# Table 3 Estimates of vaccine effectiveness ($${\varvec{V}}{\varvec{E}}$$) under non-differentially imperfect sensitivity and high cumulative risk of infection in absence of false-positive events

True Estimation adjusted for $${se}_{0}={se}_{1}=0.04$$ Naïve estimation
$$VE$$ $$\widehat{VE}$$ $$\widehat{SE}$$ $${SE}_{\widehat{VE}}$$ $${\sqrt{MSE}}_{\widehat{VE}}$$ Bias Cov $$\widehat{VE}$$ $$\widehat{SE}$$ $${SE}_{\widehat{VE}}$$ $${\sqrt{MSE}}_{\widehat{VE}}$$ Bias Cov
Cohort of 50,000 individuals (30% vaccinated at season onset)
10% 10% 0.05 0.10 0.10  ± 0 67% 4% 0.05 0.05 0.08 − 6 82%
30% 30% 0.04 0.08 0.08  ± 0 70% 15% 0.05 0.05 0.16 − 15 11%
50% 50% 0.03 0.05 0.05  ± 0 75% 30% 0.04 0.04 0.20 − 20 0%
70% 70% 0.02 0.03 0.03  ± 0 80% 51% 0.03 0.03 0.19 − 19 0%
90% 90% 0.01 0.01 0.01  ± 0 88% 81% 0.02 0.02 0.09 − 9 0%
Cohort of 1,000,000 individuals (50% vaccinated at season onset)
10% 10% 0.01 0.02 0.02  ± 0 66% 4% 0.01 0.01 0.06 − 6 0%
30% 30% 0.01 0.02 0.02  ± 0 69% 15% 0.01 0.01 0.15 − 15 0%
50% 50% 0.01 0.01 0.01  ± 0 71% 30% 0.01 0.01 0.20 − 20 0%
70% 70% 0.00 0.01 0.01  ± 0 75% 52% 0.01 0.01 0.18 − 18 0%
90% 90% 0.00 0.00 0.00  ± 0 83% 81% 0.00 0.00 0.09 − 9 0%
1. Mean of the vaccine effectiveness estimates ($$\widehat{VE}$$), mean of the standard error estimates ($$\widehat{SE}$$), standard error of the vaccine effectiveness estimates ($${SE}_{\widehat{VE}}$$), root-mean-squared error of the vaccine effectiveness estimates ($${\sqrt{MSE}}_{\widehat{VE}}$$), bias in percentage points, and empirical coverage probability (Cov) of the 95% confidence intervals when estimating vaccine effectiveness from 104 repeated data sets under non-differential sensitivity ($${se}_{0}={se}_{1}$$) of 0.04 and a cumulative risk of 0.81 in the unvaccinated in absence of false-positive events. Naïve estimation was conducted under the incorrect assumption of perfect sensitivity ($${se}_{0}={se}_{1}=1$$)