Relationship between haemagglutination-inhibiting antibody titres and clinical protection against influenza: development and application of a bayesian random-effects model

Table 2 Impact of vaccination status and vaccine strain on the estimation of HI-related protection:

Model name^$	ALL	STRAIN	ALL_V	VAC	HOB
Number of subjects	5899	5899	4162	4162	1032
Number of flu cases	1304	1304	782	782	383
Parameter Estimates*
μ _a [95% CI]	2.844 [2.25;3.36]	2.964 [2.27;3.53]	2.344 [1.49;3.14]	2.615 [1.63;3.56]	3.385 [1.53;5.27]
σ _a [95% CI]	0.845 [0.44;1.41]	0.85 [0.42;1.43]	0.944 [0.33;1.69]	1.06 [0.37;2]	1.415 [0.28;5.37]
μ _b [95% CI]	1.299 [1;1.69]	1.404 [1.04;1.91]	1.061 [0.77;1.48]	1.205 [0.81;1.69]	2.102 [-0.27;6.36]
σ _b [95% CI]	0.376 [0.1;0.76]	0.386 [0.07;0.81]	0.275 [0.05;0.66]	0.206 [0.01;0.62]	2.102 [0.19;11.93]
α_c [95% CI]		-0.467 [-1.72;0.81]		-1.04 [-2.93;0.7]
β _c [95% CI]		-0.305 [-1.06;0.42]		-0.377 [-0.98;0.23]
E[λ _i] [95% CI]	0.482 [0.41;0.57]	0.481 [0.41;0.57]	0.497 [0.39;0.61]	0.531 [0.41;0.67]	0.726 [0.64;0.81]
E[μ _i] [95% CI]	3.116 [2.93;3.26]	3.117 [2.94;3.26]	3.129 [2.91;3.3]	3.13 [2.91;3.3]	3.157 [2.96;3.35]
E[σ _i] [95% CI]	0.752 [0.69;0.82]	0.752 [0.69;0.82]	0.775 [0.71;0.85]	0.773 [0.71;0.85]	0.181 [0.16;0.21]
DIC	4667.0	4667.0	3074.0	3077.0	964.2

$. ALL: All datasets and no covariate, STRAIN: All datasets + 1 covariate for virus strain (reference category: type A virus), ALL_V: datasets with information on vaccination status, VAC: datasets with information on vaccination status + 1 covariate for vaccination status (reference category: vaccinated), HOB: data reported in Hobson et al. [5], no covariate
* Reported values for each parameter: posterior mean value and 95% credible interval

ISSN: 1471-2288