Instrumental variables (IVs) are widely used to study the causal effect of an exposure on an outcome in the presence of unmeasured confounding. IVs require an instrument, a variable that (a) is associated with the exposure, (b) has no direct effect on the outcome except through the exposure, and (c) is not related to unmeasured confounders. Unfortunately, finding variables that satisfy conditions b or c can be challenging in practice. This article reviews works where instruments may not satisfy conditions b or c, which we refer to as invalid instruments. We review identification and inference under different violations of b or c, specifically under linear models, nonlinear models, and heteroskedastic models. We conclude with an empirical comparison of various methods by reanalyzing the effect of body mass index on systolic blood pressure from the UK Biobank.

中文翻译：

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使用无效工具进行识别和推理


工具变量 （IV） 广泛用于研究在存在未测量的混杂因素的情况下暴露对结果的因果影响。IV 需要一种工具，一个变量，该变量 （a） 与暴露相关，（b） 除通过暴露外对结果没有直接影响，以及 （c） 与未测量的混杂因素无关。不幸的是，在实践中，找到满足条件 b 或 c 的变量可能具有挑战性。本文回顾了工具可能不满足条件 b 或 c 的工作，我们称之为无效工具。我们回顾了在不同违反 b 或 c 的情况下的识别和推理，特别是在线性模型、非线性模型和异方差模型下。我们通过重新分析体重指数对英国生物样本库收缩压的影响，对各种方法进行了实证比较。