Graphical Models for Recovering Probabilistic and Causal Queries from Missing Data

We address the problem of deciding whether a causal or probabilistic query is estimable from data corrupted by missing entries, given a model of missingness process. We extend the results of Mohan et al. [2013] by presenting more general conditions for recovering probabilistic queries of the form P (y|x) and P (y, x) as well as causal queries of the form P (y|do(x)). We show that causal queries may be recoverable even when the factors in their identifying estimands are not recoverable. Specifically, we derive graphical conditions for recovering causal effects of the form P (y|do(x)) when Y and its missingness mechanism are not d-separable. Finally, we apply our results to problems of attrition and characterize the recovery of causal effects from data corrupted by attrition.