Causal diagrams and change variables

Background: The true change in the value of a variable between two time points is often assumed to be a cause or an effect of interest. To our knowledge, this assumption is based on intuition, rather than on any formal theoretical justification. Methods: We used causal directed acyclic graphs to explore the causal properties of a change variable, and critically examined competing structures. Results: Based on the proposed causal structure, a change variable (true change) is no more than a derived variable. It does not cause anything and is not of causal interest. Conclusions: A true change is not a variable in the physical world. Therefore, modelling the change between two time points is justified only in a few situations.