Modeling directly from antibody levels

library(serosv)

Mixture model

Proposed model

Two-component mixture model for test result Z with Z_j(j = {I, S}) being the latent mixing component having density f_j(z_j|θ_j) and with π_TRUE(a) being the age-dependent mixing probability can be represented as

f(z|z_I, z_S, a) = (1 − π_TRUE(a))f_S(z_S|θ_S) + π_TRUE(a)f_I(z_I|θ_I)

The mean E(Z|a) thus equals

μ(a) = (1 − π_TRUE(a))μ_S + π_TRUE(a)μ_I

From which the true prevalence can be calculated by

$$ \pi_{\text{TRUE}}(a) = \frac{\mu(a) - \mu_S}{\mu_I - \mu_S} $$

Force of infection can then be calculated by

$$ \lambda_{TRUE} = \frac{\mu'(a)}{\mu_I - \mu(a)} $$

Fitting data

To fit the mixture data, use mixture_model function

df <- vzv_be_2001_2003[vzv_be_2001_2003$age < 40.5,]
df <- df[order(df$age),]
data <- df$VZVmIUml
model <- mixture_model(antibody_level = data)
#> Warning in mix(data, starting_values, dist = "norm"): The optimization process
#> terminated because either the estimates are approximate local optimal solution
#> or steptol is too small
model$info
#> 
#> Parameters:
#>       pi    mu  sigma
#> 1 0.1088 2.349 0.6804
#> 2 0.8912 6.439 0.9437
#> 
#> Distribution:
#> [1] "norm"
#> 
#> Constraints:
#>    conpi    conmu consigma 
#>   "NONE"   "NONE"   "NONE"

plot(model)

sero-prevalence and FOI can then be esimated using function estimate_from_mixture

est_mixture <- estimate_from_mixture(df$age, data, mixture_model = model, threshold_status = df$seropositive, sp=83, monotonize = FALSE)
plot(est_mixture)
#> Warning: No shared levels found between `names(values)` of the manual scale and the
#> data's fill values.

- Mixture model