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：非实验研究中有时会使用负对照变量来检测隐藏因素导致的混杂效应。负对照结局（NCO）是指虽受暴露-结局效应中未观测混杂因素影响，但不受暴露因果作用影响的结局变量。Tchetgen Tchetgen (2013) 提出了对照结局校准方法（COCA）作为正式的NCO反事实方法，用于检测并校正残余混杂偏倚。在识别过程中，COCA将NCO视为目标无治疗反事实结局的误差代理变量，通过将NCO对无治疗反事实变量进行回归分析，并结合假设个体因果效应恒定的秩保持结构模型实现识别。本研究建立了处理组平均因果效应的非参数COCA识别方法，无需秩保持假设，因此可容纳个体间不受限制的效应异质性。该非参数识别结果具有重要实践意义：与近期提出的依赖一对混杂代理变量进行识别的近端因果推断不同，本研究仅需单一代理变量即可实现混杂控制。针对COCA估计，我们提出三种独立策略：(i) 扩展倾向得分法，(ii) 结局桥函数法，及(iii) 双重稳健法。最后，通过评估巴西寨卡病毒暴发对出生率的因果影响实例，展示了所提方法的应用效果。