Depicting deterministic variables within directed acyclic graphs (DAGs): An aid for identifying and interpreting causal effects involving derived variables and compositional data

Deterministic variables are variables that are functionally determined by one or more parent variables. They commonly arise when a variable has been functionally created from one or more parent variables, as with derived variables, 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 derived variables and/or compositional data. We propose a two-step approach in which all variables are initially considered, and a choice is made whether to focus on the deterministic variable or its determining parents.

Depicting deterministic variables within DAGs brings several benefits. It is easier to identify and avoid misinterpreting tautological associations, i.e., self-fulfilling associations between deterministic variables and their parents, or between sibling variables with shared parents. In compositional data, it is easier to understand the consequences of conditioning on the ‘whole’ variable, and correctly identify total and relative causal effects. For derived variables, it encourages greater consideration of the target estimand and greater scrutiny of the consistency and exchangeability assumptions.

DAGs with deterministic variables are a useful aid for planning and interpreting analyses involving derived variables and/or compositional data.