Glossary

5.4 Directed acyclic graphs (DAGs) and causal diagrams

7 min read•august 14, 2024

Directed acyclic graphs (DAGs) are powerful tools in epidemiology for visualizing causal relationships between variables. They help researchers identify potential sources of bias and guide statistical analysis, making complex causal structures easier to understand and communicate.

In the context of causation and , DAGs provide a framework for representing assumptions about how variables interact. By mapping out these relationships, researchers can better plan their studies, choose appropriate methods, and interpret results with greater clarity and confidence.

Directed Acyclic Graphs for Causal Inference

Definition and Purpose

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  • Directed acyclic graphs (DAGs) are graphical representations of causal relationships between variables, where represent variables and directed represent causal relationships
  • DAGs are used in causal inference to visually represent and communicate assumptions about the causal structure of a system, helping to identify potential sources of bias and guide the selection of appropriate statistical methods
  • DAGs are acyclic, meaning that there are no feedback loops or cycles in the graph, and the edges are directed, indicating the direction of the causal relationship between variables (e.g., smoking → lung cancer)
  • DAGs can be used to represent both observed and unobserved variables, as well as the relationships between them, allowing for a more comprehensive understanding of the causal structure (e.g., including latent variables such as genetic predisposition)
  • By explicitly representing the causal assumptions underlying a research question, DAGs can help researchers to identify potential variables, mediators, and colliders, and to develop appropriate strategies for addressing them in statistical analyses (e.g., adjusting for confounders, conducting mediation analysis)

Role in Causal Inference

  • DAGs provide a framework for formally representing and communicating causal assumptions, promoting transparency and facilitating discussion among researchers
  • By visually depicting the causal relationships between variables, DAGs can help researchers identify potential sources of bias, such as confounding, mediation, or bias, and develop strategies to address them
  • DAGs can guide the selection of appropriate statistical methods for estimating causal effects, such as adjustment for confounders, mediation analysis, or the use of instrumental variables (e.g., propensity score matching, structural equation modeling)
  • The use of DAGs encourages researchers to explicitly consider and justify their causal assumptions, promoting a more rigorous and transparent approach to causal inference
  • DAGs can be used to assess the of causal effects and to determine the minimal sufficient for estimating causal effects from observational data (e.g., using the )

Components of a DAG

Nodes and Edges

  • Nodes in a DAG represent variables, which can be either observed (measured) or unobserved (latent) (e.g., age, sex, blood pressure, socioeconomic status)
  • Directed edges in a DAG represent causal relationships between variables, with the arrow pointing from the cause to the effect (e.g., age → blood pressure)
  • The absence of a directed edge between two nodes indicates that there is no direct causal relationship between the corresponding variables
  • A path in a DAG is a sequence of edges connecting two nodes, which can be either directed (following the direction of the arrows) or undirected (ignoring the direction of the arrows)

Familial Relationships

  • A node is a parent of another node if there is a directed edge from the former to the latter, and a child if there is a directed edge from the latter to the former (e.g., age is a parent of blood pressure, blood pressure is a child of age)
  • A node is an ancestor of another node if there is a directed path from the former to the latter, and a descendant if there is a directed path from the latter to the former (e.g., age is an ancestor of cardiovascular disease, cardiovascular disease is a descendant of age)
  • These familial relationships between nodes in a DAG are essential for understanding the causal structure and identifying potential sources of bias

Causal Paths and Associations

  • A causal path in a DAG is a directed path from one node to another, representing a direct or indirect causal relationship between the corresponding variables (e.g., age → blood pressure → cardiovascular disease)
  • An association between two variables in a DAG can arise from a causal path, confounding, or collider bias
  • Understanding the types of paths and associations in a DAG is crucial for identifying potential sources of bias and selecting appropriate statistical methods for causal inference

Confounding, Mediation, and Collider Bias in DAGs

Confounding

  • Confounding occurs when a variable influences both the exposure and the outcome, creating a spurious association between them. In a DAG, confounding is represented by a common cause of both the exposure and the outcome (e.g., age influencing both smoking and lung cancer)
  • Confounding can lead to biased estimates of causal effects if not properly addressed in the analysis
  • DAGs can help identify potential confounders by examining the paths between the exposure and outcome variables and looking for common causes

Mediation

  • Mediation occurs when the effect of an exposure on an outcome is partially or fully transmitted through an intermediate variable (the ). In a DAG, mediation is represented by a directed path from the exposure to the outcome via the mediator (e.g., smoking → lung inflammation → lung cancer)
  • Mediation analysis can be used to decompose the total effect of an exposure on an outcome into direct and indirect effects
  • DAGs can help identify potential mediators and guide the selection of appropriate methods for mediation analysis

Collider Bias

  • Collider bias occurs when conditioning on a common effect of two variables (the collider) induces a spurious association between them. In a DAG, collider bias is represented by two arrows pointing into the same node (e.g., smoking ← lung cancer → asbestos exposure)
  • Conditioning on a collider can create a non-causal association between its causes, leading to biased estimates of causal effects
  • DAGs can help identify potential colliders and guide decisions about conditioning or stratification in the analysis

Identifying and Addressing Bias

  • DAGs can be used to identify potential confounders, mediators, and colliders by examining the paths between variables and the direction of the arrows
  • By explicitly representing these causal relationships, DAGs can guide the selection of appropriate statistical methods for estimating causal effects, such as adjustment for confounders, mediation analysis, or the use of instrumental variables
  • Researchers can use DAGs to assess the potential impact of unmeasured confounding or measurement error on their estimates of causal effects
  • DAGs can also help researchers identify situations where causal effects are not identifiable from observational data, prompting the need for alternative study designs or additional assumptions

DAGs for Epidemiological Research

Constructing DAGs

  • Begin by identifying the key variables relevant to the research question, including the exposure, outcome, and potential confounders, mediators, and effect modifiers (e.g., in a study of the effect of physical activity on cardiovascular disease, relevant variables might include age, sex, diet, and smoking status)
  • Represent each variable as a node in the DAG, and draw directed edges between nodes to represent the hypothesized causal relationships based on prior knowledge and subject matter expertise
  • Consider the temporal ordering of variables when drawing edges, as causes must precede their effects
  • Include both measured and unmeasured variables in the DAG, as omitting important variables can lead to biased estimates of causal effects

Refining and Analyzing DAGs

  • Examine the DAG for potential sources of bias, such as confounding, mediation, or collider bias, by tracing the paths between variables and considering the direction of the arrows
  • If necessary, refine the DAG by adding or removing variables or edges to better represent the causal structure and address potential sources of bias (e.g., adding a previously omitted confounder or removing an edge based on new evidence)
  • Use the final DAG to guide the selection of appropriate statistical methods for estimating causal effects, such as adjustment for confounders, mediation analysis, or the use of instrumental variables (e.g., using the backdoor criterion to identify minimal sufficient adjustment sets)

Interpretation and Limitations

  • Interpret the results of the statistical analysis in light of the causal assumptions represented in the DAG, and consider the limitations and potential alternative explanations for the findings
  • Acknowledge that DAGs are based on the researcher's assumptions and subject matter knowledge, and that alternative DAGs may be plausible
  • Consider the potential impact of unmeasured confounding, measurement error, or violations of causal assumptions on the validity of the estimates
  • Use sensitivity analyses to assess the robustness of the findings to alternative causal assumptions or potential sources of bias (e.g., simulating the impact of unmeasured confounding)

Examples in Epidemiological Research

  • DAGs have been used in epidemiological studies to investigate causal relationships between various exposures and health outcomes, such as the effect of air pollution on respiratory health, the impact of social determinants on health inequalities, and the causal linking diet and physical activity to obesity and chronic diseases
  • In a study of the effect of maternal smoking on birth outcomes, a DAG could be used to represent the causal relationships between maternal smoking, birth weight, gestational age, and potential confounders such as maternal age, socioeconomic status, and prenatal care
  • A DAG could be used to guide the analysis of the causal effect of a public health , such as a smoking cessation program, on health outcomes, by representing the causal pathways through which the intervention may influence behavior and health, as well as potential effect modifiers and sources of bias

Key Terms to Review (18)

Adjustment Sets: Adjustment sets refer to a collection of variables that can be controlled or adjusted for in order to estimate causal effects accurately in observational studies. By identifying and including the right adjustment sets in analysis, researchers can help to mitigate confounding biases that may distort the relationship between exposure and outcome. Understanding how to determine these sets is crucial when using directed acyclic graphs (DAGs) and causal diagrams to elucidate the underlying causal structure of a system.
Backdoor Criterion: The backdoor criterion is a method used in causal inference to determine whether a variable can be adjusted for to identify a causal effect between an exposure and an outcome. It is particularly useful in directed acyclic graphs (DAGs), where it helps identify potential confounding variables that, when controlled for, can lead to an unbiased estimate of the causal effect. This criterion focuses on finding paths that go 'backwards' into the exposure, ensuring that any associations observed are not confounded by other variables.
Causal Diagram: A causal diagram is a visual representation that illustrates the relationships between variables in a way that helps identify causal connections. These diagrams are crucial for understanding the pathways through which an exposure might affect an outcome, thereby clarifying the assumptions and potential confounding factors in causal inference. By mapping out these relationships, causal diagrams assist in better study design and analysis in epidemiology.
Causal inference: Causal inference is the process of determining whether a relationship between two variables is causal, meaning that one variable directly influences the other. This concept is crucial for understanding the underlying mechanisms of disease and the impact of exposures on health outcomes, helping researchers differentiate between correlation and causation.
Causal pathway: A causal pathway refers to the sequence of events or mechanisms through which a causal agent leads to an outcome. This concept is crucial in understanding how exposures, risk factors, and other influences can result in health outcomes, allowing researchers to identify direct and indirect relationships between variables. Mapping these pathways helps in pinpointing potential intervention points for disease prevention and health promotion.
Collider: A collider is a variable in a causal diagram or directed acyclic graph (DAG) that is influenced by two or more other variables. This means that the collider can create a spurious association between those variables when they are conditioned upon. Understanding colliders is essential for identifying the proper relationships between variables and avoiding misleading conclusions in causal inference.
Confounding: Confounding occurs when the relationship between an exposure and an outcome is distorted by the presence of another variable that is related to both. This can lead to incorrect conclusions about the true nature of the relationship being studied, making it crucial to identify and control for confounders in research.
Directed acyclic graph: A directed acyclic graph (DAG) is a finite directed graph with no directed cycles, meaning that it consists of nodes connected by edges that have a direction and cannot loop back on themselves. DAGs are used to represent causal relationships between variables in epidemiology, helping to visualize and understand the influence of one variable on another without confounding factors creating feedback loops.
Edges: In the context of directed acyclic graphs (DAGs) and causal diagrams, edges are the connections that represent relationships between variables. They show how one variable can influence or relate to another, directing the flow of information or causation in the graph. Each edge typically has a direction, indicating the nature of the relationship, and plays a crucial role in understanding causal inference.
Identifiability: Identifiability refers to the ability to determine the unique values of parameters in a model based on observed data. In causal inference, it helps to ascertain whether a causal effect can be reliably estimated from the data available, emphasizing the importance of correctly specifying models and understanding relationships among variables.
Intervention: Intervention refers to a purposeful action or set of actions aimed at altering a health-related outcome, often implemented to prevent, control, or treat disease. It plays a crucial role in experimental studies where researchers evaluate the effects of specific treatments or exposures on participants' health. Understanding interventions is also vital in visualizing causal relationships in directed acyclic graphs, as they can indicate how changing one factor might impact another within a population.
Judea Pearl: Judea Pearl is a renowned computer scientist and philosopher, known for his foundational work in the fields of causal inference and artificial intelligence. His research has significantly influenced the development of the counterfactual model and the use of directed acyclic graphs (DAGs) in understanding causal relationships. Pearl's theories provide essential tools for analyzing how interventions can affect outcomes in various domains, particularly in epidemiology.
M. Elizabeth Hall: M. Elizabeth Hall is an influential epidemiologist known for her work in causal inference and the application of directed acyclic graphs (DAGs) in understanding complex relationships between variables in epidemiological research. Her contributions have significantly advanced the methodologies used to clarify causal relationships, particularly in public health studies, making her a key figure in the development and popularization of DAGs as tools for better causal reasoning.
Mediator: A mediator is a variable that explains the relationship between an independent variable and a dependent variable by providing a pathway through which the effect occurs. Mediators are essential for understanding the mechanisms underlying causal relationships, as they help clarify how or why one variable affects another. By identifying mediators, researchers can gain insights into the process of causation, which is crucial for developing effective interventions and policies.
Nodes: In the context of directed acyclic graphs (DAGs) and causal diagrams, nodes represent variables or entities that can influence or be influenced by other variables. Each node is a point within the graph that signifies a specific factor, such as an exposure, outcome, or confounder, establishing a framework for understanding causal relationships. Nodes are connected by directed edges, indicating the direction of influence or causation between these variables.
Non-causal pathway: A non-causal pathway refers to a relationship or connection between variables that does not imply a direct cause-and-effect relationship. Instead, it highlights how certain variables may be associated due to confounding factors, measurement errors, or other influences that do not represent a causal mechanism. Understanding non-causal pathways is crucial in the analysis of directed acyclic graphs (DAGs) and causal diagrams, as they help differentiate true causal relationships from mere associations.
Pathways: In the context of epidemiology, pathways refer to the routes through which exposure to a causal factor leads to an outcome, illustrating how different variables interact in a causal framework. Understanding these pathways is crucial for identifying direct and indirect effects of various determinants on health outcomes, allowing researchers to establish clear connections in complex systems.
Sufficiency: Sufficiency refers to a condition in causal inference where the presence of a factor (or a set of factors) is enough to produce an effect or outcome. In epidemiology, understanding sufficiency is crucial for determining how certain exposures can lead to health outcomes, helping to identify causal relationships and pathways. It plays a vital role in constructing causal diagrams and directed acyclic graphs (DAGs) by illustrating the necessary conditions for certain effects to occur.
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