Depicting deterministic variables within directed acyclic graphs (DAGs): An aid for identifying and interpreting causal effects involving tautological associations, composition
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BACKGROUND: Deterministic variables are variables that are fully explained by one or more parent variables. They commonly arise when a variable has been algebraically constructed from one or more parent variables, known as transformed variables and composite variables respectively, and in compositional data, where the 'whole' variable is determined from its 'parts'. This article introduces how deterministic variables may be depicted within directed acyclic graphs (DAGs) to help with identifying and interpreting causal effects involving tautological associations, compositional data, and composite variables. DEVELOPMENT: This article proposes a two-step approach to the handling of deterministic variables when identifying and interpreting causal effects. First, a 'full' DAG is drawn that includes all deterministic variables and all determining parents. For clarity, deterministic variables should be depicted with double-outlined nodes and all their incoming arcs should be double-lined. Next, an explicit choice should be made whether to focus on the deterministic variable(s) or the determining parents. APPLICATION: Depicting deterministic variables within DAGs bring several benefits. It is easier to identify and avoid misinterpreting tautological associations, i.e., self-fulfilling associations between variables with shared algebraic parent variables. In compositional data, it is easier to understand the consequences of conditioning on the 'whole' variable, and in turn correctly identify total and relative causal effects. For composite variables, it encourages greater consideration of the target estimand and whether the consistency and exchangeability assumptions can be satisfied. CONCLUSION: DAGs with deterministic variables are a useful aid for planning and/or interpreting analyses involving transformed variables, compositional data, and/or composite variables.
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