The case$^2$ study, also referred to as the case-case study design, is a valuable approach for conducting inference for treatment effects. Unlike traditional case-control studies, the case$^2$ design compares treatment in two types of cases with the same disease. A key quantity of interest is the attributable effect, which is the number of cases of disease among treated units which are caused by the treatment. Two key assumptions that are usually made for making inferences about the attributable effect in case$^2$ studies are 1.) treatment does not cause the second type of case, and 2.) the treatment does not alter an individual's case type. However, these assumptions are not realistic in many real-data applications. In this article, we present a sensitivity analysis framework to scrutinize the impact of deviations from these assumptions on obtained results. We also include sensitivity analyses related to the assumption of unmeasured confounding, recognizing the potential bias introduced by unobserved covariates. The proposed methodology is exemplified through an investigation into whether having violent behavior in the last year of life increases suicide risk via 1993 National Mortality Followback Survey dataset.

翻译：病例²研究，亦称病例-病例研究设计，是一种用于进行治疗效果推断的重要方法。与传统病例对照研究不同，病例²设计比较的是患有相同疾病的两种类型病例的治疗情况。一个关键关注量是可归因效应，即在接受治疗的个体中由治疗导致的疾病病例数。在病例²研究中，为推断可归因效应通常做出的两个关键假设是：1.) 治疗不会导致第二种类型的病例；2.) 治疗不会改变个体的病例类型。然而，在许多实际数据应用中，这些假设并不现实。本文提出了一个敏感性分析框架，用于审视偏离这些假设对所得结果的影响。我们还纳入了与未测量混杂假设相关的敏感性分析，以识别未观测协变量可能引入的偏倚。通过使用1993年全国死亡率追踪调查数据集，研究生命最后一年是否存在暴力行为是否会增加自杀风险，对所提出的方法进行了示例说明。