Sensitivity Analysis for Quantiles of Hidden Biases in Matched Observational Studies

Causal conclusions from observational studies may be sensitive to unmeasured confounding. In such cases, a sensitivity analysis is often conducted, which tries to infer the minimum amount of hidden biases or the minimum strength of unmeasured confounding needed in order to explain away the observed association between treatment and outcome. 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 in matched observational studies. It investigates what magnitude the maximum of hidden biases from all matched sets needs to be in order to explain away the observed association. However, such a sensitivity analysis can be overly conservative and pessimistic, especially when investigators suspect that some matched sets may have exceptionally large hidden biases. In this article, 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, the proposed sensitivity analysis is simultaneously valid across all quantiles of hidden biases 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. In addition, we demonstrate that the proposed sensitivity analysis also works for bounded null hypotheses when the test statistic satisfies certain properties. An R package implementing the proposed approach is available online. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.观察性研究得出的因果结论可能对未测量混杂（unmeasured confounding）敏感。在此类情形下，通常会开展敏感性分析（sensitivity analysis），旨在推断为消解观测到的处理与结局间的关联所需的最小隐藏偏倚规模，或未测量混杂的最小强度。若所需偏倚规模较大，则提示处理很可能存在显著效应。罗森鲍姆敏感性分析（Rosenbaum sensitivity analysis）是匹配观察性研究中开展敏感性分析的现代经典方法，该方法旨在明确需达到多大的所有匹配组隐藏偏倚最大值，才能消解观测到的关联。但此类敏感性分析可能过于保守与悲观，尤其当研究者推测部分匹配组存在异常偏大的隐藏偏倚时。本文中，我们将罗森鲍姆的分析框架进行推广，针对所有匹配组的隐藏偏倚分位数开展敏感性分析——分位数相较最大值具备更强的稳健性。此外，所提出的敏感性分析可同时在所有隐藏偏倚分位数下保持有效性，相当于为传统敏感性分析额外增添了一项“免费午餐”式的增益。所提方法适用于通用结局、通用匹配研究以及通用检验统计量场景。此外，我们还证明了当检验统计量满足特定性质时，所提敏感性分析同样可适用于有界原假设（bounded null hypotheses）场景。一款实现所提方法的R包（R package）已在线发布。本文的补充材料亦已在线发布，其中包含可用于复现研究成果的标准化材料说明。