  Confounding bias, missing data, and selection bias are three common obstacles
to valid causal inference in the data sciences. Covariate adjustment is the
most pervasive technique for recovering casual effects from confounding bias.
In this paper, we introduce a covariate adjustment formulation for controlling
confounding bias in the presence of missing-not-at-random data and develop a
necessary and sufficient condition for recovering causal effects using the
adjustment. We also introduce an adjustment formulation for controlling both
confounding and selection biases in the presence of missing data and develop a
necessary and sufficient condition for valid adjustment. Furthermore, we
present an algorithm that lists all valid adjustment sets and an algorithm that
finds a valid adjustment set containing the minimum number of variables, which
are useful for researchers interested in selecting adjustment sets with desired
properties.
