Does having firearms in the home increase suicide risk? To test this hypothesis, a matched case-control study can be performed, in which suicide case subjects are compared to living controls who are similar in observed covariates in terms of their retrospective exposure to firearms at home. In this application, cases can be defined using a broad case definition (suicide) or a narrow case definition (suicide occurred at home). The broad case definition offers a larger number of cases but the narrow case definition may offer a larger effect size. Moreover, restricting to the narrow case definition may introduce selection bias (i.e., bias due to selecting samples based on characteristics affected by the treatment) because exposure to firearms in the home may affect the location of suicide and thus the type of a case a subject is. We propose a new sensitivity analysis framework for combining broad and narrow case definitions in matched case-control studies, that considers the unmeasured confounding bias and selection bias simultaneously. We develop a valid randomization-based testing procedure using only the narrow case matched sets when the effect of the unmeasured confounder on receiving treatment and the effect of the treatment on case definition among the always-cases are controlled by sensitivity parameters. We then use the Bonferroni method to combine the testing procedures using the broad and narrow case definitions. With the proposed methods, we find robust evidence that having firearms at home increases suicide risk.

翻译：为检验“家庭中存放枪支是否增加自杀风险”这一假设，可采用配对病例对照研究：将自杀病例与在观测协变量上相似的健康对照者进行比较，回顾性评估其家中枪支暴露情况。在此类研究中，病例可采用宽泛定义（自杀）或严格定义（在家自杀）。宽泛定义可提供更多病例数量，但严格定义可能产生更大的效应量。然而，若仅关注严格定义，可能引入选择偏倚（即因依据受处理影响的特征选择样本而产生的偏倚），因为家庭枪支暴露可能影响自杀地点，进而决定病例类型。我们提出一种新的敏感性分析框架，将宽泛与严格病例定义在配对病例对照研究中相结合，同时考虑未测量混杂偏倚与选择偏倚。通过将未测量混杂因素对接受处理的影响及处理对“始终病例”中病例定义的影响用敏感性参数控制，我们开发了仅使用严格病例配对组的有效随机化检验流程，并采用Bonferroni方法整合宽泛与严格病例定义的检验结果。应用所提方法，我们获得稳健证据表明：家庭中存放枪支会增加自杀风险。