Testing if higher contact among vaccinated can be a mechanism for observed negative vaccine effectiveness.

Evidence from early observational studies suggested negative vaccine effectiveness (${V}_{Eff}$) for the SARS-CoV-2 Omicron variant. Since true ${V}_{Eff}$ is unlikely to be negative, we explored how differences in contact among vaccinated persons (e.g. potentially from the implementation of vaccine mandates), could lead to observed negative ${V}_{Eff}$. Using an $SEIR$transmission model, we examined how vaccinated contact heterogeneity, defined as an increase in the contact rate only between vaccinated individuals, interacted with two mechanisms of vaccine efficacy: vaccine efficacy against susceptibility (${VE}_S$) and vaccine efficacy against infectiousness (${VE}_I$), to produce underestimated and in some cases, negative measurements of ${V}_{Eff}$. We found that vaccinated contact heterogeneity led to negative estimates when ${VE}_I$, and especially ${VE}_S,$ were low. Moreover, we determined that when contact heterogeneity was very high, ${V}_{Eff}$ could still be underestimated given relatively high vaccine efficacies (0.7) although its effect on ${V}_{Eff}$ was strongly reduced. We also found that this contact heterogeneity mechanism generated a signature temporal pattern: the largest underestimates and negative measurements of ${V}_{Eff}$ occurred during epidemic growth. Overall, our research illustrates how vaccinated contact heterogeneity could have feasibly produced negative measurements during the Omicron period and highlights its general ability to bias observational studies of ${V}_{Eff}$.