Conditions for Non-Confounding and Collapsibility within Causal Diagrams

In observational studies, the phenomenon of confounding bias often leads to errors in the evaluation of causal effects, which in turn affects the accuracy of conclusions in causal inference. This paper details the properties of these two concepts of non-confounding and collapsibility in evaluating the true causal effects and proposes several conditions for non-confounding and collapsibility with knowledge of the constructed causal diagrams. In order to give characterizations for these conditions, we introduce the concepts of linearly ordered set and stability under conditioning and studies on certain properties. Based on the above arguments, we finally present sufficient conditions for non-confounding and collapsibility, respectively.