Randomization Inference and Sensitivity Analysis for Composite Null Hypotheses With Binary Outcomes in Matched Observational Studies

We present methods for conducting hypothesis testing and sensitivity analyses for composite null hypotheses in matched observational studies when outcomes are binary. Causal estimands discussed include the causal risk difference, causal risk ratio, and the effect ratio. We show that inference under the assumption of no unmeasured confounding can be performed by solving an integer linear program, while inference allowing for unmeasured confounding of a given strength requires solving an integer quadratic program. Through simulation studies and data examples, we demonstrate that our formulation allows these problems to be solved in an expedient manner even for large datasets and for large strata. We further exhibit that through our formulation, one can assess the impact of various assumptions about the potential outcomes on the performed inference. R scripts are provided that implement our methods. Supplementary materials for this article are available online.

本文提出针对二分类结局的匹配观察性研究中复合零假设的假设检验与敏感性分析方法。本文所讨论的因果估计量包括因果风险差、因果风险比与效应比。本文证明，在无未测混杂的假设下，可通过求解整数线性规划（integer linear program）完成统计推断；而针对允许存在给定强度未测混杂的统计推断问题，则需求解整数二次规划（integer quadratic program）。通过模拟研究与实例数据分析，本文证明所提出的建模框架即便针对大型数据集与大分层样本，仍可高效求解此类问题。此外，本文进一步表明，通过该建模框架，研究者可评估关于潜在结局的各类假设对所实施统计推断的影响。本文提供了实现所提方法的R脚本。本文的补充材料可在线获取。