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. Other information, such as the causal relations between confounders, is not required by the procedure. 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与结果之间的混杂，可以说是观察性研究设计中最重要的一步。以往的方法，如Pearl著名的后门准则，通常需要预先指定一个因果图，这在实践中往往难以实现。我们提出了一种无需预先指定图或观测变量集的混杂因素选择交互式程序。该程序通过查找我们称之为“主要调整集”的针对可能混杂变量对的方式，迭代地扩展因果图。这可以看作是对底层因果图的一系列潜在投影进行逆操作。程序以主要调整集的形式，逐步从用户那里获取结构信息，直到找到一组控制混杂的协变量，或者确定不存在这样的集合。程序不要求其他信息，例如混杂因素之间的因果关系。我们证明，如果用户在每一步都正确指定了主要调整集，我们的程序既是合理的也是完备的。