A common-cause principle for eliminating selection bias in causal estimands through covariate adjustment

Average treatment effects (ATEs) may be subject to selection bias when they are estimated among only a non-representative subset of the target population. Selection bias can sometimes be eliminated by conditioning on a “sufficient adjustment set” of covariates, even for some forms of missingness not at random (MNAR). Without requiring full specification of the causal structure, we consider sufficient adjustment sets to allow nonparametric identification of conditional ATEs in the target population. Covariates in the sufficient set may be collected among only the selected sample. We establish that if a sufficient set exists, then the set consisting of common causes of the outcome and selection, excluding the exposure and its descendants, also suffices. We establish simple graphical criteria for when a sufficient set will not exist, which could help indicate whether this is plausible for a given study. Simulations considering selection due to missing data indicated that sufficiently-adjusted complete-case analysis (CCA) can considerably outperform multiple imputation under MNAR and, if the sample size is not large, sometimes even under missingness at random. Analogous to the common-cause principle for confounding, these sufficiency results clarify when and how selection bias can be eliminated through covariate adjustment.