Recent work has focused on the potential and pitfalls of causal identification in observational studies with multiple simultaneous treatments. Building on previous work, we show that even if the conditional distribution of unmeasured confounders given treatments were known exactly, the causal effects would not in general be identifiable, although they may be partially identified. Given these results, we propose a sensitivity analysis method for characterizing the effects of potential unmeasured confounding, tailored to the multiple treatment setting, that can be used to characterize a range of causal effects that are compatible with the observed data. Our method is based on a copula factorization of the joint distribution of outcomes, treatments, and confounders, and can be layered on top of arbitrary observed data models. We propose a practical implementation of this approach making use of the Gaussian copula, and establish conditions under which causal effects can be bounded. We also describe approaches for reasoning about effects, including calibrating sensitivity parameters, quantifying robustness of effect estimates, and selecting models that are most consistent with prior hypotheses.

翻译：近期研究聚焦于多重同步处理观测研究中因果识别的潜力与局限。基于先前工作，我们证明即使给定处理条件下未测量混杂因素的条件分布已知，因果效应通常仍不可识别（尽管可能部分识别）。鉴于这些结果，我们提出一种敏感性分析方法，用于刻画潜在未测量混杂因素的影响，该方法专为多重处理场景设计，可用于表征与观测数据相容的因果效应范围。我们的方法基于结果、处理与混杂因素联合分布的copula分解，可叠加于任意观测数据模型之上。我们提出利用高斯copula实现该方法的实践方案，并建立因果效应可被界定的条件。同时，我们阐述了效应推理的多种途径，包括敏感性参数校准、效应估计稳健性量化，以及选择与先验假设最一致的模型。