发表机构
Johns Hopkins Bloomberg School of Public Health; Yale University（约翰斯·霍普金斯大学布隆伯格公共卫生学院; 耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出通过交叉代理平衡来理解近似因果推断，将治疗桥函数视为平衡条件，并证明其估计为平衡权重估计，同时为常见估计器的数值等价性提供条件。
AI 中文摘要
近似因果推断通过利用两组代理变量，在存在未测量混杂的情况下识别因果效应。识别通常依赖于桥函数，这些函数被定义为积分方程的解。然而，拟合的桥函数如何纠正混杂偏差的机制仍然不透明，难以进行解释、检查或压力测试。我们证明，治疗桥函数的定义方程本身就是一个平衡条件，具有交叉代理形式：权重是治疗混杂代理和协变量的函数，它们平衡了结果混杂代理和协变量（即，在特定治疗组中重新加权分布，以匹配各治疗组之间的分布）。通过治疗桥函数的若干现有识别路径可以被解释为提供了条件，在这些条件下，对结果代理的平衡意味着对未观测混杂的平衡，我们称之为平衡传播。利用这一框架，我们表明治疗桥函数的估计是一种平衡权重估计。最后，我们证明，对于一大类近似估计器，包括那些利用结果桥函数的估计器，也可以获得结果加权估计器形式。利用这一框架，我们提供了常见估计器数值等价的条件。
英文摘要
Proximal causal inference identifies causal effects in the presence of unmeasured confounding by drawing on two sets of proxy variables. Identification typically utilizes bridge functions, defined as solutions to integral equations. However, the mechanism by which fitted bridge functions correct for confounding bias remains opaque, offering little to interpret, inspect or stress-test. We show that the defining equation of a treatment bridge function is already a balance condition, with a cross-proxy form: the weights are functions of the treatment confounding proxies and covariates, and they balance the outcome confounding proxies and covariates (i.e., reweighting the distribution in a particular treatment arm to match the distribution across treatment arms). Several existing identification paths via a treatment bridge function can then be interpreted as providing conditions under which balance on the outcome proxies implies balance on the unobserved confounders, which we call balance propagation. Leveraging this framing, we show that estimation of the treatment bridge function is a type of balancing weight estimation. Finally, we show that an outcome-weighted estimator form can also be obtained for a large class of proximal estimators, including those that utilize an outcome bridge function. Using this framing, we provide conditions under which common estimators are numerically equivalent.
