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

Table 3 Impact of study design and diagnostic method on the estimation of HI-related protection

Model name^$	ALL	DES	DIAG	DOR
Number of subjects	5899	5899	5899	3825
Number of flu cases	1304	1304	1304	612
Parameter Estimates*
μ _α [95% CI]	2.844 [2.25;3.36]	2.55 [1.49;3.44]	2.751 [1.79;3.75]	1.594 [1.78;6.39]
σ _α[95% CI]	0.845 [0.44;1.41]	0.936 [0.49;1.56]	0.905 [0.45;1.54]	0.956 [0.23;1.88]
μ _b [95% CI]	1.299 [1;1.69]	1.222 [0.8;1.77]	1.181 [0.75;1.72]	-1.414 [3.59;1.37]
σ _β[95% CI]	0.376 [0.1;0.76]	0.412 [0.1;0.85]	0.428 [0.14;0.83]	0.211 [0.02;0.53]
Study design ^a
α _co [95% CI]		0.096 [1.23;1.44]
β _co [95% CI]		-0.021 [0.79;0.78]
α _ch [95% CI]		0.577 [0.82;1.97]
β _ch [95% CI]		0.241 [0.54;1.09]
Diagnosis ^b
α _ser [95% CI]			0.091 [1.57;1.54]
β _ser [95% CI]			0.131 [0.58;0.89]
α _ili [95% CI]			0.07 [1.65;1.36]
β _ili [95% CI]			0.415 [0.52;1.45]
E[λ _i] [95% CI]	0.482 [0.41;0.57]	0.5 [0.43;0.59]	0.491 [0.42;0.58]	0.505 [0.38;0.62]
E[μ _i] [95% CI]	3.116 [2.93;3.26]	3.115 [2.93;3.26]	3.112 [2.94;3.26]	3.168 [2.96;3.33]
E[σ _i] [95% CI]	0.752 [0.69;0.82]	0.751 [0.69;0.82]	0.751 [0.69;0.82]	0.809 [0.74;0.89]
DIC	4667.0	4670.0	4669.0	2623.0

$. 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