Combining Broad and Narrow Case Definitions in Matched Case-Control Studies: Firearms in the Home and Suicide Risk

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, which can reduce sensitivity to bias from unmeasured confounding. However, when the goal is to test whether there is a treatment effect based on the broad case definition, 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

居家持有枪支是否会提升自杀风险？为验证这一假说，可开展匹配病例对照研究（matched case-control study）：以自杀病例作为病例组，将其与在观测协变量上匹配的存活对照人群进行对比，回溯评估两组人群居家接触枪支的暴露情况。本研究中，病例可采用宽泛定义（即所有自杀案例）或狭义定义（仅指在家中发生的自杀案例）。宽泛病例定义可获得更多病例样本，但狭义病例定义往往能产生更大的效应量，进而降低研究受未观测混杂偏倚干扰的敏感性。然而，若研究目标是基于宽泛病例定义检验是否存在干预效应，仅采用狭义病例定义可能引入选择偏倚（即基于受干预影响的特征筛选样本所导致的偏倚）：因为居家接触枪支可能会影响自杀发生的地点，进而决定研究对象所属的病例类型。本研究提出一种全新的敏感性分析框架，用于匹配病例对照研究中宽泛与狭义病例定义的结合分析，该框架可同时考量未观测混杂偏倚与选择偏倚。当未观测混杂因素对干预暴露接受度的影响、以及干预对恒常病例（always-cases，即无论采用何种病例定义均会被归类为病例的研究对象）的病例分类产生的效应均通过敏感性参数加以控制时，我们开发了一种仅使用狭义病例匹配集的、基于随机化的有效检验方法。随后，我们采用邦费罗尼（Bonferroni）校正法，将基于宽泛病例定义与狭义病例定义的检验方法进行整合。通过所提出的分析方法，本研究获得了稳健的证据支持：居家持有枪支会提升自杀风险。本文的补充材料可在线获取，其中包含用于复现本研究成果的标准化材料说明。