Characterizing Influenza surveillance systems performance: application of a Bayesian hierarchical statistical model to Hong Kong surveillance data

Table 3 Summary of Pandemic and Non-pandemic Model

Data Model
❖ Data as counts	Y _j,t∼Pois(λ _j,t)
❖ Data as a proportion	$Log Y j, t ∼ N μ j, t, σ j 2$
Process Model
❖ Pandemic Model
▪ Data as counts	μ _j,t = θ _j,t ⋅ X _t + φ _j,t
▪ Data as a proportion	Log(λ _j,t) = θ _j,t ⋅ X _t + φ _j,t
▪ “Completeness”	$θ j, t = β j, t, 1 + ∑ l = 2 M β j, t, l ⋅ k l - 1, θ, t p$
▪ “Excess”	$φ j, t = a j, t, 1 + ∑ r = 2 N a j, t, r ⋅ k r - 1, φ, t p$
❖ Non-pandemic Model
▪ Data as counts and as a proportion	$Log Y j, t ∼ N μ j, t, σ j 2$
	$μ j, t = P s, j, t, 1 + P s, j, t, 2 ⋅ k 1, t np + P s, j, t, 3 ⋅ k 2, t np + P s, j, t, 4 ⋅ k 3, t np$
Parameter Model: non-informative priors
❖ Pandemic Model	$a j, t, r ∼ N μ a, σ a 2; r = 1, ...., N$
	$β j, t, l ∼ N μ β, σ β 2; r = 1, ...., M$
	$τ ≡ 1 / σ j 2 ∼ Gamma a, b$
❖ Non-pandemic Model	$P s, j, t, n ∼ N μ p, σ p 2; n = 1, 2, 3$
❖ Non-pandemic Model	τ∼Gamma(a, b)

ISSN: 1471-2458