Post-authorization observational studies play a key role in understanding COVID-19 vaccine effectiveness following the demonstration of efficacy in clinical trials. While bias due to confounding, selection bias, and misclassification can be mitigated through careful study design, unmeasured confounding is likely to remain in these observational studies. Phase III trials of COVID-19 vaccines have shown that protection from vaccination does not occur immediately, meaning that COVID-19 risk should be similar in recently vaccinated and unvaccinated individuals, in the absence of confounding or other bias. Several studies have used the estimated effectiveness among recently vaccinated individuals as a negative control exposure to detect bias in vaccine effectiveness estimates. In this paper we introduce a theoretical framework to describe the interpretation of such a bias-indicator in test-negative studies, and outline assumptions that would allow the use of recently vaccinated individuals to correct bias due to unmeasured confounding.