Estimation of Vaccine Efficacy and Critical Vaccination Coverage in Partially Observed Outbreaks

<div><p>Classical approaches to estimate vaccine efficacy are based on the assumption that a person's risk of infection does not depend on the infection status of others. This assumption is untenable for infectious disease data where such dependencies abound. We present a novel approach to estimating vaccine efficacy in a Bayesian framework using disease transmission models. The methodology is applied to outbreaks of mumps in primary schools in the Netherlands. The total study population consisted of 2,493 children in ten primary schools, of which 510 (20%) were known to have been infected, and 832 (33%) had unknown infection status. The apparent vaccination coverage ranged from 12% to 93%, and the apparent infection attack rate varied from 1% to 76%. Our analyses show that vaccination reduces the probability of infection per contact substantially but not perfectly ( = 0.933; 95CrI: 0.908–0.954). Mumps virus appears to be moderately transmissible in the school setting, with each case yielding an estimated 2.5 secondary cases in an unvaccinated population ( = 2.49; 95%CrI: 2.36–2.63), resulting in moderate estimates of the critical vaccination coverage (64.2%; 95%CrI: 61.7–66.7%). The indirect benefits of vaccination are highest in populations with vaccination coverage just below the critical vaccination coverage. In these populations, it is estimated that almost two infections can be prevented per vaccination. We discuss the implications for the optimal control of mumps in heterogeneously vaccinated populations.</p>