In matched observational studies with binary treatments, the Rosenbaum bounds framework is arguably the most widely used sensitivity analysis framework for assessing sensitivity to unobserved covariates. Unlike the binary treatment case, although widely needed in practice, sensitivity analysis for matched observational studies with treatment doses (i.e., non-binary treatments such as ordinal treatments or continuous treatments) still lacks solid foundations and valid methodologies. We fill in this blank by establishing theoretical foundations and novel methodologies under a generalized Rosenbaum bounds sensitivity analysis framework. First, we present a criterion for assessing the validity of sensitivity analysis in matched observational studies with treatment doses and use that criterion to justify the necessity of incorporating the treatment dose information into sensitivity analysis through generalized Rosenbaum sensitivity bounds. We also generalize Rosenbaum's classic sensitivity parameter $\Gamma$ to the non-binary treatment case and prove its sufficiency. Second, we study the asymptotic properties of sensitivity analysis by generalizing Rosenbaum's classic design sensitivity and Bahadur efficiency for testing Fisher's sharp null to the non-binary treatment case and deriving novel formulas for them. Our theoretical results showed the importance of appropriately incorporating the treatment dose into a test, which is an intrinsic distinction with the binary treatment case. Third, for testing Neyman's weak null (i.e., null sample average treatment effect), we propose the first valid sensitivity analysis procedure for matching with treatment dose through generalizing an existing optimization-based sensitivity analysis for the binary treatment case, built on the generalized Rosenbaum sensitivity bounds and large-scale mixed integer programming.

翻译：在二元治疗的匹配观察性研究中，罗森鲍姆界限框架可说是评估对未观测协变量敏感性的最广泛使用的敏感性分析框架。相较于二元治疗情形，尽管实践中需求迫切，含治疗剂量（即非二元治疗，如有序治疗或连续治疗）的匹配观察性研究的敏感性分析仍缺乏坚实理论基础与有效方法。我们通过建立广义罗森鲍姆界限敏感性分析框架下的理论基础与创新方法填补了这一空白。首先，我们提出评估含治疗剂量匹配观察性研究中敏感性分析有效性的准则，并基于该准则论证了通过广义罗森鲍姆敏感性界限将治疗剂量信息纳入敏感性分析的必要性。同时将罗森鲍姆经典敏感性参数$\Gamma$推广至非二元治疗情形，证明其充分性。其次，通过将罗森鲍姆经典设计敏感性与巴哈杜尔效率（用于检验费希尔尖锐零假设）推广至非二元治疗情形并推导新公式，研究了敏感性分析的渐近性质。理论结果表明，恰当将治疗剂量纳入检验至关重要——这与二元治疗情形存在本质区别。第三，针对内曼弱零假设（即零样本平均处理效应）的检验，我们通过推广现有针对二元治疗情形的基于优化的敏感性分析，首次提出基于广义罗森鲍姆敏感性界限与大规模混合整数规划的含治疗剂量匹配数据的有效敏感性分析方法。