In matched observational studies, the inferred causal conclusions pretending that matching has taken into account all confounding can be sensitive to unmeasured confounding. In such cases, a sensitivity analysis is often conducted, which investigates whether the observed association between treatment and outcome is due to effects caused by the treatment or it is due to hidden confounding. In general, a sensitivity analysis tries to infer the minimum amount of hidden biases needed in order to explain away the observed association between treatment and outcome, assuming that the treatment has no effect. If the needed bias is large, then the treatment is likely to have significant effects. The Rosenbaum sensitivity analysis is a modern approach for conducting sensitivity analysis for matched observational studies. It investigates what magnitude the maximum of the hidden biases from all matched sets needs to be in order to explain away the observed association, assuming that the treatment has no effect. However, such a sensitivity analysis can be overly conservative and pessimistic, especially when the investigators believe that some matched sets may have exceptionally large hidden biases. In this paper, we generalize Rosenbaum's framework to conduct sensitivity analysis on quantiles of hidden biases from all matched sets, which are more robust than the maximum. Moreover, we demonstrate that the proposed sensitivity analysis on all quantiles of hidden biases is simultaneously valid and is thus a free lunch added to the conventional sensitivity analysis. The proposed approach works for general outcomes, general matched studies and general test statistics. Finally, we demonstrate that the proposed sensitivity analysis also works for bounded null hypotheses as long as the test statistic satisfies certain properties. An R package implementing the proposed method is also available online.

翻译：在匹配观察性研究中，假定匹配已考虑所有混杂因素后推断出的因果结论可能对未观测到的混杂敏感。此时通常需进行敏感性分析，探究治疗与结局间的观测关联是由治疗效果引起，还是源于隐藏混杂。一般而言，敏感性分析试图推断在假定治疗无效应的情况下，为解释观测到的治疗-结局关联所需的最小隐藏偏倚量。若所需偏倚较大，则治疗很可能存在显著效应。Rosenbaum敏感性分析是匹配观察性研究中进行敏感性分析的现代方法，它探究在治疗无效应假设下，所有匹配集隐藏偏倚最大值需达到何种程度才能解释观测关联。然而，当研究者认为某些匹配集可能存在异常大的隐藏偏倚时，这种敏感性分析可能过于保守和悲观。本文推广了Rosenbaum框架，对所有匹配集隐藏偏倚的分位数进行敏感性分析（较最大值更具稳健性）。进一步证明，所提出的所有分位数敏感性分析同时具有有效性，相当于在传统敏感性分析基础上增加了"免费午餐"。该方法适用于一般结局、一般匹配研究及一般检验统计量。最后，我们证明只要检验统计量满足特定性质，所提出的敏感性分析对零假设有界的情况同样适用。本方法对应的R包已在线上发布。