A re-assessment of 4CMenB vaccine effectiveness against serogroup B invasive meningococcal disease in England based on an incidence model

Table 1 Comparison between candidate models

Model	Convergence diagnostics	Goodness of fit (deviance) [SE]		Vaccine effectiveness (%) [95% BCI]
Model	Maximum \(\widehat{\text{R}}\)	LOO-CV	WAIC	1 dose	2 doses	3 doses
NB1	1.00101	622.4 [28.8]	619.6 [28.4]	33.7 [13.2; 50.4]	78.7 [71.3; 84.3]	80.1 [70.4; 86.6]
P1	1.00004	622.6 [28.8]	619.9 [28.4]	33.5 [12.4; 49.7]	78.7 [71.5; 84.5]	80.1 [70.3; 86.7]
P2	1.00003	622.9 [29.1]	620.2 [28.7]	34.1 [13.4; 50.4]	78.9 [71.6; 84.4]	80.4 [70.5; 86.9]
NB2	1.00032	623.1 [29.1]	620.3 [28.7]	33.9 [12.7; 49.8]	78.9 [71.7; 84.5]	80.4 [70.7; 87.0]
NB3	1.00008	646.2 [27.0]	645.1 [26.9]	31.9 [7.7; 49.9]	76.0 [66.2; 83.2]	78.5 [66.7; 86.2]
P3	1.00005	671.3 [35.3]	669.7 [35.2]	31.1 [10.0; 47.3]	77.8 [70.5; 83.5]	78.9 [68.8; 85.9]
NB4	1.00052	675 [26.9]	633.1 [23.7]	21.1 [− 6.8; 41.7]	72.0 [60.7; 80.5]	76.2 [62.7; 85.2]
P4	1.00012	676.6 [27]	633 [23.7]	21.0 [− 6.6; 42.3]	71.9 [59.8; 80.2]	76.2 [62.2; 85.0]
P5	1.00011	706.3 [25.9]	641.8 [22.9]	25.6 [− 6.0; 47.7]	72.3 [58.8; 81.8]	75.0 [58.3; 85.4]
NB5	1.00038	707.1 [26]	642 [22.9]	25.8 [− 5.5; 48.6]	72.4 [58.2; 81.3]	74.9 [57.3; 85.2]

For each candidate model of the first column, the second column reports the maximum model’s \(\widehat{\text{R}}\) factor as a diagnostic criterion of Monte Carlo convergence (values near one indicate that convergence was reached for all the models). Columns three and four report goodness of fits, calculated using the leave-one-out cross-validation (LOO-CV) and the widely applicable information criterion (WAIC), here reported with their standard errors (SE). The last three columns report final estimates of VE after one to three doses using the different models. The models are ordered by their LOO-CV score. Lowest deviance values (in bold) highlight four equivalently best-fitting models, from which we selected P1 as the best (Eq. 2 in the main text), the simplest of the four

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