal interpretation of self-reported managerial survey data (Cao, 2025).
5. Common Pitfalls Specific to Health Management
Some bias patterns are particularly frequent in health management research. Four are summarised in Figure 3. (a) Berkson / admission collider: when only admitted patients are studied, a spurious association arises between two variables that share admission as a common effect. (b) Programme selection: when hospitals join accreditation or quality programmes voluntarily, participation is a collider affected by both resources and baseline quality; studying only participants opens bias. (c) Over-adjustment: controlling a mediator between intervention and outcome (for example, process adherence) understates the total effect. (d) M-structure: if a variable measured before exposure — seemingly harmless — is a collider between two unmeasured causes, controlling for it opens a closed path and creates bias; this shows why the rule “adjust for every pre-exposure variable” is wrong (Arah, 2019; Pearce, 2018).
Figure 3. Four bias patterns common in health management research. (a) Berkson / admission collider (DS = disease severity, SL = staff load). (b) Programme selection (HR = hospital resources, BQ = baseline quality). (c) Over-adjustment by controlling a mediator. (d) M-structure: controlling a seemingly harmless M opens bias (U₁, U₂ are unmeasured causes).
The common lesson of these pitfalls is that selection bias usually arises from conditioning on a collider. In health management, voluntary participation, restricting the sample to admitted patients, or studying only survey responders all fall into this category and are hard to spot without a DAG (Arah, 2019; Campos, 2020). Because matching can itself be a source of bias, drawing a DAG is not sufficient on its own in matched designs; the paths opened by matching must also be considered (Pearce, 2018).
6. Unmeasured Confounding and Sensitivity
A DAG forces one to display not only measured but also unmeasurable confounders. In the running example, a variable such as organisational safety culture may affect both staffing decisions and adverse events, yet go unmeasured in routine data. Because an unmeasured confounder cannot be adjusted for, the estimate carries residual confounding (Figure 4). The correct response is not to ignore this confounding but to acknowledge it explicitly and to present a sensitivity analysis (for example, the E-value) showing how strong an unmeasured confounder would have to be to explain away the result (Krishna, 2025). The validity of methods that estimate the average treatment effect from observational data (for example, inverse-probability weighting based on the propensity score) rests on the same no-unmeasured-confounding assumption, which the DAG makes visible (Sun, 2025).
Figure 4. Unmeasured confounding. U (for example, organisational safety culture) affects both nurse staffing (N) and adverse events (AE) but cannot be adjusted for because it is unmeasured (dashed arrows mark unmeasurable paths). The result should be reported together with a sensitivity analysis.
7. Beyond Effect Estimation: Descriptive, Prediction and Structural Equation Studies
The usefulness of DAGs is not limited to effect estimation. In descriptive studies (for example, estimating a rate or incidence) and in prediction / risk modelling, they clarify decisions about which variables to include. Whether the total causal effect of an intervention is identifiable from the data can also be assessed with a DAG (Myers, 2024); in analysing composite endpoints (for example, the combination of hospital admission and death) the risk of understating the interventional effect can be made visible with a DAG (Jahn-Eimermacher, 2017). Extensions have also been proposed for features the standard DAG does not directly capture, such as interaction (Nilsson, 2021). DAG approaches are likewise used in prognostic-factor studies (Hoorntje, 2019).
A particularly important bridge for the health management literature is that between DAGs and structural equation models (CB-SEM and PLS-SEM). In these models, the choice of control variables is often driven by convention or convenience; a DAG, by contrast, provides a principled answer to the question “why is this variable here?” for every control in the structural model: only confounders on back-door paths should be controlled, while mediators and colliders should not be entered as controls. Moreover, DAGs are non-parametric causal models that require no assumptions about the functional form of relationships, complementing the parametric structure of SEM (Balgi, 2025). Probabilistic graphical models such as Bayesian networks are likewise built on a DAG topology and encode conditional independencies through that structure (Varando, 2025). Learning structure from data (causal discovery) offers a complement to expert-driven building, but it should be remembered that moving from data to structure requires a substantial leap of assumption (Vowels, 2023; Zuo, 2024).
8. How to Report a DAG: Workflow and Checklist
The value of a DAG is realised only when it is reported clearly. Reporting in applied health research has often been shown to be inadequate: of studies that reported using DAGs, only about one-fifth stated their target estimand and roughly half reported the adjustment set implied by the DAG, while two-thirds made at least one DAG available (Tennant, 2021). Because many of the assumptions a DAG encodes can remain implicit, frameworks such as DAGWOOD have been proposed that explicitly display alternative hidden assumptions (branch DAGs) around the root DAG (Haber, 2022). Good reporting follows a workflow spanning building, interpreting and presenting (Figure 5) and can be audited with the checklist below (Table 1).
Figure 5. The workflow of a DAG from building to reporting: defining the question, listing variables, drawing arrows, reading the adjustment set, adjusting for that set only, and reporting the DAG together with its assumptions.
Table 1. A DAG reporting checklist for health management studies.
| # | Item to be reported |
| 1 | Is the research question defined as a clear exposure and outcome, and is the target estimand (e.g., the total effect) stated? |
| 2 | Is the DAG on which the study rests presented as a figure? |
| 3 | Is the rationale for the nodes and arrows in the DAG (theory, evidence or expert judgement) given? |
| 4 | Is the data source and measurement of each variable (administrative record, survey, etc.) described? |
| 5 | Is the minimal sufficient adjustment set stated explicitly, and was only that set adjusted for in the analysis? |
| 6 | Is it shown that mediators and colliders were not adjusted for by mistake (was over-adjustment avoided)? |
| 7 | Are sources of selection bias (voluntary participation, survey response, hospital admission) addressed in the DAG? |
| 8 | Are unmeasured confounders acknowledged explicitly, and is a sensitivity analysis (e.g., the E-value) reported? |
| 9 | Are measurement error and missing data, where relevant, represented in the DAG? |
| 10 | Are the software used (e.g., DAGitty) and the location where the DAG is shared (appendix/repository) stated? |
9. Limitations
DAGs are powerful but not magical; several limitations should be kept in mind. First, a DAG encodes the researcher’s assumptions, not the truth; the validity of an estimate depends on how closely the DAG matches the true data-generating process. For this reason it is argued that DAGs should not monopolise epidemiological (and managerial) reasoning or become the only valid framework (Krieger, 2016). Second, classical DAGs represent the relationship between measurements at discrete time points, whereas real causal mechanisms are often continuously operating processes; this tension calls for careful judgement about how far DAGs can be “believed” (Aalen, 2016). Third, DAGs cannot directly represent cycles or feedback relationships, which is a constraint in feedback-laden systems such as health systems. Finally, a DAG is no substitute for good study design; a correct DAG will not rescue a poorly designed study.
10. Conclusion and Key Messages
The directed acyclic graph is a low-cost, high-return thinking tool for the health management researcher. In a field that works with observational and administrative data, a DAG makes explicit, auditable and open to debate which variables are controlled for — and which are not — and why (Rodrigues, 2022). The three key messages of this guide are: (i) what to adjust for is determined not by the data but by the causal structure — adjust for confounders, not for mediators or colliders; (ii) in health management the sources of selection bias (voluntary participation, survey response, hospital admission) are usually collider structures that are hard to see without a DAG; and (iii) the value of a DAG is realised only when its assumptions, adjustment set and sensitivity to unmeasured confounding are reported explicitly (Feeney, 2025; Tennant, 2021). For the tool to take root in the health management literature, both a terminological consensus and applied examples — built on local data sources and reported in an evidence-based, transparent manner — are needed.
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