ABSTRACT We investigate the behavior of the Lasso for selecting invalid instruments in linear instrumental variables models for estimating causal effects of exposures on outcomes, as proposed recently by Kang et al. Invalid instruments are such that they fail the exclusion restriction and enter the model as explanatory variables. We show that for this setup, the Lasso may not consistently select the invalid instruments if these are relatively strong. We propose a median estimator that is consistent when less than 50% of the instruments are invalid, and its consistency does not depend on the relative strength of the instruments, or their correlation structure. We show that this estimator can be used for adaptive Lasso estimation, with the resulting estimator having oracle properties. The methods are applied to a Mendelian randomization study to estimate the causal effect of body mass index (BMI) on diastolic blood pressure, using data on individuals from the UK Biobank, with 96 single nucleotide polymorphisms as potential instruments for BMI. Supplementary materials for this article are available online.

中文翻译：

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Lasso 在一些无效仪器的仪器变量估计中的应用

摘要 我们研究了 Lasso 在线性工具变量模型中选择无效工具以估计暴露对结果的因果影响的行为，正如 Kang 等人最近提出的。无效工具是指它们未能通过排除限制并作为解释变量进入模型。我们表明，对于此设置，如果这些工具相对强大，套索可能不会始终选择无效工具。我们提出了一个中位数估计量，当少于 50% 的工具无效时是一致的，其一致性不依赖于工具的相对强度或其相关结构。我们表明该估计器可用于自适应套索估计，由此产生的估计器具有预言机属性。这些方法被应用于孟德尔随机化研究，以估计体重指数 (BMI) 对舒张压的因果影响，使用来自英国生物银行的个人数据，其中 96 个单核苷酸多态性作为 BMI 的潜在工具。本文的补充材料可在线获取。