Combining Broad and Narrow Case Definitions in Matched Case-Control Studies
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In a matched case-control study, cases are compared to noncases, who are similar in observed covariates, in terms of their retrospective exposure to a treatment to assess the impact of the treatment on the outcome. In the absence of a gold standard case definition, there is often a broad case definition and a narrow case definition. The broad case definition offers a larger sample size of cases but the narrow case definition may offer a larger effect size. Restricting to the narrow case definition may introduce selection bias because the treatment may affect the type of a case a subject is. In this article, 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. We also study comprehensively the proposed testing procedures' sensitivity to unmeasured biases using the design sensitivity and extensive power analyses. Our method is applied to study whether having firearms at home increases suicide risk.
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