We study causal inference under case-control and case-population sampling. Specifically, we focus on the binary-outcome and binary-treatment case, where the parameters of interest are causal relative and attributable risks defined via the potential outcome framework. It is shown that strong ignorability is not always as powerful as it is under random sampling and that certain monotonicity assumptions yield comparable results in terms of sharp identified intervals. Specifically, the usual odds ratio is shown to be a sharp identified upper bound on causal relative risk under the monotone treatment response and monotone treatment selection assumptions. We offer algorithms for inference on the causal parameters that are aggregated over the true population distribution of the covariates. We show the usefulness of our approach by studying three empirical examples: the benefit of attending private school for entering a prestigious university in Pakistan; the relationship between staying in school and getting involved with drug-trafficking gangs in Brazil; and the link between physicians' hours and size of the group practice in the United States.

翻译：我们研究了病例对照和病例群体抽样下的因果推断。具体而言，重点关注二值结果和二值处理的情况，感兴趣的参数是通过潜在结果框架定义的因果相对风险与归因风险。研究表明，强可忽略性在随机抽样下的效力并非总是显著，而某些单调性假设在尖锐识别区间方面可产生可比结果。具体来说，在单调处理响应和单调处理选择假设下，通常的比值比被证明是因果相对风险的尖锐识别上界。我们提出了基于协变量真实总体分布聚合的因果参数推断算法。通过三个实证案例验证了该方法的实用性：巴基斯坦私立学校对进入名校的益处；巴西辍学与参与贩毒团伙的关系；以及美国医生工作时间与团体诊所规模之间的联系。