Model Setup
Here is my basic planned setup of the model. I will fit linear mixed effects models predicting VE as a function of some combination of parameters associated with fixed and random effects.
The general model is defined as:
\[ \begin{aligned} Y_{i,s,t} &= \beta_0 + \sum_{j=2}^p\beta_jx_{j,i} + (\beta_1 + b_t^{(x_1t)})x_{1,i} + b_s^{(s)} +b_t^{(t)} + \epsilon_{i,s,t}\\ \end{aligned} \]
| Term | Interpretation |
|---|---|
| \(\beta_0\) | Fixed intercept |
| \(\beta_j\) | Fixed slopes for predictors \(x_j, j \ge2\) |
| \(b_s^{(s)} \sim \mathcal{N}(0,\sigma^2_s)\) | Random intercept for influenza season \(s\) |
| \(b_t^{(t)} \sim \mathcal{N}(0, \sigma^2_t)\) | Random intercept for influenza type/subtype/lineage \(t\) |
| \(b_t^{(x_1t)} \sim \mathcal{N}(0, \sigma^2_{x_1t})\) | Random slope for antigenic distance predictor \(x_1\), varying by subtype \(t\) |
| \(\epsilon_{i,s,t} \sim \mathcal{N}(0, \sigma^2_\epsilon)\) | Residual |
Fixed Effects
| Predictor | Interpretation |
|---|---|
| \(d\) | Antigenic distance between vaccine and circulating strain |
| \(a\) | Age group |
| \(r\) | Region (should this be a random effect?) |
| \(p\) | Proportion of infections caused by subtype/lineage \(t\) |
| \(r\) | Number of consecutive years relevant vaccine strain has been included in vaccine as of season \(s\) |
| \(c\) | Antigenic distance between this season’s (\(s\)) and last season’s relevant vaccine strain |