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Does having firearms in the home increase suicide risk? To test thishypothesis, a matched case-control study can be performed, in which suicidecase subjects are compared to living controls who are similar in observedcovariates in terms of their retrospective exposure to firearms at home. Inthis application, cases can be defined using a broad case definition (suicide)or a narrow case definition (suicide occurred at home). The broad casedefinition offers a larger number of cases but the narrow case definition mayoffer a larger effect size. Moreover, restricting to the narrow case definitionmay introduce selection bias (i.e., bias due to selecting samples based oncharacteristics affected by the treatment) because exposure to firearms in thehome may affect the location of suicide and thus the type of a case a subjectis. We propose a new sensitivity analysis framework for combining broad andnarrow case definitions in matched case-control studies, that considers theunmeasured confounding bias and selection bias simultaneously. We develop avalid randomization-based testing procedure using only the narrow case matchedsets when the effect of the unmeasured confounder on receiving treatment andthe effect of the treatment on case definition among the always-cases arecontrolled by sensitivity parameters. We then use the Bonferroni method tocombine the testing procedures using the broad and narrow case definitions.With the proposed methods, we find robust evidence that having firearms at homeincreases suicide risk.

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