Imputation without nightMARs: Graphical criteria for valid imputation of missing data

By revisiting imputation from the modern perspective of missing data graphs, we correct common guidance about which auxiliary variables should be included in an imputation model. We propose a generalized definition of missing at random (MAR), termed z-MAR, which distinguishes analysis variables from auxiliary variables included only in the imputation model. We derive a corresponding graphical condition, the m-backdoor criterion, which characterizes when a broad class of MAR-based imputation models yields valid inferences. In a sense we formalize, the m-backdoor criterion is both necessary and sufficient for valid imputation. Whereas common guidance is to include all available auxiliary variables in the imputation model, our results show that some auxiliary variables (e.g., colliders) can exacerbate bias. Thus, the modeled auxiliary variables should be restricted, at minimum, to those that causally affect either the incomplete variables or the missingness indicators. This set will always suffice to ensure valid imputation, if any sufficient set does exist among the candidate auxiliary variables. Applying this result does not require full knowledge of the graph. We demonstrate these results through simulations and an empirical application to the Stockholm Public Health Cohort, where including a presumed collider in the imputation model substantially altered estimates.