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

TL;DR

This paper introduces a new sensitivity analysis framework for matched case-control studies that combines broad and narrow case definitions, addressing biases and providing robust evidence on firearms increasing suicide risk.

Contribution

It develops a novel method to jointly analyze broad and narrow case definitions in matched studies, accounting for unmeasured confounding and selection biases.

Findings

Robust evidence that firearms in the home increase suicide risk.

New statistical method combining broad and narrow case definitions.

Addresses bias issues in case-control studies.

Abstract

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.