Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome. Existing confidence intervals for causal effects based on instrumental variables assume that all of the putative instrumental variables are valid; a valid instrumental variable is a variable that affects the outcome only by affecting the treatment and is not related to unmeasured confounders. However, in practice, some of the putative instrumental variables are likely to be invalid. This paper presents two tools to conduct valid inference and tests in the presence of invalid instruments. First, we propose a simple and general approach to construct confidence intervals based on taking unions of well-known confidence intervals. Second, we propose a novel test for the null causal effect based on a collider bias. Our two proposals outperform traditional instrumental variable confidence intervals when invalid instruments are present and can also be used as a sensitivity analysis when there is concern that instrumental variables assumptions are violated. The new approach is applied to a Mendelian randomization study on the causal effect of low-density lipoprotein on globulin levels.

中文翻译：

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两个强大的工具，用于推断无效工具的因果效应

工具变量已被广泛用于估计治疗对结果的因果影响。基于工具变量的因果效应的现有置信区间假设所有假定的工具变量都是有效的；有效的工具变量是仅通过影响治疗来影响结果且与未测量的混杂因素无关的变量。然而，在实践中，一些假定的工具变量很可能是无效的。本文提出了两种工具来在存在无效工具的情况下进行有效推理和测试。首先，我们提出了一种简单而通用的方法来构建基于已知置信区间联合的置信区间。其次，我们提出了一种基于对撞机偏差的无效因果效应的新测试。当存在无效工具时，我们的两个建议优于传统的工具变量置信区间，并且在担心违反工具变量假设时也可以用作敏感性分析。新方法应用于孟德尔随机化研究，研究低密度脂蛋白对球蛋白水平的因果影响。