Causal inference from observational data often rests on the unverifiable assumption of no unmeasured confounding. Recently, Tchetgen Tchetgen and colleagues have introduced proximal inference to leverage negative control outcomes and exposures as proxies to adjust for bias from unmeasured confounding. However, some of the key assumptions that proximal inference relies on are themselves empirically untestable. Additionally, the impact of violations of proximal inference assumptions on the bias of effect estimates is not well understood. In this paper, we derive bias formulas for proximal inference estimators under a linear structural equation model data generating process. These results are a first step toward sensitivity analysis and quantitative bias analysis of proximal inference estimators. While limited to a particular family of data generating processes, our results may offer some more general insight into the behavior of proximal inference estimators.

中文翻译：

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违反近端识别假设的偏差公式

来自观察数据的因果推断通常建立在无法验证的假设之上，即没有不可测量的混杂因素。最近，Tchetgen Tchetgen 及其同事引入了近端推理，以利用负控制结果和暴露作为代理来调整来自无法测量的混杂因素的偏差。然而，近端推理所依赖的一些关键假设本身在经验上是不可检验的。此外，违反近端推理假设对效果估计偏差的影响尚不清楚。在本文中，我们推导了线性结构方程模型数据生成过程下的近端推理估计器的偏差公式。这些结果是对近端推理估计器的敏感性分析和定量偏差分析的第一步。