Abstract：
When analyzing a selected sample from a general population, selection bias can arise relative to the causal average treatment effect (ATE) for the general population, and also relative to the ATE for the selected sample itself. We provide simple graphical rules that indicate: (1) if a selected-sample analysis will be unbiased for each ATE; (2) whether adjusting for certain covariates could eliminate selection bias. The rules can easily be checked in a standard single-world intervention graph. When the treatment could affect selection, a third estimand of potential scientific interest is the \"net treatment difference\", namely the net change in outcomes that would occur for the selected sample if all members of the general population were treated versus not treated, including any effects of the treatment on which individuals are in the selected sample . We provide graphical rules for this estimand as well. We decompose bias in a selected-sample analysis relative to the general-population ATE into: (1) \"internal bias\" relative to the net treatment difference; (2) \"net-external bias\", a discrepancy between the net treatment difference and the general-population ATE. Each bias can be assessed unambiguously via a distinct graphical rule, providing new conceptual insight into the mechanisms by which certain causal structures produce selection bias.
摘要：
当从一般人群中分析选定的样本时，相对于一般人群的因果平均治疗效应(ATE)，可能会出现选择偏差，并且还相对于所选样品本身的ATE。我们提供了简单的图形规则，表明：（1）对于每个ATE，所选样本分析是否无偏；（2）调整某些协变量是否可以消除选择偏差。可以在标准的单世界干预图中轻松检查规则。当治疗可能影响选择时，潜在科学兴趣的第三个估计是“净治疗差异”，即，如果普通人群的所有成员都接受治疗与不接受治疗，所选样本将发生的结果净变化，包括所选样本中个体的任何治疗效果。我们还为此估计提供了图形规则。我们将选定样本分析中相对于一般人群ATE的偏倚分解为：（1）相对于净治疗差异的“内部偏倚”；（2）“净外部偏倚”，净治疗差异与一般人群ATE之间存在差异。每个偏见都可以通过不同的图形规则进行明确的评估，为某些因果结构产生选择偏差的机制提供新的概念性见解。
