Influenza viruses undergo frequent antigenic changes. As a result, the viruses circulating change within and between seasons, and the composition of the influenza vaccine is updated annually. Thus, estimation of the vaccine's effectiveness is not constant across seasons. In order to provide annual estimates of the influenza vaccine's effectiveness, health departments have increasingly adopted the "test-negative design," using enhanced data from routine surveillance systems. In this design, patients presenting to participating general practitioners with influenza-like illness are swabbed for laboratory testing; those testing positive for influenza virus are defined as cases, and those testing negative form the comparison group. Data on patients' vaccination histories and confounder profiles are also collected. Vaccine effectiveness is estimated from the odds ratio comparing the odds of testing positive for influenza among vaccinated patients and unvaccinated patients, adjusting for confounders. The test-negative design is purported to reduce bias associated with confounding by health-care-seeking behavior and misclassification of cases. In this paper, we use directed acyclic graphs to characterize potential biases in studies of influenza vaccine effectiveness using the test-negative design. We show how studies using this design can avoid or minimize bias and where bias may be introduced with particular study design variations.