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：在非实验研究中，有时会使用阴性对照变量来检测隐藏因素导致的混杂效应。阴性对照结局（NCO）是一种受到暴露对关注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）提出了控制结局校准方法（COCA），作为一种正式的NCO反事实方法，用于检测和校正残留混杂偏倚。为了识别，COCA将NCO视为关注结局的无处理反事实的一个含误差代理变量，并将NCO对无处理反事实进行回归，同时结合一个秩保持结构模型，该模型假设个体水平的因果效应为常数。在本研究中，我们在无需秩保持假设的条件下，建立了处理组平均因果效应的非参数COCA识别方法，因此允许跨单位存在不受限制的效应异质性。这一非参数识别结果具有重要的实际意义，因为它提供了单代理混杂控制，而近期提出的近端因果推断依赖于一对混杂代理变量进行识别。对于COCA的估计，我们提出了三种不同的策略：（i）扩展倾向得分方法，（ii）结局桥函数方法，以及（iii）双重稳健方法。最后，我们在一项评估巴西寨卡病毒暴发对出生率因果影响的应用中展示了所提出的方法。