  The case$^2$ study, also referred to as the case-case study design, is a
valuable approach for conducting inference for treatment effects. Unlike
traditional case-control studies, the case$^2$ design compares treatment in two
types of cases with the same disease. A key quantity of interest is the
attributable effect, which is the number of cases of disease among treated
units which are caused by the treatment. Two key assumptions that are usually
made for making inferences about the attributable effect in case$^2$ studies
are 1.) treatment does not cause the second type of case, and 2.) the treatment
does not alter an individual's case type. However, these assumptions are not
realistic in many real-data applications. In this article, we present a
sensitivity analysis framework to scrutinize the impact of deviations from
these assumptions on obtained results. We also include sensitivity analyses
related to the assumption of unmeasured confounding, recognizing the potential
bias introduced by unobserved covariates. The proposed methodology is
exemplified through an investigation into whether having violent behavior in
the last year of life increases suicide risk via 1993 National Mortality
Followback Survey dataset.
