Estimating the average causal effect (ACE) using observational data is a key focus in causal inference for which missing data present an important challenge. Multiple imputation (MI) is a widely used method for handling missing data and can yield unbiased estimates when the imputation is compatible with the substantive analysis. One of the advantages of MI is its scope to include so-called "auxiliary variables", defined as variables associated with incomplete variables that are excluded from the substantive analysis. Although many studies have looked at the use of auxiliary variables in MI for improving precision, the study of auxiliary variables that are necessary for the identifiability (or "recoverability") of the ACE in the presence of missing data has been scant. In this work, we investigate the use of auxiliary variables, both mediators and non-mediators, across a range of typical univariable and multivariable missingness mechanisms depicted by missingness directed acyclic graphs (m-DAGs). For each setting, we derive recoverability results, then evaluate MI-based and complete-case methods for estimating the ACE using correctly specified g-computation, considering different strategies for incorporating auxiliary variables and varying degrees of compatibility for MI models. Based on findings from the simulation studies, we provide practical guidance, highlighting that distinguishing appropriately between mediator and non-mediator auxiliary variables is important to avoid bias as is the use of compatible and flexible (non-parametric) MI methods that incorporate these variables.

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