We consider the problem of identifying a conditional causal effect through covariate adjustment. We focus on the setting where the causal graph is known up to one of two types of graphs: a maximally oriented partially directed acyclic graph (MPDAG) or a partial ancestral graph (PAG). Both MPDAGs and PAGs represent equivalence classes of possible underlying causal models. After defining adjustment sets in this setting, we provide a necessary and sufficient graphical criterion -- the conditional adjustment criterion -- for finding these sets under conditioning on variables unaffected by treatment. We further provide explicit sets from the graph that satisfy the conditional adjustment criterion, and therefore, can be used as adjustment sets for conditional causal effect identification.

翻译：我们考虑了通过协变量调整来识别条件因果效应的问题。我们重点关注因果图已知且属于以下两种类型之一的设定：最大定向部分有向无环图（MPDAG）或部分祖先图（PAG）。MPDAG和PAG均表示可能存在的潜在因果模型的等价类。在此设定下定义调整集后，我们提出了一种必要且充分的图形准则——条件调整准则——用于在治疗变量不受影响的条件下，通过调节变量找到这些调整集。我们进一步从图中给出了满足条件调整准则的显式集合，因此这些集合可用作条件因果效应识别的调整集。