On the Graphical Rules for Recovering the Average Treatment Effect Under Selection Bias

Selection bias is a major obstacle toward valid causal inference in epidemiology. Over the past decade, several graphical rules based on causal diagrams have been proposed as sufficient identification conditions for addressing selection bias and recovering causal effects. However, these simple graphical rules are typically coupled with specific identification strategies and estimators. In this article, we show two important cases of selection bias that fall outside the scope of these existing simple rules and their estimators: one case where selection is a descendant of a collider of the treatment and the outcome, and the other case where selection is affected by a mediator. To address selection bias and recover the marginal average treatment effect in these two cases, we propose an alternative set of graphical rules and construct identification formulas using g-computation and inverse probability weighting (IPW) based on single-world intervention graphs (SWIGs), leveraging external information from individuals outside the selected sample. We conduct simulation studies to verify the performance of the estimators when the traditional crude selected-sample analysis (i.e., complete-case analysis) yields erroneous conclusions that contradict the truth. We emphasize that identifying causal effects in the presence of selection bias depends critically on both the target estimand and the availability of external information.