Negative control variables are sometimes used in non-experimental studies to detect the presence of confounding by hidden factors. A negative control outcome (NCO) is an outcome that is influenced by unobserved confounders of the exposure effects on the outcome in view, but is not causally impacted by the exposure. Tchetgen Tchetgen (2013) introduced the Control Outcome Calibration Approach (COCA) as a formal NCO counterfactual method to detect and correct for residual confounding bias. For identification, COCA treats the NCO as an error-prone proxy of the treatment-free counterfactual outcome of interest, and involves regressing the NCO on the treatment-free counterfactual, together with a rank-preserving structural model which assumes a constant individual-level causal effect. In this work, we establish nonparametric COCA identification for the average causal effect for the treated, without requiring rank-preservation, therefore accommodating unrestricted effect heterogeneity across units. This nonparametric identification result has important practical implications, as it provides single proxy confounding control, in contrast to recently proposed proximal causal inference, which relies for identification on a pair of confounding proxies. For COCA estimation we propose three separate strategies: (i) an extended propensity score approach, (ii) an outcome bridge function approach, and (iii) a doubly-robust approach. Finally, we illustrate the proposed methods in an application evaluating the causal impact of a Zika virus outbreak on birth rate in Brazil.

翻译：非实验研究中有时使用阴性对照变量来检测隐藏因素导致的混杂。阴性对照结局（NCO）是指受暴露对目标结局效应中未观测混杂因素影响，但不受暴露因果影响的结局。Tchetgen Tchetgen（2013）提出了对照结局校准方法（COCA），作为一种正式的NCO反事实方法，用于检测和纠正残留混杂偏倚。在识别方面，COCA将NCO视为目标治疗无关反事实结局的易错代理，通过将NCO对治疗无关反事实进行回归，并结合假设个体层面因果效应恒定的保秩结构模型。本研究建立了接受处理者平均因果效应的非参数COCA识别方法，无需保秩假设，因此允许跨单位存在无限制的效应异质性。这一非参数识别结果具有重要实践意义，因为它实现了单代理混杂控制，而近期提出的近端因果推断需依赖一对混杂代理进行识别。针对COCA估计，我们提出三种独立策略：（i）扩展倾向评分方法，（ii）结局桥函数方法，以及（iii）双重稳健方法。最后，我们通过评估寨卡病毒疫情对巴西出生率的因果影响的应用案例来展示所提方法。