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.