Estimate Time-To-Infection (TTI) Vaccination Effect When TTI for Unvaccinated Group is Unknown

The COVID-19 pandemic has caused significant morbidity and mortality, as well as social and economic disruption worldwide in general and USA in particular. In order to reduce these effects, a global effort to develop effective vaccines against the COVID-19 virus has produced various options with the effectiveness assessed on the rate of infection between vaccinated and unvaccinated groups, which has been used for important policy decision-making on vaccination effectiveness ever since. However, the rate of infection is an over-simplified index in assessing the vaccination effectiveness overall, which should be strengthened to address the duration of protection with time-to-infection effect. The fundamental challenge in estimating the vaccination effect over time is that the time-to-infection for unvaccinated group is unknown due to nonexistent vaccination time. This paper is then aimed to fill this knowledge gap to propose a Weibull regression model. This model treats the nonexistent vaccination time for the unvaccinated group as nuisance parameters and estimates the vaccination effectiveness along with these nuisance parameters. The performance of the proposed approach and its properties are empirically investigated through a simulation study, and its applicability is illustrated using a real-data example from the Arizona State University COVID-19 serological prevalence data.