Causal inference necessarily relies upon untestable assumptions; hence, it is crucial to assess the robustness of obtained results to violations of identification assumptions. However, such sensitivity analysis is only occasionally undertaken in practice, as many existing methods only apply to relatively simple models and their results are often difficult to interpret. We take a more flexible approach to sensitivity analysis and view it as a constrained stochastic optimization problem. This work focuses on sensitivity analysis for a linear causal effect when an unmeasured confounder and a potential instrument are present. We show how the bias of the OLS and TSLS estimands can be expressed in terms of partial correlations. Leveraging the algebraic rules that relate different partial correlations, practitioners can specify intuitive sensitivity models which bound the bias. We further show that the heuristic "plug-in" sensitivity interval may not have any confidence guarantees; instead, we propose a bootstrap approach to construct sensitivity intervals which perform well in numerical simulations. We illustrate the proposed methods with a real study on the causal effect of education on earnings and provide user-friendly visualization tools.

翻译：因果推断必然依赖于无法检验的假设；因此，评估所得结果对识别假设违反的稳健性至关重要。然而，由于现有方法大多仅适用于相对简单的模型且其结果往往难以解释，这种敏感性分析在实践中很少被采用。本文采用更灵活的方法看待敏感性分析，将其视为一个带约束的随机优化问题。本工作聚焦于存在未测量混杂变量和潜在工具变量时线性因果效应的敏感性分析。我们展示了OLS和TSLS估计量的偏差如何用偏相关系数表示。通过利用关联不同偏相关系数的代数规则，研究者可以指定直观的敏感性模型来约束偏差。我们进一步证明启发式"插入法"敏感性区间可能缺乏任何置信度保证；相反，我们提出了一种自举法来构建敏感性区间，该区间在数值模拟中表现良好。我们通过一项关于教育对收入因果效应的实际研究展示了所提出的方法，并提供了用户友好的可视化工具。