Summary Two-stage least squares estimation is popular for structural equation models with unmeasured confounders. In such models, both the outcome and the exposure are assumed to follow linear models conditional on the measured confounders and instrumental variable, which is related to the outcome only via its relation with the exposure. We consider data where both the outcome and the exposure may be incompletely observed, with particular attention to the case where both are censored event times. A general class of two-stage minimum distance estimators is proposed that separately fits linear models for the outcome and exposure and then uses a minimum distance criterion based on the reduced-form model for the outcome to estimate the regression parameters of interest. An optimal minimum distance estimator is identified which may be superior to the usual two-stage least squares estimator with fully observed data. Simulation studies demonstrate that the proposed methods perform well with realistic sample sizes. Their practical utility is illustrated in a study of the comparative effectiveness of colon cancer treatments, where the effect of chemotherapy on censored survival times may be confounded with patient status.

中文翻译：

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结构工具变量模型的两阶段估计

总结 两阶段最小二乘估计在具有未测量混杂因素的结构方程模型中很流行。在这样的模型中，假设结果和暴露都遵循线性模型，条件是测量的混杂因素和工具变量，它仅通过与暴露的关系与结果相关。我们考虑结果和暴露都可能未完全观察到的数据，特别注意两者都是审查事件时间的情况。提出了一类通用的两阶段最小距离估计器，分别拟合结果和暴露的线性模型，然后使用基于结果的简化形式模型的最小距离标准来估计感兴趣的回归参数。确定了一个最佳最小距离估计器，该估计器可能优于具有完全观察数据的通常的两阶段最小二乘估计器。模拟研究表明，所提出的方法在实际样本量下表现良好。一项关于结肠癌治疗比较有效性的研究说明了它们的实用性，其中化疗对截尾生存时间的影响可能与患者状态相混淆。