Confounder selection, namely choosing a set of covariates to control for confounding between a treatment and an outcome, is arguably the most important step in the design of observational studies. Previous methods, such as Pearl's celebrated back-door criterion, typically require pre-specifying a causal graph, which can often be difficult in practice. We propose an interactive procedure for confounder selection that does not require pre-specifying the graph or the set of observed variables. This procedure iteratively expands the causal graph by finding what we call "primary adjustment sets" for a pair of possibly confounded variables. This can be viewed as inverting a sequence of latent projections of the underlying causal graph. Structural information in the form of primary adjustment sets is elicited from the user, bit by bit, until either a set of covariates are found to control for confounding or it can be determined that no such set exists. We show that if the user correctly specifies the primary adjustment sets in every step, our procedure is both sound and complete.

翻译：混杂因素选择，即选择一组协变量来控制处理变量与结果变量之间的混杂效应，可以说是观察性研究设计中最关键的步骤。先前的方法（如Pearl著名的后门准则）通常需要预先指定一个因果图，而这在实践中往往难以实现。本文提出了一种无需预先指定因果图或观测变量集合的交互式混杂因素选择程序。该程序通过寻找我们称之为一对可能混杂变量的"主调整集"来迭代扩展因果图。这可以看作是对潜在因果图进行一系列潜在投影的逆操作。程序逐步从用户处获取以主调整集形式呈现的结构信息，直到找到一组能够控制混杂效应的协变量，或确定不存在这样的协变量集合。我们证明，如果用户在每一步都能正确指定主调整集，该程序既是可靠的也是完备的。