The front-door criterion can be used to identify and compute causal effects despite the existence of unmeasured confounders between a treatment and outcome. However, the key assumptions -- (i) the existence of a variable (or set of variables) that fully mediates the effect of the treatment on the outcome, and (ii) which simultaneously does not suffer from similar issues of confounding as the treatment-outcome pair -- are often deemed implausible. This paper explores the testability of these assumptions. We show that under mild conditions involving an auxiliary variable, the assumptions encoded in the front-door model (and simple extensions of it) may be tested via generalized equality constraints a.k.a Verma constraints. We propose two goodness-of-fit tests based on this observation, and evaluate the efficacy of our proposal on real and synthetic data. We also provide theoretical and empirical comparisons to instrumental variable approaches to handling unmeasured confounding.

翻译：尽管在治疗和结果之间存在着未测的混淆因素,但前门标准可以用来确定和计算因果关系。然而,关键假设 -- -- (一) 存在充分调节治疗对结果的影响的变数(或一组变数),以及(二) 同时没有受到与治疗结果对等相混淆的类似问题的影响 -- -- 往往被认为是不可信的。本文探讨了这些假设的可检验性。我们表明,在涉及辅助变量的温和条件下,在前门模式(及其简单扩展)编码的假设可以通过普遍平等限制(a.k.a Verma)进行测试。我们建议基于这一观察进行两种有利测试,并评估我们关于真实和合成数据的建议的有效性。我们还提供理论和经验方面的比较,用以指导处理无法计量的相混淆的变数方法。