Graphical Criteria for Efficient Total Effect Estimation Via Adjustment in Causal Linear Models

Covariate adjustment is a commonly used method for total causal effect estimation. In recent years, graphical criteria have been developed to identify all valid sets, that is, covariate sets can be this purpose. Different typically provide estimates of varying accuracies. Restricting ourselves linear models, we introduce criterion compare the asymptotic variances provided by certain sets. We employ result develop two further tools. First, simple variance reducing pruning procedure any given set. Second, give characterization set provides optimal among Our results depend only on structure and not specific error or edge coefficients underlying model. They applied directed acyclic graphs (DAGs), completed partially (CPDAGs) maximally oriented (maximal PDAGs). present simulations real data example support our show their practical applicability.