Estimating causal effects of continuous treatments is a common problem in practice, for example, in studying average dose-response functions. Classical analyses typically assume that all confounders are fully observed, whereas in real-world applications, unmeasured confounding often persists. In this article, we propose a novel framework for the identification of average dose-response functions using instrumental variables, thereby mitigating bias induced by unobserved confounders. We introduce the concept of a uniform regular weighting function and consider covering the treatment space with a finite collection of open sets. On each of these sets, such a weighting function exists, allowing us to identify the average dose-response function locally within the corresponding region. For estimation, we propose an augmented inverse probability weighted score for continuous treatments with instrumental variables under a debiased machine learning framework, and provide practical guidance to adaptively establish regular weighting functions from the data. We further establish the asymptotic properties when the average dose-response function is estimated via kernel regression or empirical risk minimization. Finally, we conduct both simulation and empirical studies to assess the finite-sample performance of the proposed methods.

翻译：估计连续治疗效果的因果效应是实践中的常见问题，例如在研究平均剂量反应函数时。经典分析通常假设所有混杂变量均被完全观测，而实际应用中往往存在未测量的混杂因素。本文提出一种利用工具变量识别平均剂量反应函数的新框架，从而减轻未观测混杂导致的偏倚。我们引入均匀正则加权函数的概念，并考虑用有限个开集覆盖治疗空间。在每个开集上均存在此类加权函数，从而能够在对应区域内局部识别平均剂量反应函数。在估计方面，我们提出一种连续治疗效果下基于工具变量的增广逆概率加权评分方法，该方法建立在去偏机器学习框架之上，并给出了从数据中自适应构建正则加权函数的实践指导。进一步地，我们建立了基于核回归或经验风险最小化估计平均剂量反应函数的渐近性质。最后，通过模拟和实证研究评估了所提方法的有限样本性能。