To ensure reliable causal conclusions from observational (i.e., non-randomized) studies, researchers routinely conduct sensitivity analysis to assess robustness to hidden bias due to unmeasured confounding. In matched observational studies (one of the most widely used observational study designs), two foundational concepts, design sensitivity and Bahadur-Rosenbaum efficiency, are used to quantify the robustness of test statistics and study designs in sensitivity analyses. Unfortunately, these measures of robustness are not developed for non-binary treatments (e.g., continuous or ordinal treatments) and consequently, prevailing recommendations about robust tests may be misleading. In this work, we provide a unified framework to quantify robustness of test statistics and study designs that are agnostic to treatment types. We first present a negative result about a popular, ad-hoc approach based on dichotomizing the treatment variable. Next, we introduce a universal, nearly sufficient sensitivity parameter that is agnostic to the underlying treatment type. We then generalize and derive all-in-one formulas for design sensitivity and Bahadur-Rosenbaum efficiency that can be used for any treatment type. We also propose a general data-adaptive approach to combine candidate test statistics to enhance robustness against unmeasured confounding. Extensive simulation studies and a data application illustrate our proposed framework. For practice, our results yield new, previously undiscovered insights about the robustness of tests and study designs in matched observational studies, especially when investigators are faced with non-binary treatment.sed sensitivity analysis for the binary treatment case, built on the generalized Rosenbaum sensitivity bounds and large-scale mixed integer programming.

翻译：为确保从观察性（即非随机化）研究中得出可靠的因果结论，研究者通常进行敏感性分析，以评估因未测量混杂因素导致的潜在偏倚的稳健性。在匹配观察性研究（最广泛使用的观察性研究设计之一）中，设计敏感性和Bahadur-Rosenbaum效率这两个基础概念被用于量化敏感性分析中检验统计量与研究设计的稳健性。遗憾的是，这些稳健性度量并未针对非二值处理（如连续或有序处理）进行开发，因此当前关于稳健检验的建议可能存在误导性。本研究提出了一个统一框架，用于量化与处理类型无关的检验统计量及研究设计的稳健性。我们首先展示了一种基于处理变量二值化的常用临时方法的负面结果。接着，我们引入了一个与底层处理类型无关的通用、近乎充分的敏感性参数。随后，我们推广并推导了适用于任意处理类型的设计敏感性和Bahadur-Rosenbaum效率的一体化公式。我们还提出了一种通用的数据自适应方法，用于整合候选检验统计量以增强对未测量混杂因素的稳健性。大量的模拟研究和数据应用验证了我们提出的框架。在实践中，我们的结果为匹配观察性研究中检验及研究设计的稳健性提供了新的、先前未被发现的见解，尤其当研究者面临非二值处理时。该工作扩展了二值处理情况下的敏感性分析，基于广义Rosenbaum敏感性边界和大规模混合整数规划方法。