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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%
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 (\({se}_{0}={se}_{1}=1\) )
