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How does one come up with the DAG for a structural causal model from observational data?
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The construction of DAGs mainly relies on expert knowledge of how variables/sets of variables are related. In other words, DAGs are used to encode the expert's a priori assumptions about relationships between and among variables in causal structures. Using directed edges and nodes, an expert can visually represent their beliefs of the causal relationships between variables.

The first step in creating a causal DAG is to diagram the investigators' understanding of the relationships and dependencies among variables. Construction of DAGs should not be limited to measured variables from available data; they must be constructed independent of available data and of background knowledge of the causal network linking treatment to the outcome.

The most important aspect of constructing a causal DAG is to include on the DAG any common cause of any other two variables on the DAG. Variables that only causally influence one other variable (exogenous variables) may be included or omitted from the DAG, but common causes must be included for the DAG to be considered causal.

The absence of any path between two nodes in a DAG indicates that the variables are not causally related (i.e., that manipulation of one variable does not cause a change in the value of the other variable).

Investigators may not agree on a single DAG to represent a complex clinical question; when this occurs, multiple DAGs may be constructed and statistical associations observed from available data may be used to evaluate the consistency of observed probability distributions with the proposed DAGs. Statistical analyses may be undertaken as informed by different DAGs, and the results can be compared.

Source: Sauer B, VanderWeele TJ. Use of Directed Acyclic Graphs. In: Velentgas P, Dreyer NA, Nourjah P, et al., editors. Developing a Protocol for Observational Comparative Effectiveness Research: A User's Guide. Rockville (MD): Agency for Healthcare Research and Quality (US); 2013 Jan. Supplement 2. Available from: https://www.ncbi.nlm.nih.gov/books/NBK126189/
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