Identification and Estimation of Vaccine Effectiveness in the Test-Negative Design Under Equi-confounding

The test-negative design (TND) is widely used to evaluate vaccine effectiveness in real-world settings. In a TND study, individuals with similar symptoms who seek care are tested, and effectiveness is estimated by comparing vaccination histories of test-positive cases and test-negative controls. The TND is often justified on the grounds that it reduces confounding due to unmeasured health-seeking behavior, although this has not been formally described using potential outcomes. At the same time, concerns persist that conditioning on test receipt can introduce selection bias. We provide a formal justification of the TND under an assumption of odds ratio equi-confounding, where unmeasured confounders affect test-positive and test-negative individuals equivalently on the odds ratio scale. Health-seeking behavior is one plausible example. We also show that these results hold under the outcome-dependent sampling used in TNDs. We discuss the design implications of the equi-confounding assumption and provide alternative estimators for the marginal risk ratio among the vaccinated under equi-confounding, including outcome modeling and inverse probability weighting estimators as well as a semiparametric estimator that is doubly robust. When equi-confounding does not hold, we suggest a straightforward sensitivity analysis that parameterizes the magnitude of the deviation on the odds ratio scale. A simulation study evaluates the empirical performance of our proposed estimators under a wide range of scenarios. Finally, we discuss broader uses of test-negative outcomes to de-bias cohort studies in which testing is triggered by symptoms.