Testable implications of outcome-independent missingness not at random in covariates

SummaryA common aim of empirical research is to regress an outcome on a set of covariates, when some covariates are subject to missingness. If the probability of missingness is conditionally independent of the outcome, given the covariates, then a complete-case analysis is unbiased for parameters conditional on covariates. We derive all testable constraints that such outcome-independent missingness not at random implies on the observed data distribution, for settings where both the outcome and covariates are categorical. By assessing if these constraints are violated for a particular observed data distribution, the analyst can infer whether the assumption of outcome-independent missingness not at random is violated for that distribution. The constraints are formulated implicitly, in terms of consistency requirements on certain linear equation systems. We also derive explicit inequality constraints that are more easily assessable, but also more permissive than the implicit constraints.