Sensitivity analysis asks how strong unmeasured confounding needs to be to explain away an observational study's conclusion. The conventional approach in matched studies conducts inference conditional upon the potential outcomes as well as both observed and unobserved confounders, and then finds the worst-case distribution for the conditional treatment assignments across all possible realizations of the unobserved confounder. The resulting worst-case allocation imagines strong, near perfect, correlations between the potential outcomes and hidden bias. We propose a stochastic sensitivity analysis that instead targets inference conditional upon potential outcomes and observed confounders while treating the hidden confounders as random with unknown conditional laws. Rather than finding the worst-case realizations for the hidden confounders, we instead determine the worst-case conditional law over a broad class of distributions. This preserves the adversarial spirit of sensitivity analysis while allowing for imperfect alignment between hidden bias and potential outcomes to a degree controlled by a scalar sensitivity parameter. We consider restrictions to both an interpretable class with no parametric assumptions and a Bernoulli class of conditional laws. Design sensitivity calculations and real-data demonstrations illustrate that allowing for even a small degree of stochasticity can materially increase reported robustness to hidden bias relative to the conventional approach.

翻译：摘要：敏感性分析探讨未测量的混杂因素需要达到何种强度才能推翻观察性研究的结论。匹配研究中的传统方法基于潜在结果及已观测与未观测混杂因素的条件推断，然后针对未观测混杂因素的所有可能实现，寻找条件处理分配的最坏情况分布。由此得到的最坏情况分配假设潜在结果与隐藏偏差之间存在强烈且近乎完美的相关性。我们提出一种随机敏感性分析方法，转而基于潜在结果和已观测混杂因素进行条件推断，同时将隐藏混杂因素视为随机变量且其条件分布未知。该方法并非寻找隐藏混杂因素的最坏情况实现，而是确定一类广泛分布中最坏情况的条件分布。这既保留了敏感性分析对抗性核心思想，又允许隐藏偏差与潜在结果之间存在由标量敏感性参数控制的不完全匹配。我们同时考虑无需参数假设的可解释类别与伯努利条件分布类别的约束条件。设计敏感性计算与真实数据演示表明，相对于传统方法，即使允许极小程度的随机性，也能显著提升对隐藏偏差的稳健性报告。