Instrumental variable approaches have gained popularity for estimating causal effects in the presence of unmeasured confounding. However, the availability of instrumental variables in the primary population is often challenged due to stringent and untestable assumptions. This paper presents a novel method to identify and estimate causal effects in the primary population by utilizing instrumental variables from the auxiliary population, incorporating a structural equation model, even in scenarios with nonlinear treatment effects. Our approach involves using two datasets: one from the primary population with joint observations of treatment and outcome, and another from the auxiliary population providing information about the instrument and treatment. Our strategy differs from most existing methods by not depending on the simultaneous measurements of instrument and outcome. The central idea for identifying causal effects is to establish a valid substitute through the auxiliary population, addressing unmeasured confounding. This is achieved by developing a control function and projecting it onto the function space spanned by the treatment variable. We then propose a three-step estimator for estimating causal effects and derive its asymptotic results. We illustrate the proposed estimator through simulation studies, and the results demonstrate favorable performance. We also conduct a real data analysis to evaluate the causal effect between vitamin D status and BMI.

翻译：工具变量方法在存在未观测混杂因素的情况下估计因果效应已获得广泛认可。然而，由于严苛且无法检验的假设条件，在主要人群中获取有效工具变量往往面临挑战。本文提出一种新方法，通过整合结构方程模型，即使是在非线性处理效应的情景下，也能利用辅助人群中的工具变量识别并估计主要人群中的因果效应。我们的方法涉及两个数据集：一个来自主要人群，包含处理变量与结果变量的联合观测值；另一个来自辅助人群，提供工具变量与处理变量的相关信息。与现有多数方法不同，本策略不依赖工具变量和结果变量的同步测量。识别因果效应的核心思想是通过辅助人群构建有效替代变量，以应对未观测混杂因素。具体通过建立控制函数并将其投影到由处理变量张成的函数空间中实现。随后我们提出三步估计量来估计因果效应，并推导其渐近性质。通过模拟研究验证所提估计量的性能，结果表明其具有良好表现。我们还在真实数据分析中评估了维生素D状态与身体质量指数之间的因果效应。