Sensitivity Analysis for the Test-Negative Design

The test-negative design has become popular for evaluating the effectiveness of post-licensure vaccines using observational data. In addition to its logistical convenience for data collection, the design is also believed to control for the differential health-care-seeking behavior between vaccinated and unvaccinated individuals, an important while often unmeasured confounder of the vaccination–infection relationship. Hence, the design has been employed routinely to monitor seasonal flu vaccines and more recently to measure COVID-19 vaccine effectiveness. Despite its popularity, the design has been questioned, particularly about its ability to fully control for unmeasured confounding. In this paper, we explore deviations from a perfect test-negative design, and propose various sensitivity analysis methods for estimating the effect of vaccination measured by the causal odds ratio in the subpopulation of individuals with good health-care-seeking behavior. We start with point identification of the causal odds ratio, comparing different forms of identification assumptions and their corresponding estimands. We then propose two approaches for conducting sensitivity analysis, addressing the influence of unmeasured confounding in two different ways. Specifically, one approach investigates partial control for unmeasured confounding, while the other examines the impact of unmeasured confounding on both vaccination and infection. Furthermore, we combine them to provide narrower bounds on the causal odds ratio, and further sharpen the bounds by restricting the treatment effect heterogeneity. Finally, we apply the proposed methods to evaluate the effectiveness of COVID-19 vaccines using observational data from test-negative designs.