A note on compatibility for inference with missing data in the presence of auxiliary covariates.

Imputation and inference (or analysis) models that cannot be true simultaneously are frequently used in practice when missing outcomes are present. In these situations, the conclusions can be misleading depending on how "different" the implicit inference model, induced by the imputation model, is from the inference model actually used. We introduce model-based compatibility (MBC) and compare two MBC approaches to a non-MBC approach and explore the inferential validity of the latter in a simple case. In addition, we evaluate more complex cases through a series of simulation studies. Overall, we recommend caution when making inferences using a non-MBC analysis and point out when the inferential "cost" is the largest.