Use of the test-negative design to estimate the protective effect of a scalar immune measure: a simulation analysis

Exposure-proximal antibody levels, or scalar correlates of protection (COPs), are increasingly used to assess infection risk following vaccination or prior infection. A version of the test-negative design (TND), adapted from vaccine effectiveness studies, has been proposed to estimate this relationship, but its validity for continuous immune measures under realistic epidemic conditions remains unclear. We used individual-based transmission models incorporating waning and boosting immunity and simulated two scenarios: one with homogenous baseline risk and another with a high-risk group. Infection risk was modeled as a function of COP, both linearly and nonlinearly. Test-negative design samples were drawn from single or multiple days and analyzed using logistic regression and generalized additive models (GAMs). Model validity, defined as the ability to recover the true COP-infection incidence rate ratio relationship, was evaluated using mean absolute error. Transformed logistic regression recovered the true relationship when the correct functional form was known, including in the presence of confounding. When the parametric model was misspecified, GAMs outperformed logistic regression, particularly with large sample sizes and broad COP coverage. Because the true functional form is often unknown, flexible semiparametric approaches may be preferred in well-powered TND studies with antibody measurements.