On the Graphical Rules for Recovering the Average Treatment Effect Under Selection Bias
Yichi Zhang, Haidong Lu
[stat.ME]
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 the 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 cannot be addressed by 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 the mediator. To address selection bias and recover average treatment effect in these two cases, we propose an alternative set of graphical rules and construct identification formulas by the g-computation and the inverse probability weighting (IPW) methods based on single-world intervention graphs (SWIGs). 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 contradictory to the truth.