Sensitivity Analysis for Attributable Effects in Case$^2$ Studies

TL;DR

This paper develops a sensitivity analysis framework for case$^2$ studies to assess how violations of key assumptions and unmeasured confounding affect estimates of attributable effects, with an application to violence and suicide risk.

Contribution

It introduces a novel sensitivity analysis method for case$^2$ studies that accounts for assumption violations and unmeasured confounding.

Findings

Framework reveals the robustness of attributable effect estimates under assumption deviations.

Application shows the impact of violent behavior on suicide risk.

Method enhances validity of causal inferences in case$^2$ study designs.

Abstract

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.