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Estimation adjusted for \({se}_{0}={se}_{1}=0.04\) , \(\kappa ={10}^{-6}\)
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%
0.09
0.11
0.11
± 0
92%
8%
0.09
0.09
0.09
− 2
95%
30%
30%
0.08
0.09
0.09
± 0
92%
26%
0.08
0.08
0.09
− 4
95%
50%
50%
0.06
0.07
0.07
± 0
93%
46%
0.07
0.07
0.08
− 4
93%
70%
69%
0.05
0.05
0.05
− 1
94%
66%
0.05
0.05
0.07
− 4
90%
90%
89%
0.03
0.03
0.03
− 1
96%
87%
0.03
0.03
0.04
− 3
88%
Cohort of 1,000,000 individuals (50% vaccinated at season onset)
10%
10%
0.02
0.02
0.02
± 0
92%
9%
0.02
0.02
0.02
− 1
89%
30%
30%
0.02
0.02
0.02
± 0
91%
27%
0.02
0.02
0.04
− 3
44%
50%
50%
0.01
0.01
0.01
± 0
93%
46%
0.01
0.01
0.05
− 4
7%
70%
70%
0.01
0.01
0.01
± 0
94%
66%
0.01
0.01
0.04
− 4
0%
90%
90%
0.00
0.00
0.00
± 0
94%
87%
0.01
0.01
0.03
− 3
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 given non-differential sensitivity (\({se}_{0}={se}_{1}\) ) of 0.04 and a cumulative risk of 0.25 in the unvaccinated. The false-positive events occurred at rate \(\kappa ={10}^{-6}\) (per person-day) corresponding to a false-positive proportion of 2% among the unvaccinated. Naïve estimation was conducted under the incorrect assumptions of perfect sensitivity (\({se}_{0}={se}_{1}=1\) ) and absence of false positives (\(\kappa =0\) )
